ON THE iMPROVEMENT OF LATTICE PERFECT {ON IN HSG’H PUMTY ZiNC CRYSTALS GROWN FROM THE MELT Thesis fur the Dogma 0! M. S. MICHIGAN STATE UNIVERSITY - Chi Kwan Chyunfg 1%2 ' ‘ guests This is to certify that the thesis entitled ON THE IMPROVEMENT OF LATTICE PERFECTION IN HIGH PURITY ZINC CRYSTALS GROWN FROM THE MELT presented by Chi Kwun Chyung has been accepted towards fulfillment of the requirements for Master's degree in Metallurgical Engineering [:4 ’3/ 4/ j/flm / //a{or professor/ *1 LIBRARY LI M’chigan State University ON THE IMPROVEMENT OF LATTICE PERFECTION IN HIGH PURITY ZINC CRYSTALS GROWN FROM THE MELT by Chi Kwun Chyung A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Metallurgy, Mechanics and Material Science 1962 ON THE IMPROVEMENT OF LATTICE PERFECTION IN HIGH PURITY ZINC CRYSTALS GROWN FROM THE MELT by Chi Kwun Chyung High purity zinc single crystals of controlled orienta- tion have been grown by improving the soft—mold technique. Improvement in crystal perfection was made by (a) minimizing radial thermal stresses during the growth and cooling to room temperature; (b) preventing the propagation of sub-boundaries from the seed. The best crystals grown were substantially free from sub-boundaries, except a few polygonization sub-boundaries near the free surface. Total dislocation density of such crystals was found to be in the range of 6-9xlO4 cm-z, as revealed by etch figures on sections nearly parallel to the prism plane. The disorientation of the polygonization sub- boundaries ranges from 5 to 30 seconds of arc. The pseudo Kossel patterns of the crystals produced by the divergent X-ray method showed qualitative agreement with the results obtained by the etching technique on crystal perfection. Chi Kwun Chyung The etching technique was capable of measuring much smaller sub-boundary disorientation than the X—ray technique. ACKNOWLEDGEMENTS The author wishes to express gratitude to Dr. William E. Taylor for the guidance in this work. The helpful sug— gestions and encouragements given by Dr. C. T. Wei are also gratefully acknowledged. The entire staff of the Department of Metallurgy, Mechanics and Material Science are thanked for their assistance and helpful discussions. The author wishes to express special gratitude to Mr. and Mrs. Fred R. Fitzpatrick for their spiritual guidance. Finally, he would like to thank the Atomic Energy Commission for the financial helps granted under the Contract #AT (ll-l)-1042. ii TABLE OF CONTENTS Page INTRODUCTION . . . . . . . . . . . . . . . . 1 THEORY AND BACKGROUND . . . . . . . . . . . 8 EXPERIMENTAL . . . . . . . . . . . . . . . . 21 RESULTS AND DISCUSSION . . . . . . . . . . . 39 CONCLUSIONS . . . . . . . . . . . . . . . . 65 RECOMMENDATIONS . . . . . . . . . . . . . . 67 REFERENCES . . . . . . . . . . . . . . . . . 70 iii lO & ll. 12. 13. LIST OF FIGURES The effective stresses causing plastic flow in the case of radial heat flow . . . . . . . Furnace set-up (schematic) . . . . . . . . . Crucible design . . . . . . . . . . . . . . . Crystal growth specimens . . . . . . . . . . a) Offset specimen b) Standard specimen Orientations of the crystals and the seeds with their designations . . . . . . . . . . . Furnace set-up . . . . . . . . . . . . . . . Furnace control panel . . . . . . . . . . . . Acid string saw . . . . . . . . . . . . . . Crystallographic arrangements of sub-boundaries 500x . . . . . . . . . . . . . . . . . . . . . Crystallographic arrangements of sub- boundaries. 500x . . . . . . . . . . . . . . Sub—boundaries propagated from the seed. 500x. Background dislocations revealed on: a) the cross sectional surface. 500x . . . . . b) the surface parallel to the growth direction. 500x . . . . . . . . . . . . Sub-boundary etching on: a) the cross sectional surface. 500x . . b) the surface parallel to the growth direction. 500x . . . . . . . . . . . . iv Page 11 33 34 34 35 36 37 38 55 55 56 57 57 58 58 Figure 14. 15. 16. 17. 18. Page Effect of crucible size on sub-boundary forma- tion near a corner of the cross sectional surface. 500x . . . . . . . . . . . . . . . . . 59 a) crystal grown in the crucible A b) crystal grown in the crucible B Sub—boundaries on the cross sectional surface 35x . . . . . . . . . . . . . . . . . . . . . . 60 Typical sub-boundaries formed at the faster COOling rate (2 mm/min.) 320x . . . . . . . . . 61 Microfocus x-ray back-reflection pattern of the crystal Y O O O O O O O O O O O O O O O O O O O 62 Microfocus x-ray back-reflection pattern of the crystal C . . . . . . . . . . . . . . . . . . . 63 I. INTRODUCTION The existence of imperfections in crystal structure has long been recognized. As early as 1912, Laue found that the intensities of X—ray diffraction spots were not in agreement with the simple theory based on the perfectly arranged crys- tal lattice. Darwin explained the intensities in terms of "mosaic" structure in which perfect lattice blocks of finite size are slightly disoriented with respect to each other (1). In 1934 Buerger introduced the concept of lineage structure (2). The idea was based on the fact that if inhomogeneous warping occurs between neighboring regions of a crystal dur- ing the growth, low angle boundaries are formed at which the crystal orientation changes discontinuously. Meanwhile in the same year, Taylor (3) and Orowan (4) introduced, independently, the concept of dislocations. This concept was proposed to account for the large discrepancies between the theoretical and experimentally observed strength of crystals. Since then, the theory of dislocations has had a great success in explaining many other properties of crystals. With gradual development in the experimental techniques of observing dislocations, the theory of dislocations made a giant stride toward the better understanding of crystalline materials. In the meantime, the growth of crystals free of dislocations became one of the most pursued subjects which might bring still further understanding in the nature of dislocations. During the past decade, the growth of dislocation--free crystals reached the realm of possibility. Dash has grown dislocation--free silicon crystals (5). The growth of per- fect germanium crystals soon followed (6). However, the growth of dislocation-~free metallic crystals has not been reported until recently. Elbaum and Howe (9) have grown aluminum crystals free of dislocations in the core. The portions of the crystals free of dislocations were less than about 0.5 mm in diameter. Perfect metallic crystals of sub- stantially large size have not been grown. The growth of perfect metallic crystals would be a difficult task indeed in light of the fact that metals are extremely susceptible to plastic deformation by thermally or mechanically induced stresses during growth as well as during cooling to room temperature. Much effort in growing perfect crystals from the melt has centered around the elimination of the four most impor— tant sources of dislocations (5, 6, 7, 8, ll, 12, l3, 16, 18). They are: 1) seed, 2) collapsing vacancy disks, 3) thermal stresses, and 4) impurities. The mechanism of collapsing vacancy disks for the forma- tion of dislocations in crystals grown from the melt has become a center of considerable speculation in recent years. Theoretical calculations made by Schoeck and Tiller (28) show that this mechanism could not account for the formation of "striation" type sub-boundaries. It was noted earlier that Frank's mechanism for striation formation (29) requires that the dislocation loops, once formed behind the interface, must be able to climb towards the moving interface at such a rate that they can catch up with it. The rough calculations made for the climb rate of dislocation loops in metals by Elbaum (8), Schoeck and Tiller (28) differ as much as five orders within the range of typical thermal conditions of careful growth. The aluminum crystals grown by Howe and Elbaum, free of dislocations in the portions of less than about 0.5 mm in diameter, contained dislocation in the surface layers. The presence of dislocations in the surface layers raises a doubt as to whether the observations can be accounted entirely by the vacancy condensation mechanism. In the meantime, thermal stress is known to be capable of introducing dislocations in crystals, if such stress is large enough. Therefore, it is of interest to improve the degree of perfection in metallic crystals grown from the melt by eliminating thermal stresses under proper growth condition. A similar approach has been initiated by Noggle (15) in his solf—mold technique in which radial heat loss is minimized by soft mold materials of high thermal insulation. The alu- minum crystals grown by this technique show comparable degree of perfection to that of crystals grown by strain annealing (20, 21). This is a promising result and should be further improved. In this work, attempts were made to improve the soft-mold technique, thus improve the perfection of metallic crystals grown. Special emphasis was made on eliminating sub-boundaries. If sub-boundaries could be eliminated, it would be a critical test for Schoeck and Tiller's contention in which they argue that Frank's mechanism for lineage for- mation is inapplicable (28). The first systematic study on the lineage structures in metal crystals was made by Tetsoonian and Chalmers (16). They have termed the lineage structure as "striations" and were the first ones to propose a mechanism for its formation. Some interesting observations were made on the striations present in tin (99.987 per cent pure) crystals. At slow growth rate the striations tend to form in a direction parallel to the direction of heat flow, regardless of the crystallographic orientation of the crystal. An incubation distance is necessary before striations can form in those parts of the crystal into which they are not propagated from pre-existing striations. They then explain the formation of the striations in terms of a vacancy condensation mechanism. This implies that the striations do not necessarily propa- gate from the seed. They also observed that the difference of orientation between neighboring striations is always a rotation of about 1/4 to 50 about an axis nearly parallel to specimen axis. The density of dislocations contained in striation sub-boundaries was found to be of the order of 107 cm"2 which was based on the relation 9 = g., where 6 is the angle of disorientation, b is the Burger's vector and h is the spacing between the dislocations in the array. Total dislocation density was of the order of 108 cm-Z. Tetsoonian and Chalmers have grown striation-free crys- tals by reducing temperature gradients. Aust and Chalmers (32) have also grown striation—free crystals by controlling the shape of the solid-liquid interface. The interfaces convex to the liquid and inclined to the specimen axis were used. However, it is doubtful as to whether sub-boundaries of very small disorientation were absent when the dislocation density is of the order of 108 cm-2 (32). Aluminum single crystals grown by the Noggle's soft- mold technique were much more perfect, as examined by X-ray diffraction (20). Here the dislocation density in sub- boundaries was about 105 cm-Z. The total dislocation density in these crystals was about 106 cm-Z. Later Kelly and wei (21) also investigated the perfection of aluminum crystals, grown by Noggle's method, using the fine X-ray beam tech- nique of Schultz. The misorientation of the sub—boundaries in the crystals varied from 1 to 20 minutes of arc. The high perfection of these aluminum crystals was attributed to the low thermal conductivity of the mold. Thus, the reduction in thermal strain during the growth seemed to result in greater perfection. However, no mechanism for the formation of striation type sub-boundaries due to thermal strain has been proposed. The techniques of observing dislocations have been grad- ually developing. Many X—ray diffraction methods have been divised. Noggle and Koehler (20), Kelly and Wei (21), Guinier (22), Lang (23) all used X-ray diffraction in one way or other. The estimations of dislocation densities made by Noggle and Koehler are at best semi-quantitative. The studies of sub-boundaries (21, 22, 23) raise question as to whether sub—boundaries are completely detectable by the X-ray techniques. Recently, etching techniques were developed to reveal individual dislocations and established at least an approxi- mate one-to-one correspondence between dislocations and the etch figures. For the high purity zinc used in this experi- ment, the etching and polishing solutions developed by Vreeland et al. (10) were used. II. THEORY AND BACKGROUND In the following, the formation of dislocations and their arrays in the crystals grown from the melt by the Bridgeman technique will be discussed with special emphasis on metallic crystals. There is an enormous amount of literature published on the subject concerning the sources of dislocations in the cyrstals grown from the melt. It has been generally accepted that there are five distinct mechanisms for the formation of dislocations. They are: l) propagation of dislocations from a seed onto the growing crystals, 2) formation of dislocations due to thermal stress, 3) formation of dislocations by vacancy condensation, 4) formation of dislocations due to local segre- gation of impurities that produce a change in lattice parameter, 5) dendritic growth. The last two mechanisms will not be treated here, under the assumption of high purity of the material and of growth conditions under which dendritic growth does not take place. 8 The theoretical prediction of dislocation formation by vacancy condensation has not been experimentally verified and will not be further considered. Hence, the first two mechanisms will be treated in the following. General theory will be discussed for a crystal in general, but special emphasis will be made on the metallic crystals grown from the melt. 1) Seed One obvious source of dislocations is the seed. When- ever a seed crystal contains dislocations which intersect the solid-liquid interface, these dislocations will propa- gate into the newly forming solid. This is a consequence of the fact that dislocations can only terminate at a free sur— face, by combining with dislocations of opposite sign, or by closing on themselves. Dislocations originating from the seed will be intro- duced into the crystal in two ways as the crystal grows; first by propagation by growth, and second by generation of dislocations by thermal stresses in the seed and propagation of these by growth (5, 18). Selection of a seed with a preferred crystallographic orientation can improve the crystal perfection in two ways: 10 a) A seed crystal with "hard" orientation. Such a seed can raise the critical stress value at which plastic deformation takes place. Thus, the number of plasti— cally generated dislocations during and after the growth will be minimized or eliminated. b) A seed crystal with a favorable orientation which will allow dislocations to grow out of the crystal. Dislocations tend to lie on certain crystallographic planes, such as slip planes. Also dislocations and their arrays tend to align themselves along the crystal axis (usually direction of heat flow) at slow growth rate, and along certain crystallographic direction at fast growth rate (5, l4, 16, 20, 21, 24). These properties can be used in selecting the seed such that dislocations can be driven out of the crystal. For example, a seed crystal in which the slip plane makes preferred angle with the crystal axis can be selected. Then the dislocations lying on the slip plane can be driven out of the crystal at fast growth rate. Dash (5) has utilized this principle in growing dislocation- free silicon single crystals. 11 2) Thermal Stress The effect of thermal stresses on the crystals grown from the melt is relatively well understood. Billig (36) and Penning (32,33) studied the thermal stresses in Si and Ge in terms of etch pit densities. Such studies in metal crystals have not been studied. Effect of such stresses would be much greater in metal crystals. It is easily under— standable that the effects are material, although they differ Thermal stresses would be tion is uniform throughout the generally fulfilled during the room temperature. exists, place and may be considered as part is due to thermal expansion, strain." similar in both types of in extent. zero if temperature distribu- This is not entire crystal. growth and the cooling to If a non—uniform temperature distribution the displacement of a point in the lattice takes consisting two parts. One the other is the "thermal Thermal strain is the consequence of the fact that displacement due to thermal expansion is not possible without interference with its surroundings. Thermal strain is nec— essary to keep the different expansions in different parts compatible with each other, if continuous. the lattice is to remain 12 When the thermal strain is very small, it may be entirely elastic. Beyond a certain critical value, which varies with the type of material and the temperature, thermal strain can— not remain elastic and will be relieved by plastic flow with generation of new dislocations. Furthermore, if plastic deformation takes place to accommodate non-uniform thermal expansion of a crystal, the reverse process will take place when the crystal is brought back to a uniform temperature, say room temperature. Plastic flow will again take place and more dislocations will be generated. In general, however, the proportion of elastic strain will be larger at room tempera- ture because the stress necessary to produce a dislocation increases as temperature decreases. In metals, the stress necessary to produce plastic flow is usually much lower than in semi-metals. Thus, the dis- location density produced by thermal strain in metal crystals will be even higher than in Si and Ge. This problem has not yet been investigated experimentally. a) Radial temperature gradient. If there is radial heat loss from a growing crystal, the shape of the liquid-solid interface would be convex into the solid. Stresses can be introduced in such a crystal, having 13 temperature variations because of dimensional changes associated with thermal coefficient of expansion. Thus, if the surface is allowed to cool to establish a temperature gradient between the center and the surface, the outer por- tion of the crystal will tend to shrink, but will be pre- vented from doing so by the warmer inner core. Accordingly, the surface layers are stretched and the core compressed. If such stresses exceed a critical value, plastic flow takes place and dislocations will be generated. In the case of low cooling rates the parabolic stress distribution in a simple round bar is represented by the following equations (32): r2 oz = (4 —E'- 2)O R r2 0 = (3 ——'- l)o 6 R2 0 r2 . or - ( £5 - 1) 00, 1 GET K where o ‘ g'hR l-v exp (-2h'E t) 14 in which h is a constant determining the rate of cooling, TO the initial temperature, R the outer radius of the crys- tal and K the diffusivity of the material. The stress tensor can be simplified by taking into account the fact that all shear stresses are zero when a hydrostatic pressure is applied. Hence one may subtract from the normal stresses a hydrostatic pressure of magnitude 0 as long as plastic flow is concerned. 6 The two remaining stresses 0' = o - o and o' = o -o r r 9 z z a in radial and axial direc— tions respectively are shown in Fig. A as a function of r. The net stress giving IqfifESSQU en plastic flow is a radial compression at the surface and an axial compression in ———»-' c. 51 *1 the center. 2 -———” Thus, 0' = -2 E—'o r 2 ‘Nh Fig. A O H l p... Q 0 The effective stresses 2 causing plastic flow in the case of radial heat flow. 15 b) Non—linear axial temperature gradient A non-homogeneous axial temperature gradient may arise from the radial heat loss. It may also exist in a growing crystal when it is withdrawn quickly during growth. Under such circumstance, shear strain er may not be zero, where r and 2 represent the radial and the axial direc— tion, respectively. Such a strain destroys the symmetry of stress pattern with respect to a plane perpendicular to the axis (32, 33). The er can cause a slip non-symmetric with respect to the crystal axis, if a normal stress component, for example oz, is present. The er is always accompanied by a z-dependent oz as follows directly from the equilibrium condition. Such stresses and strains are not readily calculated for quenching when a crystal is quickly withdrawn from the melt. Only a qualitative analysis is available to explain the effect of non—uniform axial temperature gradient. c) Thermal stresses during crystal growth. In the Bridgeman technique, there are two main sources of thermal stresses during the growth. Radial and non- linear axial temperature gradients will result from (a) a non-zero growth rate, and (b) radial heat loss. 16 There is no need for further explanations on the radial . . . 8T heat loss. Even if ax1al temperature gradient gg'were con- stant in equilibrium condition (before the growth), a term 32% Will be introduced in the temperature distribution as soon as growth takes place (32). The stresses induced by these deviations will be mini- mized when radial heat loss is prevented and the growth rate is slow. Under an ideal condition, the shape of the liquid- solid interface is perfectly planar which implies no thermal stresses are induced. Formation of Sub-boundaries Since Frank (14) proposed that suitable networks of dislocations can account for any type of misorientation in any direction between neighboring blocks of mosaic structure, many kinds of substructures have been studied. It is cus- tomary to divide these substructures into two categories, depending on their origin and mode of formation. The first category includes the substructures that arise from a par— ticular arrangements of dislocations, which are either formed during or after solidification. The second category includes the substructures arising from a specific distri- bution of impurities. In the following, only the first category will be treated. 17 There are two proposed mechanisms by which sub—bound- aries can be formed. First, when dislocation density is high enough there is a tendency for dislocations to arrange themselves into two—dimensional arrays forming a system of sub—boundaries (18, 35). At the relatively high tempera- ture prevailing behind the interface, the dislocation mobil— ity would be fairly high. These dislocations, as pointed out by Cottrell (35), would have a tendency to assemble into arrays of dislocations of the same sign, each dislocation lying in a different plane. Faster cooling rates reduce the time during which dislocation mobility is sufficient to per- mit the formation of sub-boundaries. The second mechanism was developed first by Frank (29) who suggested the vacancy collapse mechanism to account for the formation of lineage boundaries. As mentioned earlier, this mechanism has not been experimentally verified, and thus will not be treated here. It is known that thermal stresses are responsible for the formation of sub-boundaries. Washburn and Nadeau (19) observed the complex dislocation arrays were formed locally when the growing crystal was in contact with the crucible wall during the growth. They attributed the formation of the sub-boundaries to the thermal stresses resulting from 18 different thermal contractions of the crystal and the cru- cible wall. However, there have been no detailed mechanisms proposed for the formation of sub—boundaries due to the thermal stresses in the crystals grown from the melt. The formation of the striation type sub—boundaries studied by Chalmers et al. (16, 31) in tin crystals of 99.987% purity was explained in terms of the Frank's mechan- ism of collapsing vacancy disks. In view of the relatively high impurity content of the material, such an explanation may not be fully justified. The estimated density of the dislocations in the crystals was of the order of 108 cm-Z. The work of Noggle and Koehler (20) and of Kelly and wei (21) on aluminum single crystals grown by the soft-mold technique showed much higher degree of perfection in those crystals. The x-ray estimation of the total dislocation density was of the order of 106 cm-Z. The misorientation of the sub—boundaries present in the Al crystals ranged from 1 to 20 minutes of arc. Such a high degree of perfection in the crystal might have resulted from low thermal stresses in the soft-mold technique. The radial insulation by the soft- mold material (levigated alumina powder) seems to be directly responsible for the high degree of perfection. l9 Chalmers et al. (16, 31) have grown striation-free crystals of tin and aluminum. One method is based on the property that the striation width will increase to the com— parable dimension of the crystal when the rate of growth and temperature gradient is small enough. Another method used two properties of striations; l) the dependence of the striation on the crystallographic orientation and the rate of growth of the crystal, and 2) the incubation distance necessary before striations form in those parts of the crys— tal into which they are not propagated from pre-existing striations. Here they controlled the thermal conditions such that, first, the solid-liquid interface is convex to the liquid, and second, the interface is inclined to the specimen axis. In the first condition, the convex interface was obtained by a slight radial heat input. At slow growth rates, the striations tend to align themselves with the direction of heat flow, which is normal to the interface. Thus, striations can grow out of the crystal. In the second condition, the principle is the same as in the first case. Thus, the striations will tend to align themselves perpendicular to the interface if the maximum distance from the interface to the external surface of the crystal is larger than the incubation distance. 20 It is, however, hard to conceive a crystal free of sub- boundaries when the dislocation density is of the order of _ 4 _ 108 cm 2. Even when the density is as low as 10 cm 2 the I randomly distributed dislocations have a tendency to align themselves toward small angle boundaries (18). III. EXPERIMENTAL 1. Equipments a) Furnace arrangement. A modified Bridgeman technique was used in growing zinc crystals of controlled orientation. In this technique, the growing crystal remained stationary in the region between two furnaces where a constant axial temperature gradient was maintained during the growth. The crystal growth consisted of three stages of operation; soaking, solidification, and subsequent cooling to room temperature. Two type MK—lOO4-S Hevi-Duty electric furnaces were vertically mounted with a separation of l-l/2" between them. A zirconia tube with an inside diameter of 1-1/ " was inser- ted vertically into the furnaces. The gap between the two furnaces was insulated with spun fiber glass. The schematic drawing of the furnace arrangement is shown in Fig. l. The actual furnace arrangement is shown in Fig. 5. A general View of the instrument panel is shown in Fig. 6. All the control instruments used were manufactured by Minneapolis—Honeywell Company. The upper furnace temperature is controlled by a model SY153R10 recording controller. An axial temperature gradient can be maintained by setting the 21 22 corresponding temperature difference on the set point unit (model 62-R-lOO-D). Any deviation from the difference is indicated in the deviation amplifier (model 62-R-237-A). The recording controller features two modes of opera- tion; soaking and program cooling. A desired soaking period (0-6 hours) can be set at a desired temperature setting. After the soaking period, program cooling takes place line- arly at a desired rate, while a constant temperature differ- ence is maintained between the two furnaces. The span of program cooling can be changed. Most of the crystals have been grown with the span of 10 millivolts, corresponding to a temperature range of 250 degree centigrade. Fig. 1 also shows the position of the crucible and the internal arrangements. The crucible is suspended by alumel wire in a position such that the bottom 1" of the specimen is in the lower furnace and the top 1-1/2" is in the upper furnace. In the crucible, two thermal blocks T1 and T2 are in contact with the two ends of the specimen. Thermocouples are placed near the T1 and T2 blocks thus establishing an axial temperature gradient. Crucibles A and B in Fig. 2 were made of graphite and can be split vertically into halves in order to minimize mishandling of the grown crystals during the unpacking process. The dimensions of the crucibles 23 are given in Fig. 2. The soft-mold material is alumina powder (500 mesh) mixed with about 2 wt per cent of graphite powder. The mixture is tamped around the zinc charge and the thermal block Tl. An inert atmosphere in the furnace tube was provided by having a continuous flow of dry nitrogen. Furthermore, carbon was mixed in the mold material to provide a deoxidiz— ing atmosphere. b) Acid String Saw An acid string saw shown in Fig. 7 was used to cut the grown zinc crystals without introducing any mechanical stresses. Nitric acid (about 40%) was used and its delivery was made by means of Saran string. A 6 rpm Bodine electric motor drives a 2-1/2" long crank arm. One end of the Saran string is attached to the crank arm and a weight is attached to the other end to give some tension to the thread. The string is guided by narrow grooves in the middle of the faces of round spools, two of which are immersed in the nitric acid bath. In order to make a better delivery of the acid, the string is doubly laid. The cutting speed depends on the acid concentration and the amount of the acid delivered by the Saran string. 24 2. Experimental Procedure The material used in growing the crystal specimen is 99.999+% Purity zinc obtained from New Jersey Zinc Company. It was obtained in the form of round rod of 3/8“ in diameter. The round rod was rolled and machined to the standard sample dimensions given in Fig. 3a. The bottom 1” of the specimen can be replaced by a seed of known orientation. The seed was welded to the specimen with an acetylene torch or a gas torch using ammonium chloride as a flux. Before and after the welding, the surface of the specimen was cleaned by immersing it in dilute hydrochloric acid. The specimen was then placed nithe small conical hole in the center of the top face of the thermal block T The 2. alumina powder mixture was tamped around the specimen, the top face of which was in contact with the thermal block T1. The packed crucible was then suspended by alumel wire, so that the bottom 1" of the specimen was in the lower furnace and the top l-l/2" was in the upper furnace. The furnace was preheated to the desired temperature before placing the crucible into the furnace tube. Next, the charge was soaked for some hours to obtain a temperature dis- tribution as uniform as possible. At the end of the soaking 25 period, the charge was program cooled linearly at a given rate, while maintaining the constant axial temperature gradient. Typical growth settings are as follows: Upper furnace temperature 4750C Lower furnace temperature 3550C Soaking period 3—1/2 hrs. Growth rate 1 mm/min. At the typical settings, the standard sample has the trace of the liquid-solid interface in the seed at 1/2 t 1/8" from the bottom end of the sample. The trace of the inter- face indicates the demarcation line above which the sample has been molten during the soaking period. The trace is easily visible to the naked eye. The grown sample was etched in concentrated hydro— chloric acid. Visual examinations of the etched surfaces were made to determine if there are visible sub—boundaries. The crystal was then cut by means of the acid saw to dimen- sions convenient for subsequent microscopic examinations. Some difficulties were encountered in obtaining a flat sur- face by the acid saw. All the samples were cut to reveal the surfaces nearly parallel to {lOIO} type planes. 26 The samples were glued to plexiglas (acrylic plastic) plates (1/10” thick) of appropriate size with plastic adhe— sive. Subsequent handling of the sample was done entirely by handling the plastic plate. The sample was next etched to reveal dislocations on {lOIO} surfaces. Metallographic examination was made on Bausch and Lomb Research Metallograph, and photomicrographs were taken using standard techniques. Polishinqiand Etching of Dislocations Present experiment requires polishing and etching solu- tions which are suitable for undecorated high purity zinc single crystals. It has been found that the solutions de- veloped by Vreeland et al. (10) were suitable for the purpose. The solutions are: P—l 160 gr CrO3 20 gr Na2804 500 ml distilled water P—2 Equal parts of: Methanol 30A H202 conc. HNO3 P-3 160 gr CrO 3 500 ml distilled water 27 E One part: 1 gr Hg(N03)2 1 ml conc. HNO3 500 ml H20 Two parts: distilled water The polishing procedure: 1. Dip with mild agitation in solution P—l for 20— 100 sec. 2. Dip occasionally in solution P—2 to accelerate the polishing process. 3. Dip finally in solution P-2 to remove the CrO3 film. The etching procedure: 1. Dip with mild agitation in solution E, 5—6 sec. 2. Dip with mild agitation in solution P-l, 5-6 sec. 3. Dip with mild agitation in solution P-3, 2—3 sec. 4. Rinse in running tap water. 5. Rinse in running distilled water. 6. Dry in an air blast. Best results are obtained when the polishing procedure is immediately followed by the etching procedure. The formation of etch pips is due to the rapid diffu- sion Of mercury to dislocation sites over the polished sur— face, and the diffused mercury retards the rate of polishing. In order to verify the validity of the etching tech- nique, a series of experiments was made. The results were in complete agreement with the qualitative observations of 28 the dislocation etch patterns made by Vreeland et al. This may be considered to be sufficient evidence to make quanti— tative observations meaningful, since Vreeland et al. have established one-to-one correspondence between the etch pips and the dislocations by the same etching technique. Using the etching technique, a study of distributions of dislocations and sub—boundaries was made. Various sec- tions of the grown crystals were etched and the etch patterns, as revealed on {TOTO} planes, were studied. The samples of orientation 2-1 were studied on cross—section surfaces per- pendicular to the growth direction. The samples of orien— tation of 1-1 were cut to expose the cross-section surfaces making an angle of 300 with the horizontal cross-section. In the later case, the side surfaces (OlIO) parallel to the growth direction were also observed with or without cutting by acid. In the Fig. 4, the observed surfaces of the sam- ples of orientations 1-1 and 2-1 are cross—hatched with red color. Surfaces parallel to <10IO> planes in the samples of different orientations were cut and observed similarly. Such surfaces were cut carefully so that exposed surfaces were within :10 of the crystallographic planes of {IDIO} as determined by the X—ray back-reflection method. The back- 29 reflection technique may have an uncertainty of :20 in it- self. Thus the maximum angular deviation was :30 from the <10IO} plane. Vreeland et al. have shown that good etch patterns can be obtained on the surfaces making an angle as large as 5.50 from the prism plane. They have also shown that etch pips were observable on the surface as much as 150 from the prism plane. Therefore it is quite allowable to deviate as much as :30 from the prism plane, so far as etching of dislocation is concerned. A series of experiments was carried out in order to improve the crystal perfection. Emphasis was placed on 1) minimizing the thermal stress during and after the growth by minimizing the radial heat loss, 2) preventing the propagation of sub-boundaries from the seed by the offset method. In the following, these will be discussed further. Reduction in Radial Heat Loss a) By a conduction sleeve with external insulation around it. The purpose of installing the conduction sleeve around the entire length of the crucible is to improve axial heat conduction, thus to reduce the radial heat loss. The radial heat loss will be further reduced if the conduction sleeve is effectively insulated. Steel plate of thickness 0.1" 30 was wrapped around the furnace tube. The 6" steel sleeve was long enough to cover the whole length of the crucible. The insulation was done by wrapping the portion of the furnace tube between the upper and lower furnaces with spun fiberglass. The combination of the conduction sleeve and the insu— lation should result in a greatly reduced radial heat loss and an increased uniformity in the axial temperature gradient. b) By increasing the crucible size. By increasing the crucible size, the thickness of the insulating alumina mixture is increased. Two crucibles A and B whose dimensions are given in Fig. 2 were used using specimens of the same size. The thickness of the alumina insulation in the crucible B is about twice that of the crucible A. The effects of (a) and (b) were studied in terms of dislocation density and sub-boundary distribution. Elimination of Sub-boundaries-Offset Method The purpose of the offset method is to prevent the pro— pagation of sub-boundaries from the seed. The technique of eliminating the sub—boundaries is to make them grow out to free surfaces. This is possible, since the sub—boundaries 31 tend to align themselves along the growth direction at slow growth rate. Zinc specimens were machined in the shape shown in Fig. 3b. The "S" shaped constricted portion is such that no vertical straight lines can be drawn on the flat surface from the seed without crossing free surfaces. In Fig. 3b, the sub-boundaries running in the direction perpendicular to the flat surface, would be eliminated pro- vided they grow in the direction parallel to the growth axis. The crystal grown in this manner would be free of the sub—boundaries running perpendicular to the flat surface. But the sub—boundaries running parallel to the flat surface would still remain in the crystal. NOW a seed was obtained from the crystal. But the seed was rotated 900 about the specimen axis and welded to another offset sample which was subsequently grown. New the remaining sub—boundaries would grow out to free surfaces, thus leaving the second crystal free from sub— boundaries propagating from the seed. This offset method can be used more than once to insure a crystal free from the sub-boundaries propagating from the seed. It must be noted that the offset method would be most 32 effective in eliminating the sub-boundaries only if there are no newly formed sub—boundaries during the growth. How- ever, one must concede a possibility of sub—boundary forma- tion by rearrangements of the randomly distributed disloca— tions, so long as the dislocation mobility is not zero. Zinc sample 4” long 33 Alumel wire Conduction sleeve '7111771’r / V ,~ Crucible // / I I / / ‘J//"‘”T/C control I T/C differential "‘T/C differential Seed 1" long LIXI.- - I \ l \ \_ '. \ O " " 0‘ '7: 1.. ‘ o '3‘. o :‘f'. . \\ l . . \\I ~ ' Z / O k Insulator : Alumina “‘,_lll_ powder Fig. l. I11 /\/2 T Zirco tube &T' l 2. Thermal blocks Furnace setup (schematic) 34 l"/ j ! / » E 3 K V / j l’/ ;*—Zf*/F“E? 3 b . ’I / / 58' j j Crucible A: X = 5/8" i / / E /‘ ,/ /' / / C . _ .. j [I / Cruc1ble B: x - 7/8 / F73 C / / 1,, L ___:r__ __.._.L_. Fig. 2. Crucible design. __T___-H , __"T_ I} lili. 5 i 71/ I [fig] 7” 52—4 cogs—+- .. "“1277 2,3.” 1 4‘ i A I E U E 4— |” I ; r2: J--- 5 .L” \N' 1 1 ..,; a” ., III ! Pkg/6 I i . l_-I_ u -7. hurl n ca.) (19) Fig. 3 (a) Standard specimen. (b) Offset specimen. 35 Growth direction (2.770] . 4‘2 ' 05 .. E 3:37 fll%\>‘. MUD %:EML2.4woooD .ngd . I, ‘0). K0170) I 30 I l i \ l (@001)§\ /--/ /"2 /"‘3 Growth direction Micro] {72 I 0,7 'LI'LL’ 1' 1 -—- .— 7 --02|d7 l l l / , ' (000/) W/ (7'2 7'0) 2-/ 2‘2 2‘3 l L 2 l I / : «AW—(000 / ) //// I I Growth direction “(GOO/’7 027g? l (000/) \ %\ : +472. To) 4955'..2‘5. I I “74 :1“ a ’1 d 7~ I l f ( '070) (lOTO) 3 "l 4- 'I Fig. 4. Orientations of the crystals and the seeds and their designations. 36 Furnace setup. 5. Fig. 37 Fig. 6. Furnace control panel. 38 Fig. 7. Acid string saw. IV. RESULTS AND DISCUSSION In the following, the results of the metallographic inspection of the zinc single crystals will be discussed in terms of the photomicrographs of the dislocation etch fig- ures as revealed on the prism plans. Before any attempts were made for the improvement of the perfection of the crystals, a study was made on the distri— butions of dislocations and sub-boundaries in the crystals. The results of the study are summarized in Figs. 8 through 13. The etch patterns, shown in Figs. 8 and 9, show that the sub—boundaries tend to align themselves such that their traces in the {IDIO} plane are along the crystallographic directions of <2I10> and (0001). Generally speaking, the sub-boundaries running in the direction (0001) have greater tendency to be straight, as shown in Fig. 9. These sub- boundaries are usually interconnected by means of short, but almost perpendicular branches. It can also be observed that the <2IIO> direction is immediately identifiable, since the etch pips are elongated in the direction, showing the cry- stallographic symmetry. Along the relatively large angle boundaries, the dis- location etch pips are overlapped. It is extremely difficult 39 40 to resolve or to count individual pips along such sub- boundaries. When such sub-boundaries are present, an uncertainty arises in the expression of the degree of perfection of the crystal in terms of dislocation density. Elimination of such boundaries not only improves the perfection of a crystal, but also the perfection can be expressed more accurately and meaningfully. Fig. 10 shows sub—boundaries aligned nearly in [2IIO] direction in a sample with the orientation 2-1. In order to determine whether they have grown from the seed, samples with the orientation 2-2 and 2-3 have been grown from seeds obtained from the sample 2-1. The seeds were rotated 450 and 900 about the growth direction and welded to the standard zinc specimens to grow the sample 2-2 and 2-3, respectively. The sample 2-2 was then examined on the horizontal cross-section and is shown in Fig. 11. One large sub-boundary has been retained and makes an angle of about 450 with the cross sectional edges, indicating it is still running nearly in [ZIIO] direction. There are no sub- boundaries parallel to the cross sectional edges throughout the observed surface. A further evidence can be shown similarly when a crystal of the orientation 2-3 was 41 examined. Here sub-boundaries (not shown) are still running in [ZIIO] direction as well as [0001] direction. This clearly indicates the sub-boundaries are propa- gating from the seed. Therefore, if such sub-boundaries were to be eliminated from a grown crystal, they must be prevented from growing into the crystal from the seed. Next, several samples of the orientation l-l have been observed on the cross-section (lOIO) and the side faces (OlIO). The cross-section makes an angle of 300 from the horizontal cross-section. The side surfaces were observed in as—grown as well as acid-cut conditions. Background density of dislocations in the cross section surface (lOIO) is of the order of 7x104 cm-2 (ranging from 5.6 - 8.0 x 104 cm-z), while that of the side surface (OlIO) is about 2x104 cm"2 (ranging from 1.5 — 2.4x104 cm-Z). Thus the dislocation density in the cross sectional surface is about 4 times that in the side surface. In some cases, the difference is as much as one order. Fig. 12 shows the typical background densities of the two surfaces, as revealed on (1010) planes of the sample with the orientation l-l. In these photomicrographs, there is a difference of a fac- tor of about 4 in the dislocation densities. This particular crystal is one of the improved crystals, but similar 42 observations can be made for unimproved crystals. More striking differences are observable in the sub- boundary distributions. Far greater numbers of sub- boundaries are observable on the cross-section than the side face where a few sub-boundaries are observable occa- sionally. The reason for this can be seen in Fig. 13. The sub-boundary labeled P in both photomicrographs is the same one. But it is hardly recognizable in Fig. 13b. These observations of differences in dislocation den- sities and number of sub-boundaries in the two surfaces suggest that most of the dislocation lines grow parallel to the growth direction. This is a qualitative agreement with the observations made on the melt-grown single crystals (20, 21). Noggle and Koehler found that the number of sub- boundaries parallel to the growth direction is on an average three times those perpendicular to the direction. Kelly and wei also found that dislocation lines run parallel to the growth direction. In view of these facts, it would be misleading to de- termine the dislocation density by observing {TOTO} planes parallel to the growth direction. 43 1) Reduction in Radial Heat Loss a) Effect of the conduction sleeve with external insulation around it. Changes in the background dislocation densities in the crystals grown in crucible A have been studied before and after the installation of the conduction sleeve and the in— sulation. Before the installation the background densities varied considerably from one place to another, ranging from 1 to 5x105 cm-z. This value is roughly in agreement with the reported values of dislocation densities of Zn single crystals grown by Bridgeman technique (10, 37). After the installation, distribution of the background dislocations became more uniform and the densities were con— sistently about 5-7x104 cm-Z. This is a reduction in the dislocation density as much as one order. Furthermore, the deviations from the average value are much smaller due to the uniformity of the background dislocations. Consequently, the average values became more meaningful and thus more representative, so far as the background dislocation den- sity is concerned. However, the effect on sub-boundary formation is not immediately noticeable. This subject needs more experimen- tal data to conclude if there is any effect. 44 b) Effect of the crucible size. From studies with the original Bridgeman furnace, it was learned that zinc single crystals can be grown consistently only when the minimum clearance between the wall and the crystal exceeds about 1/16 of an inch. Since the alumina mixture is packed between the crucible wall and the charge, the larger clearance implies greater insulation on account of the soft-mold material. Crucible A was able to grow consistently single crystals of 7/16" x 0.1" in its cross—section. In this case, the clearance is about 1/8". For a charge of the same size, crucible B provides a clearance of about 1/4". Several single crystals grown in crucible A under the growth of a temperature gradient of 100 C/cm and a growth rate of about 1 mm/min. were examined. The cross sections show large numbers of sub-boundaries, which were not propa- gated from the seed, near the corners. Such sub-boundaries are nearly parallel to both edges of the cross section, as shown in Fig. 14a. Their appearance is quite different from those which have been propagated from the seed. Next, another crystal of the same size was grown in crucible B in which the thickness of the insulation is about twice as much. The growth condition was the same as before. 45 When this second crystal was examined, there were no such sub-boundaries as in the case of crucible A. Fig. 14b shows a similar corner of the cross section of the sample grown in crucible B. The exact mechanism of formation of such sub-boundaries is not clear. But it is quite obvious that thermal stress is responsible for the formation. The greater insulation in crucible B apparently reduced the radial temperature gradient, and hence the thermal stress, to a sufficient extent to prevent the formation of sub-boundaries near the corners. It is not immediately noticeable if there is any im- provement in the background density. 2) Elimination of Sub-boundaries by the Offset Method Several samples with orientations of lrl and 1-2 were grown by the offset method and the etched surfaces (10I0) were observed as usual. It has been found that the follow— ing procedure is most effective in eliminating the sub- boundaries in both directions. The procedure: i) Use a seed with orientation 2-1 to grow a crystal of orientation 2—3 with offset. 46 ii) Obtain a seed with the orientation 2—3 from the grown crystal. iii) Use the seed (the orientation 2-3) to grow a crystal of the orientation 2-1 with offset. By procedure 1, the sub-boundaries running in [ZIIO] direction have been effectively, but not completely elimin- ated. The sub-boundaries running in [0001] direction and some short segments of sub-boundaries running in [ZIIO] direction were retained. Examinations on the cross-section surfaces of the "S" shaped constricted region were made on the bottom portion and the top portion of the "S" region. The surfaces in the bottom portion revealed that there are sub-boundaries running all the way across the surface in the [ZIIO] direction. Sub-boundaries in the top portion are short segments running in the [ZIIO] direction near the free surfaces, indicating the sub-boundaries running all the way across the surface have been eliminated by the offset. The retained sub—boundaries running in the [0001] direction in the crystal of orientation 2-3 are usually localized to one side of the crystal, leaving the other side substantially low in the number of such sub-boundaries. The region of low sub-boundary density is sometimes large enough to cut a seed of l/ " in width. The seed obtained 47 in this way has the orientation 2-3 and was used to grow the crystal of orientation 2-1 with offset. This process eliminates the sub—boundaries running in the [0001] direction. The crystals grown in this manner are substantially free from sub-boundaries, except some short segments of polygonized sub-boundaries. The linear density of disloca- tions along the polygonized sub-boundaries is of the order l-leO3 cm-l. The disorientation ranges from 5 sec. to 30 sec. Most of the sub-boundaries have a disorientation of about 10 sec. The average distance between the sub- boundaries is about 2 mm. In some cases, it is as large as 3.5 mm. In Fig. 15, a cross sectional surface (10I0) of the crystal of orientation 1-1 is shown. Some difficulties in focusing the whole cross section were encountered in the central region. This is due to the fact that acid—cut surface is not perfectly flat. Nevertheless, some traces of sub-boundaries can be seen even in the dark region and there are no larger sub-boundaries than ones in the bright region. The disorientation of the sub—boundaries labeled P1 is about 10". That of P2 is about 25". There are some sub-boundaries aligned nearly in the [ZIIO] direction. The disorientation of the P3 is about 5". The amount of sub- boundaries running the [ZIIO] direction is negligible compared to the polygonized sub—boundaries. 48 The sub-boundaries P4 and P5 are not clearly defined. Large numbers of dislocations are concentrated along the arrays. It seems as if the dislocations are in the process of forming more clearly defined sub-boundaries. If suffi- cient time were given by slower growth rate, the percen- tage of such sub-boundaries (P and P5) would decrease be- 4 cause the concentrated dislocations would align themselves toward more clearly defined arrays. At faster growth rate of 2 mm/min., the sub-boundaries become more diffused and the background density increases somewhat. Fig. 16 shows some typical cases. It is interesting to note that the polygonized sub- boundary increases in its disorientation as it traces from the interior to the free surface. This is the general case, and P . P4’ 5 as can be observed in the sub-boundaries P1’ P2, The central region of the crystal is almost free from sub—boundaries. Somehow, the dislocations near free surface seem to have higher mobility than those in the inner portion of the crystal. This may be so because the thermal stresses, which reach the maximum values at the free surface, would serve as the driving force for the climb or the simple glide of dis- locations or both. The driving force would be greater for 49 the dislocations near the surface, thus resulting in great- er amount of polygonization. It is difficult to say which mechanism, climb or simple glide, is operating. If the thermal stresses are responsible for the forma- tion of such polygonized sub-boundaries, a sufficient reduc- tion in the thermal stresses during the growth should pre- vent the formation of such sub-boundaries. This would be an interesting and worthwhile topic to be investigated further. The average length of the polygonized sub—boundaries is about 0.6 mm/mm2 or 6 cm/sz. Since the linear density of dislocations in the sub-boundaries ranges from 1 to 5x103 cm-l, the dislocation density due to the sub-boun- daries would be in the range of 6-30x103 cm-z. The observed total dislocation density is about 6-9x104 cm-Z. This is about one order of improvement over the crystals grown at the beginning of this work. Moreover, this is a substantial improvement over the densities reported in the literature. Vreeland et al. (10) have reported the density of l-lelO5 cm.2 in high purity zinc crystals grown by the Bridgeman technique. Noggle and Koehler (20) have reported 6 the density of the order of 10 cm-2 in the aluminum cry- stals grown by the soft-mold technique. 50 The value of sub-boundary disorientations in Al crystals grown by the soft-mold technique, reported by Kelly and wei ranges from 1' to 20' of arc, as determined by the micro- focus X-ray technique of Schultz. In this work, the value has been improved to about 5" to 30" of arc in the best crystals. The etching technique is capable of measuring the dis- orientations up to 30" rather accurately at a magnification of 100 x. It would be of interest to examine the crystals grown in this work by a sensitive X-ray technique in order to confirm, at least qualitatively, the results obtained by the etching technique. Figs. 17 and 18 show the pseudo Kossel patterns of crystals Y and C, respectively. Both crystals have the same orientation 2-1, and the patterns were taken with the x-ray beam perpendicular to the basal plane. The x-ray target was copper and a nickel filter was used. The expo- sure was the same in both cases. Crystal C was grown from a seed crystal of orientation 2-3 and the offset method was used. Crystal Y was grown from a seed 2-1 without the offset. The pseudo Kossel lines are very sensitive to any deviation from perfect crystal (53). Such imperfections 51 are indicated by an increase in intensity, or a displace- ment of the pattern as a whole. Sometimes many types of discontinuities, such as gaps, overlaps and local line- shifting, are observable in the pattern due to the imper- fections. The sub-boundaries between slightly disoriented regions are indicated by gaps if they form ridges on the surface, or as overlaps if they form valleys. Local lattice rotation is sometimes registered on the film as local line- shifting of the pseudo Kossel pattern, depending on the axis of rotation. Fig. 17 shows many discontinuities which arise due to the presence of the corresponding sub-boundaries at which the Bragg condition of reflection is not satisfied. The size of the gap, overlap, or line-shifting, represents the size of the sub-boundary disorientation. The doublets are due to the KOLl and Kaz. A close examination reveals the following: (a) There are large numbers of discontinuities in the pattern of crystal C, represented mostly by gaps and line-shiftings, especially in the circular rings which correspond to the basal plane. In contrast, there is no such observable discontinuity in the pattern of crystal C. This clearly indicates that crystal C does not contain such large sub-boundaries as in crystal Y. 52 (b) Most of the images of sub-boundaries in the pattern of crystal Y intercept the Kossel lines vertically, indi- cating that they are aligned along the growth direction. The difference of orientation between neighboring sub- grains is a rotation of about 10' about an axis nearly parallel to the growth direction. This supports the previous observation made by the etching technique that most of the sub-boundaries tend to run nearly parallel to the growth direction. (c) Despite the fact that the x-ray patterns were taken under the condition of same exposure, the reflection lines of the crystal Y are much stronger and broader. This is a further proof that the crystal C is much higher in the lattice perfection than the crystal Y. A reasonable estimation shows that sub-boundary dis- orientations of about 1' of arc can be detected in the x-ray pattern of crystal C. This value may be as high as several minutes of arc in case of the crystal Y due to the stronger and broader reflection lines. The largest gaps found in the pattern of crystal Y correspond to about 20' of arc. Along the reflection lines in the pattern of the crystal C, some localized intensity variations can be observed. This may well be due to the localized imperfections in the 53 corresponding crystallographic planes. The imperfections could be very small angle boundaries or even some disloca- tion lines. It is difficult to say which of the two types of imperfections are responsible for such intensity varia- tions. The Schultz technique can be used for the study of such imperfections in greater detail. All in all, the x-ray patterns of the crystals Y and C prove that the offset method, when properly employed, is capable of eliminating the large sub-boundaries which pro— pagate from the seed, thus resulting in crystals substan- tially free from sub-boundaries. This supports the previous observations made by the etching technique. In summary, Table I shows all the grown crystals and the results of microscopic examination of the crystals. The axial temperature gradient is about 100 C/cm for all the crystals. Crystals no. 31 and 33 are the best crystals and they are substantially free from sub-boundaries. The cross sectional prism planes of the crystals are shown in Figs. 15 and 16, respectively. It is important to note that the offset method alone does not insure a crystal free from sub-boundaries in it- self. In case of the crystal no. 2, the offset method alone did not improve the crystal perfection. However, in case 54 of crystals no. 31 and 33, all other improvements (such as the conduction sleeve, the insulation, the larger crucible, and the selection of good seed, etc.) are combined with the offset method to give the best results. In case of crystal no. 37, all the improvements without the offset method are not able to produce a sub—boundary free crystal. Crystal no. 37 reveals rather extensive sub-boundary distribution, despite the fact that the seed crystal was obtained from the crystal no. 33 which is one of the best crystals. The sub-boundaries present in crystal no. 37 might have origi- nated from the welding of the seed to the polycrystalline specimen. This emphasizes again the importance of the off- set method in eliminating the sub-boundaries. 55 <2Il0> (0001) (10I0) Fig. 8. Crystallographic arrangements of sub-boundaries. 500x <0001> <21I0> (10Io) Fig. 9. Crystallographic arrangements of sub-boundaries. 500x 56 (10I0) Fig. 10. Sample with the orientation of 2-1. (10I0) Fig. 11. Sample with the orientation of 2-2. Sub-boundaries propagated from the seed. 320x 57 [2II0] ——P- (10I0) (a) Cross sectional surface. [ZIIO] _—*. (10I0) (b) Surface parallel to the growth direction. Fig. 12. Background dislocations revealed on the cross sectional and the surface parallel to the growth direction of the crystal with the orientation 101. 500x. The crystal no. 31. 58 (10I0) (a) Cross sectional surface. (10I0) (b) Surface parallel to the growth direction. Fig. 13. Sub-boundary etching on the cross sectional and the surface parallel to the growth direction of the crystal of the orientation l-l. 500x. The crystal no. 31. 59 (10I0) (a) Crystal grown in the crucible A (10I0) (b) Crystal grown in the crucible B Fig. 14. Effect of crucible size on sub-boundary formation near a corner of the cross sectional surface. 500x [ZIIO] ll 1 mm Fig. 15. 6O Sub—boundaries on the (1010) cross sectional surface. 35x 61 (b) (10i0) Fig. 16. Typical sub-boundaries formed at the faster cooling rate (2 mm/min.). 320x. The crystal no. 33. 62 Growth direction <10i0> (0001).L beam Fig. 17. Crystal Y. Microfocus x—ray back-reflection. 63 A Growth direction <10I0> (OOOl).L beam Fig. 18. Crystal C. Microfocus x-ray back-reflection. mfimumro CBC-2w 02: mo laud-Chasm OUNHHSm COHSUOm mmOHU + .H H4QHU .QHNHQVOE 2 2 2 2 mm .0 MIN HIN ¢M MN .022 Hmum>uo 3.62820 20 2822.222 32 302 See-m __ .. ._ o .2 TN 2-N om NM .0: Hmumthuo 20 2o 2822.222 E _. 02282-21 ._ __ _. o .N m-N 2-N mm >fimqop *v om .92 2.330 302 12.28,. . 02x03 _. ._ m o .2 M2 2-2 2 MN .oc Hmumro is HO COHHHOAH An; 2 2 m®> 2 2 O .H MIN MIN MN mm .o: 139:0 MO COMHHOQ Adv 2 2 2 2 2 O .0 MIN HIN VN 32282. H2322 . 32 32022-223 302+ “3 _. __ on __ < _. 2-N m-N NM um£BoEOm II U®>OHQEM 2 mm?» 2 «ca 2 HIH MIH OM II 2 2 2 2 m 2 .—.IN HIN NM II 2 2 2 2 2 O .H MIN NIN ON - __ eons-m on 3.2 _. o .2 2-N 2-N 2.2 - ._ __ mm; on < mm .o 2-2 2-2 N u- ozmsouxo mofixm-H on oc < mm .0 2-2 2-2 H pmom mo 53.20 c0322 N50 U0 253.3de m .8 .228 .2578 52282.20 on was mxH-maom 3.3.0.5 23322020 1.308 M 96on HU .2930 >Hmpcs0b 253800-2220 20m .pcoo 02;. $05.20 fiBonw nbdm padouwxumm :30 mo 02mm V. CONCLUSIONS Highly perfect zinc single crystals of controlled orien— tations have been grown by improving the soft-mold technique. a) b) The total dislocation density in the crystals is 4 —2 found to be about 6-9x10 cm . The crystals are substantially free from sub— boundaries, except a few polygonized boundaries whose disorientations range from 5 to 30 sec. of . 3 -l . . arc, corresponding to l-5x10 cm in the linear density of dislocations. The average distance between the sub-boundaries is about 2 mm. The sub-boundaries propagating from the seed can be eliminated by the offset method, under the condition in which no new sub—boundaries form during the growth. The thermally induced stresses during the growth and the cooling to room temperature were substantially reduced by: a) improving the axial heat conduction by the steel conduction sleeve; preventing the radial heat loss by increasing the thermal insulation; 65 66 c) providing a constant and uniform axial temperature gradient. The polygonized sub-boundary increases in its disorien- tation as it traces from the interior to the free surface. The etching technique is capable of measuring the dis- orientation of up to about 30 seconds of arc rather accurately at the magnification of 100x. The dislocation lines and the sub—boundaries tend to run nearly parallel to the growth direction. The pseudo Kossel patterns produced by the divergent X-ray method show a corresponding degree of crystal perfection to that of the etching technique. VI. RECOMMENDATIONS More refinements are needed in the crystal growth tech- nique, and more data must be obtained for the growth of greater lattice perfection. The present work does not prove that the thermally in- duced stresses are entirely responsible for the formation of dislocations and their arrays in zinc. It does not even prove that the thermally induced stresses are minimized. Thus, more attempts should be made to reduce the stresses even further: 1. Increasing the radial insulation by: a) using the soft—mold material of lower thermal con— ductivity. b) using larger crucible or smaller charge, thus increasing the thickness of thermal insulation. 2. Increasing the range of program cooling. The zinc crystals grown in this work have been program cooled down to about 280°C. By extending the range of the program cooling to room temperature, the thermally induced stresses during the cooling would be reduced even further. The effect of welding has not been well understood throughout this work. At no other occasion have the seed 67 68 crystals been subjected to such severe thermal stresses as during the welding. Such severe stresses are bound to have some effects on the distribution of dislocations in the seed crystal. In fact, this may well be the reason why the best crystals have not been obtained without employing the offset method. Thus, more recommendations are in order: 3. Development of a technique in which welding is not required for the controlled orientation of the seed, using the same growth technique. Use of the Czochralski technique in which no welding is required. In addition, there are some experiments which may be worthwhile for improvement of the crystal perfection. 5. Use of the seed crystals of the orientations 3-1 and 4-1 (refer to Fig. 4). The dislocations lying in the basal plane would grow out of the crystal, resulting in a crystal free from the dislocations, provided that no new disloca- tions form during and after the growth. Here a ques— tion as to how the stresses, induced thermally or mechanically, would act on the weakness of the crystals accompanying the orientations 3—1 and 4-1. 69 Use of seed crystals in which most of the dislocation lines run nearly perpendicular to the specimen axis. Such a seed can be obtained by cutting the pre- grown crystals horizontally. 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