I'5 .5 "Ln“ 2? , .' w Afi_ ' T Mali-f 94"?" I‘II'- ' III I r J 5"" I' ' 3;} "5"12' '1': "Lib 3 ' III,,II 5" :~: “3:: I "'f‘HW' (“$5 "MA.“ .Ir MIEIIW « '3'1'1'I'3I I“? ":3; ‘ ‘i' '3'}? "’“' I "' '3» I . ,5". .' I KIWI -.I\' U“: .‘ I' L ' . I I ".‘ '\ " ”up“?! I. 1‘1"“ '5"..i #6 "J I “‘1" . n I. L". 3"'I'V“1f(|" "' | . ‘I “I... .’.I. I ‘5"? "'c'}"‘fj' 'IZE' Suit." ‘l‘lul'fifi ta...“ {5' | .. I . _~ ‘rWI'I' I Lyffiin M i l"".+_."'|":1 H! . '.I ‘y 3 .. ‘ ' ' ' I'g'" 3‘. 7' M-B'OJ (“3'5 "'.I' 1"{IJI' II; II .:<‘I‘II:? ." '1'?""'":'-"""I"S;' 5"." ' T H L; 1-,»: £89 a o I ’JJJZS'] ‘ ‘ Bin-‘--u~‘,v—a “wfié- l...°.I .94. L .I"..' ’-‘ 9’5” : V wd‘di' This is to certify that the dissertation entitled The Sample Dependency of the Low Temperature Electrical Resistivity of Dilute Copper-Silver Alloys, Silver, and Palladium presented by John William Zwart has been accepted towards fulfillment of the requirements for Ph.D. Physics degree in I / ’Major professor P.A. Schroeder Date April 1, 1985 MS U i: an Affirmative Action/Equal Opportunity Institution 0-1277! MSU LIBRARIES m RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. THE SAMPLE DEPENDENCY or THE Low TEMPERATURE ELECTRICAL RESISTIVITY or DILUTE COPPER-SILVER ALLOYS, SILVER, AND PALLADIUM By John William Zwart A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 1985 ABSTRACT THE SAMPLE DEPENDENCY OF . THE LOW TEMPERATURE ELECTRICAL RESISTIVITY OF DILUTE COPPER-SILVER ALLOYS, SILVER, AND PALLADIUM By John William Zwart Measurements were made of the low temperature resistivity of dilute copper-silver alloys, silver and palladium metals in the annealed and strained states. The measurements were made using a current comparator bridge circuit with a SQUID null detector. The dilute copper-silver alloy measurements were made between 0.1 K and 1.0 K and revealed that the change in the electron- electron scattering term in the resistivity with the addition of dislocations is in qualitative agreement with theoretical predictions. The measurements on the high purity silver sample were made over the same temperature range and indicate that anomalous behavior in the resistivity near 0.3 K is not due to the pres- ence of dislocations. Measurements on palladium in the range 1.5 to 8 K reveal a decrease in the coefficient of the electron-electron scattering term and an increase in a higher power term with sample deformation. Measurements made of the susceptibility of palladium in the annealed and deformed states indicate that the electron-electron scattering term in the electrical resistivity is not magnetic in origin. An investigation John William Zwart into a method of producing high purity palladium samples indicates that melting palladium in chlorine gas removes iron. The method also substantially reduces the iron content of molten gold. The reduction of iron oxide with hydrogen was found to be a necessary step for chlorine annealing to be effective with gold. This dissertation is dedicated to my wife, Laurey, whose loving support made it all possible. 11 ACKNOWLEDGMENTS It is a pleasure to thank both Dr. P.A. Schroeder and Dr. W.P. Pratt Jr. for their supervision and help during the dissertation work, particularly for the many late nights spent in data collection. I wish to thank my guidance committee for their help, especially Dr. C.L. Foiles for discussions about palladium. I also wish to thank former graduate students Dr. Mark Haerle and Dr. Vern Heinen for their help in learning to use the two dilution refrigerators. I wish to thank my colleages at Dordt College for helping me to develop a Christian perspective towards my understanding of physics. A special thanks to Nolan Van Gaalen for moral support, and to James Mahaffy for teaching me how to word process. Thanks to my family for their support and encouragement and love. Thanks too to Jim and Joyce Snay for being such good friends. Finally, I wish to thank Michigan State University and the National Science foundation for financial support. 111 TABLE OF CONTENTS Page LIST OF TABLESOOOOO0..00......OOO0.000000000COOOOOCOOOOOOOV1 LIST OF FIGURESOOOOOOOOOOI0.....0...OOOOOOOOOOOOOOOOOIOOOV11 INTRODUCTIONOOOO0.0...0.0..0.0.00..OOOOOOOOOOOOOO0.0.0.0...1 CHAPTER 1 CHAPTER 2 CHAPTER 3 CHAPTER 4 THE LOW TEMPERATURE RESISTIVITY OF DILUTE COPPER- SILVER ALLOYS INTRODUCTION AND THEORY.........................3 IntrOdUCtionocoo...cooooooooooooooooooooooooo03 ThEOPYoooooocoococo...o000.000.00.0000000000004 EXPERIMENTAL PROCEDUREOOO...0.0.0.000000000000015 Preparation of the CuAg samples..............15 sample measurementsOOOO0.0.0.000000000000000021 RESULTS AND ANALYSISOO...OOOOOOOOOOOOOOCOOOOOOOSB COUCIUSiODSoooocoo.cooococoa-00.000000000000047 THE LOW TEMPERATURE RESISTIVITY ANOMALY IN HIGH PURITY SILVER INTRODUCTION AND THEORY.o0000.00.00.0000000000049 IntrOdUCtionoo.noo.coocoo.0.0000000000000000049 Theory.......................................49 EXPERIMENTAL PROCEDURE...00000000000000.000000060 Sample Fraparation...........................60 Sample Measurements..........................62 RESULTS AND ANALYSIS.nooo00.000000000000000000064 C0n01usionaooooooooooooooo0.0000000000000000070 Addendum.ono...ooooooooooo0.0000000000000000071 THE LOW TEMPERATURE RESISTIVITY AND SUSCEPTIBILITY OF PALLADIUM INTRODUCTION AND THEORY.00......0.0.0.00000000072 IntPOduction.O...IO...COO...0.0.000000000000072 Theory....0.0....00O...00.00.00.000000000000074 EXPERIMENTAL PROCEDURE...OOOOOOOOCOOOOOOOOOOOOOBO Sample Preparation...........................BO Sample Measurements..........................82 RESULTS AND ANALYSIS.O...00.0.0000000000000000087 CODCIUBiODSooooooooooooooooooooooooooooooooooge THE PURIFICATION OF PALLADIUM AND GOLD USING CHLORINE GAS . INTRODUCTION AND THEORY.0.00000000000000000000104 IntrOduction0.00.0000000000000000000000000.0104 ThEOPYQQooooooooooooooo000.00.000.0000000000104 1V EXPERIMENTAL PROCEDUREOOO...0.0.00.00.000.00000000000106 sample Measurements..00....0.00.0.0.000000000000000109 RESULTS AND DISCUSSION.I0.0.0.00...0.0.0.000000000000115 COUCIUSionSo000000.a000000000000000000.000000000000119 LIST OF REFERENCESOOI.0..0....OO0.0.0...0.0.0.00000000000122 TABLE 1.1 2.1 3.1 3.2 3.3 LIST OF TABLES PAGE Resistivity results for the annealed and strained QyAg alloys. The values for the samples abeled CRAB-1 and finAg-Z are from SteerIWYk MoeeoooooooeeBB The residual resistivity and electron mean free path for the annealed and strained states of the high purity Ag crysmloO0.0...O...0.0.00000000000000066 Residual resistivity and the coefficient of the T2 term in the resistivity for the samples of Pd and Pd alloys reported in the literature.............73 p , A, and B for samples Pd-A, Pd-B, and Pd-C 18 the annealed and strained states..................91 and x%d(see Eq. 3.6) and C (see Eq. 3.7) x f8r the and Fe samples. Axo is the increase in xc,upon straining................................101 vi LIST OF FIGURES FIGURE PAGE 1.1 1.2 1.3 1.6 1.7 1.8 1.9 2.2 Sample configurations of (a) gyAg A-1, 2 and (b) QyAg A-B, 4. The dashed line indicates where the unused mounting lug was clipped off..................18 Diagram of the circuit used for the 4 probe measurements at 4.2 K. The solid dots indicate 801der connECtioDBOOOOOO...OOOOOOOOOOOOOOOOOOOO0.00.023 Diagram of the bridge circuit used in the resistivity measurements.............................25 P/Po Versus T for sample CUAS A-4ereeooeeeooooooaoo34 Plot of ( 0(4. 2K)/2TC) AC/ AT versus '1‘ for sample QyAg A—4 in its annealed (a) and strained States (8’ t, u. V)....O...0.00000000000IOOOOOOOOOOO.35 Plot of versus impuritg concentration f r samples Qfiflg A-2, A-4 and t e Steenvyk.gt_31 samples guAg 1, 2.00...O....0.000.000.000.0000000000040 Gorter-Nordheim type plot of 0 versus 1/po for samples QnAg A-2, 4..............................42 A versus p /p s for the CuAg samples. The solid sbeois assume a 9 contribution of 0.1 nilcm top and the open 8 mbols assume a 0.55 n ncm contPEbution. The so id curve is the theoretical prediction of Equation 1.5 and the dashed curve is a modified version of the predictioni.OI.COO...0.0.0.0...00.0.0000000000000000043 A versus 01 1 . The solid line is Equation 1. 26. The 98118 End open symbols assume a pdis contribution of 0 and 0.55 ntlcm to Po respe0t1V91y-oeeoooaoee:oeoooooo00000900000000.00000046 The resistivity derivative data for the RRR . 20,000 Ag sample of Steenwyk.........................51 Unpublished 9(T) data for the high purity Au12 sample run earlier by the author's research group....52 vii 2.3 2.4 2.5 2.6 2.7 3.2 3.3 3.4 3.5 3.6 3.7 The temperature derivatives of the resistivity contributions due to dislocations predicted by Equations 2.1-2.4. (a) Equations 2.1, 2.2, 2.4 as indicated. (b) Equation 2.2 for variousB as ifldiCBtEd-eaeosoooeeoooeseee000.000.00.0000000000055 Two fits to the Steenwyk Ag derivative data based on the derivative of Equation 2.4 plus terms reflecting electron-electron and electron-phonon scattering contributions.............57 Derivative Of the Au12 Pealstvity data...............59 (a) Sample oonfi uration of the high purity Ag single crystal. (b) Cross section of measurement region.OOOOOOOOOOOOOOOOOOOOO0.00.0.00.00000000000000061 The resistivity derivative data for the annealed state (0) and after the first (0) and second (I) Strain1n35000000000oeoeeeocoooooooo00000000000000.00065 Smooth curves representing the derggative resistivity data for K of Yu et al for various diameter samples. The electron mean free path 18 given 38 0.2mm.0..0.00.00.00.0000000000069 Schematic drawing of the apparatus used for the Pd resistivity measurements..........................83 The Eemperature dependent part of the resistivity vs T for T < 3.7 K for sample Pd-C in the annealed state a (0) and in the strained states 8 (O), t (.), U (U), v (‘).............o.............88 ( p-»p )/'r2 plotted versus T3 for T < 8.5 K for safiple Pd-C under the same conditions as Figure 3.2.0.00000000000000000000.000.00.00000000000089 Variations of A and B with for the annealed samples (open symbols) and sgrained samples (full symbols of Pd-A (0,0), Pd-B (-,n) and Pd-C (A,O).....92 Susceptibility of pure Pg samples Pd-S1 (0,0) and Pd-SZ (‘,A) versus T in the annealed (full symbols) and strained (open symbols) states....96 Susceptibility of Pd (20 ppm Fe) versus 1/T in the annealed (0) and strained (0) states.............99 Susceptibility of Pd (106 ppm Fe) versus 1/T in the annealed (0) and strained (o) states............100 viii 4.1 4.2 4.3 4.4 4.5 Plot of Count Rate vs Mass fog a progressively etched bead of Pd doped with 9Fe. The uncertainty in the count rate is roughly the diameter of the dot................................108 The apparatus used for the C12 annealing...........110 (a) The graphite sample holder used for the C1 annealing, shown with the alumina or cible use to hold the Pd. (b) The nested quartz tubes used to hold the Au...................112 The reduction in Fe concentration in Pd as a function of time the molten metal spent in C1 . The dashed line re resents the results f0; 8 solid sample annea Ed at 1100.Coooooooooooooo117 The reduction of Fe concentration in an oxidized Au sample as a function of the time the molten metal spent in a 10% H - 90% Ar mixture. The removal of the Fe was gone by C12 annealing........120 ix INTRODUCTION The resistivity of a metal is a measure of the scattering of the current carrying charges. Early theories which made predictions of how the resistivity varies with sample temperature usually assumed ideal crystals which are infinite in extent; contain no impurities, vacancies, or interstitials; and have no extended defects such as dislocations or grain boundaries. However, real samples may contain some or all of these deviations from the ideal crystal to some extent and the theories had to be modified to account for these differences. The first approximation is that the introduction of a new source of scattering adds a term to the resistivity, but that the other contributions are unchanged, that is, the total resistivity is the sum of independent terms, each representing a different scattering mechanism. This is known as Matthiessen's rule. In many cases, Matthiessen's rule describestthe data quite well., Deviations from Matthiessen's rule exist. For example, the addition of impurities to a sample may modify the electron-electron scattering term in the resistivity. Theories have been formulated to describe this behavior. The most recent advances in describing the resistivity 2 of real samples consider the interactions which take place when more than one scattering mechanism is added to the sample. In this dissertation, the effect adding dislocations to a sample has on the low temperature resistivity is investigated. In Chapter 1, experiments on dilute copper- silver alloys are described. The experiments were carried out to test a prediction on the influence that impurities and dislocations have on the electron-electron scattering term. Chapter 2 describes an experiment to test the hypothesis that dislocations are responsible for a previously unexplained anomaly in the low temperature resistivity of high purity silver. The effect dislocations have on the low temperature resistivity and magnetic susceptibility of palladium is discussed in Chapter 3, and the results are discussed in terms of the existing theories proposed to describe the low temperature resistivity. One result is the desirability of having an extremely pure palladium sample. In Chapter 4. a new method of removing iron from palladium is described. The method is also applied to gold. CHAPTER 1 THE LOW TEMPERATURE RESISTIVITY OF DILUTE COPPER-SILVER ALLOYS INTRODUCTION AND THEORY Introduction There has been considerable interest in the sample dependence of the electrical resistivity in the noble metals: copper, silver, and gold. As experimental techniques and theoretical predictions become more refined, interesting and complex behavior is found in these metals. The subject of this section of the dissertation is an experimental study of the effects of impurities and dislocations on the electron-electron scattering term in the resistivity of copper. Only very recently have measurement techniques of sufficiently high precision been available to enable these measurements to be made. The signature of the electron-electron scattering term in the resistivity is a temperature variation of T2. The reported experimentally measured coefficients of this T2 term vary over about a factor of two"""3 for pure copper samples. This sample dependence has prompted theoretical investigations, primarily by Bergmann, Kaveh, and Wiser, and Kaveh and \\Yiser,4"10 into these deviations. The theory advanced by these authors predicting 3 that the relative amounts of impurity and dislocation scattering determine the coefficient, leadsto the present experimental study. Theory According to Matthiessen's rule, the temperature dependent electrical resistivity of metals can be expressed as the sum of independent terms: 98 Po + Pee(T) + Pep(T) + °'°. (1.1) (5 is the residual resistivity, a temperature independent term, which is due to electrons scattering from static crystal imperfections such as impurities, other point defects, dislocations, grain boundaries, etc. For a perfect crystal, this term would be zero, and the sample's resistivity would go to zero as the temperature goes to zero. However, in real samples at low temperatures, this term is actually the dominant contribution to the resistivity. The electron-electron scattering term (T) is flee extremely small -- about 10'5 Pb at 1 K, and thus requires high precision measurements for its isolation. As mentioned in the introduction, its temperature dependence is T2. This term will be discussed in more detail below. The electron-phonon scattering term, Igp(T) has a temperature dependence with a higher power of T at low temperatures, going as (T/GD)N where 9D is the Debye temperature, with N typically in the range of 4 - 5. Thus, low temperatures are needed to isolate the electron-electron scattering term, since this higher power term will dominate the electron-electron term as the temperature increases. The presence of the Debye temperature in the denominator makes copper the obvious choice to study electron-electron scattering, since it has the highest Debye temperature of the noble metals, ensuring that the electron-phonon term will become negligible at temperatures higher than in silver or gold. The dots in Equation 1.1 indicate the possibility of other temperature dependent terms due to other, scattering mechanisms, such as the Kondo effect, or surface scattering. For temperatures which are low enough that the electron-phonon contribution to the electrical resistivity is negligibly small, the expected temperature dependence for the electrical resistivity is, p= pa + AT2. (1.2) At first thought, it may seem that the electron- electron scattering term would be a large rather than a small contribution to the resistivity. After all, there are many conduction electrons in copper, and the Coulomb interaction is strong, even though it is screened in the crystal. However, the conduction electrons obey the Pauli exclusion principle, which severely limits the electrons available for the interaction. Electrons with energies of a few kBT below the Fermi level are frozen in due to the conservation of energy requirement for the collision, because the electrons must be scattered into unoccupied states. The conservation of energy requirement also limits the states into which the electrons can be scattered to those within a few kBT above the Fermi level. Since the number of electrons available for scattering and the number of states available for scattering into both increase linearly with temperature, the net electron-electron scattering rate, and hence the resistivity goes as T2. A more complete (and rigorous) treatment of this result may be found in Ashcroft and Mermin.11 A further factor which limits the magnitude of the electron-electron resistivity contribution is the conservation of momentum. In a normal (or N) scattering process the total electron momentum is conserved. In the free electron model (spherical Fermi surface), all the electrons are of the same effective mass. When the electron moments before the collision equals the momenta after the collision, the net electron velocity is conserved, so the electrical current is not degraded. Hence, the scattering event is not resistive. It is only for the less probable umklapp (or U) processes (in which the total electron momemtum before the collision differs from the total electron momentum after the collision by a reciprocal lattice vector) that resistive scattering occurs. Although copper's Fermi surface deviates from being entirely spherical in the neck regions, the bulk of the conduction electrons are on the nearly spherical belly regions, and most N scattering events are not resistive. Calculations of the electron-electron resistivity coefficent, A, have been performed by Lawrence12, Black13, and MacDonald and Laubitz14. Their predictions are 76, 27-39, and 28 ftlcm/Kz, respectively MacDonald later15 calculated 19 filcm/K2 for A. The uncertainties in these calculations are fairly large, and the spread in the experimental values (which fall between the extreme predictions) does not provide any support for any of the theories in particular. If the samples strictly followed Matthiessen's rule, the experimentally determined values of A should be the same, that is, sample independent. However, deviations from Matthiessen's rule (DMR) are well known, see for example the review articles by Bass16 and Cimberle g£_glj7. Typically, the temperature dependent part of the resistivity depends on the residual resistivity p . In the theory to be discussed below, the electron-electron scattering term is assumed to depend not only on PO but on the source of P0- The theory put forward by Bergmann, Kaveh, and iliser5'7'8 and Kaveh and Wiser4'6’9'1o is the most developed in terms of predictions for the behavior of A, so the remainder of this resistivity theory discussion will focus on their prediction. Since much of the background is discussed in great detail by Steenwyk18 it will not be reviewed here. The theory advanced by the above authors considers the role of impurities and dislocations on the deviation from equilibrium of the electron distribution function upon the application of an external electric field. The problem is treated by considering the relaxation time approximation to the Boltzmann equation, a standard method of attack.11 The relaxation time, 7(k), is a time characterizing the return to equilibrium upon the removal of external fields. As indicated, it is, in general, k dependent. As discussed earlier, only those electrons near the Fermi surface are able to scatter, so the k's involved will be on or near the Fermi surface. To solve for the electron-electron scattering component . of the resistivity for real samples, Kaveh and Wiser6 consider the sample's relaxation time to have four contributions: normal electron-electron scattering, umklapp electron-electron scattering, electron-impurity scattering, and electron-dislocation scattering, each with its own relaxation time. It should be pointed out that the terms 'impurity' and 'dislocation' are generalized to mean isotropic and anisotropic scatterers, so that 'dislocations' could be stacking faults, grain boundaries, dislocations, or any other extended defect.6 This generalization will be important when the experimental data is considered. The assumption is made that the dominant k dependence for the relaxation time is due to electron-dislocation scattering. The R dependence of the N and U electron- electron scattering relaxation times is neglected, as is any k dependence of electron-impurity scattering. Thus, with these assumptions, the relaxation time of a perfect crystal is isotropic, and with the introduction of impurities, the relaxation time remains isotropic. When dislocations are added, the relaxation time becomes anisotropic. The amount of anisotropy in the relaxation time depends then on the relative amounts of impurities and dislocations. The contributions of impurities and dislocations to the residual resistivity 95 are used as measures of the concentrations of impurities and dislocations. In this model, the N electron-electron scattering doesn't degrade the current, but these events do redistribute the electrons by scattering them into different states on the Fermi surface. If TC?) is constant, that is i? independent, there is no resistivity change. However, if 7(k) is R dependent (as when dislocations are present), then N electron-electron scattering can contribute to the resistivity by driving the electrons into regions of greater electron-dislocation scattering.6 Thus, it might be said that the presence of dislocations 'turns on' the 10 N electron-electron resistivity. The form of the relaxation time including impurity and dislocation contributions is found via a variational solution to the Boltzmann equation.5 The N and U electron-electron and impurity scattering events are assumed to be k independent, and a parameterized form is assumed for the dislocation scattering. If a'f independent form is assumed for the dislocation relaxation time as well, it is found that the major contribution to the resistivity integral for dislocation scattering is from the non-spherical regions of the Fermi surface. Since the variational theorem states the correct form for the relaxation time minimizes the dislocation scattering integral, the dislocation relaxation time must be smaller in the non-spherical regions of the Fermi surface. This leads to the form: Tdis = Tb[V(f)/Vp]n (1.3) which uses the fact that v(k) is less than the Fermi velocity VF in the non-spherical portions of the Fermi surface. The exponent n serves as the variational parameter. The value of n which minimizes the variational formulation of the resistivity is calculated as a function of pdis/pimp' where pdis and pimp are the dislocation and impurity contributions to the residual resistivity, that is, PC e 9318 + pimp' It was 11 found that as pdis/ pimp increases, n rises rapidly from 0 to about 2 for the noble metals, leveling out near pdis/pimp : 1' To actually find the form of the resistivity as a function 0f pdis/pimp requires an integration of the Boltzmann equation over the Fermi surface. This was not carried out for the noble metals, but Bergmann, Kaveh, and Wiser5 estimate the size of the enhancement of A. This estimate is carried out in terms of the fractional umklapp scattering parameter A, which is a measure of the scattering events' effectiveness in degrading the current. Ais defined as the ratio of the scattering-probability weighted average of the difference between incoming electrons' velocities and the outgoing electrons' velocities to the weighted average of the incoming electons' velocities,12 As <:v1 + v2 - v3 - v4:2w>/<:2v:2:w> (1.4) A: 0 would mean that scattering does not change the net electron velocity, so that the scattering is not resistive. (A: 1 would imply maximum degradation of the current.13 Aincludes primarily the U scattering events and also those N scattering events which take place on the non-spherical regions of the Fermi surface. Calculations (such as Black13) indicate that the U contribution to A is about half of the maximum possible N 12 contribution if N scattering events were resistive. So if the introduction of dislocations would cause all N scattering events to contribute to the electron-electron resistivity, the maximum enhancement would increase A by about a factor of three over the U value. They suggest that the presence of dislocations would at most increase the N contribution to roughly 10% of its maximum value, so the enhancement of A should be about 30%, with a factor of two 8, these authors drop the uncertainty. In a later paper latter comment, suggesting a factor of three enhancement for A. To sum up, as a sample is strained, the value of ‘his/ pimp increases. Accompanying this, the value of the variational parameter rapidly changes at first, and then levels out near ”dis/pimp a 1, implying a rapid change in A until ‘his equals pimp' with an increase in A of up to a factor of three. After the experiment discussed in this chapter was performed, Kaveh and Wiser9 made a prediction for the functional form of A in terms of pimp, pd“, using the form calculated for the alkali metals,6 but with parameters appropriate for copper. For the lower bound of A, they use a high temperature value of A calculated by MacDonald and Laubitz14 modified by 51 to account for phonon mediation terms15, yielding A a 27 fiZcm K'Z. Assuming a factor of three increase for a heavily strained sample gives the upper bound of 81 filcm K'z. The 13 predicted expression for A is: A = 27[1 + 2/(1 + pimp/pais)2] rszcm K'2 (1.5) In addition to the resistivity measurements made to experimentally check the above theoretical prediction, measurements of the thermoelectric ratio, C, were made. G is defined by: . G=I/é E=0 (1.6) where I is the electrical current through the sample necessary to null out the thermal voltage induced by the heat current 0 through the sample. C is positive if I and 0 are in the same direction. The thermoelectric power (thermopower) S is related to G by: S a GLT (1.7) where L is the Lorenz ratio and T is the temperature. Experimentally, it is much easier to measure C than S, since S measurements require precise measurements of small temperature differences. According to the Gorter-Nordheim rule, if more than one scattering mechanism exists, the diffusion thermopower is given by: s . ( p1/p)S1 + ( Pz/P)82 + ' ' ° (1.8) 14 with Pi and S1 being the resistivity and characteristic thermopower associated with scattering mechanism 1. p is the total resistivity. Using Equation 1.7, and considering only scattering by impurities and dislocations, Equation 1.8 may be rewritten: G e ( Pimp/p)Gimp * ( ”dis/p)cd18 (1.9) Since, in this experiment Po is the dominant contribution to the resistivity, (>may be replaced with 00. Also, if a term (Pimp/Pam‘s“ is added and subtracted from Equation 1.9, and the relation pb e “dis + pimp is used, Equation 1.9 can be re-written 88: G = Gar. + (pimp/po)(cimp ' Gdie’° (1.10) As is clear from Equation 1.10, a Gorter-Nordheim type plot of C vs. 1/pO should yield a straight line, and will yield information on the relative impurity contribution to the resistivity. 15 EXPERIMENTAL PROCEDURE Preparation of the QuAg samples The QgAg samples were prepared by melting ASARCO19 99.999+% pure copper rod and Cominco20 99.9999% pure silver shot in a graphite crucible which was held by a quartz support in the coils of a Lepel RF induction furnace. The induction furnace coil is contained in an evacuable can and may be rotated to pour the crucible contents into a mold. A small glass window in the top of the can allows one to monitor the sample temperature by means of an optical pyrometer. Initially, the graphite was soaked in a solution of 30% HNO3 in distilled water to remove contaminants and then out-gassed by heating in the induction furnace to a temperature of 1450°C while pumping with a diffusion pump. First, a master slug of 3.82 atomic 5 silver in copper was prepared. A piece of the ASARCO copper rod was cut with a Jeweler's saw and heavily etched in nitric acid to remove contaminants introduced by sawing. The resulting 14.92 g piece of copper rod was placed in the crucible with 1.034 g of the Cominco silver shot. The copper and silver were heated to a slight glow (700 - 800 0C) while pumping with the diffusion pump to remove any surface contamination. After cooling, the can was filled with approximately 1/3 atmosphere of argon gas and the copper and silver melted 16 together and poured into a previously etched cold copper mold. This slug was lightly etched, heated under vacuum to a slight glow, cooled, and remelted under argon. It was then allowed to cool in the graphite crucible. After lightly etching the mold and out-gassing the graphite crucible, a piece of the ASARCO copper rod was prepared, melted, and poured into the the mold using the the method outlined above. It was then remelted and repoured to gain facility with the pouring. This pure copper slug was used to make the samples' potential arms (see below). The slug ggAg A was prepared from 36.86 g of heavily etched ASARCO copper rod and 0.2433 g of the master slug. The pieces were cut from the master slug with a CuBe cutter to avoid iron contamination. Again the pieces were heated to a slight glow while pumping and allowed to cool. After backfilling with approximately 1/3 atmosphere of argon, the pieces were melted together and poured into the mold. This slug was remelted and repoured in the same manner to insure sample homogeniety. The resulting slug, QgAg A, was nominally 0.025 at. S silver in copper. The pure copper slug produced earlier was rolled out into a thick wire on CuBe rollers and then drawn through tungsten oxide dies to a diameter of 0.031 inches. Likewise, the slug ggAg A was rolled out and drawn to a 0.061 inch diameter wire. Four segments, each about 10 cm long, were cut from the center region of this wire with CuBe cutters, producing samples QgAg A-1, 2, 3, 4. 17 Pieces of the pure copper wire, about 2.5 cm in length, were spot-welded to the samples to act as potential lead contacts. It was necessary to use high purity copper for the potential arms because the the total resistance of the sample and potential arms ultimately limits the sensitivity of the measurement (see below). In addition, samples ggAg A-2 and 4 had pieces of the Cu 0.025 at. 1 Ag wire spot-welded to the center of the sample region to be used for connection to the dilution refrigerator if temperature gradients across the sample became a problem in making the measurements (see Figure 1.1). When samples QgAg A-1 and 2 showed no temperature gradient problems, these addtional tabs were cut off about 0.5 cm from the samples. The samples were then lightly etched in dilute nitric acid, rinsed with distilled water, and given a final rinse with ethanol to speed drying. A 22 mm 0.D. Vycor21 tube was cleaned in the same manner. When the samples and tube were dry, the samples were placed into the tube and the tube placed into a tube furnace for annealing. At one end of the tube, a connection was made to a mechanical and diffusion pump system, and to the other end of the tube an adjustable leak was attached, so that a low pressure of air could be introduced to allow oxygen annealing to oxidize any iron impurities, thus removing the large Kondo contribution to the resistivity, which would mask the electron-electron scattering term.22 After raising the temperature to 920°C, the 18 Silver Mounting Lugs .42.... /\ — e] L. \ / Potential E _ Arms 1i} . l G Heaters RAMs (a) (b) _._._1+H_._.. Figure 1.1 Sample configurations of (a) CuAg A-1, 2 and (b) CuAg A-3, 4. The dasEEd line indicates where the unused mounting arm was clipped off. 19 adjustable leak was opened to a pressure of 3.2 x 10'4 Torr. The samples were annealed for 2 1/4 days, during which the pressure remained in the range of 3.2 - 4.8 x 10'4 Torr. Then the temperature was slowly reduced to 500°C and the leak closed. The temperature was the slowly reduced to room temperature. When the Vycor tube was removed, it was noted that the ends of the furnace had not been packed with glass wool, which resulted in non-uniform annealing temperatures. So samples CuAg A-3 and 4 , which were nearest to the ends of the furnace, were reannealed in the same manner in a new Vycor tube for 2 days at 940°C. After a brief etch in dilute nitric acid to remove surface discoloration, silver mounting lugs were spot welded to one end of each of the samples to allow attachment to the dilution refrigerators. Current and potential leads of 0.05 mm diameter Niomax23 wire were soldered in place. Niomax consists of superconducting (at measurement temperatures) NbTi filaments in a CuNi matrix. To insure good superconducting solder contacts, the ends of the Niomax were prepared by heating them with a very hot soldering iron in a ball of molten lead-tin solder, alternating with several applications of flux. When the CuNi matrix was dissolved, the ball of molten solder was allowed to cool slightly and the Niomax withdrawn, leaving the NbTi filaments embedded in lead-tin solder. The samples had spots tinned with lead-tin solder for the current and potential leads. Then the Niomax 20 leads were soldered in place with Rose's alloy, a low melting temperature solder, taking care not to melt the lead-tin solder on the Niomax or overly heat the sample. Finally, heaters were soldered to the ends of the samples opposite the mounting lugs to be used for 0 measurements. The G heaters were 4 kc) Dale24 resistors wrapped in heavy copper wire and painted with GE 7031 varnish25 to insure good thermal contact to the samples. Current leads for the G heaters were also 0.05 mm Niomax. The potential, current, and G heater leads were twisted pairwise to reduce any stray voltages that might be induced in the bridge circuit used to make the resistivity measurements. To introduce dislocations into the samples, the samples were strained at room temperature by stretching them by hand, with a maximum elongation of about 15% for the most heavily deformed sample. Rider and Foxon26 found that the vacancy contribution to the resistivity was negligible compared to the dislocation contribution for samples strained at room temperature. The letter 'a' is used to- denote the sample run in its annealed state, and 's, t, u, v' refer to subsequent strainings. After each straining, 4 probe measurements were made to determine the new All, ‘2.2K’ and to check the contact resistances. The samples were strained and run until they broke upon straining. Attempts to repair the samples by spot welding them together or reconnecting the potential arms failed. 21 Apparently the act of spot welding drives in magnetic impurities which gives rise to the Kondo effect, masking the much smaller electron-electron scattering term. Sample 4 also broke, but was salvagable by using the cut off center connection as a potential arm. After the series of measurements were completed, the center sections of samples 2 and 4 were sent to Schwartzkopf Microanalytical Laboratory27 for analysis of Ag concentration. Sample measurements Because the bridge circuit used to make the resistivity measurements only measures ratios of resistance, independent measurements must be made to determine the sample's geometrical factor and its resistivity at a particular temperature. The room temperature resistance and 4.2 K resistance were measured using a standard 4 probe configuration. The resistivity at 4.2 K is given by: ”4.2K “ R4.2K (“1) (1.11) where R4 2K is the resistance at 4.2 K. The geometrical factor, All, is the sample cross-sectional area divided by the distance between potential contacts and is given by: A/1= p R room temp/ room temp (1 12) using the room temperature resistivity of pure copper, . 1.72 x 10'5 com.28 proom temp 22 The 4.2 K measurements were made by immersing the samples in liquid helium. Figure 1.2 shows the circuit used. Several voltage measurements were made at each current setting, reversing the current direction to eliminate any stray offset voltages. Three or four current settings between 0.1 A and 1.0 A were used. The room temperature 4 probe measurements were made similarly, but the current and potential contacts were made directly to the sample, bypassing the Niomax leads to allow the currents necessary to make a good measurement. While the sample was immersed in the liquid helium, a check was made to determine if the solder contacts were indeed superconducting. The current was sent through the leads labeled V' and the voltage measured across V. Thus, the total resistance of the sample region, potential arms, solder contacts, and Niomax was measured. Likewise, by passing current through 'the leads I and measuring the ‘ voltage across I', the current lead contacts were checked. If the currents necessary to drive the contacts normal 'exceeded 100 mA (the largest current used in the resistivity measurements) the samples were mounted in one of the dilution refrigerators for measuring. The two dilution refrigerators (which will be referred to as the Pratt and Bass refrigerators, PR and BR respectively) are quite similar in operation, with the PR cooling to approximately 13 mK and the BR cooling to 60 mK minimum temperatures. For a general discussion of dilution 23 E I HP 62638 Regulated ‘199rrent Supply Reversing SWItch HP 3450A Digital Multimeter Standard Resistor Keithly 180 Digital Nanovoltmeter I. I V. V V V. I I. “Niomax Leads '“—————-{_ ' ‘ Sample \ Niomax Leads / Figure 1.2 Diagram of the circuit used for the 4 probe measurements at 4.2 K. The solid dots indicate solder connections. 24 refrigerators see the review article by Lounasma29, and for details of these particular refrigerators see Heinen30 (PR) and Haerle31 (BR). The samples were run in pairs in a resistance bridge circuit as discussed by Edmunds gt_gl°2 (see Figure 1.3), with one serving as reference. The sample and reference are cooled by the dilution refrigerator mixing chamber, which has an attached heater. Between the sample and reference mounting lugs and the mixing chamber are a pair of heaters (4 kil Dale resistors), the upper and lower heaters, which are separated by a weak thermal link made of Ag 0.1 at. 5 Au, which has an electrical resistance of about 55 pi). Resistance thermometers Tref and Tsam monitor the temperature of reference and sample. The BR differs from the PR in that an additional resistance is in series with the sample and reference. This additional resistance is made of an indium-tin alloy of a composition such that it has a superconducting transition temperature of 3.8 K. The resistance of the alloy at 4.2 K is known, so it can be used to make an additional ig gitg measurement of the 4.2 K resistances of the sample and reference. In all cases it confirmed the independent 4 Probe results. At normal measurement temperatures, this resistor is superconducting and so the sensitivity of the bridge circuit is not degraded. Another difference between the two dilution 25 Thermal Dilution Refrigerator Connection Mixing Chamber with Electrical Isolation II Upper UPPerDfl scum i—fl Heater Heater Controller Rw--l % l I €Rw-l Lower ‘ Lower HeaterCZj—_' R ‘P_{:3Heater - Sn/In _ Q SQUID (BR only) r*/: l 47‘?" ’ i I Reference I l Sample Thermometer l I Thermometer C:}—- l '-E:J l__ .J ‘ IRef Reference Sample ISam G Heater G Heater Figure 1.3 Diagram of the bridge circuit used in the resistivity measurements. 26 refrigerators is that the mating surfaces for the mounting lugs are horizontal in the PR and vertical in the BR, so a pair of solid silver adapters were made for the BR. These adapters had copper thermometer mounts spot-welded in place. The sample thermometer mount had places for additional thermometers, and on several of the runs, thermometers were calibrated versus the BR sample thermometer to be used on other apparatus. The sample thermometers on both refrigerators are germanium resistance thermometers, labeled R7 (PR) 33, and CRT-2 (BR).:54 These thermometers were previously calibrated using National Bureau of Standards Superconducting Fixed Point Devices SRM767 and SRM768. The susceptibility of CNN (cerium magnesium nitrate) and 10% CNN 90% LMN (lanthanum magnesium nitrate) were used to interpolate between the fixed points. The data for each thermometer were fit to: 9 log R 8 An (108 T)no O n: (1.13) CRT-2 had different fits for the temperature ranges T (0.5 K and 0.5 K < T < 1.3 K. For details of the calibrations see Heinen30 (R7) and Haerle31 (CRT-2). They estimate the temperature given by R7 is within 0.7% of the actual temperature, and by CRT-2 within 15-25. The resistance of each thermometer was monitored by a resistance bridge (R7) or a conductance bridge (CRT-2). 27 The reference thermometers R4 (PR) and SRT-1 (BR) are 100£ISpeer35 carbon resistors which were calibrated versus R7 and CRT-2 respectively. The calibration was accomplished by heating the mixing chamber and assuming that in equilibrium the sample and reference were at the same temperature. The resistance versus temperature results, measured with a resistance bridge (R4) or conductance bridge (SRT-1), were plotted and the graphs used to determine the temperatures. On each subsequent experimental run, a few points of the calibration were rechecked, which allowed corrections for resistance variations due to thermal cycling. These secondary calibrations were estimated to be within 5 mK at 0.1 K and within 20 mK at 1.0 K. The output of the reference thermometer measuring bridge is sent to a temperature controller which regulates the current through the mixing chamber heater, maintaining a constant reference temperature. The sample temperature was varied by changing the current through the heater below the weak thermal link (the lower heater). The high precision resistivity measurements are accomplished with a modified commercial current comparator system described by Edmunds gt_gl°2. The current comparator system allows one to pick a master current (50 mA was used for each of these runs) and then set the ratio of a slave current to the master current. This ratio, C, can be varied between 0 and 1.9999999. so that to obtain maximum sensitivity in the resistivity measurements, the resistances 28 of the sample and reference should be within a factor of 2 of each other. The current ratio, C, is adjusted so that the potential drops across the sample and reference are equal, as indicated by the SQUID null detector. Several current reversals were used to eliminate thermal emfs. When the voltages are balanced: I R reeref g Isam sam ' (1,14) 0r, rearranging this relation, R I sam 8 ref g C. I . ref sam (1.15) So, if the temperature of the reference were fixed, and the temperature of the sample varied, measuring C as a function of temperature, C(T), would allow one to calculate P(T) from C(T), Rref' earlier. However, this direct method of finding P(T) has and the 4 probe data taken some experimental drawbacks. Rref cannot be fixed at a single temperature for the entire sample measurement range of about 0.1 K to 1.0 K due to the experimental set-up. The temperature of the reference resistor is held fixed by a temperature controller which sends a current to a resistive heater attached to the mixing chamber. The temperature controller monitors the resistance of the reference thermometer and adjusts the heat going to the mixing chamber reference to hold the temperature fixed. Since the 29 temperature controller heats the mixing chamber, the temperature of Rref sets the minimum temperature for the sample as well. Also, when the sample is heated and this heat travels to the mixing chamber, the temperature controller reduces the current to the mixing chamber heater to maintain the reference resistor temperature. So, when the heat going to the sample's lower heater exceeds the heat sent to the mixing chamber originally, the temperature controller can no longer maintain the temperature of R Therefore, instead of being able to keep the ref’ reference at a single fixed temperature while the sample temperature is varied over the range of interest, the reference temperature can only be held for a more limited range of sample temperatures. Thus, to calculate P(T) directly from C(T) data, one would need to know R precisely at several ref temperatures. To avoid these problems, differences in C are considered. If at some temperature T1, C1 ' Rsam(T1)/Rref(Tref) (1.16) and at T2 8 T1 + AT, C2 is defined similarly, and if AC 2 C2 - C1, then: .113. Rref(Tref) Rsam(T2) ' Rsam(T1) 3% C1AT Rsam(T1) Rref(Tref) AT Rsam(T2) ' Rsam(T1) Rsam(T1) A T 3O = A“sam(T) p (T ) AT sam 1 (1.17) Since for these samples Po >> P- no (even at 1 K PO/(P - p0) is about 105). and if AT is small then: JAC— = .J_ 9.2 C AT po (31‘ , (1.18) For a particular reference temperature, a series of C measurements were made over the accessible range of sample temperatures. Then,.AC/CAT was calculated using consecutive values for C and T. Typically AT was about 50 mK. In each experimental run, it was necessary to use three or four different values of Tref' With the elimination of the reference resistance from the data by taking differences, it is possible to interchange the roles of sample and reference and run two samples in each run. As a secondary check on the temperature of the sample, use is made of the weak thermal link separating the upper and lower heaters. By switching the heat from the lower heater (at which point the sample is at temperature T) to the upper heater and measuring a new sample temperature T', the electrical resistance of the weak thermal link is calculated by the Wiedemann-Franz law11, by writing it in the form 31 R = (Lo Tave AT)/O w-l (1.19) where Rw-l is the resistance of the weak link, L0 is the Sommerfeld value of the Lorenz: ratio, 2.445 x 10'"8 (V/K)2, Tave is the average of T and T', .AT is the difference, and 0 is the heat flow through the weak thermal link when the heat is flowing through the lower heater. Generally the calculated values of Rw-l were merely compared to the known values of R However, in one w-l' case (CuAg A-4a), the known value was used, with the assumption of constant T' to calculate new values of T. Use of these corrected temperatures merely reduced the scatter in the data, but did not effect the overall temperature dependence of the derivative data with temperature. This method of taking the data is somewhat different from the method outlined in Edmunds gt_gl?2, in which after regulating at Tref' the temperature difference .AT used in the resistivity derivative calculation is produced by switching the heater current from the lower to upper heater. A new reference temperature is used for each pair of points used in calculating the resistivity derivative. While this method has the advantage that AT is the same in the derivative calculation and the Wiedemann-Franz law check, allowing a direct comparison, it does have some disadvantages. First, if P(T) is to be recovered directly from the C data (as opposed to integrating the derivative data), the new Rref must be 32 known at many values of Tref’ instead of just three or four. Secondly, since it uses a new reference temperature for each pair of C points, time must be spent waiting for the system to come to equilibrium. Thirdly, it requires two balances of the bridge for each derivative, which also can take a considerable time. The method outlined above has the additional advantage of being somewhat self correcting, in that if a value of C measured is actually too high or low, the AC's calculated using the C's measured just before and just after will be affected in opposite directions, i.e. one will be high and the other low. Thus only the scatter in the derivative data is increased. The final measurements made on the samples were the G measurements. For these measurements, the master current from the current comparator was disconnected from the system and shorted. After noting the output value of the SQUID null detector system, a small current (on the order of a few microamps) was passed through the G heater, sending a heat current, Q, along the sample. The resulting shift in the SQUID output, due to the thermal voltage induced, was nulled out by sending an electric current through the sample. Then, the heater current and sample current were removed and the SQUID output checked, to make sure that the starting point of the SQUID output had not shifted during the measurment. 33 RESULTS AND ANALYSIS In Figure 1.4, a plot of NPO versus temperature is shown for a typical sample run, that of CuAg A-4u. The solid curve is given by P/Po - 1 + (A/Pb)T2 with A and po given in Table 1.1. It is clear that the dominant temperature dependence is T2, however, there are small variations at the lower temperatures. Since these variations are on the order of 1 ppm and the precision of the current comparator is about 0.1 ppm, these variations are non-negligible. Figure 1.5 shows the data plotted in a different manner. If 9-90 + ATZ, then using Equation 1.18 p(4.2 K) AC P(4.2 K) dp 1 dp = -——- . .—— ——— a A. 2TC AT 2T po dT 2T dT (1.20) Figure 1.5 is a plot of ( P(4.2K)/2TC)AC/ AT versus T for sample CuAg A-4 in its annealed and strained states. Any variation from a purely T2 temperature dependence will show up as a deviation from a horizontal line that has A as its intercept. It is clear that the deviation at the lower temperatures occurs for all the states of sample 4. Similar downturns of the data from the horizontal line are visible in the plots for the other samples which are not shown. A few of the lowest temperature points, which are consistent with the downturns, have been deleted from the plot to allow for appropriate vertical scaling. Other high precision measurements made on pure metals show deviations 34 20- 08—- - 0 0.2 0.4 0 o 0.8 700 Figure 1.4 All)o versus T for sample C_uAg L0 A-4u L2 35 I I i 7 j T' T ,1 T I ‘20 ‘ v V O t J O V 100 — } ' i 80 -— ' 0 Cu Ag A-‘l 60 - ' e 3 40 — . ‘ 1 I u 20 [- ' J 'V 120 T o ' . o m0 . ‘ '~4~s i ' ' Figure 1.5 Plot of ( P(4.2K)/2TC) AC/AT versus T for sample CuAg A-4 in its annealed (a) and strained-states (s, t, u, v). 36 from the horizontal line at low temperatures when the data is plotted in the same way. However, the effect is an upturn in Ag18 (and chapter 2), K31, and Au36. These upturns may be explicable in terms of dislocation flutter.37 The effect seems to increase enormously in K with deformation. The absence of this effect in the QgAg alloys may be due to pinning of dislocations by impurities, so that higher frequencies and energies are involved. The effect would be shifted to higher temperatures where it would be lost in the comparatively large electron-phonon contribution to the resistivity. There is some evidence of flutter effects between 2 and 3 K in some Cu alloys.38’39 Possible explanations for the downturn are the Kondo effect and a contribution to the resistivity proposed by Al'tshuler and Aronov4O based on the interference of electron-electron scattering and electron scattering off of static impurities. The latter effect has been generalized by Fleurov, Kondratenko, and Kozlov41 to include scattering off of vibrating impurities as well. This effect adds an additional temperature dependence to the resistivity of the form -CT1/2, that is, the resistivity at low temperatures is given by: p: "o - CT1/2 + AT2. (1.21) The addition of the Kondo effect gives a resistivity of the form: 37 p = po — B 1n T + AT2. (1.22) Unfortunately, the data are not precise enough to distinguish between the two forms. However, the observed effect is orders of magnitude greater than either of the predictions of Al'tshuler and Aronov or Fleurov gt_gl, leading one to suspect the Kondo effect is more likely. Application of a longitudinal magnetic field would allow one to distinguish between the Kondo and the other effect,40 but this was not experimentally feasible at the time. The values of A obtained by ignoring the lower temperature points are listed in Table 1.1 together with the dilute alloy data of Steenwyk gt_gl.2 Less emphasis should be placed on the Steenwyk results, since his values of A are the result of fitting data taken at higher temperatures, where the electron-electron contribution is much smaller than the electron-phonon contribution to the resistivity. Indeed, his values of A reverse order as strain is increased when the form of the electron-phonon term is varied slightly.18 As predicted by Bergmann gt_gl° and Kaveh and Wiser,6 A does increase with strain for a given sample, and that for the annealed samples, A decreases with impurity concentration. However, since the dilute alloys should all be in the impurity dominated scattering region before straining, they should all have the same value of A, which is certainly not the case. 38 Table 1.1 Resistivity results for the annealed and strained CuAg alloys. The values for the samples Tabeied Quip-1 and gghg-z are from Steenwyk et a1. Impurity . concentration 90 A Sample (at 5 Ag) (n 0 cm) (f 0 cm K'z) a CuAg A-1a 0.024 1.99 e 0.06 not measured gfiAg A-1s 6.92 e 0.21 94 + 8 b CUAS A-28 00016 1042 i 0006 36 i 2 CEAg A-Zs 1.65 e 0.05 37 t 1 CEAg A-2t 1.94 e 0.06 37 e 1 §§Ag A-2u 2.87 e 0.09 51 e 2 a CuAg A-3a 0.011 1.22 t 0.05 not measured QEAO A-3s 1.33 t 0.06 56 t 3 b CuAg A-4a 0.012 1.15 t 0.09 53 ¢,4 EEAg A-4s 1.67 e 0.05 57 e 2 CfiAg A-4t 2.63 e 0.08 69 t 2 CfiAg A-4u 5.07 t 0.15 101 e 4 §§Ag A-4v 7.29 s 0.22 121 s 4 c CuAg 1a 0.1 6.46 14 e 6 CfiAg 1s 9.47 36 t 7 CEAg 1t 11.95 59 e 7 EEAg 1v 17.70 45 i 1 c CuAg 2a 0.025 2.23 35 e 1 §§Ag Zn 3.50 47 t 1 a b Estimated from Figure 1.6 27 As measured by Schwarzkopf Microanalytical Nominal value 39 The data arenotconsistent with the earlier Bergmann gt_gl§ paper which appears to predict saturation in A for ‘Hmp/pdis of about 1 instead of the 0.1 that their later prediction9 makes. The absence of saturation for the most strained samples is more consistent with the later prediction, which was made after the experimental work was finished. Comparing the experimental data to the Kaveh and Wiser prediction requires an assumption about the contributions of isotropic and anisotropic scattering to the residual resistivity. One can only measure go,'which is the sum of the two terms, P = P +P . 0 dis imp (1.23) So, since these two contributions cannot be separated experimentally, one must assume a value of pimp for each sample. Clearly, 0 5 pimp g pann’ where pann is the value of (E for the annealed sample. As an upper bound for pimp’ the assumption was made (as did Kaveh and Wiser9) that 0.1 nizcm of pann is due to dislocations, and so pimp a pann - 0.1 nilcm for each sample. The lower bound for pimp is suggested by Figure 1.6. For zero concentration, 00 is about 0.55 nu cm. This is assigned entirely to a pd18 contribution to pann' If one considers that the precipitation of iron oxide during the annealing process may strain the sample upon cooling, this may be a reasonable assumption. Also 4O 90.41969 h) () J 31 * 0 0.04 0.08 0.12 conc. (01.? 0A9). Figure 1. 6 Plot ofp n versus impurity concentration for samplgg CuAg A- 2, 4 and the Steenwyk et al samples CuAg 1, 2. 41 these samples are polycrystalline, and grain boundaries behave as dislocations in the theory of Kaveh and Wiser6 The C data supports the supposition that there is a large dislocation contribution for the annealed samples. Below 1 K, G was constant for each sample, i.e. the therm0power is linear in T. In Figure 1.7, a Gorter- Nordheim type plot of G versus 1/pb for samples ggAg A-2 and 4 is shown. As expected from Equation 1.10, the relation is linear. The zero intercept, corresponding to infinite dislocation resistivity, gives the characteristic G for dislocations in copper, Gdis - +0.66 V'1, which agrees with Pearson's42 characteristic thermopower S for dislocations in copper. The slope of each line is given by (Gimp - Gdis) pimp' The slope for sample 2 is -2.3 nilcm/V and for sample 4, -1.1 ntlcm/V. Taking the ratio of these yields pZimp/p4imp s 2.1. When compared with /p4ann c 1.23 from Table 1.1, p2ann this is inconsistent with pann impurities. Indeed, the G slope ratio is consistent with being largely due to P318 in the annealed samples of about 0.85 nilcm. Figure 1.8 shows a plot of A versuslfimp/Pais. The solid symbols use the upper bound for pimp and the open symbols use the lower bound value. The error bars have been omitted from the open symbols for clarity. The solid line is the Kaveh and Wiser9 prediction. It is clear that in this form the predicted dependence of A is not experimentally verified. 42 + 1.0 , I I -CuAg A-2 'CuAg A-4 +0.6 ._ .1? + 0.2 — _. 3 0 -0.2 - -O.6 — -1 o l ' 0 0.2 0.4 06 0,3 Q," (:1 Gem)" '1 Figure 1. 7 Gorter-Nordheim type plot of 0 versus 1/00 for samples CuAg A- -2, 4. 43 .coupouoosn on» no coums0> omquucos 0 ma 0>s=o cognac on» can m.r coduoouw no couuouomsa ”moduocoona on» ma 0>L=o mason one cowouaanqcvcoo son“: mm.o m ossmomnmmooahm coco one one q 0» son“: v.0 no coausmhsucoo mamcowmmmo muonazm canon one .mmfiosom m<=o on» com o moods < m.r whomam . ..mQ\o§Q 8. o. p 3 3.0 _:____J __:____ _ __:____ _ _:_____ _ W . 1.. IIIIII 11...!) 8 I/ 1 4 l m m o/ o 3 I b o 4 m m o V I . r. m m . / cow m x o o z/ m I. / SJ J/ .Ibw .NO<:U4 0// TI pD(3UO m :— .?< 3:6. / .n-< o500 K) can be accounted for by a spin-flucuation temperature of 190 K; 2) A and x both increase with the introduction of Ni impurities°°'78 which produce local spin fluctuations: 3) the presence of paramagnons explains why singlet superconductivity in supressed in Pd even though the electron-phonon coupling constant suggests it should occur.79 Irradiation of Pd with He ions can produce superconductivity and reduces x°.3°'31 If the introduction of dislocations into Pd influences the formation of paramagnons, then it is probable that A is affected. Also the effect should influence X in the same fashion. That is, if the introduction of dislocations were to produce local spin fluctuations, as is the case with the introduction of Ni impurities, then both A and x should increase. If the presence of dislocations quenches the formation of paramagnons, as is the case with irradiation, then both A and x should decrease. The problem is then, is it mainly Coulombic s-d 80 scattering producing A, or is it paramagnon scattering? An answer may lie in the calculations of MacDonald.82 MacDonald has produce a formalism which includes both contributions, and feels that a quantitative investigation into electron-electron scattering in non-simple metals is practical, but no calculation of this sort has been made for Pd. EXPERIMENTAL PROCEDURE Sample Preparation The samples used in the resistivity measurements, Pd-A, Pd-B, and Pd-C were fabricated from 1 mm diameter wire from Johnson Matthey Chemicals Limited.83 Potential arms of the same material were spot-welded about 3 cm apart. Since it is known that annealing in air substantially reduces the low temperature resistivity of Pd,84 all the samples were annealed in air. Samples Pd-A and Pd-B were annealed by passing a current of about 30 A through the samples, which raised them to about 975°C as measured by an optical pyrometer. Pd-A was held at this temperature for 40 minutes, and then slowly cooled to room temperature over about 7 hours by slowly reducing the current. Pd-B was held for 70 minutes at this temperature and slowly cooled in the same manner. The current connections were counter- weighted to avoid straining the samples during the cooling. Pd-C was annealed by clamping one end of the sample in a Cu block and flame heating the block for several minutes, 81 raising the sample temperature to roughly the same as the other samples. It was then allowed to slowly cool by reducing the heating of the Cu block. Niomax current and potential leads were attached to the samples in the same manner as the QgAg samples discussed in chapter 1. No mounting lugs were attached to the samples. The samples Pd-A, Pd-B, and Pd-C were strained by stretching them at room temperature. Again the postscript 'a' is used to denote the annealed sample, and 's, t, u, v' refer to subsequent strained states. The pure Pd samples used for the susceptibility measurements, Pd S-1 and Pd S-2, were made from pieces of the same wire used to make the resistivity samples which were annealed in the same manner as Pd-C. The samples were spark cut from from the end of the wire furthest from the Cu block. The spark cut end was heavily etched with aqua regia to remove any contaminants introduced in the spark cutting. Two Pd samples containing Fe were also made for susceptibility measurements. Sample Pd (106 ppm Fe) was produced by melting some of the Johnson Matthey Pd wire with the appropriate amount of Fe sponge (also from Johnson Matthey) in an alumina crucible in an RF induction furnace under vacuum. The resulting slug was inverted and remelted twice to insure sample homogeniety. The sample was spark cut from the slug. Sample Pd (20 ppm Fe) was spark cut from . 82 a slug of on-hand material. Both samples were etched with aqua regia to remove surface contaminants introduced in spark cutting. Dislocations were introduced into the susceptibility samples by rolling them through stainless steel rollers until the samples were about twice their initial length. They were rinsed with solvent and heavily etched with aqua regia. Sample Measurements The same apparatus used for the QgAg samples was used to measure the room temperature and 4.2 K resistances of the samples to determine the geometrical factor and P4.2, again using several currents with current reversals at each current. Since the T2 contribution to the resistivity is much larger in Pd than Cu, the T2 term is the dominant temperature dependent term up to much higher temperatures, enabling the resistivity measurements to be made in a conventional He4 cryostat. The system used is one built by Steenwyk18 with some minor modifications to the sample holders. Figure 3.1 shows the layout used. This is similar to the dilution refrigerator layout, except that the mixing chamber is replaced with a ”1 K pot", which is filled with liquid He from the main bath by opening and then closing a needle valve. The 1 K pot is then pumped with a large volume mechanical pump, lowering the temperature to 83 l K Pot Thermal Connection with Electrical Isolation -——-——0 Heater Heater SQUID Reference Sample Thermometer Thermometer [:J— 1—{3 L. .J Iref Eeference Sampli‘] Isam J" “L Figure 3.1 Schematic drawing of the apparatus used for the Pd resistivity measurements. 84 near 1 K. The other difference between the dilution refrigerator and this apparatus is that the temperature controller heats the reference holder's heater instead of one mounted on the mixing chamber. This difference allows the sample to be at a lower temperature than the reference. Again, the role of sample and reference can be interchanged. The Pd samples were run pairwise in most cases, however, for some of the last measurements on PdeC, the reference was made of commercial Cu wire, since the samples Pd-A and B had broken in attempting to strain them further. The samples and references were held in place by clamping them at one end to an OFHC Cu block, which contained a thermometer and heater, the heater being closer to the 1 K pot. The positions of the two samples will be referred to as the 'sample position' and 'reference position' although the roles were interchangable. Both sample and reference position thermometers were germanium resistance thermometers, monitored with conductance bridges. The sample position thermometer was a Cryocal germanium resistance thermometer, calibrated above 1.5 K by the manufacturer in 0.1 K increments. An additional decimal place in the temperature was obtained by linear interpolation between these points. The reference thermometer was calibrated by the author in the apparatus by mounting it a Cu block with the sample thermometer and 85 plotting the conductance vs temperature results. The same current comparator used in the previous sam/Bref' the ratio of the resistances of sample and reference. However, measurements was used to find C c R since in this apparatus, the reference could be held at a fixed temperature while the sample's temperature varied over the entire range of interest, the differences method used to analyze the data in the previous measurements on CuAg and Ag was not used. For these measurements, the sample serving as reference was held at about 2 K, and C(T) measured for the sample, over a temperature range of about 1.5 K to 8 K. Above 8 K the superconducting leads went normal, rendering the SQUID insensitive to differences in the potential drops across sample and reference. Since the temperature dependence of the resistivity is so large in Pd, C was measured for each sample to 1 part in 105 to 1 part in 106 instead of the full sensitivity available with the current comparator. These C(T) data were least squares fit to: 2 N C s C + C T + C T 0 1 2 (3.3) Sample Pd-C showed the largest temperature deviation from the T2 dependence and yielded N - 5. For Pd-A and Pd-B, the deviation from purely T2 dependence was not as large and resulted in large uncertainties for N. The C data were then fit to: 86 c = C'O + c'1T2 + C'2T5 (3.4) for each of the samples. Within their uncertainties, CO and C'O were the same, as were C1 and C'1, that is to say, the dominant temperature dependence is T2, with a much smaller additional higher power term. To convert these coefficients to resistivity coefficients, the 4-probe data were used. Since C(T) was found for both the reference and the sample, the resistance of the reference at the temperature at which it was held is given by Rref(Tref)'R(4'2K)[Cref(Tref)/Cref(4'2K) (3.5) Multiplying the coefficients of Equation 3.4 by this resistance, gives the resistance of the sample as a function of temperature. When the reference was the Cu one, the 4.2 K result was used directly, since the change in resistance is negligibly small for the temperature difference. As a check, the resistance of the sample was calculated at T . 4.2 K and compared to the 4-probe 4.2 K measurement. In all cases they agreed. Multiplying the resistance coefficients by the geometrical factor determined by the 4-probe results converted the fit to resistivity in the form: 2 5 p8 p 4» AT '1' ET 0 ° (3.6) 87 The susceptibility measurements were performed on an SHE Corporation85 Model 905 SQUID equipped susceptometer. A 1 k0 field was used for all sample measurements. Six measurements were made at each temperature, and the results averaged. The pure Pd susceptibility results were least-squares fit to: X= X0 + X1T2 (3.7) which is the form of Equation 3.2, and the ggFe results least-squares fit to: X: X + C/T ° (5.8) since for the low Fe concentrations used, the magnetic Curie temperatures are negligibly small. RESULTS AND ANALYSIS Figure 3.2 shows the temperature dependent part of the resistivity of sample Pd-C plotted versus T2 for T < 3.7 K to show that in this region the T2 behavior is well obeyed. It is obvious that A, the slope of these lines, decreases with sample strain. Also, as the amount of strain increases, departures from T2 appear. Figure 3.3 shows (P- PO)/T2 versus T3 for 1.5 x < T < 8.5 x showing the behavior is close to T5. This T5 term 86 may be associated with electron-phonon scattering. Again it is clear that A, here the vertical intercept, 88 1 1 I l— ] fl 1 l 0.7 "’ 0 Pd Co I- O ‘ . .1 0 1 . D U a 00‘ - ‘ v .- OJ '- - E b - 9 S303-- - .5 as - ~- I Q. . 0.3 '- - 0.3 "' .— 00' — - M J J J 1 J 1 J I l 0 4 IO 20 Figure 3.2 The temperature gapendent part of the resistivity vs T for T < 3.7 K for sample Pd-C in the annealed state a (0) and in the strained states a (O), t (I), u (o), v(A). 89 —( er I :2 r ‘ E 9 <3 r 3 42— 7 69 IF- Q "" .1 38 - ' ‘ A 34 ‘ _ 1 1 J 1 1 O 200 400 600 13 (10") Figure 3.3 ( P- P )/T2 plotted versus T3 for for T 2 8.5 K for sample Pd-C under the same conditions as Figure 3.2. 90 decreases with strain. On the other hand, B, the coefficient of the T5 term and here the slope of these lines, increases with strain. Table 3.2 lists the values of po, A, and B for the samples run. Figure 3.4 shows the behavior of A and B as a function of the residual resistivity 1%. The curves shown on the figure are merely to guide the eye through the points for each sample. Consider first the behavior of the annealed samples only. 90 decreases with increasing annealing time. At the same time, increased annealing time results in smaller values of A. Secondly, it is obvious from the plot that for a given sample, strain increases as, decreases A, and increases B. Since the largest A belongs to the annealed state of the sample which has the shortest annealing time, it appears that the annealing in air that these samples received was sufficient to reduce the number of dislocations and that the longer annealing times perhaps removed or pacified some sort of impurity. This behavior of A and B is opposite of that for Cu2 (and Chapter 1). In Cu, A increases with strain and the electron-phonon scattering term decreases. As seen in Chapter 1, the behavior of Cu is theoretically explained by the different anisotropies of electron- electron, impurity, dislocation, and electron-phonon scattering. For the electron-electron scattering AT2 term in Cu, the argument is that electron-electron and electron- 91 -C in the annealed and strained states. :8, A, and B for samples Pd-A, Pd-B, and Table 3.2 A(p mom/K2) B(fncm/K5) P°(n 9cm) Sample 999 000 22 0 0 0 nw0.000 titi... 494 39535 O O O O 0 68900 11 988 000 15 0 0 0 0.0.000 ..¢.z..¢ 719 45739 0 O O O "(Ala/.53 44333 92 12 *1 I I 1 1 7 t at - <5 4 4L- - d: O 1 1 1 1 1 5° 1 l ’7 ‘1 I .. - -1 if 40 x E d? g 30" '- < °'Pd A 20_ DIPd B .— ' (“Pd C 10 I l L I l 0 4 8 12 18 20 24 Po (nflcm) Figure 3.4 Variations of A and B with p .for the annealed samples (open symbolg) and and strained samples (full symbols) of Pd-A (0,0), Pd-B (0,0) and Pd'C (‘,A) 0 93 impurity scattering are both rather isotropic, and the addition of the anisotropic dislocation scattering changes the electron distribution function away from that characteristic of electron-electron and impurity scattering, leading to an increase in A. For the electron-phonon scattering term, the addition of dislocation scattering is to change the electron distribution function from that characteristic of impurity scattering alone to one more like phonon scattering alone, and thus decreases the electron-phonon scattering. If Pd is to be explained by this picture, strain must produce a change in the distribution function less like that characteristic of phonon scattering alone. Pinski gt_gl77 have shown that anisotropy effects can have a large influence on the calculated resistivities for Pd, but only consider anisotropy to the extent that different sheets of the Fermi surface may be displaced by different amounts. If the behavior of Pd is to be explained by a varying anisotropy picture, scattering anisotropies much different from those of Cu must be assumed. If, on the other hand, the AT2 term is primarily due to electron-paramagnon scattering, the results could be explained by hypothesizing that dislocations quench the formation of paramagnons,thus eliminating this sort of scattering. Schindler and Rice68 and Rice78 have calculated the the temperature dependence of electron- 94 paramagnon scattering and find that the low temperature contribution to the resistivity is of the form ppara e AT2 - B'TS. (3.9) If the electron-phonon term also has approximately a T5 dependence, the measured 8 would be°the sum of the positive electron-phonon term and the negative electron-paramagnon term. If sample strain quenches the paramagnon formation and reduces A and B', the rise in the measured B'is explained as well as the decrease in A. Schindler and Rice have also calculated how A should scale with the static magnetic susceptibility X0, when Pd is alloyed with low concentrations of Ni. The presence of the Ni produces local spin-fluctuations and increases both A and x0. They predict that A should vary as x02, but treat the effect of the Ni as increasing the average Coulomb interaction between the d-electrons. That is, the presence of the Ni impurities produces an overall enhancement of the paramagnons. Lederer and Mills86 have calculated how A should scale with X0 for enhancement of the Coulomb interaction in the vicinity of the Ni impurities only and find that A varies as x0, which more closely explains the Schindler and Rice data. If the effect of dislocations is to quench the formation of paramagnons, then the static susceptibility should decrease with sample strain. As mentioned earlier in the chapter, Stritzker80 95 found that low temperature irradiation caused Pd to become a superconductor. He argues that irradiation could cause a smearing out of the density of states at the Fermi level, reducing the Stoner enhancement factor, and thus quenching the paramagnons. Meyer and Stritzker81 measured the low temperature susceptibility before and after low temperature irradiation for a Pd 0.35 at % Fe sample and did find a marked reduction in the susceptibility in the Pd host. (The Fe was added to enhance the signal in their susceptometer.) The results of the susceptibility measurements made in the present study are shown in Figure 3.5, where the measurements on two pure Pd samples in the annealed and strained states are plotted as a function of T2, as expected from Equation 3.2. The small departures at the low end from the T2 dependence are probably due to magnetic impurities in the sample. The fits to the annealed sample data give (x(T) - x(0))/ x(0) . 0.51 x 10‘4 T2 and 0.50 x 10'4 T2 for Pd-S1 and Pd-sz compared to the value of 0.26 x 10'4T2 of Manuel and St. Quinton87 quoted by Beal-Monod75, giving a slightly better agreement with the theoretical prediction of 0.47 x 10'4T2. x0, combined with the result of Anderson88 for the Pauli susceptibility yield a Stoner enhancement factor of 8.4. However, the interesting result is that, contrary to expectations, the static susceptibility increased as the 96 12 .V O X (p. emulg) I I I I I I I Pd 5-1 0 annealed ° strained Pd 5-2 Aannealed A strained Figure 3.5 400 800 1200 Susceptibility of pure Pg samples Pd-S1 (0,0) and Pd-SZ (4,0) versus T in the annealed (full symbols) and strained (open symbols) states. 97 sample was strained. A similar increase with deformation in the susceptiblity of Pd has been noted by Deryagin 33 2189 at an unspecified temperature. Jarlborg and Freeman90 have calculated x for various elastic deformations and show that in all cases x0 substantially increases. This is due to a slight broadening of the density of states which increases the density of states at the Fermi level. Since the coefficient of the T2 term in the susceptibility depends on the more sensitive first and second derivatives of the density of states (see Equations 3.2 and 3.7) is is reasonable that these exhibit a larger relative change than x0. Thus the susceptibility measurements do not seem to support the idea that the introduction of dislocations to Pd quenches the formation of paramagnons. The difference between these results and the irradiation results of Meyer and Stritzker may mean that irradiation produces a substantially different type of disorder than straining the sample. Meyer and Stritzker mention the role interstitials play in smearing out the density of states. Another possibility is that the presence of Fe may influence the susceptibilty of the host Pd in a way not accounted for in their mean field type analysis of their data. To test this, two Pd samples containing Fe were run in the annealed and strained states, albeit with much lower Fe concentration. These samples were the Pd (20 ppm Fe) and Pd (106 ppm Fe) samples whose susceptibilities are shown in 98 Figures 3.6 and 3.7. The plots show X versus 1/T and are linear as expected from Equation 3.8. The 1/T - O intercept is the susceptibility of the Pd host. The upturn at small 1/T is due to the T2 term in the Pd susceptibility which is not accounted for in Equation 3.8. The effect of the strain is clear. Straining increases X0 for Pd and has little or no influence on the Curie constant. The susceptibility data is summarized in Table 3.3. Conclusions The following observations were made: First, annealing in air reduces both p0 and A for Pd samples. Second, straining a sample increases 5%, decreases A, and increases 8. Third, x0 increases when Pd and PdFe is strained. Fourth, (X(T) - X°)/T2 decreases with strain for Pd. If it is meaningful to discuss the scattering as solely due to Baber or paramagnon scattering mechanisms, then the decrease in A with an increase in ‘8 upon straining would not seem to support the electron-paramagnon scattering 68'86 which relate argument, since the theories to date A to xo predict that increasing x0 will accompany increasing A. On the other hand, a Kaveh-Wiser type anisotropy argument applied to the Baber mechanism would require unexpected anistropies and its not clear as to how it may apply to the case where two classes of electrons of different effective masses interact. Perhaps the 99 Pd 20 ppm Fe 7.2 3’ a 5 3 7.0 X 6.8 6.6 ° ' ' I J 000 O0] U02 1" (K") Figure 3.6 Susceptibility of Pd (20 ppm Fe) versus 1/T in the annealed (0) and strained (0) states. 100 12" Pd lOdpmee " X In emu/g) 6 '- 0- J l l J .0 0.1 0.2 T" (K") Figure 3.7 Susceptibility of Pd (106 ppm Fe) versus 1/T in the annealed (0) and strained (0) states. 101 Table 3.3 )9 and X1 (see Eq 3.6) and C (see Eq. .7) for the Pd and PdFe samples. ‘Axo is the increase in X0 upon straining. Sample xo(uemu/g) x1(10'10emu/gK2) Axo P8381 annealed 6.517 2.004 0.402 strained 6.919 1.828 Pd-S2 annealed 6.558 1.949 strained 6.857 1.643 0.299 Sample xo(pemu/g) C (nemu K /g) .Axo Pd (20 ppm Fe) annealed 6.65 2.56 strained 6.79 2.57 0.14 Pd (106 ppm Fe) annealed 6.5 15.49 8 strained 7.00 15.45 0.42 102 calculation proposed by MacDonald will provide an answer to the question. The secondary reason for making these measurements was to understand the variation of A reported in the literature. It is clear that the state of the sample has a considerable effect on A. A change in PD of about 4 nilcm will change A by about 10 pizcm/Kz which is appreciable when compared to the variation in A seen in Table 3.1. But most researchers make measurements on well annealed samples, and the lowest value of A reported is for the 0.43 nilcm residual resistivity sample of Webb gt_gl§9 which, based on po, would not seem to have the high number of dislocations necessary to drive the sample's A down to its value of 15.9 pilcm/KZ. If the strain quenches I paramagnons, one would expect that the absolute concentration of dislocations to be of importance. If a Kaveh-Wiser type changing anisotropy scheme is correct, then it may be the relative concentration of impurities that is the important quantity. A very low Po sample may still be in the dislocation dominated limit. The interesting experiment to perform next would be to take an extremely pure sample, such as the Webb gt_gl sample and strain it, measuring A before and after. If it is already in the dislocation dominated region and the relative anisotropy picture picture is correct, then A should change very little. If the effect is primarily due to spin fluctuations, A may still have a sizable decrease. In the 103 next chapter, a method of producing very high purity Pd samples will investigated. CHAPTER 4 THE PURIFICATION OF PALLADIUM AND GOLD USING CHLORINE GAS INTRODUCTION AND THEORY Introduction In the previous chapter, one reason for producing high purity Pd samples was discussed. In this chapter, a method of purification is studied that removes Fe impurities from Au and Pd, Fe being one of the most common impurities in both Pd and Au. In addition to wanting high purity Pd samples to further investigate the role of dislocations in the temperature dependence of the resistivity, there is another reason for wanting high purity Pd samples. There exist theoretical predictions that Pd might exhibit p-wave superconductivity, but because of the sensitivity of p-state pairing to impurity scattering, it is necessary to have an extremely pure sample.91 Theory To date, the Pd samples with the highest RRR have been prepared by annealing in 02 or air.84 For Au, annealing in this manner also increases the RRR, but the role of O2 is to oxidize the oxidizable impurities and to cluster the impurities, reducing their effect on the 104 105 resisitivity, but not necessarily removing them from the sample.92 In 1970, Walker93 reported results on the removal of Fe impurities from Au, by annealing in a reduced atmosphere Of C12. Although chlorine gas reacts with Au, at temperatures above about 300°C the compounds AuCl and AuCl3 are not stable. 0n the other hand, both FeCl2 and FeCl3 are stable and volatile just above these temperatures. Thus, by heating the Au to an appropriate temperature, and introducing C12, the Fe on the sample surface will combine with the 012, and leave the sample to plate out on a cooler region of the apparatus. However, since the appearance of the Fe on the surface is essentially a diffusion limited process, the Fe removal was carried out at a much higher temperature, 850°C. With an 8 hour Cl2 anneal, Walker was able to reduce the Fe concentration in a 0.08 mm diameter Au wire by a factor of 200 as determined by spectroscopic analysis. The same technique should be applicable to Pd. PdCl2 decomposes at 500°C, and so if the 012 is introduced above this temperature, it should be possible to remove the Fe impurities. However, no such attempt is noted in the literature. Kopp94 and Stesmans92 both conducted studies on the effect of 012 annealing on the transport properties of Au. However, the analysis of the effects on the resistivity is complicated by surface scattering in 106 their thin samples. Also, the transport measurements are not capable of distinguishing between removal of impurities and the pacification of them, that is, reducing their total scattering cross section by forming chlorides and/or clustering in the sample. Stesmans noted aging effects on the RRR which be attributed to changes in grain boundary scattering with time. In 1982, Cutler95 studied the effects of 012 annealing on Au using radioactive tracing techniques. She doped Au with 59Fe or 54Mn and found both were removed with Cl2 annealing. This technique offers quick, straight-forward proof of whether the impurity is removed instead of pacified, and is the one adopted for these measurements. EXPERIMENTAL PROCEDURE The Pd and Au samples used in this study were doped with 59Fe. 59Fe has a half-life of 45 days and emits readily detectable Y-rays of 1.1 and 1.3 MeV. Since the Pd and Au need not be of ultra-high purity for the purposes of this study, scraps of high purity materials left over from previous sample preparations were used. The 59Fe was obtained from New England Nuclear Corporation96 and came as ferric chloride in 0.5 M hydrochloric acid, with an initial activity of 0.1 mCurie for 0.1 ml of solution. The Pd and Au samples were rolled out into foils and 107 given a light etch in aqua regia to remove surface contamination. Since the activity of the 59Fe solution was much higher than necessary for the measurements, a small amount of the radioactive solution was mixed with a photographic wetting agent. This was painted onto the fails with a small brush, after which the foils were placed in an open test tube, which was placed in a dessicator for thorough drying. The Pd and Au samples were handled separately. After drying, the foils were placed in quartz tubes. The Pd foils were sealed in the tube under 1/4 atmosphere of 10% H2 - 90% Ar gas mixture and placed in a tube furnace set at 1100°c for 11 days so the unoxidized 59Fe would diffuse into the foils. Upon opening the furnace, it was observed that the foils had melted, resulting in small beads of Pd doped with the 59Fe, possibly due to an overshooting of the set temperature of the furnace. The beads were no more than 1 mm in diameter. One of the beads was progressivly etched, with the mass measured and activity counted after each etch, as shown in Figure 4.1. This study indicated that the concentration of 59Fe was reasonably uniform throughout the bead. The Au foils were under melted under the 10% H2 - 90% Ar gas mixture in a pair of nested quartz tubes in the apparatus used for the 012 annealing (see Figures 4.2 and 403 (b) )0 108 1200 , r ‘1' .E i 800- — O G) E E 400— g d :3 C) CD 0 I J l 0 8 16 24 32 mass (mg) Figure 4.1 Plot of Count Rate vs Mass fogga progressively etched bead of Pd doped with Fe. The uncertainty in the count rate is roughly the diameter of the dot. 109 Sample measurements The activity counting was done with a 2"x2" sodium iodide detector powered by an Eberline Mini-Scaler. The signal output was sent to a Tracor Northern Multichannel Analyzer, and only those signals falling within an energy window encompassing the Vbrays emitted by the 59Fe were counted. The detector was housed in lead shielding to reduce the background rate. Counts were generally made for 10 minutes, and background counts made just before or after the sample counts were subtracted. The apparatus used for the C12 annealing is shown in Figure 4.2. The apparatus is connected to a pumping system consisting of a mechanical pump and liquid N2 cold-trapped diffusion pump, equipped with thermocouple and ionization pressure gauges. It also has a valved input for the introduction of the 10% H2 - 90; Ar gas mix used to reduce any oxidized Fe so that the Cl2 anneal is effective (see results section). Connected to the pumping system via a quick connect is a valved pyrex manifold. Attached to the manifold are a thermocouple pressure gauge, the chlorine storage bottle, and the quartz tube in which the sample annealing was done. All O-ring seals in the valves and connections were coated with Fluorolube Grease GR-90.97 The graphite sample holder was supported inside the quartz tube by a smaller diameter quartz tube, and held in the center of the quartz 110 Thermocouple Pressure Gauge Quick Connect To Pumping System and Ar-H2 Input ‘— Valves’/////' Quick Connects Graphite Sample Holder so.../// 00000 K / \J I Chlorine Bottle ‘ RF Induction Furnace Coils Figure 4.2 The apparatus used for the C12 annealing. 111 tube by small quartz centering rods. All surfaces of the support structure were fire-polished to avoid scratching the inside of the quartz tube. Figure 4.3 (a) is a cut-away drawing of the graphite sample holder. The Pd samples were held in an alumina crucible. It is important to use a high grade of alumina, low purity alumina was found to break down at the temperatures used for the Pd anneals (over 1550°C). The hole drilled beneath the crucible was necessary to pump out the region below the crucible, since the crucible fit the graphite rather closely. In earlier versions, in which the hole was not drilled, the alumina crucible tended to float to the top of the graphite when the sample region was heated. Figure 4.3 (b) shows the method used to hold the Au samples. They were placed between a pair of nested quartz tubes, with the inside tube held above the sample by a few dimples in the outside tube. This method of holding the sample had the benefit of having nearly all of the 59Fe plate out on the upper surfaces of the nested tubes instead of the outer quartz tube shown in Figure 4.2. Before being used in the annealing measurement, the graphite and quartz tubes were cleaned by soaking in aqua regia and given thorough rinses in distilled water. The system was assembled and pumped out using the diffusion pump, usually overnight. The system was then heated with the RF furnace to temperatures above the annealing 112 Graphite I I Sample I Holder l | I 1 Alumina I Crucible I l l I l Quartz Centering Rod \\\I ‘_ I 1:: I I L. " .J Quartz I ll ' Support Tube 1 lI /I& /' L 1 (a) (b) Figure 4.3 (a) The graphite sample holder used for the Cl annealin , shown with the alumina crEcible use to hold the Pd. (b) The nested quartz tubes used to hold the Au. 115 temperature and held until thoroughly out-gassed. All temperatures were measured with an optical pyrometer. However, since the outer quartz tube darkened as the graphite was heated, the temperatures measured with the optical pyrometer are lower than the actual temperatures. The annealing procedure was performed in the following way. The Pd sample was weighed and counted, and then placed in the previously out-gassed alumina crucible. The system was pumped down to a pressure of a few mTorr with the diffusion pump and the system was heated with the RF furnace to about 800°C. Since heating the sample and holder would raise the pressure slightly, pumping with the diffusion pump continued until the pressure dropped back down to about 10 mTorr. Then 700-800 mTorr of the HZ-Ar gas mixture was introduced to the sample region and the temperature raised to 1200°C (;,100°C). The gas mixture was allowed to remain for several minutes to reduce any oxidized Fe. This short reduction time is sufficient to reduce any oxides near the surface of the sample, and the 59Fe in the interior of the sample should be oxide free after the preparation of the sample. The HZ-Ar mixture was then pumped out and 600-800 mTorr of Cl2 was introduced to the sample region by a brief opening of the valve on the storage bottle. The temperature of the sample was then raised to the annealing temperature. After the annealing had taken place for the appropriate amount of time, the C12 was frozen in the bottom of the outer 114 quartz tube by immersing the end of the tube in liquid N The RF furnace was shut off, and after the sample 2. and graphite had cooled to room temperature, the 012 was returned to the storage battle, by immersing the bottle in liquid N2 and allowing the end of the outer quartz tube to warm up. The Au annealing was performed in a similar manner, except that the Au was contained in nested quartz tubes as previously noted, the Hz-Ar mixture was introduced at about 850°C, and the temperature was not raised for the reduction of the oxide. After the C12 had been returned to the storage battle, the outer quartz tube, with the quick connect attached, was removed and taken to the radioactive material handling area and the sample removed for weighing and counting. In the case of the Au samples, a quick etch with aqua regia was done before the weighing and counting, since removal of the sample from the nested tubes might possibly cause some of the plated-out 59Fe to be picked up by the sample. To determine the importance of the H2 reduction, one of the Au samples was deliberatly oxidized by melting it in a reduced pressure of air for about 4 minutes and then 012 annealed. Then Hz-Ar annealing and C12 annealing were alternated, both taking place at temperatures just above melting. 115 RESULTS AND DISCUSSION The first run on Pd was an anneal performed on a foil prepared by Cutler. The Cl2 anneal took place at 1100°C for 61 minutes. While sucessful in the sense that the count rate/mass dropped from (181 ¢_1)/mg min to (89.; 3)/mg min, meaning a 50% reduction in Fe concentration, the results were not that useful in terms of sample preparation, as the mass of the sample dropped by 80%, from 9.27 mg to 1.79 mg, due to the high vapor pressure of Pd. Counts were made on the quartz outer tube, quick connect, and graphite sample holder, indicating that the 59Fe had plated out only on the outer tube just above the region where the graphite was held. The tube was cleaned out with aqua regia and again out-gassed. For the next run, advantage was taken of the fact that while the vapor pressure increases somewhat upon the melting of Pd, the diffusion of Fe is much more rapid in the molten metal. Five of the small beads of Pd doped with 59Fe, produced earlier, with a total mass of 65.7 mg, were placed in the out-gassed crucible. The same annealing procedure described above was used, except the Pd temperature was raised just above its melting temperature of 1550°C for the C12 anneal (while the optical pyrometer measurement of the temperature is somewhat inaccurate due to tube darkening, by using welding goggles it is easy to 116 observe when the sample melts). The sample was held in the molten state for 4 minutes in the C12. After cooling, the resulting single ball of Pd was removed, weighed, and counted. This same sample was then replaced in the apparatus and rerun with the molten sample in contact with 012 for an additional 10 minutes. If the assumption is made that the Fe must appear on the surface of the sample in order for the 012 to remove it, then the concentration reduction is essentially a diffusion limited process and the concentration should decrease exponentially with time (see, for example Jost9°). Figure 4.4 shows the results for Cl2 annealing of molten Pd. The abscissa represents the time spent in Cl2 while the sample was molten, not the total time the C12 was in contact with the Pd (which is a few minutes longer) since the removal of Fe is much slower when the Pd is solid. The point corresponding to the second run is plotted at the total time the molten sample spent in contact with C12. Accompanying this 75% reduction in Fe concentration in 14 minutes is a 50% reduction in sample mass, far better than the results for the solid Pd. An estimate of the diffusion coefficient of Fe in Pd above its melting temperature can be made from the plot. The sample was roughly spherical with a diameter of about 2 mm. Jost98 gives an expression relating the average concentration as a function of time for spherical geometry, 117 A 1 p on normalized count rate / mass 8 0 3L. 15 7 Phi“ Figure 4.4 The reduction in Fe concentration in Pd as a function of time the molten metal spent in Cl . The dashed line represegts the results f0; a sample annealed at 1100 . 118 assuming initial uniform concentration. The average concentration is proportional to exp(-x2Dt/R2) where R is the sample radius and D is the diffusion coefficient. The data yield D a 2 x 10’6 cmZ/s with perhaps a factor of 5 uncertainty since the sample was in contact with the alumina crucible. Also, since the sample lost mass during the run, the surface area of the Pd changed during the annealing. The reaction rate of 012 with Fe is also neglected. The first Au run was upon a piece of not very active Au foil left over from Cutler's experiments. An anneal of molten Au in the presence of Cl2 for 30 minutes dropped the count rate to one indistinguishable from background, so a second run on a more active sample was performed for a shorter time. The 20 minute anneal on a 3.018 g sample caused only a 6 mg loss of sample. The count rate/mass dropped from (6328.1,15)/g min to (15.: 1)/s min, a reduction of over a factor of 400 in the Fe concentration, in a time far shorter than was necessary for this reduction in solid Au. A rough estimate of the diffusion coefficient is D s 6 x 10'5 cm2/s. The final Au run was done on a deliberately oxidized sample, of mass 0.90 g. After the sample was oxidized by melting under a reduced atmosphere of air, a 012 anneal on the molten metal was performed. The count rate/mass was unchanged. Then the sample was melted under HZ-Ar, followed byea nearly 20 minute Cl2 anneal, which is long 119 enough to remove nearly all the free 59Fe. The sample was weighed and its activity counted, and the process repeated. The results are shown in Figure 4.5, where the activity is plotted versus total time spent under the HZ-Ar mixture. The diffusion coefficient for oxidized Fe in molten Au is roughly 9 x 10'6 cmZ/s. As shown in the plot, the limiting factor for the removal of Fe from Au which has undergone oxidation is the reduction of the oxidized Fe. Perhaps the presence of oxidized Fe is the reason why Barnard gt_3199 found Fe effects in the resistivity of an Au sample which was melted under C12. Conclusions For the first time, C12 annealing has been demonstrated to remove Fe from Pd. Annealing the molten metal, as opposed to the solid, improves the Fe reduction versus mass loss ratio. In Au, the application of 012 to the molten metal, rather than the solid metal, greatly reduces the time necessary to remove a given amount of Fe. The reduction of the oxides in the sample is important for 012 annealing to be effective. The next step is to use these methods to produce high purity Au and Pd samples. Probably the best method would be to purify an initial quantity of the Pd or Au using the methods outlined above. Next, the samples would be made, 120 0.1 normalized count rate / mass 1 1 0.010 20 40 1 (min) Figure 4.5 The reduction of Fe concentration in an oxidized Au sample as a function of the time the molten metal spent in a 10% H - 90% Ar mixture. The removal of the Fe was gone by Cl2 annealing. 121 followed by a 012 anneal below the melting point to remove any surface Fe introduced in the handling and shaping of the sample. 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