CHARACTERIZATION OF MICROSTRUCTURE AND SLIP BEHAVIOR OF NIOBIUM USED TO FABRICATE ACCELERATOR CAVITIES By Di Kang A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Materials Sci ence and Engineering Doctor of Philosophy 201 9 ABSTRACT CHARACTERIZATION OF MICROSTRUCTURE AND SLIP BEHAVIOR OF NIOBIUM USED TO FABRICATE ACCELERATOR CAVITIES By Di Kang Large grain niobium (Nb) has been used to fabricate superconducting radiofrequenc y (SRF) cavities for particle accelerators over the past couple of decades, as a promising alternative to the well - established but expensive approach of using rolled polycryst alline sheet Nb. While the large grain approach to make cavities provides a redu ced cost process, the performance is comparable to fine grain cavities . Cavities fabricated from both approaches exhibit variability in performance, a costly yet common issue . Understanding the origin of the variability will enable informed design decisi ons to be made, which necessitates studying the underlying physical metallurgy of Nb. One source of the variability is the starting material for fabricating cavities . Large and fine grain Nb was characterized to determine if ingots have commonalities and examine how different ingots result in heteogeneity in the microstructure of rolled sheets . Eight large grain ingots were analyzed using electron backscatter diffracti on (EBSD) and Laue X - ray diffraction. The lack of similarity in crystal orientations an d grain boundary misorientations of the ingots suggest s random orientation nucleation / growth, which gives rise to variability in subsequent forming and processing . Fine grain rolled Nb sheets to be used for the Facility for Rare Isotope Beams (FRIB) were evaluated using tensile tests and EBSD to ensure the acceptability of the material. With these data, performance variability in future FRIB cavities can be traced t o the initial microstructure. While the mechanical properties and texture vary significan tly from one batch to another, correlations between texture, microstructure, and mechanical properties are generally weak. A multi - crystal rolling experiment was devised to investigate the connection between ingot and sheet microstructure. Wedged pieces f rom an ingot were rolled flat, from which samples with different amounts of cold work were extracted and analyzed with EBSD before and after annealing . B ands with orientations different from the parent grains developed due to rolling, and small grains nuc leated from the bands upon annealing. The banding and recrystallization patterns approximate those observed in sheets subj ected to more rolling passes, which implies that the microstructural heterogeneity in the rolled sheets originated from the randomly oriented large grains in the ingots. Hot spots are regions in a cavity with a localized temperature increase that may destr oy the superconducting state. To identify sources of hot spots and performance variability in large grain cavities, EBSD was used to examine the cross - sections at the equator and iris of a cavity half - cell. The results suggest that cavity surface damage ( locations with higher dislocation content reflected by greater orientation gradients ) associated with the friction from deep drawing depends on crystal orientation, and the magnitude of such damage is different at the iris and equator . The orienta tion gradients at the equator were not uniformly removed after annealing at 1000 ºC/2hr. This explains why the equator is more susceptible to hot spots in additional to it having a higher magnetic field and suggests that annealing at higher temperatures o r longer times may be necessary. Modeling microstructural evolution during cavity processing can help predict performance variability and re duce the number of trial and error experiments. A f undamental understanding of deformation mechanisms of Nb is need ed to establish such a model. For this purpose, two sets of single crystals with the same orientations were extracted from a n ingot slice, and one set was heat treated to alter the initial condition. Both sets of samples were deformed to about 40% engine ering strain in uniaxial tension. The d ifferences in flow stress, crystal rotation, and active slip systems between the two sets are likely due to the removal of preexisting dislocations caused by the anneal . iv ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy , Office of High Energy Physics, through Grant No. DE - S0004222. I would like to express my sincere appreciation for my advisor Dr. Thomas Bieler for his mento rship , support, encourage ment, understanding, and patience throughout the years. It would have been impossible for me to be where I am without him. I have gone through several struggles, and he has always giv en me a hand. His natural curiosit y , enthusiasm for science , and approach to life have influenced me greatly . I would also like to express my deep gratitude for my guidance committee members Dr. Martin Crimp, Dr. Carl Boehlert, and Dr. Neil Wright for th e ir devotion, insights into my research, and con stant feedback on how I can improve . I would also like to thank my collaborators , Chris Compton at the Facility for Rare Isotope Beams and G igi Ciovati at Jefferson Lab , for their tremendous assistance with my experiment s as well as numerous valuable discussions . I would also like to thank my fellow graduate students for their friendship , inspiration, and help over the past years. Finally, I would like to thank my parents for always believing in me and prov iding me with unconditional support during tough times. v TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ........................ vii LIST OF FIGURES ................................ ................................ ................................ ..................... viii I. INTRODUCTION ................................ ................................ ................................ ............... 1 II. LITERATURE REVIEW ................................ ................................ ................................ .... 4 a. Accelerator Technology and Niobium ................................ ................................ ................. 4 b. Progress in Improving Cavity Performance ................................ ................................ ......... 6 c. Dislocations and Cavity Performance ................................ ................................ .................. 8 d. Ingot Produ ction and Initial Grain Orientation ................................ ................................ .. 13 e. Large Grain Approach to Forming Cavities ................................ ................................ ...... 20 f. Microstructure of Fine Grain Nb Sheets ................................ ................................ ............ 22 g. Cavity Fabrication and Surface Studies ................................ ................................ ............. 27 h. Active Slip Systems in Nb ................................ ................................ ................................ . 32 i. Observ ation of Dislocations in Nb ................................ ................................ ..................... 42 j. Evaluation of GNDs using cross - correlation EBSD ................................ .......................... 45 k. Opportunities for Research ................................ ................................ ................................ 47 III. MATERIALS AND METHODS ................................ ................................ ....................... 50 a. Large Grain Nb Ingots Characterized by EBSD and Laue Camera ................................ ... 50 b. Fine Grain Nb Sheets Characterized by EBSD and Mechanical Tests .............................. 57 c. Rolled Multi - Crystal Nb Samples Charact erized by EBSD and Laue Camera ................. 59 d. Nb Cavity Samples Characterized by EBSD ................................ ................................ ..... 62 e. Nb Single Crystals Characterized by in - Situ Tensile Tests ................................ ............... 65 IV. RESULTS ................................ ................................ ................................ .......................... 70 a. Crystal Orientation of Large Grain Nb Ingots ................................ ................................ ... 70 b. Texture and Stress - Strain Behavior of Fine Grain Nb Sheets ................................ ........... 99 c. Microstructure of Rolled Nb Samples ................................ ................................ ............. 107 d. Evolution of Microstructure in Nb Cavity Samples ................................ ........................ 112 e. Slip an d Crystal Rotation in Heat - Treated Nb Single Crystals ................................ ........ 119 V. DISCUSSION ................................ ................................ ................................ .................. 137 a. Preferred Orientation and Orientation Stability in Large Gr ain Nb Ingots ..................... 137 b. Texture/Property Relationship in Fine Grain Nb Sheets ................................ ................. 146 c. Connection between Ingot and Sheet Microstructure ................................ ...................... 148 d. Effects of Processing History on Cavity Surface Damage ................................ .............. 149 e. Effects of Heat Treatment on Preferred Slip Systems in Nb ................................ ........... 154 VI. CONCLUSIONS ................................ ................................ ................................ .............. 162 vi VII. RECOMMENDATIONS FOR FUTURE WORK ................................ .......................... 165 APPENDIX ................................ ................................ ................................ ................................ . 167 BIBLIOGRAPHY ................................ ................................ ................................ ....................... 188 vii LIST OF TABLES Table 1: Information of ingots and their short names used in this work, ranked by ingot size. ... 52 Table 2: Orientations in Bunge Euler angles (°) for the Ningxia ingot slice. The numbering is the same as Figure 24. ................................ ................................ ................................ ......................... 70 Table 3: Or ientations in Bunge Euler angles (°) for the CBMM - NSCL ingot slice. The numbering is the same as Figure 24. There are varying differences between EBSD and Laue measurements of the same g rains (discussed later). ................................ ................................ ............................. 71 Table 4: Orientations in Bunge Euler angles (°) for the CBMM - H1 and CBMM - H2 ingot slices. The numbering is the same as Figure 25. The two slices are nearly identical in orientations. .... 71 Table 5: Orientations in Bunge Euler angles (°) for the TD - 1 and TD - 2 ingot slices. The numbering mounting error. ................................ ................................ ................................ ................................ .............. 71 Table 6: Orientations in Bunge Euler angles (°) for the Heraeus ingot at locations shown in Figure 25. Orientation variation in grain 1 is small based upon five measurements. ............................. 72 Table 7: Orientations in Bunge Euler angles (°) for the Niowave ingot a t locations shown in Figure 26. Orientations do not vary much in the longitudinal direction of the ingot. After etching, the orientation of seven locations changed 1 - 2 º , but the orientation gradients associated with the milling bands are still present. ................................ ................................ ................................ ...... 73 Table 8: Orientation spread for grains with multiple Laue measurements, estimated using the average orientations (Figure 43) as the r eference. The intragranular orientation variation is small compared to the Ningxia ingot (shown later). ................................ ................................ .............. 87 Table 9: Summary of observed slip planes from slip trace analyses for as - received and heat - treated samples, with {112} planes in the first line, and {110} planes in the second line for each orientation. The heat - treated samples exhibited more {110} slip than the a s - received samples. The numbers in parentheses indicate the Schmid facto r rank (as illustrated in Figure 71) for a given slip system, and the first slip system whose Schmid factor rank is different between the two samples is indicated in the left column. ................................ ................................ ................................ ....................... 126 Table 10 : Orientation evolution with deformation for the annealed samples T1 and V1. Numbers in red are the difference between the i nitial and final orientation, which shows that T1 has a greater crystal rotation than V1. ................................ ................................ ................................ .............. 136 viii LIST OF FIGURES Figure 1: Example of a 7 - cell cavity. Blue arrows on top indicate polarity changes of the electro - magnet ic fields within the cells [ adapted from Figure I - 1 in reference [ 16] ]. ................................ 6 Figur e 2: Q 0 vs. E pk measured on a 1.3 GHz single cell cavity before and after baking at 100 °C for 48 hours. The bake moved the Q - slope to higher accelerating fields and increased the Q value [Figure 1 (b) in reference [22]]. ................................ ................................ ................................ ...... 8 Figure 3: in a cavity. The green color corresponds to a misorientation of 2°, and blue is 0° [Figure 14 in reference [26]]. ................................ ................................ ................................ ................................ 9 Figure 4: Local average misorientation (LAM) calculations using the 2nd near est neighbor sampling area for the point at the center, LAM averages the misorientations of all its neighboring points (connected by short white lines) within the kernel [Figure 3 in reference [126]]. ............. 10 Figure 5: Corresponding histograms for the LAM maps shown in Figure 3 [Figure 15 in reference [26]]. ................................ ................................ ................................ ................................ .............. 11 Figure 6: Thermal conductivity as a function of temperature for a bi - crystal sa mple. The original phonon peak (blue arrow) on grain 2 disappeared after 15% strain, but i t was fully restored after a 1000 °C/2hr heat treatment [adapted from slide 5 in reference [32]]. ................................ .......... 13 Figure 7: Schematic of the electron beam melting equipment to produce and to purify Nb ingots [Figure 2 in reference [38]]. ................................ ................................ ................................ .......... 15 Figure 8: Ultrasonic tomography of a Nb ingot. No. 1 is near the bottom of the ingot, and No. 48 is near the top [Figure 3 in reference [44]]. ................................ ................................ .................. 17 Figure 9: Electron channeling contrast image of a sample from an as - received Nb ingot showi ng contrast arising from dislocations [Figure 8 in reference [24]]. ................................ ................... 19 Figure 10: Flow diagram of SRF cavity fabrication using fine grain or large grain Nb (courtesy of W.C. Heraeus, Germany) [adapted from Figure 6 in reference [37]]. ................................ .......... 21 Figure 11: Orientation maps of the full thickness of Nb tensile specimens from (a) Wah - Chang as - received ILC sh eet (b) Wah - Chang as - received ILC sheet after annealing (c) Tokyo - Denkai as - received sheet [Figure 2 in reference [63]]. ................................ ................................ .................. 25 Figure 12: A half - cell (right) formed from a large grain ingot slice (left) by deep drawing, and a schematic of the process is shown in the middle [adapted from Figure 8 in reference [37]]. ...... 27 ix Figure 13: Representative inverse pole figures from EBSD measurements on different samples. The orientation spread is greatest after deformation and is least in t he recrystallized condition [adapted from Figure 9 in reference [24]]. ................................ ................................ .................... 29 Figure 14: Dependence of achievable ac celerating gradient on the thickness of material removed from surface, measured on a fine grain cavity [adapted from Figure 3 in reference [76]]. .......... 30 Figure 15: Change in local average misorientations (LAMs) on cavi ty samples due to baking. In each case, measurements were made on the same sample before and after baking in ultra - high vacuum [Figure 2 in reference [27 ]]. ................................ ................................ ............................ 31 Figure 16: A schematic diagram showing a [111] bcc screw dislocation with its Burgers vector and line dir ection out of the page, and the effect of core relaxation on a slip trace: a) The core may relax on either three symmetric {112} planes (dashed lines) or three symmetric {110} planes (solid lines). Motion of the dislocation can leave a trace on a surface indicating the slip plane for: b) {112} re laxation, the screw dislocation may frequently cross slip on two of the three {112} relaxation planes (each change in plane marked by a circle), while following a high resolved shear stress plane (fine dotted line) . c) For {110} relaxation, the screw disl ocation may frequently cross slip on two of the {110} planes, while following a high resolved shear stress plane [Figure II - 13 in reference [16]]. ................................ ................................ ................................ .......................... 36 Figure 17: Initial tensile axes for D&F and Ningxia samples on a stereograp hic projection section. The boundaries mark where the Schmid factors are equal between two {110} sli p systems (solid lines), two {112} slip systems (dashed lines), a {110} and a {112} slip system (dotted lines). The boundary is colored green for the same slip direction, and red for intersecting slip directions. Slip systems whose Schmid factors are gre atest in the area between the boundaries are labeled [Figure V - 9 in reference [16]]. ................................ ................................ ................................ .................. 41 Figure 18: TEM micrograp hs of (a) dislocation cell structure in a Nb sample cold rolled to 50% (45,000× magnification) (b) dislocation networks in a Nb sample rolled to 98% and annealed at 900 °C/1h (44,000× magnification) [Figure 5 and Figure 9 in reference [110]]. ......................... 43 Figure 19: (a) Electron channeling contrast (ECC) image of dislocations near an indent (b) GND density map of the same are a generated from CC - EBSD showing si milar dislocation distribution (c) Dislocation density map calculated by counting dislocations in the ECC image [Figure 3 in reference [119]]. ................................ ................................ ................................ ............................ 46 Figure 20: Road map showing the interconnections of research activities outlined above. Letters a - e in parentheses correspond to the section headings in the next three chapters. ....................... 49 Figure 21: Schematic of the EBSD configuration. The electron beam interacts with a sample that is tilted 70° from th e beam axis. Red arrows indicate the coordinate systems used for the crystal orientation. Backscatter electrons form diffraction patterns on the EBS D camera, which are then processed by a computer equipped with data acquisition and analysis software. Th e electron beam trajectory is also controlled by the computer [adapted from Figure 1.3 in reference [124] and Figure II - 15 in reference [16]]. ................................ ................................ ................................ ................. 50 x Figure 22: Laue camera equipped with area detector, showi ng how an ingot slice was mounted to determine crystal orientations [Figure 3 in reference [122]]. ................................ ....................... 51 Figure 23: A typical Laue pattern (left) and the indexing user interface (right) [Figure 4 in reference [122]]. ................................ ................................ ................................ ................................ ............ 52 Figure 24: Images of ingot slices characterized by EBSD. Dashed lines identify the location of faint grain boundaries. The numbers on the image s of the ingots indicate ID s of the grains whose crystal orientation will be reported later. The scale bar is common to both images. ................... 53 Fi gure 25: Images of ingot slices characterized by Laue camera. The grid on the CBMM - NSCL slice illustrates how 57 measurements were systematically made with a step size of 1 inch. The TD - 1 slice was measured similarly using a step size of 2 inches, yieldi ng 19 data points (detailed in). For the Heraeus, CBMM - H1, and TD - 1 slices, the numbers provide approximate locations of the orientation measurements (reported later). The scale bar is common to all images. ............. 55 Figure 26: Image of a slab cut along the longitudinal direction of an ingot (prepared by Niowave). The dimensions are 70 cm (W) × 22 cm (H) × 1 cm (T). Te n closely spaced Laue measurements (a - j) were made in addition to the numbered locations. Scan j was about half way between locations 2 and 27 [adapted from Figure 3 in refer ence [123]] . ................................ ................... 5 6 Figure 27: Layout of acceptance crite ria list (ACL) samples extracted from (a) Tokyo - Denkai and (b) Ningxia sheets. The Tokyo - Denkai samples are oriented 45° with respect to th e rolling direction, while the Ningxia samples are either perpendicular or parallel to the rolling direction. The d imensions are the same for each type of samples and are shown on the Tokyo - Denkai drawing. All units are in inches except for the square sa mples in (a) [adapted from Figure 14 in reference [61]]. ................................ ................................ ................................ ................................ .............. 58 the Niowave ingot used for the rolling experiment. The green dotted line indicates that the sample was cut in half part way through the rolling process due to developing a curved strip. ................................ ................................ ......... 60 End slice S1 was cut next to the top edge of the rolled piece, and its corr es ponding orientation map and the sense of rolling are shown on the right. The cross - sections of samples A2 and A6 were examined for the effects of rolling and annealing. ................................ ................................ ....... 61 Figure 30: Locations of three samples extracted from a half - cell formed by JLab. The locations of grain boundaries (GB) and a neck are indicated in the blown - up images in Figure 31. Numbers pro vide approximate locations of EBSD scans on the equator and iris [adapted from Figure 2 in reference [126]]. ................................ ................................ ................................ ............................ 63 Figure 31: Secondary electron images of the 6 areas examined by EBSD. Gr ain boundaries and the neck are marked in accordance with Figure 30. The numbering is also the same as Figure 30 [adapted from Figure 4 in reference [126]. ................................ ................................ ................... 64 xi Figure 32: Layout of single crystal tensile samples extracted from the Ningxia ingot slice. The dimensions are shown on the left. The location of s amples P1 and P3 are shown as examples of the labeling strategy [adapted from Figure III - 3 in reference [16]]. ................................ ............. 66 Figure 33: Experimental setup of the in - situ tensile tests. Sample W is shown as an example. Left tensile load frame mounted inside the MIRA3 SEM chamber, right plan view of the sample [ada pted from Figure 3.2 in reference [131]. ................................ ................................ ................ 68 Figure 34 : Illustration of how orientation maps were generated using the TD - 1 ingot slice. Red dots indicate app roximate locations of the 19 measurements that are two inches apart, and each pixel in the 30x30 grid was assigned the measured orientation closest to i t within a grain. ........ 75 Figure 35: Normal direction orientation maps for the CBMM - H1, Heraeus, Ning xia, and TD - 1 ingot slices, as labeled. Annotations provide angle and rotation axis for grain boundary misorientations, with CSL boundaries identified with thick black boundaries and red text. The red arrow on the Heraeus slice identifies the perimeter g rain that has the same orientation as the center grain. The high angle (> 15º) grain boundaries are identified with thi n black lines. The scale and legend are common to all maps. ................................ ................................ ................................ ... 77 Figure 36: Normal direction orientation maps for the CBMM - NSCL slice measured by EBSD (left) and Laue camera (right). Annota tions provide angle and rotation axis for grain boundary misorientations, with CSL boundaries identified with thick black boundaries and red text. The discrepancy between the two methods will be addressed in the Discussion chapter. The scale and legend a re common to both maps. ................................ ................................ ................................ 78 Figure 3 7: Transverse (in got growth) direction orientation map for the Niowave ingot slab. Annotations provide angle and rotation axis for grain boundary misorientations. The red arrow identifies the perimeter grain that has the same orientation as the center on e. The high angl e (> 15º) grain boundaries are identified with thin black lines. There is no CSL boundary in this ingot. ................................ ................................ ................................ ................................ ....................... 79 Figure 38: Grain boundary misorientation distribution functions (MODFs) for the CBMM - H1 and TD - is a trend for grain boundary misorientations t o fall between 35 - 55 º . ................................ .......... 80 Figure 39: Grain boundary MODFs for the Ningxia and Heraeus ingot slices. Misorientat ions for grain boundary misorientations to fall between 35 - 55º. ................................ ................................ ................................ .................. 81 Figure 40: Grain boundary MODFs for the CBMM - NSCL and Niowave ingots. Misorientations misorientations to fall between 35 - 55º. ................................ ................................ ......................... 82 xii Figure 41: Density pole figures for each ingot plotted using the same color scale. Orientations of dominant grains are evident by the three red <100> poles for the Heraeus and Niowave ingots. The ingots lack commonality in orientation distributions. ................................ ........................... 84 Figure 42: Ingot growth (sheet normal) direction discrete inverse pole figures for each ingot. There is a lack of near <111> orientations among the ingots. ................................ ................................ 85 Figure 43: Illustration of how orientation variation is estimated from multiple Laue measurements within a grain. The orientation deviation map on the left uses the average orientation of each grain as a referenc e. For example, the largest deviation for grain 1 is in the range of 2.5 - 3° (dark yellow), and the upper bound value (3°) is assigned to this grain as its orientation spread. ...................... 86 Figure 44: Orientation gradients along the 18 - mm gauge length of three tens ile samples extracted from the Ningxia ingot slice. Y1 has the largest orientation gr adient due to a low angle boundary near its right end. ................................ ................................ ................................ ........................... 89 Figure 45: Orientation variation in Euler angles for t he three samples shown in Figure 44. ....... 90 Figure 46: Grain reference orientation deviation maps showing fine scale orientation gradients for samples Y1 and U1 based on the average orientation at the center. The directionality of banding is consistent for sample U1, but less so for sample Y1. The color scale is common to all maps. 91 Figure 47: Selected fine scale orientation patterns of the as - cut samples overlaid onto the image of the Ningxia slice. Black dashed lin es highl ight the original grain boundaries. The color scale for the maps is the same as Figure 46. There is no consistency in the directionality of the banding with respect to the ingot. ................................ ................................ ................................ ............... 92 Figure 48: Fine scale orientation patterns from roughly the same regions for samples P1 and Q1 before and after an 800 °C/2h anneal. The anneal did not alter the patterning by much. The color scale is the same as Figure 46. ................................ ................................ ................................ ...... 93 Figure 49: Orientation deviation maps (based upon points with minim um KAM) of the heat - trea ted samples S2 and T2 before deformation but after electropolishing and annealing. There are no fine scale orientation gradients like those in the as - cut samples. The color scale is the same as Figure 46. ................................ ................................ ................................ ................................ .................. 94 Figure 50: Half - cell deep drawn from the CBMM - H2 ingot slice. Orientations measured before and aft er deformation are overlaid onto th e image (black before, yellow after). Note that the numbering of locations (hand - written on the half - cell) is different from Figure 25. The orientations did not change much after deep drawing, except for location 10 (9.8 º difference). The red boxes indicate locations for which the Laue patterns will be compared before and after deep drawing (Figure 51) [adapted from Figure 2 in reference [123]]. ................................ .............................. 95 Figure 51: Laue diffraction patterns before and after deep drawing at locations 1, 5, and 7 shown in red boxes in Figure 50. The spots visible on the undeformed ingot slice (left three) are not as xiii visible and more smeared after deformation (right three). A example is shown in red circles at location 7. ................................ ................................ ................................ ................................ ...... 96 Figure 52: Laue di ffraction patterns at positions e and d from the Niowave ingot (Figure 26). The left pattern shows dis tinct spots in the middle of a milling band, while the right one shows smearing of spots from the edge of a milling band. ................................ ................................ ..................... 97 Figure 53: Laue diffraction patterns at positions 7, 18, and 25 from the Ni owave ingot (Figure 26) before and after a 100 µm etch. The spot s became sharper after etching. The 1 - 2 º orientation change is due to mounting error and the removal of a machined surface layer. ........................... 98 Figure 54: Sheet normal direction orientation maps, engineering stress - strain curves, and density pole figure s for the Tokyo - Denkai samples with extreme tensile properties. The loading direction is either horizontal, or in and out of the page with respect to the orientation maps. There is an inverse correlation between grain size and yield strength [adapted fro m slide 18 in reference [139]]. ................................ ................................ ................................ ................................ ..................... 101 Figure 55: Engine ering stress - strain curves for 23 Ningxia samples that were either perpendicular (red curves) or parallel (blue curves) to the rolling direction [adapted from slide 16 in reference [13 9]]. The yield strength vs. grain size correlation applies to the two e xtreme samples, but not to every other sample. ................................ ................................ ................................ ..................... 102 Fig ure 56: UTS vs. average grain size (equivalent diameter from EBSD analysis) scatter plots for Tokyo - Denkai samples (above) and Ningxia samples (below). A weak negative correlation is present. On average, the Tokyo - Denkai samples have higher UTS than the Ningxia samples [adapted from slide 17 in reference [139]]. ................................ ................................ ................ 103 Figure 57: Maximum ODF intensity v - 2 = 45° slice (from 0 - 90°) for Tokyo - Denkai (above) and Ningxia (below) samples [adapted from slide 20 in reference [139]]. ................................ ................................ ................................ ................................ ..................... 105 Figure 58: f - 2 = 45° for To kyo - Denkai (above) and Ningxia (below) samples. Little correlation is present [adapted from slide 21 in reference [139]]. ................................ ................................ ................................ ................................ ..................... 106 Figure 59: Orientation map of a region on the cross - section of sample A2 with ~68% reduction. The original orientatio n is shown on the top right corner. An original grain boundary i s present in the upper area. The average confidence index (CI) before cleanup is 0.45 for this dataset. The legend on the top left applies to all following orientation maps unless otherwise specified. ..... 107 Figure 60: Orientation map of a region on the cross - section of sample A2 with ~76% reduction. F urther deformation bands with distinct orientations developed, and the original orientation is no longer traceable. The average CI before cleanup is 0.54 for this dataset. ................................ . 108 xiv Figure 61: Orientation map of a region on the cross - section of sample A6 with ~92% reduction. The horizontal bands of different orientatio ns and black zones in the middle resemble the layere d structure observed in sheet material. The average CI before cleanup is 0.13 for this dataset. .. 109 Figure 62: Orientation maps from matching areas on sample A2 with ~68% redu ction (shown in Figure 59) before and after annealing at 800 ºC/2hr. Small grains emerged inside the lower large grain due to the anneal, with orientations different from the parent grain. H owever, these minority orientations are the same within the pink and dark green regions. ................................ ............. 110 Figure 63: Orientat ion ma ps from matching areas on sample A2 with ~76% reduction (shown in Figure 60) before and after annealing at 800 ºC/2hr. Similar to Figure 62, small grains with green orientations emerged on the right from the deformation bands because of the anneal. The s cattered new grains again have the same orientation. ................................ ................................ .............. 111 Figure 64: Normal direction orientation maps (lef t), LAM maps (middle), and IQ maps (right) for the three equator regions indicated in Figure 31. For each region, results for as - deep drawn, after heat treatment, and after BCP conditions are shown from top to bottom. The scale and legends are common to all images. Red arrows on the LAM map of Equator 2 indicates a scratch feature that disappeared after the heat treatment [adapted from Figure 5 in reference [126]]. ..................... 113 Figure 65: Normal direction orientation maps (left), LAM maps (middle), and IQ maps (ri ght) for the three iris regions indicated in Figure 31. For each region, results for as - deep drawn, after heat treatment, and after BCP conditions are shown from top to bottom. The scale is common to all images and the legends are the same as Figure 64 . A grain boundary developed in Iris 1, likely during deep drawing [Figure 6 in reference [126]] . ................................ ................................ .... 114 Figure 66: Point - to - origin (upper three) and point - to - point (lower three) misorientation profiles for the three colored li nes drawn on Equator 2 in Figure 64 . The blue ends of the colored lines in Figure 64 are the origin. In the after - BCP condition (green), the left grain exhibits an oscillation of ~2 - 3º as the line crosses the area with low angle grain boundaries. [Figur e 7 in reference [126]]. ................................ ................................ ................................ ................................ ..................... 117 Figure 67: LAM histograms of the six EBSD scans for as - deep drawn (top), after anne aling (middle), and after BCP (bottom) conditions. The horizontal scale is common for all three plots. Before annealing, the iris had higher LAM values than the equator, but the iris changed more from annealing [Figure 8 in refere nce [126]. ................................ ................................ ....................... 118 Figure 68: Engineering stress - strain cu rves of as - received (left) and heat - treated (right) samples. Orientations of tens ile axes are indicated by corresponding colors in the triangle inset, which also provides Schmid factor contours in white for {110} slip and gray for {112} slip, both scaled at 0.5, 0.499, 0.49, 0.47, 0.44, 0.40, 0.36, 0.32. Dashed lines mark boundaries w ith equal Schmid factors (orange {110} + {112} with intersecting slip directions, red {112} with intersecting slip directions, blue {110} + {112} with the same slip dir ections) [Figure 1 in reference [130]]. 119 Figure 69 : Slip trace identification on the heat - treated sample W in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the xv measured orientations, with {110} slip traces in green, and {112} in p urple. Slip traces were not apparent until ~20% engineering strain for this sample [adapted from Figure 7 in reference [58]]. ................................ ................................ ................................ ................................ ..................... 121 Figure 70: Slip systems ranked by Schmid factors (up to 8th highest) for the as - received sample T3 (above) and heat - treate d sample T2 (below). The first {110} slip system was observed in both samples and was the only apparent slip system. ................................ ................................ ......... 123 Figure 71: Slip systems ranked by Schmid factors (up to 8th highest) for the as - received sample V3 (above) and heat - treated sample V2 (below). A {110} and a {112} slip system were observed in V3, while only the most highly favored {110} slip sys tem was observed in V2. .................. 124 Figure 72: <111>, <112>, and <110> pole figures for the heat - treated sample T2 with the t ensile direction pointing out of the page. The [1 1] pole moved towards the tensile axis with increasing strain, while the [011] pole moved away from the tensile axis. This is consistent with the observed slip system (011) [1 1]. ................................ ................................ ................................ .............. 125 Figure 73: Orientation evolution with deformation for the as - received sam ple R2 and heat - treated sample R3. R2 rotated more th an R3 during deformation [adapted from Figure 6 in reference [58]]. ................................ ................................ ................................ ................................ ..................... 127 Figure 74: Prisms illustrating how the three locations of the heat - treated sample P2 (right) rotated differently with defor mation over a range of ~5 mm along the gauge len gth. The orientations at 40% strain all differed from that of the as - received sample P3 (left). The left and right regions of sample P3 had similar opposite rotations as P2. Numbers in red show misorientat ions before and after deformation in correspondi ng areas. ................................ ................................ .................. 129 Figure 75: Orientation maps from three regions for the heat - treated sample U2 before and after deformation. The left area developed orientation bands with different rotations after def ormation. Annotations on the left map provide angle and rotation axis for misorientations of the deformation - induced gra in boundaries. ................................ ................................ ................................ ........... 130 Figure 76: Inverse pole figures showing the evolution of tensile axis orientations with defor mation for as - received (triangles) and heat - treated samples (colored solid c ircles). The orientation change (º) from deformation is shown for each annealed sample. The as - received samples almost always exhibit more crystal rotation than the annealed samp les [adapted from Figure 4 in reference [130]]. ................................ ................................ ................................ ................................ ..................... 131 Figure 77: Optical images of the as - received (AR) and heat - t reated (HT) sampl es in pairs taken after deformation. The scale shown for orientation W is common to all images. Both P samples had similarly opposite sense of rotation on either side of the gauge length, based on the reflections. The two U samples neck ed at different l ocations near one of the ends of the sample. .............. 133 Figur e 78: Engineering stress - strain curves of samples T1 and V1 deformed in - situ . The arrows indicate where the tensile test was paused to collect CC - EBSD data. The initial hardening behavior for T1 is partly due to the pre - strain (~8.7%), and its plot is sh ifted to the right accordingly. .. 134 xvi Figure 79: GND distribution maps at each strain level obtained from CC - EBSD for samples T1 and V1. The before - deform ation condition for T1 is missing as it was pre - strained to about 8.7%. The orange circle on the top right indicates an area with higher preexisting GND content for V1. There is a noticeable increase in GND density for T1, and little change for V1. ....................... 135 Figure 80: Maximum Schmid factor maps for the 5 ingot slices for slip on {110}, {112}, or both families of planes based on biaxial tension. The scale shown next to the Heraeus slice is common to all maps. These maps provide an estimate of formability based on hard/soft orientations. .. 141 Figure 81: Maximum Schmid factor maps for the Niowave ingot slab for slip on {110}, {112}, or both families of planes based upon biaxial tension in a slice taken perpendicular to the longitud inal direction. Slices from this ingot would likely experience more homogeneous deformation due to the huge grain at the center. ................................ ................................ ................................ ........ 142 Figure 82: Fitted line of yield strength vs. grain size for the Ningxia samples shown in Figure 55. The shotgun scatter suggests that the Hall - Petch relationship is not well satisfied. ................... 147 Figure 83: LAM profiles in the 6 grains obtained from averaged traces on the inside and outside of the equator and iris. Damage depths up to about 200 µ m i s present in some regions, and the magnitude is different for the equator and iris, as well as for the outside and inside [Figure 9 in reference [126]]. ................................ ................................ ................................ .......................... 152 Figure 84: The table on the right list s the annealed samples in the order of increasing ratio between the primary and secondary {110} slip systems, which corresponds roughly to decreasing initial hardening rates as shown in the zoomed image on the lower left [Figure 3 in reference [121]]. 155 Figure 85: Comparison of experimental and simulation results of several annealed samples using classical, dynami c hardening, and differential - exponenti al approaches. Without accounting for the Non - Schmid effects, the modeling still shows good agreement with the experiments [Figure 15 and Figure 16 in reference [149]]. ................................ ................................ .............................. 156 Figure 86: Comparison of slip trace morphology at 40% engineering strain on the as - received and heat - treated sample X. X3 has wavier s lip traces than X2. ................................ ....................... 158 Figure 87: <111>, <112>, and <110> pole figures from three regions on the gauge length for the heat - treated samples P, Q, and R with the tensile axis pointing out of the page. The color scale for engineering strain is common and shown next to sample P. ................................ ...................... 168 Figure 88: <111>, <112>, and <110> pole figures from three regions on the gauge length for the heat - treated samples S, T, and U with the tensile axis pointing out of the page. The color scale for engineering strain is common and shown next to sample S. ................................ ...................... 169 Figure 89: <111>, <112>, and <110> pole figures from three regi ons on th e gauge length for the heat - treated samples V, W, and X with the tensile axis pointing out of the page. The color scale for engineering strain is common and shown next to sample V. ................................ ................ 170 xvii Figure 90: Slip trace identification on the heat - treated sample P in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in pu rple. ........................... 171 Figure 91: Slip tr ace identification on the heat - treated sample Q in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. ........................... 172 Figure 92: Slip trace identification on the heat - treated sample R in some of the areas examined. Observed sli p traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. ........................... 173 Figure 93: Slip trace identification on the heat - treated sample S in some o f the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measure d orientations, with {110} slip traces in green, and {112} in purple. ........................... 174 Figure 94: Slip trace identification o n the heat - treated sample T in some of the areas examined. Observed sl ip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. ........................... 175 Figure 95: Slip trace identification on the heat - treated sample U in some of the areas examined. Observed slip traces (solid line s) were match ed with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. ........................... 176 Figure 96: Slip trace identification on the heat - treated sample V in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted li nes) based on the measured orientations, with {110} slip traces in green, and {112} in purple. ........................... 177 Figure 97: Slip trace identification on the heat - treated s ample X in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. ........................... 178 Figure 98: Orientation maps from three regions for the heat - treated sample P before and after defor mation. ................................ ................................ ................................ ................................ 179 Figure 99: Orientation maps from three re gions for the heat - treated sample Q before and after deformation. ................................ ................................ ................................ ................................ 180 Figure 100: Orientation maps from three regions for the heat - treated sample R before and after deformation. ................................ ................................ ................................ ................................ 181 Figure 101: Orientation maps from three regions for the heat - treated sample S before and after deformation. ................................ ................................ ................................ ................................ 182 xviii Figure 102: Orientation maps from three regions for the heat - treated sample T before and after deformation. ................................ ................................ ................................ ................................ 183 Figure 103: Orien tation maps from three regions for the heat - treated sample U before and after deformation. ................................ ................................ ................................ ................................ 184 Figure 104: Orientation maps from three regions for the heat - treated sample V before and after deformation. ................................ ................................ ................................ ................................ 185 Figure 105: Orientation maps from three regions for the heat - treated sample W before and after deformation. ................................ ................................ ................................ ................................ 186 Figure 106: Orientation maps from three regions for the heat - treated sample X before and after deformation. ................................ ................................ ................................ ................................ 187 1 I. INTRODUC TION Particle accelerators incorporating superconducting radiofrequency (SRF) technology have a variety of scientific and industrial applications. As the performance of accelerator cavities made from niobium (Nb) approaches the theoretical limit, an incre asing number of issues have arisen that cannot be explained or tackled with conventional physics. Over recent years, much research has focused on the materials science aspects of Nb in the SRF community, following the pioneering efforts by Padamasee et al . [1, 2] . Physical understanding of the metallurgy of N b is necessary to develop a viable path to further enhance the performance of cavities while reducing their variability in performance. Material c onsiderations for SRF cavities involve three major aspects: formability, stiffness, and microstructure [3] . Good formability facilitates cavity fabrication and requires high elongation to failure ; stiffness ensures dimensional stability during cavity operation (e.g., cooling down under vacuum) and requir (dislocation configuration) dictates thermal conductivity and magnetic properties that are lin ked to cavity performance , since dislocations interfere with heat transfer and trap magnetic flux [3] . Depending on the application of a cavity, the material specification usually requires a comp romise among these factors [3] . Currently, the for mability and stiffness of Nb can be reasonably controlled by SRF cavity manufacturers, even though knowledge of the microstructure or metallurgica l state of cavities is limited. A material model that integrates the microstructure with existing physics the ories will enable a more accurate prediction of cavity performance. To build such a comprehensive model , it is vital to understand how microstruc ture evolves during cavity fabrication and how it affects 2 performance. With such a model, forming and performance issues can be anticipated or eliminated at an earlier stage, and more robust criteria for material acceptance are possible. This work addre sses some of the missing links required to establish a better material model. The initial microstructure of the material to make cavities is a prerequisite for the simulation. Then, two paths are followed first, the microstr uctural evolution during pro cessing of a cavity is investigated and correlated to its performance; second, the slip behavior is examined in the simpler case of uniaxial tension for a fundamental understanding of deformation mechanisms of Nb that govern the microstructural changes. T he insights from these studies will complement prior knowledge and provide a basis for the modeling, thus enabling design strategies that will lead to more consistent cavity performance and cost reduction. Recently, the role of dislocations in cavities has attracted increasing in the SRF community [4 - 6] . Dislocations are associated with variability in the starting Nb material, and such variability evolves during the forming process and may magnify variability durin g cavity fabrication , which eventually influences cavity performance. An improved material m odel will allow dislocation configuration in a cavity to identified as dislocations are both a component and consequence of the microstructural evolution. The scop e of this work follows five parallel storylines that will be set forth in the Materials and M ethods, Results, and Discussion chapters: (a) crystal orientation s of ingot slices, (b) texture of fine grain sheets, (c) link between the ingot and sheet microstr ucture, (d) orientation gradients in a large grain cavity, and (e) single crystal tensile tes ts. The reason for using this structure instead of having five separate chapters is that the linkages between sections a - e can be more effectively 3 communicated , p articularly in the Discussion chapter . However, this organization brings about a disadvantage of conveying five parallel studies within each chapter. 4 II. LITERATURE REVIEW a. Accelerator Technology and Niobium The quest for superconductivity began in 1892 when James Dewar invented the Dewar flask, a vessel he later used to liquefy hydrogen successfully in 1898 [7] . Heike Onnes managed to produce liquid helium in 1908 , which opened a brand - new chapter in the properties of matter at low temperature s [7, 8] . Onnes wrote in his lab notebook in 1911, as he discovered that than K [7, 9] . At that time, however, he was more into celebrating his choice of mercury to validate his theory on electrical resistivity of metals rather than realizing the birth of a new era. In 1913 , the Leiden group led by Onnes found that lead and tin were also s uperconductors, with transition temperatures close to 6 K and 4 K, respectively [8, 10] . In the same year, Onnes was awarded the Nobel Prize in Ph ysics for his extraordinary contribution to low - temperature physics [7] . The world of particle accelerators was almost developing in parallel [11] . Driven by high energy physics research, the history of accelerators can be traced back t o 1895, when Lenard observed electron scattering in gas es , signifying the transition from atomic physics to nuclear physics [11] . In the early twenties , Ernest Rutherford identified the need for atomic projectiles with much higher energy and intensity than what was naturally available [11] . A milestone was achieved in 1932 when Cockcroft and Walton split a lithium ato m with 400 kV protons [11] . A cceler ator technology entered a new stage in 1961 , as Banford and Stafford started the possibility of applying superconducting principles to proton linear accelerator [7, 12] . In this technology, superconductivity is coupled with the existing radiofrequency 5 resonators, hence the term superconducting radiofrequency (SRF). Niobium (Nb) was proposed then for assessment of its potential in the application, because it has the highest superconducting transition temperature ( T c = 9.3 K) among elem ental metals , along with other merits such as being a type II superconductor as well as having good ductility and thermal conductivi ty [12] . The first Nb accelerator cavity incorporating the SRF techno logy was developed in 196 8 at Stanford University [13] , replacing traditional lead - plated copper cavities that operate at room temperature . SRF ca vities enable high duty cycle or even continuous - wave operations with large accelerating gradients while minimizing beam impedance and power dissipation [14] . There are a variety of applications for SRF cavities , ranging from fundamental physics research , including nuclear physics and nuclear astrophysics , to high energy light sources such as those used in life science and materials science [2, 15] . At the core of an acc elerator, cavities consist of a string of ellipsoidal cells [1] . Figure 1 shows an exemplary assembly of a 7 - cell cavity [1 6] . T he largest diameter of the ellipsoid is refe rred to as the equator, and the smallest diameter is the iris [1] . With radiofrequency (RF) induction, t he electromagnetic field between each adjacent pair of cells keeps changing polarity as charged particles pass s uch that a constant accelerating d irection is maintained [17] . The polarity changes are s trategically timed to accommodate the increasing speed of particles. After travel ing through multiple cavities, subatomic particles can nearly re ach the speed of light , while larger particles can reach half the speed of light [17] . There may be tens of thousands of cavities in an accelerator such as the proposed International Linear Collider (I LC), depending on particle characteristics and the desired speed [18] . 6 b. Progress in Improving Cavity Performance The performance of a cavity is typically represented by two paramet ers the accelerating gradient ( field ) E acc and the quality factor Q 0 [1] . E acc denotes the capability of a cavity and Q 0 denotes its efficiency. The theoretical limit f or E acc is calculated to be ~ 55 MV/m for Nb cavities , based on the critical magnetic field, and the design of the ILC requires a n E acc of ~3 1 MV/m [19] . The qu ality factor Q 0 is defined as where U is the energy stored in a cavity, and P c is the energy dissipated in one RF cycle [20] . Typical Q 0 of modern cavities is on the order of 10 10 . To provide an understanding of this value, if Galileo Galile i experiment in the early 17 th century with a 1 Hz pendulum had such a Q 0 , the amplitude of the pendulum would have only decreased by about half as of today [21] . Regardless of the E acc and the highest possible Q 0 [3] . Over the years, steady improvements in both parameters have Figure 1 : Example of a 7 - cell cavity. Blue arrows on top indicate polarity changes of the electro - magnetic fields within the cells [adapted from Figure I - 1 in reference [ 16] ]. 7 been acc omplished , thanks to the growing understanding of limiting phenomena and practical solutions. The first issue identified that affect s cavit y performance was multipacting , a resonant process during which electrons build up within a small region of the cavity surface [1] . These electrons absorb RF power, making it difficult to further increase the electric field by increasing the incident RF power. T he electrons also impact cavity walls, leading to a substantial increase in temperature and eventually to thermal breakdown (discussed next) . This multipacting issue can be overcome with a proper shape design [1] . The second issue is thermal a significant energy loss that occurs when the local temperature of a cavity exceeds T c [1] . Thermal breakdown typically originates at sub - millimeter - size regions of defects, where there is a small temperature increase . This leads to a higher fraction of normally conducting electrons , i.e., instability of the superconducting state [1] . The likelihood of a the rmal breakdown can be reduced by improving the thermal conductivity of Nb [1] . Another issue is field emission, which is the emission of electrons from high electric field regions of a cavity [1] . The RF power is absorbed by t hese electrons and dissipated as heat and radiation upon impact with cavity walls. Intense field emission can initiate t hermal breakdown. Therefore, field emission sites such as surface defects, need to be prevented [1] . Finally, a Q - slope is often present at high electric fields, which is a rapid drop in Q 0 when the accelerating f ield approaches the theoretical limit , as shown in Figure 2 [18, 22] . In general, a low - temperature bake at around 120 °C dramatical ly improves the high field Q 0 , al tho ugh different mechanisms have been proposed to explain this effect and no agreement has been reached so far. 8 Thermal breakdown, field emission , and Q - slope are all closely related to defects in a cavity. A ny material imperfections that potentially lea d to issues with t he superconducting state and strong ele ctro magnetic fields are categorized as defects [1] . These include inclusions (Ta, Cu, Fe, etc. ), chemical or drying stains, balls and voids at electron beam w elds, interstitial s (O, N, C, and H ) and crystalline defects. While other defects can be eliminated via careful handling and purification processes , crystalline defects are prevalent and more difficult to control [1] . c. Dislocations and Cavity Performa nce It is hypothesized that d isloca tions have the most substantial impact on cavity performance among the various crystalline defects in Nb [23 - 25] . This section will discuss how dislocations could interfere with the operation of SRF cavities. Figure 2 : Q 0 vs. E pk measured on a 1.3 GHz single cell cavity b efore and after baking at 100 °C for 48 hours. The b ake moved the Q - slope to higher accelerating fields and increased the Q value [ Figure 1 (b) in reference [22] ]. 9 The first known mechanism is that dislocations serve as pinning centers for magnetic flux, resulting in the irreversibility of magnetization curves [1] . When an external magnetic field is applied, incoming magnetic flux is captured at pinning centers. As the magnetic field is reduced , these flux lines remain trapped, resulting in residual magnetization even when the external field vanishes. Th e only way of eliminating pinned flux is to heat the cavity to destroy the super - conducting state, which is not practical in normal operations. Trapped flux also introduces error in to measurements of the critical magnetic field H c1 a drop in the apparen t values for H c1 has been observed with post - processing steps such as etching and heat treatment , as dislocatio ns are removed [1] . Therefore, dislocations and other pinning centers (such as interstitial impurities) for magnetic flux need to be minimized in a cavity . Dislocations can also degrade the thermal conductivity of Nb, which contribute s to thermal breakdown [1] . The temperature increase due to inadequat e heat transfer introduces local thermal instability that destroys the superconducting state. Romanenko et al. found a correlation between high dislocation content and the hot regions of a cavi t y [26, 27] . Figure 3 shows the l ocal average misorientation (LAM) maps (discussed next) from two regions on a la rge grain cavity [26] . Figure 3 : (right) regions in a cavity. The green color corresponds to a misorientation of 2°, and blue is 0° [Figure 14 in reference [26] ]. 10 LAM provides an estimate of the dislocation content. For a given dat um point, LAM reports the average misorienta ti on between of all the neighboring points within a specified distance from the kernel [28] , as illustrated in Figure 4 for the 2 nd nearest neighbor sampling area. LAM information can be presented in the form of a grayscale map or a histogram. In an LAM map, each EBSD dat um point is assigned a certain shade of gray between white and black, corresponding to misorientations from 0º to a user defined maximum value. In an LAM histogram, the range of misorientations is divided into bins, and the number of observed misorientations from each pixel in each bin determi nes its number fraction. Figure 4 : Local average misorientation (LAM) calculations using the 2nd nearest neigh bor sampling area for the point at the center, LAM averages the misorientations of all its neighboring points (connected by short white lines) within the kernel [ Figure 3 in reference [126] ]. 11 The map on the left had larger LAM value s (more dislocations) , which correlated with hot regions in the cavity, while the map on the right correlated with cold r egions in the cavity [26] . Figure 5 shows corresponding histograms for the LAM maps in Figure 3 , where the cold region h as a sharper peak at a smaller misorientation angle than the hot region [26] . Dislocations in crystall ine materials exist in two forms [29, 30] . Geometrically necessary dislocations (GNDs) account for the lattice curvature arising from an unbalanced population of dislocations of one sign within a given region in a grain. Such lattice c urvature can be revealed by a LAM map, in which a larger LAM value corresponds to a higher GND density . Statistically stored dislocations (SSD s ) are slightly displaced dislocation pairs with opposite signs that do not contribute to t he overall orientation gradient. When there are adequate driving forces such as an Figure 5 : Corresponding histograms f or the LAM maps shown in Figure 3 [Figure 15 in reference [26] ]. 12 elevated temperature, neighboring SSDs with opposite signs can move towards each other and sometimes annihilate [29, 30] . Because more dislocations are categorized as SSDs as the step size increases, the GND s are semi - quantitatively revealed in the LAM maps. A proposed explanation for the dislocation - induced local heating is that dislocation lines vibrate with passing phonons (lattice vibrations, the primary conducting mechani sm in the super - conducting state) and disperse them, thereby slow ing the heat transfer [24] . This interference is most significan t when dislocation lines (both edge and screw) are aligned with the direction of heat flow [24] . Evidence for this theory was provided by Chandrasek a ran et al. , in which annealing at te mperatures above 10 00 ºC usually led to a significant restoration of phonon peaks on deformed single c ryst al and bi - c rystal samples [31 - 33] . Figure 6 shows an example of the phonon peak evolution on a bi - crystal sample that was annealed after being extracted from an ingot slice, deformed in ten sion , and annealed again. The phonon peak of grain 2 disappeared after 15% strain but completely recovered to its original position after the 1100 °C anneal [32] . Moreover, p honon peaks have been observed i n fully re crystallized fine grain samples with a low purity [34, 35] , implying that dislocations are more detrimental than impurities and grain boundaries to thermal conductivity in the superconducting state. This is another reason why it is desirable to reduce the disloc ation content in a cavity . Furthermore, near - surface dislocations may account for the benefits associated with low - temperature baking. Romanenko et al. speculated that dislocation annihilation m ight occur via a vacancy - assisted process at aroun d 120 °C, hence the performance gain [27] . However, other mechanisms such as the elimination of excess concentration of oxygen were also proposed , and more research is needed before a consensus can be reached [2] . Dislocations could still degrade cavity performance in other ways that have not yet been explored and understood. 13 For all of the reasons discussed above, one of the ultimate goals of SRF cavity proce ssing is to minimize the dislocation content in a cavity and to align the remaining dislocations perpendicular to the direction of heat flow to minimiz e phonon dispersion (maximize thermal conductivity) [24] . d. In got Production and Initial Grain Orientation To continue to push the limit of cavity performance , significant research ha s focused on materials science and surface science in the SRF community over recent years [3, 24, 36] . The Figure 6 : Thermal conductivity as a function of temperature for a bi - crystal sample. The original phonon peak (blue arrow) on grain 2 disap peared after 15% strain, but it was fully restored after a 1000 °C/2hr heat treatment [adapted from slide 5 in reference [32] ]. 14 goal is to understand the metallurgical state evolution during the cavity fabrication process, with emphases on three aspects initial crystal orientation s , deep drawing, and post - processing steps , including chemical and heat treatments. I t i s desirable to have a model that can computationally predict the final shape and microstructure (e.g., dislocation content and arrangement) within a cavity, based up on the initial crystal orientations and processing history. With such modeling, accepta nce criteria can be established or improved for materials suppliers, so that it is possible to obtain more consistent cavity performance . T hese three aspects will be introduced in the follo wing sections . Nb ingots are produced and purified by electron bea m melting in vacuum [37] . Raw Nb pellets are melted by an electron beam , and the molten Nb is collected in a water - cooled copper mold to form ingots [37, 38] . Figure 7 shows a schematic diagram of this process [38 - 40] . The ingots are purified several times by repeated electron beam melting [37, 38] . The water cooling leads to large radial and longitudinal temperature gradient s in the ingots. The resultant strain from thermal contrac tion causes dislocations to form [24] . Both the ingot production and ingot purification are done slowly at elevate d temperatures, leading to considerable grain growth , although not to the extent that all dislocations are wiped out since thermal strains occur concurrently with grain growth due to the temperature gradient in the cooling ingot . While hu ge grains are present in an as - received ingot , there has not been much success in getting a grain that extends to the full diameter of an ingot [41] . It is chall enging to control the grain orientations in a n ingot . One of the first Nb ingots that Jefferson L ab received from CBMM had a large single crystal in the center [41] . This is a desirable configuration for deep drawing since the largest strain occurs at the center and a single crystal in 15 this region can h elp enable uniform deformation . H owever, it is unclear under what condition s that ingot was grown and how it could be reproduced [41] . A study at DESY on ingot slices from three suppliers (CBMM, Heraeus, and Ningxia) further demonstrated the lack of reprod ucibility in g rain microstructures [42] . Full - penetration X - ray characterization at DESY - HASYLAB showed that the cent ral grain of the CB MM slice had good homogeneity with a near { 111 } orientation measurements at seven locations of the grain revealed minim a l fluctuations, proving high quality of the single crystal. The Heraeus ingot slice Figure 7 : Schematic of the electron beam melting equipment to produce and to purify Nb ingots [Figure 2 in reference [38] ]. 16 consisted of a big central grain with a near { 100 } orientation and small perimeter grains. The central crystal again possessed a high quality with little orientation flu ct uations. In contrast, the Ningxia slice consisted of many grains with wide ly scatter ed orientations [42] . At t he center of the slice, a signal splitting of refle ctions (indicating multiple crystals) and Debye - Scherrer rings ( indicating small crystals) we re observed in addition to the strong single crystal signal [42] . Due to the reduced number of grain boundaries in large grain Nb , it is expected that the contribution to thermal resistance from phonon scattering at grain boundaries will be much lower than f ine grain Nb [42] . The thermal conductivity of a series of fine grain, large grain , and single crystal Nb samples was measured at low temperatures. The results showed pronounced phonon peaks on the large grain and single crystal samples from Heraeus after an 800 ° C heat treatment, while no phonon peak was observed on the fine grain samples after the same heat treatment. No phon on peak was observed either on a large grain sample from Ningxia, which is likely due to its large grain consisting of many small s ub - grains. This suggests that the orientation consistency of the large grains could be essential for practical superconductivity of Nb [42] . While there may be orientation variation s in the plane of an ingot slice, orientation s along the longitudinal direct ion of an ingot appear to be quite stab le . Umezawa et al . examined 48 slices extracted from the top to the bott om of an ingot with ultrasonic tomography, as shown in Figure 8 [43, 44] . T he grain orientations were almost identical , although the positioning of grain boun daries differed slightly with each slice . They concluded that the grains grew in a colum nar manner and that the size and shape of a grain strongly depended on the orientations present at the base plate 17 [44] . This suggests that a s eeding approach may work in obtaining desirable orientatio n s for Nb ingots (discussed next) . Figure 8 : Ultrasonic tomography of a Nb ingot. No. 1 is near the bottom of the ingot, and No. 48 is near the top [Figure 3 in reference [44] ]. 18 In the pursuit of reducing the grain boundary area even further , efforts have been made to grow single crystal ingots. Heraeus investigated the growth paramete rs to reliably produce ingots with a sizeabl e cent ral grain with a specified orientation [13, 45, 46] . Several variables in electron drip melting could affect the nucleation and dissolution of grains in the liquid pool, such as the pool temperature, molten pool motion, and dripping of melt stock into the pool. The ir preliminary conclusion was that the ir melting p rocess was not stable enough to reproducibly create a central crystal of ~150 mm in diameter with a con trolled orientation throughout a whole ingot of ~ 2000 mm in length [13] . Tokyo - Denkai also attempted to grow single cryst al ingots by placing a seed crystal on to a Nb base plate before the standard melting process [13, 44] . However, u ltrasonic tomography revealed that the base pla te crystals rather than the seed determined the grain growth in the ingot . It was argued tha t a thicker seed crystal might be necessary for a successful single crystal growth [13] . DESY demonstrated that i t is possible to enlarge a single crystal without destroying its original microstructure by rolling [13, 47] . E ven after being defor med into half - cells, the enlarged single crystals still maintain ed their orienta tions normal to the surface. Annealing at 800 °C did not alter the deformed single crystals either (i.e., no recrystallization), al though { 001 } and { 110 } orientations were more stable than { 111 } orientations [13, 47] . They also observed that when the misorientation between two single crystals wa s with in 3° , they gr e w into one grain upon electron beam welding [13] . D islocations have been observed in as - received i ngots. The el ectron channeling contrast image of a sample from a n ingot slice demonstrated large populations of entangled dislocations , 19 as shown in Figure 9 [24, 48] . White regions indicat e a high dislocation density , a s electrons are backscattered towards the detector by dislocations ; black areas correspond to lattice planes that are oriented for electron channeling with little distortion by dislocations . Such clusters of dislocations res emble those observed in cold - worked metals [29] . These preexisting networks of dislocations in an ingot could have an impact on deformation and microstructural evolution during subsequent forming steps . Figure 9 : Electron channeling contr ast image of a sample from an as - received Nb ingot showing contrast arising from dislocations [Figure 8 in reference [24] ]. 20 e. Large Grain Approach to Forming Cavities There are mainly two approaches to forming a cavity. One is the well - established fine grain approach [37] , in which Nb ingots are broken dow n with forging, milling, and rolling, plus intermediate heat tre atments to retrieve formability. Sheet metal d isks of ~3 mm in thickness and ~ 35 cm in diameter are produced this way for deep drawing. A small and uniform grain size of ~50 µm is generally necessary for good formability so that no excessive surface roughing occurs during deformation [13] . Alternatively, disks can be produced by directly slici ng Nb ingots, namely the large grain approach [13, 41, 49] . Figure 10 shows a schematic diagram of the fine grain approach (above) and the large grain appr oach (below) [37] . Propos ed about two decades ago, the large grain approach quickly gained attention as it significantly reduces fabrication costs by eliminating the rolling and annealing steps, and the amount of material waste to produce disks was estimated to be 15%, compared to about 45% for standard fine grain disks [41, 43, 50] . More importantly, comparable or even better performance has been achieved from large grain cavities [13, 41, 51 - 55] . The large grain approach was a breakthrough in the cavity manufacturing ind ustry and could benefit many accelerator projects , including the ILC. 21 An apparent difference between disks obtained from the two methods is the average grain size. Fine grain disks usually have a uniform grain size of ~50 µm, while the grain size for large grain disks is much less uniform, and can be as large as 20 cm. Thus, large gr ain Nb tends to be more mechanically anisotropic , with f ormability and dimensional stability inferior to fine grain Nb . However, a study by Ciovati et al . [56] demonstrated that with proper heat treatments, the mechanical properties (evaluated by yield strength and burs t tests) of large grain cavities c ould be better than fine grain cavities. Figure 10 : Flow diagram of SRF cavity fabrication using fine grain or large grain Nb (courtesy of W.C. Her aeus, Germany) [adapted from Figure 6 in referen ce [37] ]. 22 The heterogeneous deformation of large grain ingot slices is most ly accounted for by the differences in crystal orientations [16, 57] . From established principles for body - centered cubic (bcc) materials , orientations with <111> directions normal to the surface have high flow stress (hard), yet are the most stable in deep drawing, while orientations with <100> directions normal t o the surface are soft and less stable [24] . From single crystal experiments, tension along <111> directions requires about twice as much stres s as tension in directions more than 20 away from <111> [16, 58] . L arge grain cavities may (a combination of bumps and grooves) caused by the heterogeneous deformation at and near grain boundaries. This can be overcome with appropriate mechanical processing, such as barrel polishing [3] . However, after chemical treatments, even though the grain surfaces remain mostly smooth, the difference in etch rates from one orientation to another produces steps up to 500 µm between the grains, more pro minent than t hose in fine grain cavities [3, 51] . While large grain Nb exhib its excellent ductility in uniaxial tension, its biaxial deformation properties (e.g., susceptibility to thinning ) are closer to those of fine grain material rather than single crystals [3] . Ther efore, one of the major concerns about the large grain approach is whether the cost reduction makes it worthwhile to tolerate the uncertainties in forming [24] . f. Microstru cture of F ine G rain Nb S heets As the large grain approach has not been fully industrialized due to its recent introduction into the field , most SRF cavities to date are still manufactured with fine grain Nb sheets. A critical step in produc ing these sheet s is rolling combined with heat treatments . The final microstructure of a rolled sheet is determined by both the initial grain orientations and processing history , as will be review ed in this section . 23 Rolled and heat - treated Nb sheets tend to exhibit a sa ndwich microstructure, with { 100 } orientations near the surface, and { 111 } orientations in the middle [24] . Raabe et al. observed such microstructures on polycrystalline Nb rolled to 50% and 60% reduction and a ttributed them to slip on {110} and {112} planes [59] . A similar study by Abreu et al. revealed that {100} orientations increased with the amount of deformation , but not {111} orientations [60] . T h e di screpancy may be due in part to different starting mate ria l s Raabe et al. used a weakly textured material , while Abreu et al. used a hot - rolled sheet [59, 60] . For manufacturing SRF cavities, it is desirable to have Nb sheets with consistent texture and grain size s . However, there is almost always a considerabl e variation in the sheet microstructure , e ven for suppliers wi th mass production capability and well - co ntrolled processing schedules [24, 61, 62] . For example, Jiang et al. examined ten rolled sheets from two suppliers, and al l of them had different microstructures ( e.g., gr ain size and preferred orientations) [63] . Full recrystallization that removes most dislocations generated during rolling is necessary for good formability of Nb sheets. In a study by Jiang et al. , one batch of material ( Figure 11 (a) ) was under - recrystallized compared to (b) and (c) due to the presence of elongate d grains [63] . T his batch showed greater mechanical anisotropy in tensile tests , and there were problems in deep drawing. The other two ba tches shown in Figure 11 (b) and (c) had equiaxed grains with more isotropic mechanical properties, suggesting that they would deform more homogeneously ( cause less earing ) during deep drawing [63] . T he d eformation texture of Nb can also be op timized by asymmetric rolling [6 4] . Ito et al. found that l ess elongated grains could be obtained by differential - speed r olling (different rotational speed of upper and lower rolls [65] ) with a speed ratio of 1.4 . Moreover , subsequent heat treatment 24 of asymmetric ally - rolled samples produced an equiaxed mic - fi ber ({110} orientations) , so there is less planar anisotropy in the sheets [64] . A commonality among the roll ed Nb sheets is a lack of {110} (Goss) orientations [24] . These orientations cannot be a chieved by rolling, as the stress state facili tates rotations towards orientations between {001} and {111} aligned with the sheet normal direction . However, unlike silicon s teel , where a high fraction of {110} orientations can be obtained by recrystallization after deformation , {110} orientations are rare ly observed even in annealed Nb sheets . Th e difference in recrystallization behavior despite other similarities between the two materials could be due to the existence of small particles in si licon steel s or the opposite elastic anisotropy of Nb and Fe [24] . 25 Figure 11 : Orientation maps of the full thickness of Nb tensile specimens from (a) Wah - Chang as - received ILC sheet (b) Wah - Chang as - received ILC sheet after annealing (c) T oky o - Denkai as - received sheet [Figure 2 in reference [63] ]. 26 To identify how specific orientations respond to rolling and annealing , Nb samples with much larger grain s were studied . Srinivasan et al. rolled Nb single crystals with { 001 } , {110} , and {111} or ientations to strains of 25 - 50% [66] . After deformation, t he samples were annealed at 800 ° C, 1000 °C, and 1200 °C for three h ours . The {001} and { 110 } samples exhibited good orientation stability, i.e., no recrystallization occurr ed after annealing. This is consistent with a minor hardness increase in these samples after rolling, which indicates low work hardening and s tored energy. On the other hand, the {111} samples deformed to 50% strain showed more work hardening and consequ ently, enhanced recovery in hardness after the 1000 °C and 1200 °C heat treatment , due to partial recrystallization. The greater residual hardness of these samples can be attributed to a higher GND content to accommodate the lattice curvature in non - recry stallized regions [66] . Sandim et al. also investigated orientation evolution during rolling and annealing of Nb. One of their studies used h igh - resolution electron backscatter diffraction (EBSD) to observe the subdivision of three neighboring grains in coarse - grained Nb rolled to 80% [67] . Results show strong orien tation dependence in grain fragmentation two of the grains developed deformation bands nearly parallel to the rolling direction , while the Goss - oriented third grain developed a more organized micro structure . Two other studies by Sandim et al. involved r ecrystallization of rolled large grain Nb [68, 69] . In both cases, h ighly misoriented lamellar boundaries formed due to heterogene ous deformation in rolling . Upon annealing, t hese boundaries served as nucleation sites for grains, but the original grain boundary in the less er deformed bi - crystal sample (rolled to 70%) was also confirmed to be a nucl eation site. A bnormal sub - grain gr owth was proposed to account for the formation of other grains during recrystallization [68] . 27 g. Cavity Fabrication and Surface Studies This section will introduce major steps in forming cavities from fine grain or large grain disks and review prior studies that correlate the microstructure s with the performance of cavities. The smallest unit of a cavity is a half - cell, formed by deep drawing as illustrated in Figure 12 [37] . Half - cells are typically formed by deep drawing Nb disks and are electron beam welded together at the equato r and iris to form a series of cells. A schematic configuration of deep drawing is also shown in Figure 12 [37] . After welding, the inner surface of a cavity is cleaned using buffered chemical polishing (BCP) [ 37] . The BCP solution is a mixture of phosphoric acid, hydrofluoric acid , and nitr ic acid in the ratio of 1:1:2 [70] . A typical rem to be cooled in order to minimize hydrogen contamination via diffusion [37] . Next, the cavity is heat treated in a vacuum furnace to remove most of the dislocations introduced during forming . Various s chedules have been used in the SRF community, such as Figure 12 : A half - cell (right) formed from a large grain ingot slice (left) by deep drawing, and a schematic of the process is shown in the middle [adapted from Figure 8 in reference [37] ]. 28 600 °C for 10 hours, 800 °C for two hours, and 1000 °C for two hours, and no agreement has yet been reached as to which one is the most beneficial for cavity performance [71, 72] . A thin and stable pentoxide layer tends to form on the surface of Nb with exposure to air or water. The equilibrium thickness of the oxide layer is on average ~5 nm , but is dependent on crystal orientations [3] . While the oxide itself does not great ly degrade the superconducting properties of Nb, the interface between the oxide layer and Nb can absorb contaminants , such as hydrogen [73, 74] . A vacuum anneal above 500 ºC is effective in dissolving the surface oxide into the bulk [75] . The heat tre atment also removes hydrogen co ntamination during BCP [3] . During the heat treatment of a cavity , microstructural changes occur by the mechanisms of recovery, recrystallization, or a combination o f both [24, 29] . Recovery takes place when a plastically deformed material is heated to moderate temperatures. When high purity Nb is heated to 700 - 800 °C (about 35% of its melting point), the stored strain energy from plastic deformation is first released by local rearrangements of dislocations , where nearby dislocations with opposite signs annihilate with each other. The strain energy is fu rther reduced as low angle boundaries (<5° misorientation ) begin to form [29] . Both processes require the reduction of defect structure and climb of dislocations, s o they only occur when there is enough thermal energy for local as well as long - range diffusion [24, 29] . When the heating is above a critical temperature, new g rains containing few dislocations emerge in the recovered microstructure, and grains with fewer dislocations grow into those with more dislocations [24, 29] . This is the process o f recrystallization, during which high angle grain boundaries (>10° misorientation ) are produced [29] . 29 The inverse pole figures in Figure 13 illustrate the effects of deformation and heat treatment [24] . The EBSD measurements were done on different samples for the four conditions, so they do not describe orienta tion evolution. Typically, t he orientation spread is high est in the deformed condition and drops as recrystallization occurs . The orientation spread is similar to the LAM in reflecting dislocation content, but it is a larger - scale evaluation. The modera te orientation spread in the recovered state reflects the presence of sub - grains. This F igure is a simplified representation of the evolution of dislocations along the cavity fabrication path dislocations nucleate during the ingot solidificati on due to the large thermal gradient; dislocation multiplication occurs during deep drawing through Frank - Read sources and cross slip ; annealing removes SSDs by recovery and more dislocations by recrystallization [29] . C omplete recrystallization is believed to be necessary for the optimal superconducting and mechanical properties of fine grain Nb [ 3] . Material s subjected to a small amount of deformation usually have large recrystallize d grains upon annealing , while heavily deformed single crystals annealed at low temperatures for short times tend to have small recrystallized grains, including na nocrystals. The recrystallizatio n temperature decreases with increasing purity [3] . It is also possible to achieve r ecovery without recrystallization in large grain cavit ies by annealing at low temperature s for a long time [3] . Figure 13 : Representative inverse pole figures from EBSD measurements on different samples. The orientation spread is greatest after deformation and is least in the recrystallized condition [adapted from Figu re 9 in reference [24] ]. 30 T he surface of a cavity tends to ha ve a higher dislocation content than the bulk due to the friction effects from the die in deep drawing, and a BCP etch is neces sary to remove the surface damage layer. Kneisel et al. identified the dependence of achievable accelerating gradients on the amount of material removed from the cavity surface ( Figure 14 ) [76] . The test was stopped at about 180 µm as the cavity performance was acceptable for their application. The thickness of the damage layer was estimated to be 100 - 200 µm. Therefore, removing surface material from deep drawn cavities via barrel polishing and chemical treatments has become normative in the SRF community. Romanenko et al. obs erved a striking effect of the low - temperature bake on dislocat ions [27 ] . Figure 15 shows the LAM values for small /large grain cavity samples cleaned by BCP or electropolishing (EP), before and after the bake [27] . Except for the small grain BCP case , LAM Figure 14 : Dependence of achievable accelerating gradient on the thickness of material removed from surface, measured on a fine grain cavity [adapted from Figure 3 in reference [76] ]. 31 values were noticeably lowe r after baking , suggesti ng that dislocations were removed . However , s ome grains resisted recovery/recrystallization and retained a high dislocation density [27] . Initiation of flux penetration corresponds to RF losses during cavity tests [3, 77] . After baking, the onset of flux penetration shifted towards higher fields for both hot and cold spots, whic h is consistent with prior observations on dislocation density [27] . Also, h ydride precipitates were identified on Nb samples cut from cavitie s after cryogenic RF test s , and the hydride concentration was higher on hot spots (high dislocation content ) than it was on cold spots [3] . Figure 15 : Change in local average misorientations (LAMs) on cavity samples due to baking. In each case, measurements were made on the same sample before and after baking in ultra - high vacuum [Figure 2 in reference [27] ]. 32 The high local concentrati on of hydrogen facilitated the formation of hydrides upon RF cycling [3] . This series of cavity test results again show that dislocations play a significant role in the supercon ducting behavior of Nb and that reducing the dislocation content is essential to improve t he reproducibility of cavity performance [3] . h. Active Slip Systems in Nb Slip during plastic deformation is the underlying mechanism that accounts for many of the cavity performance ph enomena previ ously discussed . This section will cover fundamental studies on slip in Nb , along with general theories on deformation in bcc metals . In the cavity fabrication process, crystal orientations, active slip systems, dislocation sub - structure, and recrystall ization during annealing are interrelated from the metallurgical perspective [24] . S lip behavior depends on how crystals are oriented with respect to the applied stress; slip and interactions of slip systems re sult in a specific dislocation substructure; the dislocation sub - structure determines how recovery and recrystallization proceed d uring heat treatments , and the remaining dislocation s may be defective regions in a cavity [26, 27, 78] . Establishing the correct model for slip systems is particularly important for predicting the microstructural evolution during the cavity fabrication process . To understand sli p during deep drawing of a large grain Nb disks , knowledg e about slip in simpler uniaxial tension of single crystal Nb is needed to provide an initial basis . Specifically, the study of slip addresses two concerns the effective / macroscopic slip planes (evident by slip trace analysis and crystal rotation), and planes on which kink pairs nucleate along dislocation lines (fundamental/atomic slip planes) [79] . 33 For bcc metals, the close - packed (hence slip) directions are <111>, but there are no close - packed planes like those in face - centered cubic metals [79] . Planes containing the close - packed direction with a decreasing order of inter - planar spacin g are {110}, {112}, and {123}. N o stable stacking faults have been found in bcc metals due to their high stacking fault energy, so no slip planes are defined by dislocation dissociations either . K ocks described in which slip occurs in <111> directions without f ollowing any particular slip planes [79, 80] . In bcc materia ls , edge dislocations have lower lat tice friction and are more mobile than screw dislocations at room temperature, so screw dislocations are the rate - controlling mechanism during plastic deformation [24] . Since the motion of screw dislocations is thermally activated, it will likely occur by nucleation of kink pairs on well - defined atomic planes [79] . Th e kink pair nucleation mechanism gives rise to the temperature and strain rate dependence o f flow stress es in bcc metals [79] . The low mobility of bcc screw dislocat ions can be partly explained by t he core relaxation theor y [81 - 85] . A <111> bcc screw dislocation core tends to spre ad onto three symmetric {110} or {112} planes, which results in a non - planar core structure and hinders the movement of screw dislocations [86] . Consequently, screw dislocation mobility i s affected by non - glide shear stresses , resulting in a violation of the Schmid law. Due to their low mobility , long and drawn - out screw dislocations are usually left behind during plastic deformation and are observable [16] . T he core relaxation in Nb depends on bot h the temperature and purity [87 - 89] . Seege r argued that fundamental slip planes change from {110} at low temperatures (<100 K) to {112} at higher temperatures due to a change in the core structure [88] . Experimental results from many bc c materials support this theory, but there are exceptions [90 - 94] . I nterstitial impurities such as 34 hydro gen stabil ize the {110} relaxation [85, 95] . SRF c avities are fabri cated from high purity Nb at room temperature, so the {112} relaxation should be favored ove r {110}. However, the forming process could lead to hydrogen contamination so that both relaxations may coexist [16] . The difference s between {110} and {112 } relaxations account for the difference s in critical resolved shear stresses between {110} and {112} planes [16 ] . In contrast, atomistic simulations of bcc metals predict that slip should occur fundamentally on {110} plan es, regardless of the interatomic potential, boundary condition s , or material purity [79] . Atomistic simulations have been successful in pre dicting mechanical properties of bcc metals, e.g., in demonstrating that non - planar screw dislocation core s lead to strong lattice resistance and thermally activated plast icity [79] . Furthermore , net {112} slip could occur by the motion of screw dislocations on alternating {110} planes , and the core structure does not straightforward ly dictate apparent slip planes [79] . Another phenomenon unique to bcc metals is the twinning/anti - twinning asymmetry, in which a smaller resolved shear stress is needed to move a screw dislocation in the twinning sense of slip than in the anti - twinning sense [86, 87, 96, 97] . This asymmetry has been attributed to the energy required to displace an atom within a given slip plane in the direction of the Burgers vector. The twinning/anti - twinning asymmetry and non - planar screw dislocation cores give rise to the non - Schmid effects in bcc metals and affect the critical resolved shear stress for a given slip system to v arying extents [86, 87, 96, 97] . Atomistic simulations have confirmed the presence of the twinning/anti - twinning asymmetry [79] . The relationship between slip systems may change with deformation due to the rotation of the crystal with respect to the applied stress. A general rule regarding work hardening is that if 35 the operating slip systems have a common slip direc tion, little hardening results; but there will be significant work hardening if the slip systems have different slip directions . For example, the inter action of intersecting <111> slip systems could l eave beh ind sessile dislocations with the resulting Burgers vector on a non - close packed {100} plane [79] . Slip trace analysis has been widely used in fundamental studies of slip . Deformation experiments lead to transport of material by dislocations onto a free surface, forming slip traces. These slip traces can be imaged in several ways , such as optical microscopy, scanning electron microscopy (SEM), and atomic force microscopy [79, 98, 99] . S lip trace analysis may be complicated by the tendency of bcc screw dislocati ons to cross slip on either {112} or {110} planes due to core relaxation [85, 95] . Figure 16 shows an illustration of this effect , where frequent change s in slip planes lead to a wavy slip t race that roughly follows the tra ce of a highly stressed plane [16] . This causes the problem o f imitation , w here cross slip occurs over a small length scale, such that the macroscopic slip trace appears straight rather than serrated and is mistaken for a slip trace of the other slip plane family. The smaller the distance between cross - slip events, which may occ ur at nanometer scale [85, 95] , the more difficult to distinguish that a slip trace was formed by a combination of two individual slip traces. 36 A limitation of slip trace analysis is that slip may be influenced by the presence of a free surface, as evidenced by studies using thin foils [79, 100, 101] . Vesely noticed on molybdenum thin foils that the activated slip systems have a Burgers vector nearly parallel to the surfac e besides having a high resolved shear stress [100, 101] . A similar outcome was obtained by Luft and Kaun [102] , who studied thin foils with different exposed faces and compared the results to thos e obtained using cylindrical rods. For the thin foils, the slip traces were determined by the subsurface dislocations, which might not be a good r epresentation of the bulk behavior. Therefore, slip trace analysis could be misleading in identifying slip p lanes for bulk plasticity [79, 100 - 102] . Figure 16 : A schematic diagram showing a [111] bcc screw dislocation with its Burgers vector and line direction out of the page, and the effect of core relaxation on a sl ip trace: a) The core may relax on either three symmetric {112} planes (dashed lines) or three symmetric {110} planes (solid lines). Motion of the dislocation can leave a trace on a surface indicating the slip plane for: b) {112} relaxation, the screw dis location may frequently cross slip on two of the three {112} relaxation planes (each c hange in plane marked by a circle), while following a high resolved shear stress plane (fine dotted line). c) For {110} relaxation, the screw dislocation may frequently cross slip on two of the {110} planes, while following a high resolved shear stress pl ane [Figure II - 13 in reference [16] ]. 37 Slip in the various bcc metals has a lot in common , al though ea ch material has its subtleties [79] . Investigation of slip in Nb started over 60 years ago when several researchers deformed single crystal Nb under different experi mental conditions [90, 94, 103 - 105] . More attention has been put into Nb over the past few decades, as it became the material of choic e to build SRF cavities. The following paragraphs will concentrate on slip in high purity Nb at room temperature, which is the condition during SRF cavity manufacturing . Maddin and Chen used optical slip trace analyses and Laue X - ray diffraction to identify slip only on {110} planes in Nb at room temperature in both tension and comp ression across the unit triangle [90] . In the work of Duesbery and Foxal l ( referred to as D&F later ), s lip was observed on either {110} or {112} planes depen ding on the stress axis and the orientation of single crystal s as detailed in [104] . Baars also investigated slip systems in Nb, and his findings will be summarized in the follo wing paragraphs [16] . Resul ts from the D&F set will be compared to the work by Baars [16] . Baars [16] ex tracted 12 sets of single crystals with different orientations from a large grain Nb ingot slice supplied by Ningxia. The orientations were chosen to initially favor a single slip system or a combination of slip systems. The interstitial impuri ty content of the Ningxia samples is high enough such that elementary slip on both {112} and {1 10} planes should be considered [16, 95] . However, the results suggest that the dominant slip systems at yield are {112}. This is based up on the interpr etation of the stress - strain behavior of a sample that was oriented to favor a single {110} slip system, but its initial hardening behavior resembled another sample that favored two intersecting {112} slip systems. Therefore , it was concluded t hat the ons et of hardening in both samples was predominantly caused by two {112} slip systems interfering with each other [16] . Furthermore, samples with larger differences between the initial resolved shear stress on 38 intersecting {112} slip systems have a lower initial hardening slope , while those with small er difference s have a higher initial harde ning slope [16] . Considering only the {110} slip systems or a combination of {110} and {112} slip systems does not give the same co rrelation on hardening . T he rotation of tensile axes can also be explained by the dominance of {112} slip systems at yield [16] . A ratio between the shear stress of the two most - stressed intersecting {112} slip systems below 1.1 correlate s well with hardening at yield, suggesting that the combined twinning /anti - twinning and non - glide shear stress effects may o nly alter the critical resolved shear stress by a small amount [16] . Thus , incorporation of many of the se de tails may not be necessary for practical models for the deformation of large grain Nb . Initial simulation results from Mapar et al. suggest that the shape change in the tensile samples can be adequately model ed ( determined by slip planes and kinematics). However, the non - Schmid effects are still needed to get the stress levels correct (shown later) [106] . The dominance of {112} slip at yield followed by {110} slip for the rest of deformation appears to comply with the theory of Seeg er et al. [16, 95] , which suggests that the core rela x ation of screw dislocation s in high purity Nb is on {112} planes , and that impurities change the core relaxation to {110} planes. This indicates that the initial interstitial impurities of ~400 at . ppm (plus hydrogen absorbed during sample preparation) did not cause a significant amount of {110} relaxation at yield, but the additional impurities absorbed during deformation in the air (due to breakdown of the surface oxide layer that allows hydrogen to get in ) changed the relaxation to {110} type [16] . The possibility that the favored slip plane could change during deformation due to absorbed impurities such as hydrogen poses a challenge to the modeling of slip in Nb [16] . 39 B ands with distinct orientations are more evident in the deformed samples favoring intersecting slip sy stems than in samples with easy glide orientations [16] . This suggests that with the same amount of strain, samples ca n have different amounts of GNDs , which could account for delayed observation of deformation band s until strains are large . Even though uniaxial tension is not the stress state for fabricating cavities, this implies t hat selecting a strategic orientation may be important for minimizing dislocation content and for ensuring that dislocations are aligned desirably in a cavity . Also , samples with higher dislocation content are more prone to recrystallization, which may lead to unexpected grains upon annealing [16] . The impurity content and experimental conditions of the D&F data set are close to the Ningxia samples, except that preexisting dislocations should be minimal in the D&F set (grown by electron beam zone melting) due to the ir anneal before deformation [16, 104] . The lower yield stress in the D&F set is consistent with their higher purity, t hough the interstitial impurity conten t is still high enough so that {110} slip must be considered [16, 104] . The D&F set shows the same trend as the Ningxia set, in which a decreasing difference in the resolved shear stresses of the intersecting most - str essed {112} slip systems at yield correlates well with the initial hardening slope [16, 104] . However, the trend is al so present in the D&F set if the intersecting most - stressed {110} slip systems or the two most - stressed systems are compared . This leaves some uncertainty about active sli p systems at yield for the D&F set [104] . Figure 17 shows a stereographic projection section of the tensile axes for both the D&F and Ningxia samples, with boundaries of equal Schmid factor (resolved shear stress) between {11 0 } and {11 2 } slip systems whose <111> slip directions are either parallel or intersecting [16] . As the twinning/anti - twinning asymmetry and non - g lide stress es could alter the critical resolved shear 40 stress, the boundaries with both s lip systems equally active may be shifted . Some of the boundaries may not even exist depending on the experimental conditions (i.e., purity and temperature). This F ig ure is useful in selecting orientations that favor specific sli p systems for further investigations into slip systems in Nb or for forming cavities [16] . Overall, the outcomes from t he Ningxia and D&F sets are consistent with dominant {112} slip at yield [16] . The o ccasional {110} slip observed at yield in the D&F set may come from imitation by frequent cross slip on {112} slip planes, though this requires that the imitating (less stressed) slip systems be activated by the twinning/anti - twinning and non - glide stress effects [16] . While dislocation motion unhindered by impuri ties tends to occur in bursts that should be visible at the scale at w hich the samples were imaged , it remains unclear if this possibility of imitation can be eliminated [1 6, 107 - 109] . 41 Figure 17 : Initial tensile axes for D&F and Ningxia samples on a stereographic projection section. The boundaries mark where the Schmid factors are equal between two {110} slip systems (soli d lines), two {112} slip systems (dashed lines), a {110} and a {112} slip system (dotted lines). The boundary is colored green for the same slip direction, and red for intersecting slip directions. Slip systems whose Schmid factors are greatest in the ar ea between the bound aries are labeled [Figure V - 9 in reference [16] ]. 42 i. Ob servation of Disloca tions in Nb Direct observation of dislocations complements slip analys e s , since it provides additional details about the deformation mechanism . D islocations in Nb have been imaged by transmission electron microscopy (TEM ) since the 1960s , as will be revie wed in this section . Stiegler et al. studied the dislocation evolution during rolling and annealing of Nb single crystals [110] . For a rolling reduction up to 10%, disloca tion entanglements were confined to a ~100 µm surface layer , while the bulk developed a distinctive cell structure 1 . With 80 % reduction , individual cells were no longer discernible [110] . After heat treatment , dislocations inside the cells moved towards the walls to form organized networks [110] . At higher temp eratures, r egions with low di slocation content were formed by sweeping of dislocations o ut of the networks facilitated by the thermal energy [110] . Figure 18 shows the cell str ucture on a 50% reduction sample and the organized dislocation networks on a 98% reduction sample that was annealed at 900 °C for an hour [110] . Bowen et al. deformed Nb s ingle crystals in uniaxial tension at room temperature and observed long clusters of edge dislocations on {112} slip planes in stage I work hardening [103] . During stage II , densely packed secondary dislocations built up within the cell structure , as in the case of rolling . A similar study by Foxall et al. also demonstrated the presence of edge dis locations in the form of dipoles and loops in stage I [94] . They further observed that dislocations in stage II were primarily distributed in tilt and twist boundaries as well as in edge multipole walls [94] . 1 No details about rolling were provided in the paper; as actua l strain history depends on roller size, sample thickness, and strain per pass, these results may not be consistent with other studies. 43 Figure 18 : TEM micrographs of (a) dislocation cell structure in a Nb sample cold rolled to 50% (45,000× magnification) (b) dislocation networks in a Nb sample r olled to 98% and annealed at 900 °C/1h (44,000× magnification) [Figure 5 and Figure 9 in reference [1 10 ]]. 44 In contrast, Ikeno et al. observed mainly screw dislocations on single crystal Nb thin foils stretched at room temperature (strain level not specified) [111] . They argued that the clusters of dislocation dipoles originated from jogs rather than from dislocation trapping . As their experiment was done in - situ , they suggested that the previously identified dislocation substructure in Nb could be partly due to artifacts during sample u nloading an d thinning [111] . Dislocations of screw character were also observed by Thompson et al. [112] on polycrystalline Nb samples deformed by cold rolling a nd drawing. Louchet et al. conducted in - situ tensile tests of Nb thin foils at different temperature s [83] . The y observed that screw dislocations dictate the deformation behavior below ~ 2 0 0 K, while the room tempe rature deformation is dominated by the motion of mixed dislocations with short , pure screw segments [83] . Chang et al. examined the interactions of glissile dislocations in Nb [113] . Even though all interactions led to sessile dislocations with <100> or <110> Burgers vectors, one interaction surprisingly facilitated slip by promoting the c ross slip of a portion of one reactant mobile <111> dislocations [113] . This implies that not all interactions of intersecting slip systems would necessarily hinder the slip process , and adds to the complexity of deformation of Nb [113] . In summary, both edge and screw dislocations in cell / wall structure s have been identified in deformed Nb samples by TEM . While it is generally believed that screw dislocati ons dictate the room temperature deformation of Nb , edge dislocations are commonly observed . Therefore, it would be desirable to characterize dislocations in Nb using nondestructive techniques such as electron channeling contrast imaging (ECCI) [114] to minimize artifacts from sample preparation , which is lacking in the literature . 45 j. Evaluation of GNDs using cross - correlation EBSD In the past decade, a cross - correlation based analysis of high - reso lution EBSD patterns has been developed , and it enables estimating GND content and arrangement in deformed material s [ 115 - 118] . The cross - correlation EBSD (CC - EBSD) method bridges the gap between localized imaging techniques such as TEM and macrosc opi c analyzing techniques such as X - ray diffraction for characterizing dislocation s [116] . In CC - EBS D, variations in elastic strain and lattice curvature are calculated from subtle shifts in the positions of zone axes and other diffraction features i n EBSD patterns , based up on a chosen reference pattern with zero or known strain [116] . Strain s as low as 10 - 4 and rotations as low as 0.006° can be resolved [116, 117] . Even if the strain is unknown for a reference pattern , the GND distributio n can still be extracted as only the gradients of strains and lattice rotations are needed for the evaluation [116] . CC - EBSD was initially applied to semiconductors due to their well - defined geometry and low dislocation density, and it has evolved to be sufficiently reliable for struc tural materials such as metals [116, 118] . Wilkins on et al. demonstrated satisfactory utility of the method for studying dislocation in four deformation modes of metallic systems nanoinde ntation, phase transformation, thermal contraction , and fatigue [116] . To better understand t he capabilities and limitations of CC - EBSD, Dunlap et al. compared the dislocation distribution s calculated from CC - EBSD with direct observations from ECCI [119] . The dislocation densitie s measured by both methods show good agreement, though the discrepanc y in spatial arrangements is more significant [119] . Figure 19 shows a comparison of ECCI and CC - EBSD from the same area near an indent , in which the approximate locations of dislocations match , 46 but there is no one - to - one correlati on [119] . The discrepancy may re sult from two aspects CC - EBSD could miss dipole s due to its inferior spatial resolution, while ECCI could miss dislocations due to invisibility criteria or may be unable to resolve clusters of dislocations [119] . Estimation of GND density using CC - EBSD may be influenced by step size a nd binning ( averag ing adjacent pixels in a pattern) [120, 121] . Jiang et al. discovered that a n increase in the step size of EBSD scans leads to lower GND density because some dislocations will be considered as SSD s [120] . GND density maps of a deformed Cu sample exhibited noticeable loss of features when the step s ize was changed from 0.5 to 2 µ m , as the d islocation cell size is about 1.5 µ m in the material [120] . T hey also found that pattern binning (up to 8x8) does not affect the calculated GND density si gnificantly , giving the potential for speeding up CC - EBSD data acquisition. Ruggles et al. modeled the change in calculated GND density as a function of step size by incorporating the transition of GNDs into SSDs due to the implicit Burgers circuit defined by step size [121] . They found a range of steps size s where the calculated GND density is nearly constant Figure 19 : (a) Electron channeling contrast (ECC) image of dislocations near an indent (b) GND density map of the same area generated from CC - EBSD showing similar dislocation distribution (c) Dislocat ion density map calculated by counting dislocations in the ECC image [Figure 3 in reference [11 9 ]]. 47 for a given sample , thus establishing robust criteria for step size selection [121] . Their simulation s also indicate a much higher portion of GNDs in heterogeneously deformed specimens than those subjected to homogeneous deformation [121] . The model provides the potential of estimating overall dislocation conten t since it accounts for SSD contribution s , which would be a significant advance in the EBSD - based dislocation analysis [121] . In brief , GND density and distribution in deformed materials can be conveniently asses sed by the CC - EBSD method . Because of the ease of use and extensive availability of EBSD systems, this method can provide considerable insights into the field of materials science and plasticity. k. Opportunities for Research As reviewed in previous sections, material studies on Nb used in SRF cavities follow ed both science (fundamental understanding) and engineering (cavity fabrication ) approach es . This combination of approaches creates opportuniti es for obtaining a deeper underst anding of the deformation mechanis ms of Nb , such that the microstructural evolution during cavity forming can be modeled , enabling prediction of cavity performance . Outlined below are efforts that have been accomplished in support of research and development programs at Michigan State University ( MSU ) : Characterization of more ingot slices add s to the literature on the initial condition of Nb ingots and could provide further insights into why microstructures are heterogeneo us in rolled polycrystalline sheets . The differences and commonalities in ingot slices from different suppliers may reveal trends to be controlled or exploited. Characterization of fine grain sheets for use in the Facility for Rare Isotope Beams (FRIB) ensures that the materials meet the specifications defined by FRIB [62 ] , and enables relationships 48 between micro structure and mechanical propert ies to be explored . Such data can also be correlated with the performance of future FRIB cavities. Then, it is possible to establish a microstructure - performance model that can si mulate cavity forming and operation , which would be valuable to the SRF community . It is desirable to identify the connection between ing ot and sheet microstructures. A rolling experiment of multi - crystals are conducted to make progress toward this goal . S amples with different amounts of cold work reduction are examined before and after annealing to find credible sources for the layered micro structure in the sheet metal. Study ing the microstructural changes during deep drawing and subsequent processing o f Nb to supplement the surface studies is valuable , as previous work focused more on cavity testing than on the metallurgical perspective . A n assessment of the effects of complex strain paths in deep drawing can be made by comparing the crystal orientatio ns of an ingot slice before and after the deformatio n. Grain orientation and d islocation substructure will be examined on samples extracted from a large grain cavity that was subjected to the same chemical and heat treatments as in a real cavity . This gi ves a measure of dislocation evolution in a cavity , which can be correlated with cavity performance results . On a more fundamental level, a f urther study of active slip systems in Nb single crystals building on the work of Baars [16] would contribute to the goal of establishing a model that can estimate the final dislocation configuration in cavit ies by predictin g the amo u nt of dislocation glide on various slip systems based upon crystal orientations . As Baars investig ated as - received single crystal s and deformed them in a conventional test frame with analysis after monotonic deformation to 40% strain , a more det ailed examination with in - situ tensile tests on a set of neighboring samples 49 from the same ingot slice that ha s been annealed provides an opportu nity to identify effects of pre - existing dislocations on slip behavior . It will also enable a more straigh t for ward interpret ation of the results of Baars in the context of a lower initial dislocation density. A road map that shows the interconnections of the above projects a nd aids visualization of the logic flow of this work is provided in Figure 20 . The l etters in parent heses (a - e) correspond to the stor ylines that will be followed in each of the Materials and methods, Results, and Discussion chapters. Figure 20 : Road map showing the interconnections of research activities outlined above . Letters a - e in parentheses correspond to the section headings in the next three cha pters. 50 III. MATERIALS AND METHODS An experimental approach is employed to establish the foundat ion for modeling the micro - structural evolution and performance of cavities, as detailed in this chapter. a. Large Grain Nb Ingots Characterized by EBSD and Laue Camera This section and correspondin g sections in the Results and Discussion chapters are based u p on previous ly published papers [122, 123] , with additional figures and details . Electron backscatter diffraction (EBSD) is a well - established techn ique for identifying crystal orientations. In EBSD, an electron beam is focused onto a flat crystalline sample whose surface normal is tilted 70° from the beam axis [124] . Electrons that are scattered by the sample in backward directions produce intersecting ( Kikuchi) patterns on a fluorescent screen (EBSD camera). These pat terns can be converted into crystal orientations through a Hough transform [124] . A schematic configuration of EBSD is shown in Figure 21 [16, 124] . Figure 21 : Schematic of the EBSD configuration. The electron beam interacts with a sample that is tilt ed 70° from the beam axis. Red arrows indicate the coordinate systems used for the crystal orientation. Backscatter electrons form diffraction patterns on the EBSD camera, which are then processed by a computer equippe d with data acquisition and analysis software. The electron beam trajectory is also controlled by the computer [adapted from Figure 1.3 in reference [124] and Figure II - 15 in reference [ 16 ]]. 51 Rather than using EBSD to characterize ingot slices as Baars did [16] , it is more practical to measure orientations using the Laue method, in which a beam of white radiation from an X - ray source shines on a sample and is diffracted law [125] . X - rays diffracted in backward directions (i.e. , with large Bragg angles) are recorded by an area detector. Figure 22 illustrates the experimental setup for Laue measurements, in which a Nb ingot slice was attached in front of the Laue camera (Photonic Science Laue X - ray Imaging S ystem, Microphotonics Inc.). The slice was supported vertically by books and held in place with double stick tape on aluminum supports to ensure that the ingot s urface is perpendicular to the X - ray beam . This way, the biggest mounting errors exists in the rotation about the ingot surface normal . The collected patterns were indexed with a semi - automatic method using OrientExpress software 3.4, based on the crystal structure of Nb, the sample to detector distance, and dimensions of the area detector. Figure 23 shows an example of a Laue diffraction pattern and the index ing user interface. Typically, five points on multiple hyperbolae need to be specified for indexing a pattern . The orientations were converted to match the EBSD software coordinate system with X pointing down and Y to the right. Figure 22 : Laue camera equipped with area detector, showing how an ingot slice was mounted to determine crystal orientations [Figure 3 in reference [122]] . 52 Seven ingot slices and a slab cut in the longitudinal direction of an ingot using wire electro - di scharge machining (EDM) were examined to identify their crystal orientations. The supplier information for each ingot is shown in Table 1 (ranked by ingot diameter/size), with a name for each that will be used later . Except for th e Niowave ingot, the ingot slices are about 3 mm in thickness. The composition (impurity elements and content ) of the ingots are unknown. Table 1 : Information of ingots and their short names used in this work, ranke d by ingot size . The Ningxia and CBMM - NSCL ingot slices ( Figure 2 4 ) were characterized by EBSD on a CamScan 44 field emission scanning electron microscope operated at 20 kV, with a working distance of 33 mm. For the Ningxia slice, a keyhole - shaped sample cont aining grains 1 - 8 were Figure 23 : A typical Laue pattern (left) and the indexing user interface (right) [Figure 4 in reference [1 22 ]]. 53 extracted by EDM from the center, as shown in Figure 2 4 . O rientations of the perimeter grains 9 and 10 were measured by the Laue method . For the CBMM - N SCL slice, four samples containing all five grains were extracted at grain boundaries on the perimeter (numbered 1 - 8). The samples were etched by buffered chemical polishing ( BCP , defined in section g of Literature Review ) after EDM to provide a surface s uitable for EBSD. Dashed lines are overlaid on some faint grain boundaries for better visibility. As the EBSD samples were much smaller than the size of the i.e., that the orientations do not var y greatly within the grains. This assumption will be assessed later. Figure 24 : Images of ingot slices characterized by EBSD. Dashed lines identify the location of faint grain boundaries. The numbers on the images of the ingots indicate IDs of the grains whose crystal orientation will be reported later. The scale bar is common to both images. 54 The Laue method was used to study the CBMM - H1, CBMM - H2, TD - 1, TD - 2, CBMM - NSCL, Heraeus ( Figure 25 ) , and Niowave ( F igure 26 ) ingot slices. The n umbers on each ingot slice indicate roughly where the orientations wer e measured. Multiple measurements were made in some of the large grains. For example, the grid overlaid on the CBMM - NSCL slice shows the approximate locations of 57 Laue measurements t hat are one inch apart, where each intersection corresponds to one measurement (excluding those beyond the image of the slice). These results were compared to EBSD data from the same ingot slice. The CBMM - H1 and CBMM - H2 slices were cut adjacent to each o ther from a n ingot, and so were the TD - 1 and TD - 2 slices. Thus, only the CBMM - H1 and TD - 1 slices are shown in Figure 25 . 55 Figure 25 : Images of ingot slices characterized by Laue camera. The grid on the CBMM - NSCL slice illustrates how 57 measurements were systematically made with a step size of 1 inch. The TD - 1 slice was measured sim ilarly using a step size of 2 inches, yielding 19 data points ( detailed in). For the Heraeus, CBMM - H1, and TD - 1 slices, the numbers provide approximate locations of the orientation measurements (reported later). The scale bar is common to all images. 56 T o identify effects of deformation on orientations and to assess changes in the sharpness of Laue diffr action spots , t he CBMM - H2 ingot slice was measured again with the Laue camera after being deep drawn into a half - cell. The surface of the Niowave ingot slab was smoothed using an end mill after a rough saw cut, and then mechanically polished to make the grains on the surface visible ( F igure 26 ). Besides the numbered locations, ten closely spaced orientations a - j were captured to the left of location 2 across two milling passes (the lower image of F igure 26 ) , where orientation j was about halfway between locations 2 and 27. Seven of the locations were examined again after removing 100 µm from the surface by etching . F igure 26 : Image of a slab cut along the longitudinal direction of an ingot (prepared by Niowave). The dimensions are 70 cm (W) × 22 cm (H) × 1 cm (T). Ten closely spaced Laue measurements (a - j) were made in addition to the number ed locations. Scan j was about half way between locations 2 and 27 [adapted from Figur e 3 in reference [1 23 ]] . 57 b. Fine Grain Nb Sheets Characteriz ed by EBSD and Mechanical Tests The facility for rare isoto pe beams ( FRIB ) is a scientific user facility under construction at MSU funded by the U.S. Department of Energy, MSU and the State of Michigan [62] . A large quantity of fine grain Nb is being used in the constru ction of the FRIB, which has been procured from two suppliers Tokyo - Denkai and Ningxia [62] . While vendors generally follow well - established material specifications for Nb, there is still a substantial variation in the properties of the incoming material. Therefore , the FRIB has developed its acceptance criteria list (A CL) to ensure the quality of Nb and to minimize potential variability issues in cavity fabrication. The ACL incl udes mechanical properties, purity, texture, surface finish, and electrical conductivity or residual resistivity ratio (RRR) [62] . At least one set of samples from each production lot we re teste d based on the ACL [62] . The samples were extracted from non - usable areas of the sheets (2 - 4 mm thick) using EDM, as shown in Figure 27 [61, 62] . The Tokyo - Denkai samples were cut 45° with respect to the rolling direction, while the Ningxia samples were either parallel or perpendicula r to the rolling direction [62] . In each set, a standard ASTM dog - bone shaped sample was deformed to fracture in un iaxial tension using an Instron 4302 lo ad frame , with a loading rate of 5 mm/min. The square samples were etched by BCP , and their cross - sections were examined by EBSD, using the CamScan microscope operated at 20 kV in stage - controlled scan mode . After E BSD, Vickers hardness were measured on the cross - sections of the square samples, using a Clark microhardness tester CM - 100 at a load of 100 g. The other sample was used for thermal conductivity measurements and will not be discussed in this work. 58 Various mechanical parameters can be extract ed from the tensile test data. Specifically, the AC L requirements are as follows [62] : 0.2% offset yield strength: >7000 psi (48.3 MPa) Tensile strength (UTS): >14000 psi (96.5 MPa) Percent elongation ( f ): >40% in longitudinal direction and >35% in transverse direction Figure 27 : Layout of acceptance criteria list (ACL) samples extracted from (a) Tokyo - Denkai and (b) Ningxia sheets. T he Tokyo - Denkai samp les are oriented 45° with respect to the rolling direction, while the Ningxia samples are either perpendicular or parallel to the rolling direction. The dimensions are the same for each type of samples and are shown on the Tokyo - Denkai drawing. All units are in inches except for the square samples in (a) [ adapted from Figure 14 in reference [61] ]. 59 The EBSD data were used to assess texture, grain size , and degree of recry stallization of the sheets [62] . The ACL requir ement is a pre dominant grain size of ASTM #5 (64 µm) with >90% recrystallization. While texture is not part of the ACL, it can be useful in understanding potential problems during cavity forming and operation. The EBSD data were cleaned up using a single iteration of grain dilation and grain confidence index (CI) standardization with a minimum grain size of 3, and points with CI > 0.1 were used to generate the maps shown later. For Vickers hardness (HV), ten dat um points were collected on each sample moun ted with one of its cross - sections (arbitrarily chosen) facing the indenter , and eight of them excluding the minimum and maximum were averaged for the hardness value reported. The ACL requires an HV of less than 60 [62] . c. Rolled Multi - Crystal Nb Samples Characterized by EBSD and Laue Camera To investigate the origin of the heterogeneous banded texture and microstructure that varies from one lot to the next in the sheet material , a multi - crystal rolling experiment was designed . A portion of a n ingot was extracted (S in Figure 28 ) , and the initial orientations of its end slices (S1 and S2) were measured using the Laue camera. Part way through the r olling process, sample S was cut in half , and each half was further rolled to a flat piece that is about 1 mm thick , yielding a gradient of rolling reductions. One of the rolled piece s ( A ) is shown in Figure 29 , where S1 is next to its top edge , and S2 is next to its bottom edge . The sense of rolling and corresponding orientation map for S1 are shown on the top r ight corner in Figure 29 . Two samples , cut from the rolled piece , were evaluated by EBSD for the effects of rolling and annealing . Sample A2 is near the right end with zero to moderate cold work reductio n , while 60 sample A6 is close to the maximum reduction region. Both samples were heat treated at 800 ºC /2hr and examined again afterward . Figure 28 : the Niowave ingot used for the rolling experimen t. The gree n dotted line indicates that the sample was cut in half part way through the rolling process due to developing a curved strip. 61 Figure 29 : about 1 mm thick rolled from the right half of sample S ( Figure 28 ) . End slice S1 was cut next to the top edge of the rolled piece , and its correspondi ng orientation map and the sense of rolling are shown on the right . The cross - sections of s amples A2 and A6 were examined for the effects of rolling and annealing. 62 d. Nb Cavity Samples Characterized by EBSD This section and corresponding sections in the Results and Discussion chapters are based upo n previously published papers [126 , 127] , with additional figures and details . U sing EDM , t hree samples were cut from two r ings trimmed from the equator and iris of a large grain half - cell prepared at Thomas Jefferson National Accelerator Facility (JLab). Two of the samples were extracted from the equator ring, and one from the iris ring, as shown in Figure 30 . All samples contained a grain boundary , and the two equator samples had earing feat ures (heterogeneous deformation) near the grain boundar y . The earing may be associated with a higher drag force due to the resistance to thinning at the grain boundar y . Figure 31 shows secondary electron images of the six cross - sectional areas examined by EBSD. The samples were mounted with the outside of the half - cell fac ing upwards. The cross - sections of the samples are the opposite s urfaces of half - cells that would be welded to other half - c ells. These surfaces were hand ground using SiC abrasive paper to remove the EDM recast layer. The relatively smooth EDM finish enabled the use of fine ab rasive paper to minimize damage from grind ing, starting with grit 1200 (particle size ~15.3 µm) and ending with grit 4000 (particle size ~2.5 µm) [128] . After grinding, the samples were given a light etch (BCP) that removed another 10 µm of material to provide a surface suitable for EBSD. The step size used for EBSD was 20 µm. The data were cleaned using the same procedure as described in the previous section, after which orientation maps were generated . 63 Figure 30 : Locations of three samples extracted from a half - cell formed by JLab. The locations of grain boundaries (GB) and a neck are indicated in the blown - up images in Figure 31 . Numbers pr ovide approximate locations of EBSD scans on the equator and iris [adapted from Figure 2 in reference [126]] . 64 After obtaining the EBSD measurements, the iris sample and one of the equator samples were heat treated at 800 º C/2hr in a vacuum furnace dedicated for Nb, and the other equator sample was heat treated at 1000 ºC/2hr. For the 1000 ºC anneal , titanium was used as a getter to minimize the uptake of hydrogen and oxygen into Nb. The same areas were scanned again to id entify the effects of annealing on the microstructure . Then, t he samples were etched wit h BCP to remove another 10 µm of material from the surface, and the same areas were examined once more to identify changes that occurred in the subsurface region. The image quality (IQ) of EBSD patterns are an indicator of grain boundaries, defect content , and surface contamination [124] . The IQ parameter is the averag e height of detected Figure 31 : Secondary electron images of the 6 areas examined by EBSD. Grain boundaries and the neck are marked in acco rdance with Figure 30 . The numbering is also the same as Figure 30 [adapted from Figure 4 in reference [126] . 65 intensity pe aks in the Hough transform (locating the bands) of an EBSD pattern [129] . Any distortions to the lattice within the diffractin g volume will produce diffraction patterns with lower IQ as the Bragg condition is no longer precise ly satisfied, resulting in a more diffuse diffract ion band [124] . As the dominant defect in a crystal, dislocations can be qualitatively assessed by an IQ map, where darker areas indicate higher dislocation content [124] . Nevertheless , IQ is affected by both GNDs and SSDs , while LAM only reflects GN Ds. Other factors such as grain boundaries , surface contam ination , and the electron channeling depth for the crystal orientation will also affect the IQ. Furthermore, IQ can be affected by EBSD imaging parameters that are often different for each scan, m ay vary smoothly over the area of a scan, and will differ from grain to grain due to different a mounts of backscatter ed electrons . Thus, the IQ map is informative when interpreted as a r elative quantity within a given scan, but less so when comparing betw een scans. Like LAM maps, IQ maps are presented in grayscale that varies linearly from black, the minimum IQ on a map , to white, the maximum IQ on a map which differs for each scan. In the R esults chapter , both LAM and IQ maps are used to assess the t otal defect content. e. Nb Single Crystals Characterized by i n - Situ Tensile Tests This section and corresponding sections in the Results and Discussion chapters are based upon previously pub lished papers [58, 130] , with additional figures and details . To investigate slip activities in Nb , twelve sets of single crystal samples were extracted from the Ningxia slice after its surface was mechanically cleaned , as shown in Figure 32 . Each set contained three parallel samples from the same grain, so the three nominally ha ve the same crystal orientation. The orientations were chosen to initially favor either a single slip system or a combination of slip systems. The methodology for orienta tion selection is detailed in [16] . A 66 letter from O to Z is designated to each set, and for the three samples in a set, number 1 denotes the one marked by a black dot, and numbers 2 and 3 foll ow downwards, as shown in the upper right schematic of Figure 32 . The dimensions of the samples are shown on the left side of Figure 32 , which is a reduced version of the ASTM E8 - 04 standard for sub - size sam ples . Figure 32 : Layout of single crystal tensile samples extracted from the Ningxia ingot slice. The dimensions are shown on the left. The location of samples P1 and P3 are shown as examples of the labeling strategy [ adapted from Figure III - 3 in reference [16] ]. 67 Samples P3, Q2, R2, S3, T3, U3, V3, W3, and X3 (as - received samples) were electro - polished by Baars (parameters provided in [16] ) and deformed monotonically to 40% engineering strain using a tensile load frame (Instron 4302), with a strain rate of 1 mm/min. Samples O1 through Z1 (set 1) were etched with BCP after being extracted from the ingot slice and annealed at 800 ºC/2h r by Compton to remove some of the dislocations formed during ingot production. They were used to assess orientation gradients within the large grains before and after annealing . Samples P2, Q3, R3, S2, T2, U2, V2, W2, and X2 (heat - treated samples) were electropolished by Baars and annealed at 800 ºC/2h r by Compton . They were deformed in - situ at 0.004 mm/se c inside a Tescan MIRA3 scanning e lectron microscope using an Ernest Fullam stage, with a strain increment of ~10% followed by c haracterization, in which slip traces and orientations were recorded at three locations along the gauge length. An example of the test setup is shown in Figure 33 [131] . The deformation behavior of heat - treated samples is compared to that of as - received samples to identify the effects of annealing . 68 Figure 33 : Experimental setup of the in - situ tensile tests. Sample W is shown as an example. Left tensile load frame mounted inside the MIRA3 SEM chamber, right plan view of the sample [adapted from Figure 3.2 in reference [131]. 69 To understand the evolution of GNDs during uniaxial tensi on and how they correlate with work hardening and crystal rotation , sampl e s T1 (in the middle of the stereographic triangle) and V1 (near the [100] - [110] boundary) were deformed in - situ for CC - EBSD analysis. EBSD patterns with 480× 480 resolution over an area of 250×250 µm 2 were recorded at each 10% strain increment , using a step size of 2 µ m and an exposure time of 0.1 s . The EBSD data were process ed with the OpenXY software to obtain GND density and distribution s at every deformation stage 2 [132] . The ca lculation is based up on equations developed by Nye and Kroner that relate derivatives of lattice distortion to dislocation content [121, 133 - 136] . The experimental meth ods described above will enable characterization of the physical metallurgy of Nb that governs cavity forming and performance , with emphases on microstructure and slip behavio r. 2 B. Dunlap and M. Crimp provided training of the CC - EBSD methodology as well as valuable insights. 70 IV. RESULTS This chapter presents observations on ingot and sheet microstructures , as well as how they are correlated based on the rolling experiment s . Such corr elation s also provide insights into how the microstructure and performance of a large grain cavity are influenced by forming and annealing . A fundamental study on slip behavi or of Nb that influences the microstructural changes is reported at the end. a. Crystal Orien tation of Large Grain Nb Ingots Table 2 through Table 7 ingot slice at locations ind icated on images of the ingots ( Figure 2 4 through F igure 26 ). While only selected orientations are shown in the t able s , all measurements are reflected in the EBSD maps and subseq uent analyses. For the CBMM - NSCL ingot slice, the Laue measurement s shown in Table 3 are closest to the EBSD sample locations, and the differences between the measurements from the two methods will be addressed later. For the Niow ave ingot, orientations of seven locations measured again after etching are shown in Table 7 . Table 2 : Orientations in Bunge Euler angles (°) for the Ningxia ingot slice. The numbering is the same as Figure 2 4 . Ningxia 1 78.0 27.2 284.9 2 105.9 7.8 239.4 3 322.7 33.1 79.3 4 294.7 25.1 83.0 5 327.0 41.9 38.5 6 186.1 37.2 172.9 7 202.4 39.2 167.0 8 132.7 26.0 266.5 9 270.6 158.5 184.7 10 244.9 139.8 153.9 71 Table 3 : Orientations in Bunge Euler angles (°) for the CBMM - NSCL ingot slice. The numbering is the same as Figure 2 4 . There are varying differences between EBSD and Laue measu rements of the same grains (discussed later). C BMM - NSCL (EBSD) CBMM - NSCL (Laue) Difference 1 167.6 140.4 167.6 168.4 142.0 179.8 11.7 2 281.9 123.7 127.8 279.1 138.0 143.2 22.4 3 158.9 143.7 184.7 156.0 148.2 180.0 5.3 4 176.4 133.3 194.7 172.2 144.4 196.5 12.5 5 171.7 159 .5 261.7 130.1 146.7 148. 7 50.1 6 188.0 136.1 188.0 169.4 140.8 179.9 14.4 7 168.3 118.0 135.3 173.6 147.7 146.5 30.9 8 155.4 142.5 245.4 152.0 138.4 233.9 10.0 Table 4 : Orientations in Bunge Euler angles (°) for the CBMM - H1 and CBMM - H2 ingot slices. The numbering is the same as Figure 25 . The two slices are nearly identical in orient ations . Table 5 : Orientations in Bunge Euler angles (°) for the TD - 1 and TD - 2 ingot slices. The numbering is the same as Figure 25 . T here is a systematic mounting error. 72 Table 6 : Orientations in Bunge Euler angles (°) for the Heraeus ingot at locations shown in Figure 25 . Orientation variation in grain 1 is small based u pon five measurements. Heraeus 1 - a 147.6 113.5 163.8 1 - b 147.0 114.5 164.4 1 - c 145.0 114.3 163.9 1 - d 146.0 114.1 164.9 1 - e 143.7 114.8 164.1 2 191.7 134.5 112.9 3 121.1 138.0 186.3 4 113.5 132.4 178.5 5 123.3 137.7 123.0 6 234.8 144.7 159.9 7 228.4 140.7 154.0 8 263.3 138.5 112.2 9 99.5 132.8 149.9 10 265.9 159.7 116.3 11 240.1 150.1 161. 3 12 304.0 133.5 187.8 13 8.7 142.8 186.6 14 350.4 130.5 124.3 15 58.9 164.9 122.2 16 340.7 130.4 158.3 17 212.1 129.5 155.4 18 179.4 112.5 122.4 73 Table 7 : Orientations in Bunge Euler angles (°) for the Niowave ingot at lo cations shown in F igure 26 . Orientations do not vary much in the longitudinal direction of the ingot. After etching, the orientation of seven locations changed 1 - 2 º , but the orientation gradients associated with the milling bands are still present. Niowave Niowave (after etching ) 1 324.3 137.3 111.7 2 323.1 136.5 111.1 3 98.2 144.0 135.3 4 323.5 136.7 111.6 5 324.3 136.1 112.5 6 323.1 137.0 111.9 323.5 135.4 110.9 7 327.7 131.4 116.6 326.7 133.3 115.3 8 332. 0 139.1 123.2 9 328.1 132.6 117.2 327.6 131.2 116.2 10 309.1 173.1 171.9 11 328.7 131.6 116.5 12 324.0 136.9 111.2 13 264.5 174.2 216.8 14 97.3 145.1 135.0 15 97.9 144.4 135.2 16 322.9 135.6 111.1 17 324.4 135.7 112.2 1 8 322.7 136.4 110.1 324.1 135.2 111.8 19 326.5 132.8 113.8 20 323.6 136.6 111.8 21 321.9 135.2 109.0 22 327.4 132.2 115.7 23 89.3 144.6 124.8 24 327.8 132.0 116.7 326.6 132.2 115.1 25 327.1 132.8 115.1 326.2 133.6 114.6 26 322.6 135. 9 110.3 323.7 135.1 111.4 27 324.8 136.4 113.5 28 329.7 140.3 121.1 74 It is evident from Table 4 that the CBMM - H1 and CBMM - H2 slices have nearly identical crystal orientations due to them being immediate ne ighbors (the maximum difference between matching locations is 1.2º) . For the TD - 1 and TD - 2 slices ( Table 5 ) , the largest difference (~3°) about the slice normal direction during m ounting ( a noticeable misalignment was later found in the fiducial marker on the two slices) . As shown in Table 6 , the orientation variation in the large grain 1 of the Heraeus slice is small , based upon five measurements. For the Niowave ingot , there is an orientation change after etching of 1.0 to 2.1° from the seven measurements in Table 7 , which could be due to mounting error and chemical removal of a machined surface . Furthermore, crystal orientations do not vary much along the longitudinal direction of the Niowave ingot the orientation spread is only 6.2° ove r a length of 70 cm. Orientation variations within the grains will be described later ( semi - quantified in Table 8 ) for measurements made on the same grain in each ingot slice. From orientations obtained from both EBSD and Laue met hods, a 30x30 grid was overlaid on the image of each ingot, and an orientation map was constru cted , where each pixel is assigned the measured orientation closest to it within a grain. An illustration of this process is shown in Figure 34 , in which an orientation map for the TD - 1 slice is generated ( Figure 35 ) using the 19 measured dat um points that are two inches apart. 75 Figure 34 : Illust r ation of how orientation maps were generated using the TD - 1 ingot slice. Red dots indicate approximate locations of the 19 measurements that are two inches apart, and each pixel in the 30x30 grid was assigned the measured orientation closest to it within a grain. 76 Figure 35 through Figure 37 show axi al growth direction orientation maps for all ingot s . Some small perimeter grains were not measured, corresponding to black areas in the maps (e.g., TD - 1) . Grain boundary misorientatio ns are annotated in the form of angle [rotation axis] on each map , with coincidence site lattice (CSL) boundaries identified in red lettering . CSL boundaries are high angle grain b oundaries (> 15º) that are more energetically favorable than random boundaries , resulting from structural periodicity in the atomic positions with in the boundary [137, 138] . Due to the resemblance between the CBMM - H1 and CBM M - H2 ingot slices, only CBMM - H1 is shown in Figure 35 ( similarly for the TD - 1 slice ). For the CBMM - NSCL ingot slice, orientation maps from both EBSD and Laue measurements are shown in Figure 36 . The orienta tion map for the Niowave ingot slab ( Figure 37 ) is presented in the sample [010] (transverse/ingot growth) direction , which corresponds to the [001] direction s in the other ingot slices. Thi s perspective also applies to the other m aps for the Niowave ingot slab shown later. Both the Heraeus and Niowave ingots have a grain near the perimeter with nearly the same orientation as the center grain. 77 Figure 35 : Normal direction orientation maps for the CBMM - H1, Heraeus, Ningxia, and TD - 1 ingot slices , as labeled . Annotations provide angle and rotation axis for grain boundary misorientations, with CSL boundaries ident ified with thick black boundaries and red text. The red arrow on the Heraeus slice identifies the perimeter grain that has the same orientation as the center grain. The high angle (> 15º) grain boundaries are identified with thin black lines. The scale and legend are common to all maps. 78 Figure 36 : Normal direction orientation maps for the CBMM - NSCL slice measured by E BSD (left) and Laue camera (right). Annotations provide angle and rotation axis for grain boundary misorientatio ns, with CSL boundaries identified with thick black boundaries and red text. The discrepancy between the two methods will be addressed in the Discussion chapter. The scale and legend are common to both maps. 79 Figure 38 through Figure 40 s how misorientation distribution function (MODF) maps for all ingots, where each inverse pole figure (IPF) triangle represents the distribution of rotation axes between neighboring grains for e ach binned angular range for grain boundary misorientation s . Th e color represents the probability of finding a rotation axis with a misorientation angle range indicated in units of times random, similar to the density pole figures shown in Figure 4 1 . The MODF maps are smoothed density plots th at represent the length of grain boundary misorientations , so for comparison, the observed misorientation axes ( shown on the orien tation maps in Figure 35 through Figure 37 ) are marked by black in Figure 38 through Figure 40 . Figure 37 : Transvers e (ingot growth) direction orientation map for the Niowave ingot slab . Annotations provide angle and rotation axis for grain boundary misorientations. The red arrow identifies the perimeter grain that has the same orientation as the center one. The high angle (> 15º) grain boundaries are identified with thin black lines. There is no CSL boundary in this ingot. 80 Figure 38 : Grain boundary misorientation distribution functions (MODFs) for the CBMM - H1 and TD - 1 ingot slices. The sp ecific m isorientations identified in Figure 35 are identified by There is a trend for grain boundary misorientations to fall between 35 - 55 º . 81 Figure 39 : Grain boundary MODFs for the Ningxia and Heraeus ingot slices. Misorientations identified in Figure 35 There is a trend for grain boundary misorientations to fall between 35 - 55º. 82 Figure 40 : Grain boundary MODFs for the CBMM - NSCL and Niowave ingots. Misorientations identified in Figure 36 and Figure 37 There is a trend for grain boundary misorientations to fall between 35 - 55º. 83 Based on the orientation maps, <001>, <011>, <111> and <112> density pole figures for each ingot are plotted using the same color scale in Figure 4 1 . These pole figures highlight dominant orientations / grains, such as those represented by the three red <001> poles in the Heraeus and Niowave ingot slices . Figure 42 shows discrete IPFs in the ingot growth direction for all ingo ts . While the orientation distribution appears to be random, there is generally a lack of near <111> orientations aligned with the i ngot growth direction. Orientation variation is commonly observed when multiple measurements are made in the same grain of the ingot slices. This variation can be semi - quantified using the TSL software (EBSD data analysis) as shown in Figure 43 , where each point corresponds to the misorientation with respect to the average orientation of a grain. These misorientations are divided into ten 0.5° bins from 0 - 5°, and the upper bound valu e for each bin is used as an estimate of the orientation variation. Table 8 lists the largest variation ( orienta tion spread) for each grain with more than one measuremen t. The orientation spread is only a couple of degrees in most grains. For example, grain 1 in the middle of the Heraeus slice was measured in 5 places as marked by 1 - a through 1 - e on the ingot image in Figure 25 , showing about 2.5° of misorientation among the orientations. This small variation is consistent with a qualitative assessment of orientation gradi ents in another Heraeus slice [42] , though the nature of the gradients was not assessed in the same way. The TD - 1 and CBMM - H1 slices also exhibited consistent orientation s , since all grains have an orientation spread of less than 2.5°. The Niowave ingot has a greater spread of 6.2° in grain 1, although it is mainly due to the much bigger ar ea evaluated. This good longitudinal orientation stability is consistent with observations in [44] and is also consistent with the negligible orientation differenc es between adjacent ingot slices such as TD - 1 and TD - 2. 84 Figure 41 : Density pole figures for each ingot plotted using the same color scale. Orientations of dominant grains are evident by the three red <100> poles for the Herae us and Niowave ingots. The ingots lack commonality in orientation distributions. 85 Figure 42 : Ingot growth (sheet normal) direction discrete inverse pole figures for each ingot. There is a lack of near <111> orientations among the ingots. 86 Figure 43 : Illustration of how orientation variation is e stimated from multiple Laue measurements within a grain. The orientation deviation map on the left uses the average orientation of each grain as a reference. For example, the largest deviation for grain 1 is in the range of 2.5 - 3° (dark yellow), and the upper bound value (3°) is assigned to this grain as its orientation spread. 87 Table 8 : Orientation spread fo r grains with multiple Laue measurements, estimated using the average orientations ( Figure 43 ) as the reference. The intragranular orientation variation is small compared to the Ningxia ingot (shown later). Ingot Grain ID Number of measurements Orientation spread (°, average) CBMM - H1 1 3 0.5 4 2 1.5 TD - 1 1 3 1 3 5 1.5 5 2 1 6 6 2.5 CBMM - NSCL 1 16 3 2 7 2.5 3 9 4.5 4 10 3.5 5 15 2 Heraeus 1 5 2.5 Niowave 1 22 6.2 3 4 3.5 10 2 3 A closer look at the large grain at the center of the Niowave ingot slab shown in F igure 26 reveals that there is a periodic oscillation in orientation s that comes from the milling band. For example, if orientation 1 1 (left side) is used as a reference, the misorientations for orientations 4, 2, and 1 along a milling band near the center are 6.4°, 6.5° , and 6.8°, respectively. Orientations 9, 24, and 22 (right side) along another milling band have much s maller misorientations of 1.6°, 1. 2° , and 1.2°, respectively. The six orientations on the right are on the same milling direction pass , which is opposite from measuremen ts on the middle and left side . The orientations are corresp ondingly similar in bands milled in the same direction. To more clearly identify this orientation periodicity , a fine step size set of orientations to the left of position 2 were measured. Using orientation 2 as a reference , the misorientation reaches 88 a peak (6.8°) around the c enter of the adjacent band (position f), and gradually drops to a small value at position j (0.7°). Orientation j is close to orientation 27, which has the same milling direction. Such oscillation is reflected in the orientation map of the Niowave ingot in Figure 37 , which shows a color change that is correlated wi th the milling pass direction. A greater orientation spread was observed in the Ningxia ingot slice as evidenced by the EBSD results from the tensile samples . O rientat ion gradients were observed on two scales. Figure 44 shows how the average orientations vary over the 18 - mm gauge length on three of the single crystal samples. This variation is plotted in Figure 45 , showi the crystal z - axis and the intervening rotation about the crystal x - axis (PHI). The average orientation gradient for the 12 samples (O1 through Z1) is 4°, although sample Y1 has a striking 14° variation across the gau ge length. A closer look at this sample suggests that there is a low angle grain boundary between the rightmost location and the adjacent one. This grain boundary was confirmed by a Laue measurement . Neglec ting th is boundary, the variation for sample Y1 is about 7°, making sample V1 the one with the largest orientation gradient of about 8° across the gauge length. 89 Figure 44 : Orientation gradients along the 18 - mm gauge length of three tensile samples extracted from the Ningxia ingot slice. Y1 has the largest orie ntation gradient due to a low angle boundary near its right end. 90 Each of the average orientation values used in Figure 44 comes from an 815x275 µm scan, in which there are also orientation gradients at the scale of 30 - 60 microns. Figure 46 shows such fine - scale orientation patterning revealed by the grain reference orientation deviation maps for samples Y1 and U1, with a color scale from blue (0°) to red (5°) (white for >5°). Th e directionality of orientation banding is consistent for sample U1, but there are several directions for the bands in sample Y1. Figure 45 : Orientation variation in Euler angles for the thre e samples shown in Figure 44 . 91 Figure 46 : Grain refere nce orientation deviation maps showing fine scale orientation gradients f or samples Y1 and U1 based on the average orientation at the center. The directionality of banding is consistent for sample U1, but less so for sample Y1. The color scale is common to all maps. 92 Figure 47 shows one fine scale orientation pattern from each sam ple in set 1 (etched by BCP and annealed, but never electropolished) examined before annealing . While there is no apparent consistency in the directionality or distance between the orientation bands, samples in the same grain tend to have similar directio ns of banding , with the exception of samples S1 and T1. This fine - scale orientation patterning did not change much after th e set 1 samples were annealed at 800 °C/2h r . Figure 48 shows roughly the same areas examined before and afte r the Figure 47 : Selected fine scale orientation patterns of the as - cut samples overlaid onto the image of the Ningxia slice. Black dashed lines highlight the original grain boundaries. The color scale for the maps is the same as Figure 46 . There is no consistency in the directionality of the banding with respect to the ingot. 93 anneal for samples P1 and Q1. However, similar patterns are absent on samples from set 2 which were electropolish ed (parameters provided in [16] ) and later annealed, examples of which are shown in Figure 49 for samples S2 and T2 ( after annealing ). Figure 48 : Fine scale orientation patterns from roughly the same regions for samples P1 and Q1 be fore and after an 800 °C/2h anneal. The anneal did not alter the patterning by much. The color scale is the same as Figure 46 . 94 Th e CBMM - H2 slice was deep drawn into a half - cell, and crystal orientations obt ained after deformation are shown in yellow in Figure 50 , at locations 1 - 12 (a different numbering is used as the locations do not always match those on the undeformed ingot slice). For comparison, orientations before deformation a t nearby locations are shown in black, and there is only a slight change in orientation in most cases. Orientations within the same grain along the radial direction were also evaluated , in that the stress state varies from iris to equator region. Three s uch pairs (12 4, 8 10, and 7 6 ha nd - drawn in Figure 50 ) were compared to their corresponding orientation s before deep drawing. The largest deviation from the original orientation is 9.8° at location 10, while for the other orientat ions the deviati on did not exceed 3.5°. Even though the crystal orientations did not change much after deformation, the Laue diffraction spots became more smeared. Figure 51 shows three examples of this effect at locations Figure 49 : Orientation deviation maps (based upon points with minimum KAM) of the heat - treated samples S2 and T2 before deformation but after electropolishing and annealing . There are no fine scale orientation gradients like those in the as - cut samples. The color scale is the same as Figure 46 . 95 1 (top) , 5 (right) , and 7 (bottom) in Figure 50 before and after deep drawing, in which individual spots are no longer discernable after de ep drawing. Figure 50 : Half - cell deep drawn from the CBMM - H2 ingot slice. Orientations measured before and after deformation are overlaid onto the image (black before, yellow after). Note that the numbering of locations ( hand - written on the hal f - cell) is different from Figure 25 . The orientations did not change much after deep drawing, except for location 10 (9.8 º difference). The red boxes indicate locations for which the Laue patterns will be compared before and after d eep drawing ( Figure 51 ) [adapted from Figure 2 in reference [123]]. 96 Figure 51 : Laue diffraction patterns before and after deep drawing at locations 1, 5, and 7 shown in red boxes in Figure 50 . The spots visible on the undeformed ingot slice (left three) are not as visible and more smeared after deformation (right three). A example is shown in red circles at location 7. 97 I n contrast , for the Niowave ingot slab whose surface was end milled, distinct diffraction spots are still visible in the middle of milling bands, and the spots are smeared only at the edge s of milling bands . Figure 52 shows an example of this with Laue diffraction patt erns near and at a milling band. After a BCP etch that removed about 100 µm from the surface, t he diffraction spots became sharper to varying extent s at the seven positions examined , examples of which are shown in Figure 53 . The spots also moved slightly after BCP , as reflected by a minor orientation change ( provided in the Figure ) . Figure 52 : Laue diffraction patterns at positions e and d from the Niowave ingot ( F igure 26 ). The left pattern shows distinct spots in the middle of a milling band, while the right one shows smearing of spots from the edge of a milling band. 98 Figure 53 : Laue diffraction patterns at positions 7, 18, and 25 from the Niowave ingot ( F igure 26 ) before and after a 100 µm etch . The spots became sharper after etching . The 1 - 2 º orientation change is due to mounting error and th e r emoval of a machined surface layer . 99 b. Texture and Stress - Strain Behavior of Fine Grain Nb Sheets Most o f the results of texture assessment of batches of Nb sheet are presented in [61] , which provides details on how each map or plot was generat ed . This section will show extreme case s and a preliminary exploration o f correlations between different parameters, as highlighted in [139] . Figure 54 shows sheet normal direction orientation maps, engineering stress - strain curves, and density pole figures for the Tokyo - Denkai sampl es , with maximum f , minimum f , maximum UTS, and minimum UTS [139] . The loading direction is either horizontal or in and out of the page with respect to the orientation maps (the ambiguity is due to the symmetry of the square samples and inadequate labeling ). The or ientation maps are deemed to be representative of the sheets, as additional EBSD scans on grips of the tensile samples (about 10 cm away) show similar microstructure to the square samples [61] . From the orientation ma ps , the sample with maximum UTS has much smaller grains than the sample with minimum UTS. The sample w ith maximum f has a strong <100> texture compo nent in the pole figures, while the sample with minimum f has a dominant <111> component . The texture intensity is higher for samples with maximum f and UTS than for samples with minimum f and UTS. All fo ur samples lack {110} orientations parallel to the sheet normal. Figure 55 shows the engineering stress - strain curves for 23 Ningxia samples that were cut either perpendicular or parallel to the rolling direction, and the orientatio n maps for samples with maximum and minimum UTS. Like the Tokyo - Denkai samples, a smaller grain size corresponds to a larger UTS. However, there is no clear relationship between the st ress - strain behavior and sample orientations with respect to the rolli ng direction. Figure 56 shows the UTS vs. average 100 grain size (calculated by the TSL software) scatt er plots for 23 Tokyo - Den kai and 23 Ningxia samples . Although some degree of correlation is present as expected, there is considera ble scatter . 101 Figure 54 : Sheet normal direction orientation maps, engineering stress - strain cu rves, and density pole figures for the Tokyo - Denkai samples with extreme tensile properties. The loading direc tion is either horizontal, or in and out of the page with respect to the orientation maps. There is an inverse correlation between grain size an d yield strength [ adapted from slide 18 in reference [139] ] . 102 Figure 55 : Engineering stress - strain curves for 23 Ningxia samples that were either perpendicular (red curves ) or parallel (blue curves ) to the rolling direction [ adapted from slide 16 in reference [139] ] . The yield strength vs. grain size correlation applies to the two extreme samples, but not to every other sample. 103 Figure 56 : UTS vs. average grain size ( e quivalent diameter from EBSD analysis ) scatter plots for Tokyo - Denkai samples (above) and Ningxia samples (below). A weak negative correlation is pr esent . On average, the Tokyo - Denkai samples have higher UTS than the Ningxia samples [ adapted from slide 17 in reference [139] ]. 104 Figure 57 shows the maximum orientation distribution function (ODF) intensity at each 2 - 65°) an 1 (0 - 180°) for Tokyo - Denkai and Ningxia samples [139] - fiber peaks are similar for both materials , with a 2 between 35° and 60° for Tokyo - Denkai, and between 35° and 55° for Ningxia. The intensity values vary considerably for both sup pliers. Figure 58 shows f vs. average ODF intensity of the - 2 = 45° for Tokyo - Denkai and Ningxia samples, where there is no apparent correlation. Other plots pursuing correlations between measur able parameters are s hown in [61] , although the correlations are eit her weak or absent. 105 Figure 57 : - 2 = 45° slice (from 0 - 90°) for Tokyo - Denkai (above) and Ningxia (below) samples [ adapted from slide 20 in reference [139] ] . 106 Figure 58 : f - 2 = 45° for Tokyo - Denkai (above) and Ning xia (below) samples. Little correlation is present [ adapted from slide 21 in reference [139] ] . 107 c. Microstructure of Ro lled Nb Sampl es Figure 59 through Figure 61 show orientation maps of the cross - sections of the rolled samples, at cold work reduction s of about 68%, 76%, and 92%, respectively. In Figure 59 , som e regions of the lower grain still exhibited the original crystal orientation at the right end of S1 with deformation bands starting to develop , and a different grain is visible along the upper edge . As the reduction increases to 76%, deformation bands be gin to dominate , and the initial orientation is hardly present, as shown in Figure 60 . At 92% reduction ( Figure 61 ), much of the area is no longer indexable, though the well - defined horizon t al bands of diffe rent orientations and black zones in the middle resemble the layer ed structure observed in the sheet material. Figure 59 : Orientation map of a region on the cross - section of sample A2 with ~68% reduction. The original orientation is shown on the top right corner. An original grain boundary is present in the upper area. The average confidence index (CI) before cleanup is 0.45 for this dataset. The legend on the top left applies to all followin g orientation maps unless otherwise specified. 108 Figure 60 : Orientation map of a region on the cross - section of sample A2 with ~76% reduction. Further deformation bands with distinct orientations developed, and the original orienta ti on is no longer traceable. The average CI before cleanup is 0.54 for this dataset. 109 Figure 62 shows orientation maps from matching areas on sample A2 with ~68% reduction before and after annealing at 800 ºC/2hr. Small grains in pink and dark green nucleated in the lower large grain as a result of the heat treatment , with orientations different from the parent grain. However, these minority orientations are the same within both the pink and dark gree n regions , as evident from the prisms shown on the small pat ches. Also, both new orientations are misoriented about 30º fro m the parent green orientation, and the rotation axis is close to <111>. The poorer quality in the orientation map after annealing is likely due to the heat treatment plus more time since the last etch which was done before the anneal . A similar comparison of orientation maps before and after annealing is shown in Figure 63 for sample A2 at ~76% reduction. Whi le recrystallization is less remarkable than in Figure 62 , the Figure 61 : Orientation map of a region on the cross - section of sample A6 with ~92% reduction. T he horizontal bands of different orientations and black zones in the middle resemble the layered structure observed in sheet material . The average CI before cleanup is 0.13 for this dataset. 110 new grains on the right still have consistent orientations , which are also similar to the dark green orientations in Figure 62 . The new orientat ions are still about 30º away from the parent orientation, although there is no longer a well - defined rotation axis. T he orientation map for s ample A6 after annealing is similarly noisy so that it is not possible to discern recrystallized grains, so it is not shown . Figure 62 : Orientation maps from matching areas on sample A2 with ~68% reduction (shown in Figure 59 ) before and after annealing at 800 ºC/2hr. Small grains emerged inside the lower large grain due to the anneal, with orientations different from the parent grain. However, these minority orientations are the sa me within the pink and dark green regions. 111 This work provides initial evidence of how the randomly oriented large grains evolve into the highly variable sheet microstructure upon rolling. W hile t his characterization is preliminary, it is representative of other measurements that are the focus of research projects being condu cted by colleagues . Figure 63 : Orientation maps from matching areas on sample A2 with ~ 76 % reduction (shown in Figure 60 ) before and after annealing at 800 ºC/2hr. Similar to Figure 62 , s mall grains with green orientations emerged on the right from the deformation bands because of the anneal . The scattered new grains again have the same orientation. 112 d. E v olution of Microstructure in Nb Cavity Samples Changes in the microstructure resulting from forming the H1/H2 cavity half illustrated in Figure 30 were assessed using normal direction orientation maps, LAM maps, and IQ maps in the left, middle, and right positions , for the equator and iris in Figure 64 and Figure 65 , respectively. Three locations on the equator and three locations on the iris are shown in the top, middle , and lower groups of images in each Figure . Within each group, the images show the as - deep drawn maps above, annealed in the middle, and re - etched following the anneal on the bottom . 113 Figure 64 : Normal direction orien tation maps (left), LAM maps (middle), and IQ maps (right) for the three equator regions indicated in Figure 31 . For each region, results for as - deep drawn, after heat treatment, and after BCP conditions are shown from top to botto m. The scale and legends are common to all images. Red arrows on the LAM map of Equator 2 indicates a scratch feature that disappeared after the heat treatment [ adapted from Figure 5 in reference [126] ] . 114 Figure 65 : Normal direct ion orientation maps (left), LAM maps (middle), and IQ maps (right) for the three iris regions indicated in Figure 31 . For each region, results for as - deep drawn, after heat treatment, and after BCP conditions are shown from top to bottom . The scale is common to all images and the legends are the same as Figure 64 . A grain boundary developed in Iris 1, likely during deep drawing [ Figure 6 in reference [126] ] . 115 On th e orientation maps, low and high angle grain boundaries are marked by white (3 - 15º) and black (>15º) lines. T he 2 nd nearest neighbor sampling area ( as illustrated in Figure 4 ) is used for the LAM maps, with a grayscale from white ( 0º) to black (2º). An individual grayscale from black (minimum IQ) to white (maximum IQ) is used for each IQ map. The LAM maps and IQ maps from matching areas are shown adjacent to each other to aid comparison. Significant orientation gradients are evi dent by the large color changes over distances of 100 - 200 µm in the orientation maps. Surface contamination, grain boundaries, and artifacts such as residual deformation from scratches are visible on the IQ maps. The darker gray regions on the LAM maps n ear the surface indicate larger LAM values than the lighter gray regions in the interior bulk area, which is evidence for surface damage. The orientation and LAM maps with grain boundaries show that the magnitude of surface damage depends on crystal orie ntations. For example, Equator 2 in Figure 64 shows that LAM values on the outside surface are greater (darker) in the right grain than in the left; the difference is even larger after annealing. The heat treatment reduced the mag nitude o f orientation gradients inside the material, as the LAM maps became lighter, representing a crystal with lower defect content. However, the heat treatment altered the orientation gradients near the surface very little. Furthermore, high LAM value s are lo cated near the surface after annealing in all areas except on the outside of the iris to the left of the grain boundary in Iris 3 ( Figure 65 ), in which the left grain was strained (thinned) more than the right grain. The re gions that did not initially possess high surface LAM values remained unchanged after annealing (except for Equator 2 in the left grain , where removal of 10 µm revealed much higher LAM values). 116 A close inspection of the orientation maps suggests that ther e is often a slight migration of grain boundaries at each stage. For example, the jog in the boundary in Equator 1 ( Figure 64 ) is at a different location in the as - deep drawn and annealed maps and is absent in the etched map. The heat treatment also led to the removal of defects on the initially polished surface in some cases, notably the disappearance of orientation gradients after annealing that were remnants of a scratch from left to right in Equator 2 ( Figure 64 ). However, what appeared to be similar scratch features in Equator 3 just above the center did not completely disappear with annealing, and the same feature with a wider breadth of misorientations was present after the 10 µm etch , which implies that this feature is a long - range defect structure that formed during deformation and was stable through the heat treatment. After etching , the LAM values became higher in several cases, an example of which is shown in the upper third of the left grain in Equator 2 in Figure 64 , where many low angle grain b oundarie s are evident by both the white boundary lines in the orientation map and the extensive black local maxima in the LAM map. Figure 66 provides a qua ntitative visua lization of this, in which the misorientation profiles for the three lines from corresponding places on the orientation maps in Figure 64 are plotted . In the after - BCP co ndition, the profile for the left grain exhibi ts a large oscillation of about 2 - 3º as the line crosses the area with many low angle grain boundaries. This effect is also evident in the etched LAM map of Iris 2 in Figure 65 , though less pronounced . 117 Figure 67 shows the LAM histograms for the six scans after deep drawing, after annealing , and after BCP. Before the heat treatment, all iris scans (dashed lines) had higher LAM values than the equator s cans (solid lines), which is consistent with the large r strain and greater amount of darker shades of gray in the as - deep drawn LAM maps. Annealing resulted in more dramatic changes in the iris than in the equator, as all LAM peaks for the iris scans moved to the left by about 0.25º. In contrast, LAM peaks for the equator scans shifted in both directions, suggesting that the recovery processes were highly variable. For example, the peak for Equator 3 moved to the rig ht after the 1000 ºC/2hr anneal, indicating h igher GND content. After etching , the LAM valu es showed no consistent relationship with the annealed state in the same areas, as a different volume of material was sampled (which was subsurface after annealing) . Figure 66 : Point - to - origin (upper three ) and point - to - point (lower three ) misorientation profiles for the three colored lines drawn on Equ ator 2 in Figure 64 . The blue ends of the colored lines in Figure 64 are the origin . In the after - BCP condition (green) , the left grain exhibits a n oscillation of ~ 2 - 3º as the line crosses the area with low angle grain boundaries. [ Figure 7 in reference [126] ] . 118 Figure 67 : LAM histograms of the six EBSD scans for as - deep drawn (top), after annealing (middle), and after BCP (bottom) conditions. The horizontal scale is common for all three plots. Before annealing, the iris had highe r LAM values than the equator, but the iris changed more from annealing [ Figure 8 in r eference [126]. 119 e. S lip and Crystal Rotation in Heat - Treated Nb Single Crystals Figure 68 shows the engineering stress - strain curves of the as - received and heat - treated samples side by side [16, 130] . The color code for the orientations is provided on the in verse pole figure on the left plot. Most samples exh ibited a stage of easy glide that is characteristic of single crystals, while orientation U showed more work - hardening than a typical poly crystal and necked before reaching the 40% engineering strain. Flow stresses and yield strengths are consistently low er after the 800 °C/2h r anneal . Also, there is no longer a slight drop in the flow stress in the heat - treated samples between yield and ~ 15% strain, which is most significant in or ientation T. Figure 68 : Engineering stress - strain curves of as - received (left) and heat - treated (right) samples. Orientations of tensile axes are indicated by corresponding colors in the triangle inset, which also provides Sch mid factor contours in white for {110} slip and gray for {112} slip, both scaled at 0.5, 0.499, 0.49, 0.47, 0.44, 0.40, 0.36, 0.32. Dashed lines mark boundaries with equal Schmid factors (orange {110} + {112} with intersecting slip direction s, red {11 2} with intersecting slip directions, blue {110} + {112} with the same slip directions) [ Figure 1 in reference [130] ] . 120 The IPF triangle inset in Figure 68 provides orientations of tensile axes with respect to the sample coordinate system, overlaid with Schmid factor contours and boundaries. Samples with tensile axes oriented close to the symmetr y boundaries where two slip systems have equal Schmid factor s (U, P, and V) are more prone to work hardening due to the interactions between intersecting slip systems, while samples with tensile axes oriented away from these boundaries tend to have a low i nitial hardening rate. The noisier stress - strain curves fo r the heat - treated samples resulted from the setting for acquiring the load data . T he resolution could have be en significantly improved by changing the unit from pounds to grams, thereby making the curves much smoother , but this was discovered too late. F or comparison with the as - received samples, slip trace analyses were performed on the heat - treated samples, an example of which is shown in Figure 69 for sample W. At each strain level (~10% increments), computed slip traces using a MATLAB code [140] based on measured orientations on the top surface were compared with observations for hi gher Schmid factor slip systems, a ssuming that the stress tensor was uniaxial tension. Traces for {112} slip are indicated with purple dashed lines, and {110} with green dashed lines on the prisms. The computed traces are in good agreement with the observed traces o n SEM images taken at three locations with 1000x magnification . 121 Figure 69 : Slip trace identification on the heat - treated sample W in some of the areas examined. Observed sl ip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in pur ple. Slip traces were not apparent until ~ 20% engineering strain for this sample [ adapted from Fi gure 7 in reference [58] ] . 122 Figure 70 and Figure 71 demonstrate how the observed slip traces are related to Schmid factors among the computed slip systems (presented in decreasing Schmid factor order up to the 8 th highest), using orientations T and V. For orientation T, the same {110} slip system with the highest Schmid factor was observed in both s amples, even though there is a small difference between the initial orientation of T2 and T3 that altered the ranked list of slip system Schmid factors. In contrast, three different slip systems were observed for orientation V in the two samples, even tho ugh the samples had the same initial Schmid factor ranking. The effect of observed slip systems on crystal rotation was assessed using <111>, <110>, and <112> pole figures, as shown in Figure 72 for sample T2. The [1 1] pole mo ved towards the tensile axis (pointing out of the page) wi th deformation, which indicates that slip in the [1 1] direction was active. Also, the [011] pole (slip plane normal) moved away from the tensile axis. This is consistent with the observed (011) [1 1] slip system as shown in Figure 70 . 123 Figure 70 : Slip systems ranked by Schmid factors (up to 8th highest) for the as - received sample T3 (above) and heat - treated sample T2 (below). The first {110} slip system was observed in both samples an d was the only apparent slip system. 124 Figure 71 : Slip systems ranked by Schmid factors (up to 8th highest) for the as - received sample V3 (above) and heat - treated sample V2 (below). A {110} and a {112} slip system were observed in V3, while only the most highly favored {110} slip system was observed in V2. 125 Figure 72 : <111>, <112>, and <110> pole figures for the heat - treated sample T2 with the tensile direction pointing out of the page. The [1 1] pole mov ed towards the tensile axis with increasing strain, while the [011] pole moved away from the tensile axis. This is consistent with the observed slip system (011) [1 1]. 126 Table 9 summarizes the slip planes associated with observed traces for the as - received and annealed samples. For each orientation, the first slip sy stem whose Schmid factor rank is different between the two samples (up to the 8 th highest) is indicated in parentheses in the left column. For example, the 2 nd highest ranking slip system is different for the two T samples ( Figure 70 ), and the ranking is the same for the V samples ( Figure 71 ). A slip system is red if it was observed in both samples. Table 9 : Summary of observed slip planes from slip trace analyses for as - received an d heat - treated samples, with {112} planes in the first line , and {110} planes in the second line for each orientation. The heat - treated samples exhibited more {110} slip than the a s - received samples. The n umbers in parentheses indicate the Schmid factor rank (as illustrated in Figure 71 ) for a given slip system , and the first slip system whose Sch mid factor rank is different between the two samples is indicated in the left column. 127 The heat treatment led to more slip on {110} planes there is evidence for slip on 12 {112} and nine {110} planes fo r the as - received samples and four {112} and 11 {110} planes for the heat - treated samples when slip systems up to the 8 th in the Schmid factor rank are considered . No anomalous slip traces (slip on a {110} plane with a low resolved shear stress [ 141] ) were observed in the se samples. Figure 73 shows the orientation evolution with deformation for the as - received sample R2 and heat - treated sample R3 , using Euler angles obtained from the center of the gauge length . The two s amples initially had a ~ 1.8° difference in orientation, but sample R2 rotated much more than sample R3 after the 40% strain. Th eir final orientations differed from each other by about 14°. Figure 73 : Orientation evolution with deformation for the as - received sample R2 and heat - treated sample R3. R2 rotated more than R3 during deformation [ adapted from Figure 6 in reference [58] ] . 128 T he heat - treated sample P2 is an outlier regarding orientatio n evolution since it exhibited dramatically different rotations from the three locations spanning ~5 mm along the gauge length. As shown in Figure 74 , it started with a slight difference in orientations across the sample, but as de formation proceeded the left and right part of the crystal rotated in opposite directions (the divergence is about 24° after deformati o n), leaving the center orientation almost unchanged even after 40% strain. In addition to the orientations obtained from [16] , areas corresponding to sample P2 were measured on P3 to evaluate whether similar counter rotations are present. Orientations from the left, middle, and right regions are shown on the bottom of Figure 74 for sample P3. The sense of rotation is similar for P2 and P3, though the magnitudes are different. Also, the orientation at the center of sample P3 is different from the prior measurement at roughly the same location. 129 Figure 74 : Prisms illustrating how the three locations of the heat - treated sample P2 (right) rotated differently with deformation over a range of ~5 mm along the gauge length. The orientations at 40% strain all differed from t hat of the as - received sample P3 (left). The left and right regions of sample P3 had similar opposite rotations as P2. Numbers in red show misorientations before an d after deformation in corresponding areas. 130 The heat - treated sample U2 is another outlier since it developed deformation bands with different orientations. Figure 75 shows the orientation maps for sample U2 from three locations before and after deformation. The deformation banding is most evident in the left region, where the rotation between alternating orientations is on the aver age ~25°, based up on four pairs of dat um points evaluated . Figure 75 : Orientation maps from three region s for the heat - treated sample U2 before and after deformation. The left area developed orientation bands with different rotations after deformation. Annotations on the left map provide angle and rotation axis for misorientations of the deformation - induce d grain boundaries. 131 Figure 76 sho ws the evolution of tensile axis orientation with deformation in inverse pole figures , using orientation s measured at the center of each sample. Triangles connected by dashed lines are used for the as - received samples, and colored dots connected by solid lines are used for the heat - treated samples. The orientation difference s before and after deformation are also shown for the heat - treated sample s . The trajectories of rotation are similar for orientation S, whereas the other orientations show varying deg rees of difference s between the as - received and heat - treated samples (X is an extreme). Figure 76 : Inverse pole figures showing the evolution of tensile axis orientations with deformation for as - received (triangles) and heat - treated samples (colored solid circles). The orientation change (º) fr om deformation is shown for each annealed sample. The as - r eceived samples almost always exhibit more crystal rotation than the annealed samples [ adapted from Figure 4 in reference [130] ] . 132 Figure 77 shows optical images of the as - received and heat - treated samples in pairs taken after deformation. Most samples exhibited similar macroscopic shape changes and shear bands with and without the heat treatment. Both orientation P samples showed an opposite sense of rotation at either end of the gauge length based on the optical reflections, consistent with the orientation data. A no table exception is orientation U, in which necking occurred at different locations for the two samples. Figure 78 shows the engineering stress - stress curves of samples T1 and V1 deformed in - situ for CC - EBSD analysis of GND density and distribution. Sample T1 was pre - strained to about 8.7%, as estimated fr om its geometry. This sample was the first experiment done by Derek Baars in prior work, and because something went wrong with the experiment, it was stopped . The detail had bee n forgotten , and the anneal also affected the strain state, so interpretation of the stress - strain curve and initial hardening behavior is not straightforward. The 8.7% pre - strain is added to the measured strain for T1 to account for the prior strain. Th e flow stress is nearly flat for T1 as it is oriented near the center of the stereographic triangle with fewer slip systems interacting with the favored slip systems, while V1 shows more hardening at larger strains because it is oriented near the [100] - [11 0] symmetric boundary where two slip systems with different Burgers vectors h ave similar Schmid factors. 133 Figure 77 : Optical images of the as - recei ved (AR) and heat - treated (HT) sample s in pairs taken after deformation . The scale shown for orientation W is common to all images. Both P samples had similarly opposite sense of rotation on either side of the gauge length, based on the reflections. The two U samples necked at different locations near one of the ends of the sample. 134 Figure 79 shows the GND maps calculated by CC - EBSD using Nye and Kroner equations at each strain level for samples T1 and V1. The map for V1 at 0% strain reflects preexisting GND s in the sample some dots and short curves in lighter blue within the circle d region suggests higher local GND content . These GNDs could serve as forest dislocations during deformation. The pre - deformation GND map for T1 is missing because the sample was pre - strained. Figure 78 : Engineering stress - strain curves of samples T1 and V1 deformed in - situ . The a rrows indicate where the tensile test was paused to collect CC - EBSD data. The initial hardening behavior for T1 is partly due to the pre - strain (~8.7%), and its plot is shifted to the right accordingly. 135 Figure 79 : GND distribution maps at each strain level obtained from CC - EBSD for sampl es T1 and V1. The before - deformation condition for T1 is missing as it was pre - strained to about 8.7%. The orange circle on the top right indicates an area with higher preexisting GND content for V1. There is a noticeable increase in GN D density for T1, and little change for V1. 136 Sample T1 shows a more pronounced increase in GND density with deformation, and the dislocations are mainly aligned with slip traces. On the other hand, hardly any increas e in GND content was detected for sam ple V1, because the color remains nearly constant. This trend in GND density change is consistent with the difference in lattice rotation shown in Table 10 sample T1 h as a greater orientation change than V1 after 40% strain, even though the change was calculated based on the orientation in the pre - strained condition (8.7% instead of 0%) for T1. Table 10 : Orientation evolution with deformation for the annealed samples T1 and V1. Numbers in red are the difference between the initial and final orientation , which shows that T1 has a greater crystal rotation than V1. T1 (annealed) V1 (annealed) 0% 0% 21.6 118.5 124.0 10% 168.7 67.3 272.9 10% 19.3 121.0 124.8 20% 180.6 62.9 269.8 20% 16.8 123.9 124.5 30% 184.0 62.0 269.6 30% 16.5 124.8 125.3 40% 184.5 61.9 269.7 15.7° 40% 16.4 125.2 126.3 9.5° The pole figures with respect to tensile axes, slip trace identification, and EBSD results for each tensile sample not shown in this section are provided in the Appendix. Th is set of experimental results shown above provide s opportunities for exploring the inter - co nnection s between various types/states of materials characterized, which will be discussed next. 137 V. DISCUS SION Th is chapter examines the underlying mechanisms which account for the heterogeneous deformation of large grains, variability in sheet texture, microstructural evolution during cavity processing , and differences in slip behavior of single crystals. a. Pre ferred Orientation and Orientation Stability in Large Grain Nb Ingots Similarities and Differences of Ingots To identify variability in the startin g material to build cavities , c rystal orientations and the distribution of orientations are compared among th e eight ingot slices. The density pole figures in Figure 4 1 show no apparent similarities, which suggests that no preferred orientation is intrinsic to ingot production. This is also supported by the discrete IPFs in Figure 42 , indicat ing that orientation formation is random in the ingots . Another common feature among the ingots is a tendency for grain boundary misorientations to fall between 35° and 55° ( denoted by black the MODFs in Figure 38 through Figure 40 ), which is consistent with the MacKenzie distribution for a complete ly random texture in cubic poly - crystal s that has a misorientation peak at 45° [142] . Furthermore, a different Heraeus ingot slice studied in [42] shows no commonality in orientation, grain boundary misorientation, or grain size with the Heraeus slice examined in this work. The se observations taken together suggest that there is a lack of preferential grain boundary mobili ty or interfacial energy that would lead to a preferred orientation or grain boundary misorientation, even for ingots from the same supplier (e.g., CBMM). The grain boundary misorientations of the ingot slices are rarely close to CSL conditions. Evaluated their corresponding tolerances [28] , the CBMM - H1, CBMM - H2, TD - 1, TD - 2, and Niowave ingot s 138 have no CSL boundaries , and the approximate fractions of CSL boundarie s for Heraeus, Ningxia , and CBMM - NSCL ingot slice s are 8%, 13%, and 5%, respectively (highlighted in black on the orientation maps in Figure 35 and Figure 36 ). This further support s the hypothesis that orientations are randomly generated, with little low energy configuration being favored . During fast so lidification, dendrites grow along <100> directions for bcc metals [143, 144] . H owever, there is no preferred orientation for slow solidification c ondition during ingot production due to the lack of a well - defined heat flow direction. Orientations nucleate randomly because the temperature gradient does not provide adequate driving fo rce to favor certain dendrite orientations. Moreover, grain bounda ry mobility is high for pure Nb, which leads to high temperature annealing condition that facilitates grain growth. Finally, slow directional solidification favors large grains parallel to the ingot growth direction. These factors combined result in rand om, elongated grains in the ingots. An interesting feature from the orientation map of the Niowave ingot ( Figure 37 ) is that one of the perimeter grains (indicated b y the red arrow) has the same orientation as the dominant center grain. This suggests that upon the start of solidification, a near single crystal orientation was established , yet some perturbations (perhaps a couple of randomly oriented dendrites that ha d disl odged from the interface) settled close to, but not at the perimeter. These orientations remained stable as the ingot grew in length, yielding elongated grains near the lower left edge , which led to an island grain within a larger growing parent cry stal . The center orientation is also present at the lower perimeter, suggesting that none of the orientations have a growth advantage or disadvantage. There is another similar orientation pair in the Heraeus slice ( Figure 35 ), whe re the center grain has nearly the same orientation as a grain to its right. This suggests that near the bottom of the ingot , these two areas may have started from the same nucleus. 139 The good longitudinal orientation stability in the Niowave ingot and in [44] suggests that it is possible to extract many ingot slices with similar orientation profiles, which is a n advantage in terms of consistency in volume produc tion of cavities. It may be practical to use a series of adjacent slices to form a set of half - cells that belong to one cavity and align them to match grain boundary locations. Electron beam welding of deformed large grains may cause recrystallization in the heat affected zone as shown in [24, 48, 145] , though the influence of welds between matched orientations has not been examined . M ore ingots need to be examined to determine whether such longitudinal orientation consistency is typical. The Ningxia ingot slice ha s the highest orie ntation gradient s among the ingots examined, as evidenced by the series of scans along the gauge length of three tensile sampl es ( Figure 44 ) . It is unclear how such orientation variation within the large grains originated. However , a different Ningxia slice studied in [42] shows similar orientation gradients , which suggests that this may be associated with the ingot production methodology. Such intragranular orientation gradients could complicate deformation behavior in the extracte d single crystal sample s (discussed later ), causing variations in deformation paths that may lead to inconsistent microstructural features, and perhaps, cavity performance. The parallel fine r scale ( ~ 30 - 60 µm) orientation gradients present in the as - recei ved Ningxia samples ( Figure 46 through Figure 48 ) are absent after electropolishing (samples S2 and T2 are shown as examples in Figure 49 ) . This impl ies that the patterning only exist ed on the surface and may be an artifact of the mechanical polishing applied to clean the surface of the slice . Figure 80 and Figure 81 show the maximum Schmid factor maps based on biaxial tension (a simplifi cation of strains likely in a formed half - cell) for each ingot slice for slip on {110}, {112}, or both families of planes ( as both are equally facile ) . These Schmid factor maps provide an 140 estimate of formability, indicating that some grain orientations ar e significantly harder than others. The lowest Schmid factor (darkest) orientations have <111> directions normal to the surface. While these orientations require greater stresses to deform, the {111} parallel to the sheet texture results i n better formab ility in other bcc metals, because the strain is more uniform than found in softer grains [24] . 141 Figure 80 : Maximum Schmid factor maps for the 5 ingot slices for sl ip on {110}, {112}, or both families of planes based on biaxial tension. The scale shown next to the Heraeus slice is common to all map s. These maps provide an estimate of formability based on hard/soft orientations. 142 Ideally, for cavity forming the mechanical properties should be isotropic in the plane of a Nb disk [37] , which is often not the case for large grain ingot sli ces as shown in Figure 80 above . It is therefore essential to examine how the initial anisotropy affects deformation. I ngot slices with more homogeneous shades of bl ue will presumably experience less heterogeneous st rain concentrated along grain boundaries during deep drawing, as the deformation resistance of the grains is similar . D ifferences in Schmid factors in grains near the center are more important due to the larger strains near the iris. As the perimeter reg ion experiences a complex strain path due to the drawing process (compression - bending - unbending - drawing), the biaxial Figure 81 : Maximum Schmid factor maps for the Niowave ingot slab for slip on {110}, {112}, or both families of planes based upon biaxial tension in a slice taken perpendicular to the longitudinal direction. Slices from this ingot would l ikely experience more homogeneous deformation due to the huge grain at the center . 143 maps are not indicative of expected heterogeneous strain evolution (a crystal plasticit y model is needed to assess this). From the Schmid factor maps in Figure 80 , the CBMM - H1 and CBMM - H2 slices should deform evenly, since no grain is intrinsically hard (dark). This wa s partly confirmed by the images of the CBMM - H2 half - cell in Figure 30 (equator) and Figure 50 (iris) , which shows mostly similar thickness in the equator and iris cross - section s , though there are several neck s /ears (the subsequent weld could even a local thickness variation) . There are no severe grain boundary ledges or surface topography either, which again indicates that all grains deformed evenly. Slices from the Niowave ingot would also likely experience more homogeneous deformation due to the hu ge grain at the center. Effect of deep drawing / milling on crystal orientation A preliminary assessment was made by comparing the crystal orientations before and after deep drawing of the CBMM - H2 slice. N o significant orientation changes were present after de ep drawing at various locations measured by Laue camera on the half - cel l ( Figure 50 ) . The smearing of Laue diffraction spots in the CBMM - H2 slice after deep drawing ( Figure 51 ) indicates that more dislocatio ns were generated during the forming process . As a result, a subsequent anneal is needed to remove defect s and improve RRR and thermal conductivity. The fact that even the brightest diffraction spots were streaked ( not sharp ) before deep drawing is unexp ected and may be related to the EDM surface of the ingot slice. I n contrast to the micro - strain in the surface layer of the deep drawn cavity due to localized friction interactions with the die , longer range macrostrains are pre sent in the Niowave longitud inal ingot. C ompared to the Laue patterns of the half - cell ( on the right side of Figure 51 ) , diffraction 144 spots are less smeared in the end - milled Niowave ingot ( Figure 53 ) except at the edge of a mi lling ban d ( location d in Figure 52 ). Instead , there was a peak shift on the surface as indicated by the difference in orientations ( Table 7 ) and position s of the diffraction spots before and after etching ( Figure 53 ) . Th is peak shift rather than broadening suggests that milling produces a more uniform macrostrain [125] . B ecause the mechanical polishing done after milling removed some surface damage, the Laue diffraction spots from the polished surface of the Niowave ingot ( Figure 53 ) are sharper than the undeformed and EDM CBMM - H2 slice on the left side of Figure 51 . Merits and limitations of EBSD and Laue metho ds A difficulty with using EBSD to characterize an ingot slice is that small pieces need to be extracted , which prevents further use of the slice to make a cavity. The Laue method serves as a nondestructive alternative of systematically measuring orientat ion s on ingot slices similar to the orientation mapping used to characterize microstructural patches. Therefore, the Laue method is suitable for production evaluation, allowing accept/reject criteria based on anticipated formability requirements . It also al lows grain orientation s in welds and in heat affected zones to be assessed [145] . Laue measurements do not need to be performed in a vacuum , which considerab ly loosens the geometrical restrictions imposed by the chamber of an electron microscope. Thus, samples with larger or more complicated dimensions can be cha racterized . Moreover, unlike EBSD in which only arbitrarily selected locations are measured , the Laue technique enables measurements from virtually anywhere on an ingot slice, and the slice can be evaluated at multiple stages along the cavity fabricati on path. Also, X - rays penetrate deeper into materials than electrons, so the 145 Laue method has a practical advantage of requiring less rigorous surface preparation as compared to EBSD. As shown in the orientati on measurements in Table 3 and the orientation maps in Figure 36 for the CBMM - NSCL i ngot slice , the discrepancies in crystal orientations from EBSD and Laue measurements are sometimes significant. This illustrates a couple of more advantages of the Laue method over EBSD. Because the ingot slice was fixed onto a flat stage in front of th e Laue camera with movements controlled by a stepper motor, mounting errors were minimized and consistent throughout the characterization process. On the other hand, for EBSD each sample was mounted and measured separately, and the crystal orientations needed to be adjusted to comply with a global coordinate system. Furthermore, it is immediately evident from Laue measurements as to how much orientations oscillate or cha nge within a large grain, while for EBSD, multiple samples would have t o be extracted for the same purpose. The precision of Laue measurements was assessed . Based on multiple operators indexing the same pattern using differently chosen peaks , an orientati on was known within 0.25° in each Euler angle, while EBSD measurements on single crystal regions show consistency in obtaining orientations with no smaller than 0.5° of certainty . This indicates that the precision of the Laue method is intrinsically as go od as, if not better than EBSD. Both methods depend on reproducibility in sample mounting, but geometrical details may affect accuracy in measurement due to the different sample size and shape. A limitation of the Laue method is that it lacks the fine s patial resolution available with EBSD, as the illuminated area on the sample is about 1 mm in diameter. This means that grains smaller than a few mm cannot be characterized easily, though this is not a problem for large grain 146 ingot slices. The disadvan ta ge of the Laue method is that it is much slower and cannot be as easily used to analyze polycrystal grain orientation s. b. Texture/Property Relationship in Fine Grain Nb Sheets While the microstructures and mechanical properties vary significantly from one sh eet to another, little texture/property correlation has been identified . Yield strength and grain size values were extracted from the Ningxi a sheet samples shown in Figure 55 to evaluate how well the Hall - Petch equation [146] is satisfied. The fitted line is shown in Figure **. T h e Hall - Petch constants 0 = 76.3 MPa and k y = 1.64 MPa·m 1/2 ) show reasonable agreement with literature values [ ], but the R 2 value is quite low, indicating considerable scatter. The gradual slope suggests that the yield strength is not highly sensitive to grain size. These observations imply that other factors such as preferred orientations have a larger influence on the yie l d strength, and this helps explain why it is hard to find one - to - one correlation between parameters extracted from the tensile tests and microstructural measurements. 147 There is sometimes a systematic difference in sample mechanical properties between t he two companies. For example, the UTS s of Tokyo - Denkai samples are slightly higher than those of Ningxia samples, as shown in the UTS vs. grain size plots in Figure 56 . This may result from their different source material and pro prietary manufacturing processes, or from how the samples were cut with respect to the rolling direction (0º or 90º for Ningxia and 45º for Tokyo - Denkai) . Larger LAM values correspond to greater GND con tent (lattice curvature/low angle grain boundaries) in the sheets, which serves as barriers for plastic deformation and should yield more work hardening and presumably higher UTS. However, the LAM vs. UTS plots exhibit shotgun scattering [61] . This again implies that the mechanical properties are a combined effect of multiple factors that have not been identified . Figure 82 : Fitted line of yield strength vs. grain si ze for the Ningxia samples shown in Figure 55 . The shotgun scatter suggests that the Hall - Petch relationship is not well satisfi ed. 148 Des pite the scatter in material properties, all samples examined met the ACL specifications. Except for the implications of cost, it may be desirable for a string of cavities to be formed using sheets with similar microstructural profiles. This assessment o f texture and mechanical properties provides a means to correlate cavity performance with a specific origin al materia ls state , so it is a resource for future learning that may lead to more meaningful ACL requirements. c. Connection between Ingot and Sheet Mic rostructure The multi - crystal rolling experiment provided evidence of how the layer cake micro - structure in sheet material originated . Also, a s shown in the rolled large grain orientation maps in Figure 59 through Figure 61 , dominant ori entations that develop from rolling are highly variable and are not always traceable to the original orientation s of large grains. However, t he similarity in the orientation of recrystallized grains despite being isolated ( Figure 62 and Figure 63 ) implies that the new grains are a systematic (not random) consequence of the deformation process. The in ability to consistently index the heavily deformed area for sample A6 with about 92% re duction ( Figure 61 ) suggest s a non - uniform stress and strain distribution, which would lead to varying recrystallization behavior in the different layers. Randomly oriented large grains combined with the complicated deforma tion state during multiple rolling passes and the not - well - understood orientations of recrystallized grains contribute to the heterogeneity in sheet microstructur e . This explains why it is rare to observe similar texture even in sheets from the same manuf acturer [24] . This rolling study is a n ongoing effort that other researchers are investigating . 149 d. Effects of Processing Histor y on Cavity Surface Damage From the shape change due to forming the iris and equator , heterogeneous deformation leads to earing , implying that the equivalent strains are different in different grain orientations . The iris experienced hoop tension and bend ing that reached an equivalent strain of about 40%. Based up on continuum finite eleme nt modeling of the forming process for cavities with similar geometry, the equator experienced a more complex history involving hoop compression and bending to an equivalent strain of about 20% [147] . The difference between the equator and iris LAM maps in Figure 64 and Figure 65 is consistent with the larger strain in the iris before annealing, the equator scans have large areas that are light gray (lower LAM values) , whereas the iris scans are dominated by darker shades of gray (higher LAM values) . Because the result i ng dislocation density in the iris was probably higher, this provided a larger driving force for recovery, which can account for the more dramatic change in the LAM maps for the iris sample after the heat treatment . No evidence for recrystallization, i.e. , the emergence of new orientations, is present after the 800 C heat treatment. This suggests that conventional furnace heating facilitates recovery and prevents recrystallization in deformed large grains. In con trast, previous studies on electron beam w elding of deformed single crystals [24, 48, 145, 148] showed that recrystallization occurred in the heat affected zone adjacent to the weld, resulting in different grain size on either side of the weld. The sample s reached the recrystalli zation temperature before too much recovery took place due to the high heating rate, so the stored dislocation defect energy was available for nucleation and growth of recrystallized grains. The grain boundary in Iris 1 in Figure 65 appears to have developed during deformation. This boundary has the highest misorientation at the inner surface and disappears with distance 150 toward the outer radius. Since the boundary has large LAM values as indicated by the da rk color, it seems to be a consequence of polygonization [2 9] , which leads to a low - energy configuration of dislocations where regularly spaced dislocations organize into low angle boundaries inclined to the slip plane. The formation of th is low angle grain boundary may be a result of the changing driving for ce for dislocation activit y with respect to the crystal orientation , because the hoop st ress is in a different crystal direction at every position in the original large grain. A larger bending strain may have occurred at this position during deep drawing , causing an unbalanced population of dislocations of one sign to form the low angle boun dary. It is also possible that a preexisting low angle grain boundary became a trap for dislocation accumulation that led to the formation of a sharper grain boundary. Evidence for this possibility is visible in Iris 2 in the middle set of orientation ma ps of Figure 65 , where there is a near vertical very low angle grain boundary to the left of center. This boundary is evident as a subtle color change in the three EBSD map s and the after annealing LAM map, but it is not evident in the as - deep drawn LAM map as it is obscured by the high LAM values . The slight migration of grain boundaries in all the orientation maps shown in Figure 64 and Figure 65 suggests that the driving force (prim arily plastic strain) for recovery was in homogeneous, so that the defect removal occurred at different rates in various parts of the crystal . T he difference in dislocation removal at the equator and iris may explain why the equator is more susceptible to forming hot spots in operating cavities [26] , as there are regions where the LAM values become higher a fter the anneal . This is also consistent with observati ons of thermal conductivity in [31 - 33] , in which a larger strain is generally associated with a more significant restoration of phonon peaks after annealing. The fact that all the after - BCP LAM histograms are more similar to each 151 other ( Figure 67 ) may reflect that th e observed material was not close to a free surface that could provide surface energy or more degrees of freedom for chang es to occur. This implies that defect removal was greater near a free surface than beneath the surface. The corresponding IQ maps in Figure 64 and Figure 65 for the equator and iris provide a contrast to the LAM maps, as they show a sum of all defect content, including impurities, vacancies, GNDs, and SSDs. In the LAM maps, there is evidence for cell boundaries distinct networks having regions between them in which there are few GNDs. The IQ maps generall y show lower IQ (darker r egions) where there is higher GND content, but the cell structures are not evident. This implies that SSDs and other defects overwhelm the contribution from GND s . Annealing increases the IQ in a way that is consistent with the de crease in the GND content , but there are also regions of high IQ that correspond with high LAM values in most maps. Because LAM values correspond to GND content , t he depth of surface damage can be estimated from the LAM maps . M ultiple traces from the su rface inward in the six grains measured using EBSD mapping were extracted and averaged. LAM profiles are plotted with depth from the surface in Figure 83 for six areas in the equator and six areas in the iris. As evident by variat ions in the plot, a ll six grains responded differently to forming. LAM values for the iris are in general higher th an the equator, consistent with overall qualitative observations. At the equator, LAM values come to a low and constant value at a smaller depth than the iris, again indicating that the dislocation content is greater at the iris. Traces starting from th e inside and outside behave differently as well ; the equator inside and iris outside reach a constant LAM value at ~60 µm, while the LAM valu es have a more gradual drop from the surface for the equator outside and iris inside. 152 Significant dislocation content is present at depths up to about 200 µm at several locations , consistent with the equator and iris LAM maps in Figure 64 and Figure 65 . This may explain why the performance of the cavity fabricated from this half - cell was not s atisfactory after an initial ~70 µm BCP, but it improved remarkably after a second ~170 µm surface removal with c entrifugal barrel polishing, BCP followed by electropolishing as described in [5, 149] . This suggests that the LAM values near the surface can be understood as a metric for damage in cavities , and once the dislocation content drops below a threshold, cavity performance is no longer affected . Comparing Figure 83 : LAM profiles in the 6 grains obtained from averaged traces on the inside and outside of the equator and iris. Damage depths up to about 200 µ m is present in some regions, and the magnitude is different for the equator and iris , as well as for the outside and inside [ Figure 9 in reference [126] ] . 153 with Figure 14 , where fine grain cavity pe rformance was still improving with 180 µm of surface removal, it appears that the damage from deep drawing occurs similarly in fine grain cavities, even though it was estimated using a different approach [76] . Romanenko et al . reported that a low - temperature bake at ~120 ºC caused a reduction in LAM values in both small and large grain cavities [27] , which is unexpected since it is generally believed that dislocations are hard to move at temperatures much below the recovery threshold. In this study, care was taken to observe the same areas before and after the anneal and surface removal, showing that GNDs in large grain Nb ar e stable and difficult to remove even after the higher temperature anneal. Furthermore, it is puzzling that the data in [27] suggests that more chang e in LAM took place in large grain material than fine grain material , when one would expect a greater presence of grain boundaries would facilitate removal of dislocations ( al though there was no indication that the same regions were measured before and aft er the bake ) . In both studies, the trends show a shift of LAM peaks to the left (smaller values) after annealin g, and the variability may arise from the heterogeneity in dislocation substructures. Thus, larger statistical sampling may be needed before a quantitative interpretation of the magnitude of the shift can be developed . T here are regions wit h stable and e ntangled dislocation microstructures that are resistant to the recovery - based removal, and the heterogeneity of these regions may account for the etch pits occasionally observed on large grain cavities that are associated with RF losses [150, 151] . A limitation of this study is that EBSD only provides information about the surface because the penetration d epth for the e lectrons is less than 1 µm. Therefore, it remains an open question as to whether the effects of annealing on the surfaces examined are a good representation of the 154 bulk. T he differences in LAM value histogram s before and after the 10 µm BCP in Figure 67 does suggest different recovery behavior between the surface and the bulk , as the surface could serve as a sink for dislocations to exit in large grain material. While the surface condition is vital for superconductivity, reducing defect content is important for bulk properties such as thermal conductivity. Hence, it is neces sary to know if dislocations in bulk have been effectively removed . e. Effects of Heat Treatment on Preferred Slip Systems in Nb The lower yield strength and flow stress after the 800 °C/2h r heat treatment in the stress - strain curves in Figure 68 are likely due to a reduced density of preexisting dislocations that were barriers to plastic deformation. The lack of a slight drop in the flow s tress between yield and ~15% strain for some of the heat - treated samples (most notably T) also su ggests lower forest dislocation content. By comparing the Schmid factor ratio between primary and secondary slip system s (with a different slip direction from primary) with the initial hardening behavior along with the observed rotation axes and slip traces , it was argued in [16] that {112} slip largely accounts for the onset of plastic deformation in the as - received samples. To assess the effect s of dislocation removal , a similar analysis was performed on the heat - treated samples, as shown in Figure 84 . Here, based on observations of slip traces and rotation axes, the {110} slip systems instead best account for the initial hardening slopes the smaller the ratio between primary and secondary {1 10} slip systems (i.e. , the more similarly they a re favored) , the more work hardening a sample tends to have. This change in the preferred slip plane suggests that the anneal may have altered the core structure of screw dislocations in the samples, possibly due to boiling out hydrogen, or that the prese nce of preexisting forest dislocations in the as - received samples makes slip on {112} planes more 155 favo rable. This is consistent with slip trace observations in Table 9 , where {110} slip systems are more prevalent in the heat - treat ed samples. Figure 84 : The table on the right lists the annealed samples in the order of increasing ratio between the primary and secondary {110} slip systems, which corresponds roughly to decreasing initial hardening rates as sho wn in the zoomed image on the lower left [ Figure 3 in reference [ 121 ] ] . 156 C rystal plasticity modeling was used to simulate the deformation of orientations P through X [ 106, 152] . The modeling attempted to extract parameters describing non - Schmid effects , but if they are there, they appear to be small in Nb. Figure 85 : Comparison of exp erimental and simulation results of several annealed samples using classical, dynamic hardening, and differential - exponential approache s. Without accounting for the Non - Schmid effects, the modeling still shows good agree ment with the experiments [ Figure 1 5 and Figure 16 in reference [149] ] . shows examples that com pare the experimental and simulation results of several annealed Ningxia samples [106, 149] , indicatin g that two different hardening rules, the dynamic hardening and differential - exponential models , can capture the broad effects of hardening but not the evolutionary details (further discussed in [106] ), none of which employ the non - Schmid appr oach. This suggests that these simpler Schmid - based models might suffice for simulating the deep drawing of large gr ain Nb. The outcome of slip trace observations summarized in Table 9 is also in line with the implication from modeling that the non - Schmid effects are small in Nb [000] . Even though the Figure 85 : Comparison of exp erimental and simulation results of several annealed samples using classical, dynamic hardening, and differential - exponential approache s. Without accounting for the Non - Schmid effects, the modeling still shows good agree ment with the experiments [ Figure 1 5 and Figure 16 in reference [149] ] . 157 MATLAB code used to calculate slip traces only considers Schmid effects, t here is a good agreement between the Schmid theory and experiments for each heat - treated sample, at least one of the top two ranking slip systems (based on Schmid factor and a global stress tensor ) was observed . For the a s - received samples, Q is the only exception with the 3 rd highest ranking slip system observed . Slip traces are not visible in most annealed samples until about 20% strain . This may be where dislocations mov e through th e crystal uniformly and exit the crystal freely at low er strains . Also, the straight slip lines differ from those observed in the as - received samples, which have a range of inclinations that indicate bursts of slip in the same direction , but on different planes. Figure 86 shows an example of the slip morphology in samples X3 ( as - received ) and X 2 (annealed) [16] . The slip traces of X3 are wavier with fewer straight portions than X2 . This suggests that t he presence of preexisting dislocations may have led to entanglements that cause bursts of slip activity on a particular slip plane , and hence, shorter lengths with the same slip trace. 158 Figure 86 : Comparison of slip trace morphology at 40% engineering strain on the as - received and heat - treated sample X . X3 has wavier slip traces than X2. 159 As shown in the evolution of tensile axes plots in Figure 76 and examples of orientations R and P in Figure 73 and Figure 74 , the as - received samples almost always exhibit more crystal rotation than the annealed samples after deformation. This impl ies that annealing caused changes in slip behavior. For example, if slip occurred alternatively on {112} and {110} planes rather t han u niform ly on {110} planes , the n orientation changes would reflect rotations about two axes rather than one, which may accoun t for larger misorientations in the as - received samples . Moreover , the slightly different initial orientations within each samp le pa ir may have also contributed to the divergence in crystal orientations at larger strain s . In general, the farther away a sample is oriented from symmetric boundaries of the stereo - graphic triangle , the less work hardening and more crystal rotation it exh ibits during deformation ( stress - strain curves in Figure 68 and rotations on inverse pole figures in Figure 76 ). This suggests that the single slip condition facilitates lattice rotation , whereas the interac tion of slip system s contributes to hardening and suppresses rotation . Crystal o rientations were captured from three areas spanning ~ 5 mm along the gauge length for the heat - treated samples, which enables assessment of how the initial orientation gradient s as illustrated in the serial of scans in Figure 44 affect deformation. However, P2 is the only sample that shows counter rotations in the three regions as shown by the prisms in Figure 74 , whereas the othe r samples all exhibit consistent rot ation directions . While this may suggest that the orientation gradients are not significant enough to cause different parts of the samples to deform differently, it may also be due to the relat ively short distance (5 mm vs. 18 mm gauge length) over which the orientations were measured , as was imposed by an instrument al limit . 160 For the CC - EBSD experiment, t he d ifference s in work hardening behavior ( Figure 78 ) and GND density ( Figure 79 ) between samples T1 and V1 suggest that GNDs are mainly responsible for crystal rotation, while hardening may be primarily accounted for by SSDs that result from the intersection of slip systems . More tests are needed to confirm this implicati on. The hints of local preexisting GNDs in sample V1 ( Figure 79 ) could partly explain its high hardening rate despite the prior anneal . The two U samples both exhibited banding with different orientations diverging from each othe r with increasing strain, as shown in Figure 75 for U2 (annealed). This phen omenon is similar to that observed in the rolled multi - crystals (e.g., Figure 60 ). The Schmid factors for rolling or biaxial tensi on are in general lower than uniaxial t ension 3 . Because U is the orientation with low Schmid factors on multiple slip systems, its stress state may be close to rolling deformation of certain orientations . This perspective may lead to an ability to predic t which orientations are more likely to show shear banding in rolling conditions. Simulating the orientation evolution during rolling is a project being conducted by a colleague (Eureka Pai Kulyadi ). For most orientations, the macroscopic shape change and deformation banding are similar between the as - received and annealed samples , as shown in the optical image s in Figure 77 . This suggests that even though the mechanistic details of deformation are poten tially different due to the heat treatment , such microscopic effects may be insignificant from the cavity manufacturing perspective. Nevertheless, changes in dislocation substructures due to varying interactions of slip systems lead to differing defect ch aracteristics that may affec t cavity performance. 3 This can be demons trated by comparing the Schmid factors for each slip system based upon uniaxial tension, plane strain compression, or biaxial deformation for the same crystal orientation. 161 In summary, the connection between randomly oriented large grains and the layered poly - crystalline micro structure in rolled sheet s has been identified from the rolling experiments . Cavity s urface damage results from heterogeneous def ormation during deep drawing and leads to different microstructure effects at the equator and iris following heat treatment . Preexisting dislocations play a critical role in the deformation of single crystals. These findings provide a physical basis for developing codes that can simulat e the microstructural evolution and recrystallization during cavity processing, which will ultimately contribute to the goal of producing cost - effective SRF cavities with consistent performance. 162 VI. CONCLUSIONS The physical m etallurgy of Nb for building SRF accelerator cavities with focuses on the microstructure and slip behavior has been investigated to identify sources of variability in cavity performance and to establish a basis for modeling cavity forming and performance. T he findings are summarized as follows : Eight Nb ingots from different suppliers were characterized by the EBSD or Laue method . T he ingots have no obvious commonalities in crystal orientation or grain boundary misorientations, suggesting that the ingot s olidification process is random and uncontrolled . The s low solidification condition and l ack of temperature gradient led to random, elongated gr ains in the ingots. Typically, t he crystal orientations do not vary by more than 1 ° / in ch along either longitu dinal or transverse directions in various ingots , yet the Ningxia ingot show s more orientation gradients than the others , likely due to their ingot manufacturing process (e.g., different thermal gradients ) . The greater intragranular orientation gradients may have also contributed to the preexisting dislocations in the extracted tensile samples. The Laue method serves as a nondestructive alternative to EBSD for measuring large grain orientation s, allowing crystal orientation s to be captured during the cav ity fabrication process . It may also be used to examine the heat affected zone of equator welds. Such orientation information is important to establish a database that can be correlated with cavity performance. Effects of plastic deformation on crystal q uality were examined . Machining processes , such as end milling , are likely to introduce a more uniform macros train , whereas the friction from deep drawing tends to produce more localized near - surface strain s . Both processes can result in surface damage t hat necessitates heat treatment or chemical removal. 163 The micros tructure and mechanical properties of the Nb material to be used for the Facility for Rare Isotope Beams (FRIB) varied in all samples from the two suppliers. Scatter plots for most pairs of t he measured parameters suggest low correlations between the texture, microstructure, and mechanical behavior , even though there is significant variability among sheets. T h is assessment provides a means to correlate future cavity performance with a specifi c m icrostructure. Preliminary results from the rolling experiment suggest a correlation between the ingot and sheet microstructure deformation bands parallel to the surface developed from rolling, and grains with random orientations nucleated after heat tre atment at 800 ºC/2hr. These observation s show how the randomly oriented large grains evolve into the highly variable banded/layered sheet texture resulting from the complex stress state of rolling and subsequent heat treatment , suggesting that the vari ability in cavity performance can be traced all the way back to the ingot , and that recrystallization may be a systematic process determined by prior orientation, strain history, and heat treatmen t. This implies that a sophisticated material model is nece ssary to predict variability in cavity performance . EBSD analyses on the iris and equator samples from a cavity half - cell show that the surface damage from deep drawing depends on crystal orientations, is different at the equator and iris, and is sever e ev en in the bulk at the iris. The iris and equator respond differently to annealing due to their different defect states. While the 800 ºC/2hr heat treatment may suffice for recovery near the iris, a longer time or higher temperature may be needed for the equator to achieve a similar degree of defect removal. The se heat treatments do not remove GND network s effectively . The da mage de pth (consisting of higher GND density) is estimated to be 200 µm and removal of this dama ged layer proves to be a pratical m ethod to improve cavity performance. The magnitude of surface damage may be similar for large grain and fine grain cavities, but further study is needed to confirm 164 this. This implies that cavity performance is directly related to the GND content present in the more highly deformed surface regions resulting from the deep drawing process, and that a more strategic deformation path and heat treatment are needed to reduce dislocations and processing cost . Nb single crystals with different orientations were de formed in uniaxial tension before and after an 800 °C/2hr anneal to study slip activ it y that is useful in modeling the deep drawing of large grain ingot slices. The results indicate that the stress - strain behavior is strongly dependent on orientations and that annealing lowered the flow stress and usually changed the preferred slip plane s from {112} to {110}, due to the removal of preexisting dislocations. This suggests that the prior strain history (hence dislocation content) has a significant impact on which slip systems are favored to operate , which in turn affects the orientation and defect evolution during cavity forming . This implies that for material models to be more effective, they must be capable of tracking the evolution of dislocation content within the material throughout the formin g process. Homogeneous slip could account for the lack of visi ble slip traces at early stages of deformation in the heat - treated samples. CC - EBSD analysis suggests that GNDs account for crystal rotation during defo rmation and hardening is caused primarily by SSDs, although more tests are needed to confirm this observation. Initial simulation s based on the single crystal stress - strain behavior suggests that a Schmid - based model can c apture the anisotropic deformatio n characteristics . 165 VII. RECOMMENDATIONS FOR FUTURE WORK Continu ing to c haracteriz e the rolling and annealing microstructure of Nb multi - crystal s will provide further insights into how sheet microstructure is linked to the original large grains and extend the p reliminary studies reported here . Additional rolled samples will be examined using EBSD before and after heat treatment at various temperatures / times . This is a n ongoing project conducted by a couple of undergraduate researcher s . The strain tensors obtai ned from the finite element modeling of deep drawing of Nb can be used to assess which slip systems were activated during deformation. This analysis will provide a means to compare the simulated and measured changes in the shape an d crystal orientation of a half - cell, which will assist in constitutive model development. A synchrotron X - ray study on the half - cell used in this work w ill address how recovery or dislocation removal occurs in the bulk and if the process is different fro m the free surface. Sam ples with grain boundaries or shape irregularities can be extracted from the remainder of the trimmed material and given the same annealing and BCP treatments. This would provide more information on the microstructural evolution during cavity processing. A similar surface damage study on a fine grain cavity half - cell would reveal the similarities and differences between the damage behavior of large grain and fine grain material. Samples have been ex tracted from a fine grain cavity provided by JLab , and pr eliminary EBSD data have been collected . This would supply another perspective on the ongoing debate of whether the large grain or fine grain approach is better for volume production of cavities. Du e to the limited number of single crystal samples studied in this work and in [16] , several orientations are still missing in the fundamental triangle. Future tests with new orientations will 166 supplement the collection of uniaxial tensile deformation of Nb and make the comparison with the D&F set more robust. This would also provide a ba sis for improving the crystal plasticity models for Nb deformation. More CC - EBSD e xperiments can be performed on the tensile samples to confirm the trend of GND evolution during deformation . The GNDs can also be resolved into different types (edge vs. scr ew) as well as onto slip planes ({110} vs. {112}). This will provide further insi ghts into the deformation mechanism of Nb. GND s can also be mapped on cavit ies as a function of processing , reinforcing the link between dislocations and cavity performance. ECCI provides a means to observe dislocations directly , so it can be used to iden tify the evolution of dislocation sub structure and content with heat treatment and deformation in the tensile samples. The outcomes can be correlated with the stress - strain behavior and slip system activities can be inferred . Fundamental understanding of dislocation evolution is also helpful in modeling the processing of cavities. This may enable strategic heat treatment schedules that would identify an optimized microstructure for cavity performance (e.g., dis locations aligned perpendicular to the heat transfer direction). This analytical approach is the subject of a paper by a collea gue (Mingmin Wang) that was published recently [153] . 167 APPENDIX 168 F igure 87 : <111>, <112>, and <110> pole figures from three regions on the gauge length for the heat - treated sample s P, Q, and R with the tensile axis pointing out of the page. The color scale for engineering strain is common and sh own next to sample P. 169 Figure 88 : <111>, <112>, and <110> pole figures from three regions on the gauge length for the heat - treated samples S, T, and U with the tensile ax is pointing out of the page. The color scale for engineering strain is common and shown next to sample S. 170 Figure 89 : <111>, <112>, and <110> pole figures from three regions on the gauge length for the heat - treated samples V, W, and X with the tensile axis pointing out of the page. The col or scale for engineering strain is common and shown next to sample V . 171 Figure 90 : Slip trace identification on the heat - treated sample P in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in pu rple. 172 Figure 91 : Slip trace identification on the heat - treated sample Q in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, w ith {110} slip traces in green, and {112} in purple. 173 Figure 92 : Slip trace identification on the heat - treated sample R in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. 174 Figure 93 : Slip tra ce identificati on on the heat - treated sample S in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. 175 Figure 94 : Slip trace identification on the heat - treated sample T in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in gree n, and {112} in purple. 176 Figure 95 : Slip tr ace identification on the heat - treated sample U in some of the areas examined. Observed slip traces (solid lines) were matched with computed traces (dotted lines) based on the measured or ientations, with {110} slip traces in green, and {112} in purple. 177 Figure 96 : Slip trace identification on the heat - treated sample V in some of the areas examined. Observed slip traces (solid lines) were matched with computed trac es (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. 178 Figure 97 : Slip tr ace identification on the heat - treated sample X in some of the areas examined. Observed slip traces (so lid lines) were matched with computed traces (dotted lines) based on the measured orientations, with {110} slip traces in green, and {112} in purple. 179 Figure 98 : Orientation maps from three regions for the heat - treated sample P bef ore and after deformation. 180 Figure 99 : Orientation maps from three regions for the heat - treated sample Q before and after deformation. 181 Figure 100 : Orientation maps from three regions for the heat - treated s ample R before and after deformation. 182 Figure 101 : Orientation maps from three regions for the heat - treated sample S before and after deformation. 183 Figure 102 : Orientation maps from three regions for the he at - treated sample T before and after deformation. 184 Figure 103 : Orientation maps from three regions for the heat - treated sample U before and after deformation. 185 Figure 104 : Orientation maps from three region s for the heat - treated sample V before and after deformation. 186 Figure 105 : Orientation maps from three regions for the heat - treated sample W before and after deformation. 187 Figure 106 : Orientation maps from three regions for the heat - treated sample X before and after deformation. 188 BIBLIOGRAPHY 189 BIBLIOGRAPHY [1] H. 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