A TEST OF THE FLYNN, BASS, AND LAZARUS THEORY USING QUENCHED PLATINUM Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY JOHN S. ZETTS ' 1971 .Mh ‘~*-~.~_.X, L“! riRY hfifiifig,3§h§§§ University " This is to certify that the thesis entitled A TEST OF THE FLYNN, BASS, AND LAZARUS THEORY USING QUENCHED PLATINUM presented by John S. Zetts has been accepted towards fulfillment of the requirements for . Eh...D_.___ degree in .EhxsmL IMMEW Major professor Date November '12, 1971 I“ amnmo av fE'II HUAB & SUNS I I 9an wow mcI ’4’? I . I .- .i.: .IICHIBIII -I r. _ <».I - ‘J I (0:. v B'NDERS II 4 ABSTRACT A TEST OF THE FLYNN, BASS, AND LAZARUS THEORY USING QUENCHED PLATINUM BY John S. Zetts We have measured the resistance quenched into platinum wires of various diameters using a variety of quench speeds in order to test the theory of vacancy annealing to sinks during a quench proposed by Flynn, Bass, and Lazarus. Fast-quench data were obtained with 16 and 10 mil diameter wires quenched into water and ice water. using two different liquid quenching systems, and with 4 mil diameter wires quenched in air. Variable- quench-speed data were obtained from: a) water, kerosene, helium gas and air quenches on a 16 mil diameter specimen: b) water, air and slow air quenches on 10 mil diameter specimens; and c) air and slow air quenches on a 4 mil diameter specimen. The fast—quench data give an effective vacancy formation energy of Ef = 1.23 i .07 eV for the 16 and John S. Zetts 10 mil specimens and Ef = 1.30 i .05 eV for the 4 mil specimen. These values are substantially lower than the best value of 1.51 eV previously obtained by Jackson. In light of this disagreement, we have examined our fast- quench data with respect to the objections raised by Jack- son concerning previous quenching experiments on platinum, but none of these objections were found to be applicable to the data. Certain data shifts observed in this study, as of yet unexplained, may be partly responsible for this disagreement. Otherwise, we have not been able to deter- mine the source of the disagreement. Analysis of the variable-quench—speed data ac- cording to the theory of Flynn et a1. show them to be con- sistent with the theory for a specimen of any one diameter by each of three tests performed. The analysis yields values for the vacancy motion energy Em which are also found to be dependent upon specimen diameter: Em = 1.55 eV for the 4 mil specimen, and Em = 1.65 eV for the 16 and 10 mil specimens. These values of Em are substantially higher than those commonly obtained from low-temperature annealing studies by Jackson and others. It is found from the John S. Zetts analysis that values of E as high as 1.50 eV are incom- f patible with our variable-quench-speed data and the theory. Because of the disagreement among our data in the values of Ef and Em for all three specimen diameters, we do not consider that the applicability of the Flynn et a1. theory to quenched platinum has been firmly estab- lished. Finally, when the possible effects of quenching strains and vacancy clustering on the data are considered, it is found that any corrections to the data dictated by these considerations would most likely only enhance the differences between our values of E and Em and those f obtained by Jackson. A TEST OF THE FLYNN, BASS, AND LAZARUS THEORY USING QUENCHED PLATINUM BY John 8.7ietts A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1971 ACKNOWLE DGEMENTS I would like to express my deepest appreciation to my advisor, Dr. Jack Bass, for his encouragement and ad- vice throughout the course of this work. Secondly, I wish to thank Dr. Ronald J. Gripshover for many helpful discus- sions, for assistance in taking much of the data, and for designing much of the electrical circuitry used in this study. Also, I would like to thank Mr. Mohsen Khoshnevisan for assistance in taking much of the data and for many helpful discussions, and Mr. Robert Specht for drawing the thesis figures. I am indebted to Dr. J. J. Jackson, Argonne National Laboratories, for several important dis- cussions, for giving me much of his unpublished data, and for sending me an additional 16 mil platinum wire. Finally, I would like to acknowledge the financial support of the Atomic Energy Commission for this research. ii TABLE OF CONTENTS LIST OF TABI‘ES O O I O O O O O O O O O O O O O O 0 LIST OF FIGURES O O O O O O O O O O O O O O O O I I. INTRODUCTION. . . . . . . . . . . . . . . . . The Vacancy Formation Energy, Ef. . . . The Simmons-Balluffi Technique. . . . . Quenching . . . . . . . . . . . . . . . The Relation of Quenching to Annealing and Self-diffusion Experiments. . . . The Theory of Flynn, Bass, and Lazarus. Previous Studies of Quenched Platinum . The Present Experiment. . . . . . . . . II. SPECIMEN PREPARATION AND QUENCHING PROCEDURE. A. B. Specimen Preparation. . . . . . . . . . Quenching Procedure . . . . . . . . . . III. APPARATUS AND ELECTRICAL CIRCUITS . . . . . . A. B. Specimen Holders and Liquid Quenching Sys tems O O O O O O O O O I O O O O 0 Electrical Circuits . . . . . . . . . . iii Page vi 12 15 22 27 3O 30 33 42 42 44 TABLE OF CONTENTS (Cont.) A. V. RESULTS--PART II, A. B. FAST QUENCH DATA . Measurements of the Quench Speed. The Quenched-in Resistance. Experimental Accuracy . Comparison with Jackson's smary O O O O O O O O Quench Speeds . . . . . Quenched-in Resistance. VI. ANALYSIS AND CONCLUSIONS. . . A. The First Test. . . . . The Second Test . . . . The Third Test. . . . . Summary and Discussion. Conclusion. . . . . . . BIBLI OGRAPHY O O O O O O O O O O O APPENDIX A: APPENDIX B: APPENDIX C: DATA SHIFTS. . . . . IMENTS ON PLATINUM. . . . . APPENDIX D: FOR VACANCIES IN PLATINUM . iv SLOWED QUENCH CHANGES IN SPECIMEN PARAMETERS AND THE MAGNITUDE OF LIQUID QUENCHING STRAINS REVIEW OF PREVIOUS QUENCHING EXPER- DEVIATIONS FROM MATTHIESSEN'S RULE Page 53 53 59 68 71 79 81 81 84 92 93 99 101 107 114 116 121 138 143 151 LIST OF TABLES Table Page I. REVIEW OF PREVIOUS WORK ON PLATINUM. . . . . 24 II. ANNEALING PROCEDURES AND RESIDUAL RESIS- TANCE RATIOS (R-RATIOS). . . . . . . . . . 73 III. BEST VALUES OF Ef AND Em DEDUCED FROM FLYNN ET AL. ANALYSIS FOR Q = 2.90 3". o o o e o 101 eff IV. VALUES OF Ef OBTAINED FROM FAST-QUENCH DATA FOR ALL THREE SPECIMEN DIAMETERS. . . 108 V. A LIST OF SEVERAL PERTINENT EXPERIMENTAL QUANTITIES FOR PREVIOUS QUENCHING STUDIES ON PMTINUMO O O O O O O O O O O O O O O O 145 LIST OF FIGURES Figure Page 1. RESISTANCE QUENCHED INTO 0.016" DIAMETER GOLD WIRES AS A FUNCTION OF QUENCH TEMPERATURE AND QUENCHING SPEED. . . . . . 18 2. LIQUID QUENCH SYSTEM I AND ASSOCIATED SPE CIMN HOLDER O O O O O O O O O O O O O O 3 7 3. LIQUID QUENCH SYSTEM II AND ASSOCIATED SPECIMEN HOLDER. . . . . . . . . . . . . . 38 4. BLOCK DIAGRAM OF CIRCUITS. . . . . . . . . . 46 5. BLOCK DIAGRAM OF AC CIRCUITS . . . . . . . . 49 6. SLOW AIR QUENCH CONTROL SYSTEM . . . . . . . SO 7. COOLING CURVES FOR 16 MIL WIRES QUENCHED INTO WATER AND KEROSENE. . . . . . . . . . 54 8. VARIATION OF INITIAL QUENCH SPEED, T, WITH QUENCH TEMPERATURE T FOR 16 AND 10 MIL WIRES QUENCHED INTO EATER AND ICE WATER. THREE OF JACKSON'S DATA POINTS HAVE BEEN INCLUDED FOR COMPARISON. . . . . . . . . . 56 9. RESISTANCE QUENCHED INTO 16 MIL WIRES FOR WATER QUENCHES USING 081 AS A FUNCTION OF INVERSE QUENCH TEMPERATURE. . . . . . . 60 10. RESISTANCE QUENCHED INTO 16 MIL SPECIMENS FOR WATER.QUENCHES USING QSII COMPARED WITH THAT OF 081 . . . . . . . . . . . . . 62 vi LIST OF FIGURES (Cont.) 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. COMPARISON OF RESISTANCE QUENCHED INTO 16 MIL SPECIMENS FOR WATER AND ICE-WATER QUENCHES WITH QSII . . . . . . . . . . . . COLLECTED QUENCH DATA FOR NINE 16 MIL SPECIMENS QUENCHED INTO WATER USING QSI (LINE A, 3 SPECIMENS) AND QSII (LINES B THROUGH F, 6 SPECIMENS). JACKSON'S WATER QUENCH DATA (LINE J) HAS BEEN INCLUDED FOR COMPARISON . . . . . . . . . . . . . . . . RESISTANCE QUENCHED INTO 10 MIL WIRES FOR WATER QUENCHES USING QSII. AIR AND FLOW- ING AIR QUENCHES WITH THE SAME SPECIMENS HAVE BEEN INCLUDED FOR COMPARISON. . . . . COOLING CURVES FOR A) AN AIR QUENCH WITH A 10 MIL SPECIMEN AND B) A SLOW AIR QUENCH WITH A 4 MIL SPECIMEN. . . . . . . . . . . VARIATION OF THE INITIAL QUENCH SPEED T WITH QUENCH TEMPERATURE Tq FOR AIR QUENCHES WITH 4, 10, AND 16 MIL SPECIMENS . . . . . VARIATION OF THE INITIAL QUENCH SPEED T WITH QUENCH TEMPERATURE Tq FOR SLOW AIR QUENCHES WITH A 10 MIL SPECIMEN. . . . . . RESISTANCE QUENCHED INTO A 16 MIL SPECIMEN AS A FUNCTION OF QUENCH TEMPERATURE AND QIIENCH SPEED O O O O O O O O O O O O O O O RESISTANCE QUENCHED INTO A 10 MIL SPECIMEN USING WATER, AIR, AND FIVE SLOW AIR QUENCH SPEEDS o o o o o o o o o o o o o o o RESISTANCE QUENCHED INTO TWO 10 MIL SPECI- MENS USING AIR, FLOWING AIR, AND 3 SLOW AIR QUENCH SPEEDS. . . . . . . . . . . . . RESISTANCE QUENCHED INTO A 4 MIL SPECIMEN USING AIR AND 5 SLOW AIR QUENCH SPEEDS . . vii Page 64 65 67 82 83 85 86 88 89 90 LIST OF FIGURES (Cont.) 21. 22. 23. 24. 25. 26. 27. 28. DETERMINATION OF Em FOR ASSUMED VALUES OF Ef FOR A 16 MIL SPECIMEN USING THE FLYNN ET ALO ANALYSIS O O O O O O O O O O O O O O DETERMINATION OF Em FOR ASSUMED VALUES OF Ef FOR A 10 MIL SPECIDdEN . o o o o o o o . DETERMINATION OF Em FOR ASSUMED VALUES OF Ef FOR A 4 MIL SPECIMEN. o o o o o o o o e VALUES OF Em DEDUCED FROM FLYNN ET AL. ANALYSIS VERSUS ASSUMED VALUES OF Ef FOR ALL THREE SPECIMEN DIAMETERS . . . . . . . FRACTIONAL QUENCHED-IN VACANCY CONCENTRATION c/c VERSUS DqT rq FOR A 16 MIL SPECIMEN USING Ef = 1.25 eV, Em ='l.65 eV, AND Q.= 2.90 eV. . o o . . o a o o o o o O a o FRACTIONAL QUENCHED-IN VACANCY CONCENTRATION C/c VERSUS DqTqTq FOR A 10 MIL SPECIMEN USING E = 1.25 eV, Em = 1.65 eV'AND Q=2.9UeV................ FRACTIONAL QUENCHED-IN VACANCY CONCENTRATION c/c VERSUS Dqthq FOR A 4 MIL SPECIMEN USING Ef = 1.35 eV, Em = 1.55 eV AND 0 = 2.90 eV. CURVES LABELED C AND S COR~ RESPOND TO FLYNN ET AL. THEORETICAL CURVES FOR VACANCY LOSS TO CYLINDRICAL AND SPHERICAL SINKS, RESPECTIVELY. . . . . . . THE RESISTANCE QUENCHED INTO GOLD AND PLAT- INUM WIRES AS A FUNCTION OF BOTH THE MEASURING TEMPERATURE AND INVERSE KELVIN QUENCH TEMPERATURE. THE DASHED LINES INDICATE THE RANGE OF QUENCHED-IN RESIS- TANCES PREVIOUSLY OBTAINED BY BASS (1964) ON GOLD AND IN THE PRESENT STUDY (SECTION IV) ON PLATINUM. . . . . . . . . . . . . . viii Page 94 95 96 100 103 104 105 155 I . INTRODUCTION A. The Vacancy Formation Energy, Bf The simplest point defect in metals is the lattice vacancy, a site in the perfect lattice from which an atom is missing. It is now well established that substantial concentrations of lattice vacancies are present in thermal equilibrium in metals just below their melting point. The fractional concentration, CV, of vacancies present at the absolute temperature T is described in terms of a quantity known as the vacancy formation energy, Ef, by (1): _ '3 /kT I . Cv — A e f . [1] Here k is Boltzmann‘s constant, and A is a constant of order unity determined by the entropy increase per va- cancy. Reasonably accurate values for cv and Ef have now been established for a number of fcc metals. Ef is found to be about 1 eV (electron volt), and cv at the 1 melting temperature is typically between 10.4 and 10-3. The two most important techniques for establishing these values have been: 1) the method of Simmons and Balluffi (2); and 2) quenching. With the method of Simmons and Balluffi, one measures cv directly. But the measurements are rarely sensitive enough to yield accurate values for E Measurements made after quenching are very sensitive f. to the presence of vacancies, but they do not measure cv directly, and can be plagued by systematic errors. To- gether these techniques have produced reliable results for a number of fee metals. Unfortunately, little is yet known about cv and Ef in bcc transition metals, which have recently been produced in sufficiently pure form to be studied. Be- cause of their high melting temperature, they cannot yet be studied with the Simmons-Balluffi technique (see sec- tion B below). This leaves only quenching. But we do not yet know enough about the importance of systematic errors in quenching experiments to be able to say that the results obtained are always reliable. And if we are to interpret data obtained with bcc metals correctly, we must know the conditions under which quenching studies yield reliable data. The most general theory which has been used to correct for systematic errors occurring in quenching studies is the theory of Flynn, Bass, and Lazarus (3), which deals with the loss of single vacancies to sinks during a quench. However, this theory has never received a truly rigorous test. It is the intent of this thesis to rigorously test this theory with quenching data ob- tained using platinum, a metal which, according to pub- lished data, should be well described by the theory. In the following sections, we first discuss the Simmons-Balluffi and quenching techniques in more detail. We then describe the method of Flynn, Bass and Lazarus, and review the previous quenching studies on Pt. Fi- nally, we outline the specific goals of this thesis. B. The Simmons-Balluffi Technique The Simmons-Balluffi technique involves measure- ments upon a sample in thermodynamic equilibrium, in which the concentration of vacancies is representative of the temperature at which the measurement is made. In theory, one could determine cv(T) by measuring any property of a metal in thermodynamic equilibrium which is affected by the presence of vacancies; e.g. electrical resistance, specific heat, sample length, etc. In most cases, how- ever, one does not know with sufficient accuracy just how this property should behave in the absence of vacancies (4). In 1959, Simmons and Balluffi (2) showed that a combination of two particular sets of measurements would allow cv(T) to be determined, without knowledge of how either property behaved in the absence of vacancies. They showed, for a cubic crystal containing small concentra- tions of randomly distributed vacancies and interstitials, that cv(T) - CI(T) = 3[AL(T)/Lo - Aa(T)/ao]. [2] Here cI is the fractional concentration of interstitials (atoms located at positions other than normal lattice sites), and AL/Lo and Aa/ao are the fractional increases in the macroscopic length and microscopic lattice parameter of the metal, respectively, as its temperature is raised from room temperature to the temperature T. Lo and a0 are therefore the values of L(T) and a(T) at room temperature. Since at high temperatures CI is nor- mally much less than Cv(2), equation 2 can be used to determine cv(T). If cv can be accurately measured over a finite temperature range, this technique can be used in conjunction with equation (1) to obtain Ef. From eqn 1 we see that a plot of the natural logarithm of c§-— 1n cv--against inverse temperature-~l/T--will yield a straight line with slope -Ef/k. Unfortunately, the use of this technique is presently limited by the sensitivity with which Aa/ao can be measured (about 1 x 10-5--Corresponding to a sen- sitivity of a few percent of the vacancy concentration at the melting point), and by the difficulty of main- taining high temperatures sufficiently constant and uniform along the specimen to produce reliable data. The second difficulty has limited application of the technique to metals which melt below 1100°C (it has thus 225;been applied to platinum). The first has limited direct determinations of Ef to very few metals (e.g. Al (9), and perhaps Pb (6), Na (7), and Au (8)). Even in these cases the uncertainty in Ef varies from at least 5% to above 10%. Thus this method has not yet been able to provide accurate values for E However, it has: f. 1) provided values for Cv at the melting temperature accurate to 5 or 10%; 2) demonstrated unequivocally the existence of vacancies and their dominance at high tem- peratures over interstitials; and 3) helped to confirm the general validity of other techniques for studying the properties of vacancies, particularly "quenching." To obtain greater sensitivity in measurements of E it is necessary to turn to other techniques. Pres— fl ently, the most sensitive method for detecting vacancies involves measuring the electrical resistance of a quenched metal at very low temperatures (typically 4.2K). We now describe this method in detail. C. Quenching Quenching involves cooling a metal rapidly from a high temperature to a low temperature at which vacancies are immobile. If the metal can be cooled rapidly enough, such that a substantial fraction of the vacancies ini- tially present in equilibrium are trapped in, then the "quenched-in" vacancies can be studied at low tempera— tures. In the last 19 years, many studies have served to demonstrate the validity of quenching as an experimental technique for studying the properties of vacancies. It is now clear that, provided sufficient care is exercised. and work is confined to samples of sufficient purity, quenching studies can provide reasonably reproducible re- sults, which yield important information concerning the properties of vacancies. In principle, the concentration of vacancies re- tained in a quenched sample could be measured directly using the field-ion-microscope, or a variation of the Simmons-Balluffi technique. If the vacancies can be caused to conglomerate into large Clusters, they can also be detected with the electron microscope. In practice, each of these procedures suffers from experimental diffi- culties, and they have not yet been able to yield reliable quantitative results. Most published studies have involved measurements of quantities which are proportional to the vacancy concentration, particularly the low temper- ature resistivity of quenched samples. In this case, one assumes that p = p.c . [3] where pi is the resistivity of a unit concentration of single vacancies. Measurements of electrical resistivity at 4.2K allow fractional vacancy concentrations as small as 10'.8 to be detected. This corresponds to a sensitiv- ity of better than 0.01% of the vacancy concentration at the melting temperature. If a specimen could be cooled rapidly enough to trap in all of the vacancies initially present at the quench temperature Tq, then, from equations (1) and (3), pv(Tq) would be given by e-Ef/kTq pv(Tq) = 01A [4] In practice, even with the fastest attainable quench speeds one usually expects some vacancy loss during the quench: the largest fractional losses occurring for the highest quench temperatures. In this case, the variation of pv(Tq) with Tq would not reproduce eqn (4) exactly, and a plot of ln pv(Tq) vs. l/Tq would, in general, not yield a straight line.. However, one can determine at least a lower limit to Ef by fitting a straight line to the lowest quench temperature portion of the data, where the fractional vacancy loss is smallest. In this case it would be more accurate to describe the slope of this line . . . eff , In terms of an effective formation energy, E , which f may not be equal to Ef. In order to determine Ef, it is necessary to correct for vacancy loss during the quench. In principle, this can be done by quenching the specimen with a series of quench speeds, and then extrapolating the data to “infinitely fast" quench speed. However, the validity of such extrapolations can be affected by two experimental difficulties inherent in quenching; l) va- cancy complexing, and 2) quenching strains. 1) vacancy complexing: Since vacancies in fcc metals are known to attract each other (9), some vacancies will be present in equilibrium in the form of small va- cancy clusters. Because of the increasing stability of 10 these Clusters at lower temperatures (10), their number and size are likely to increase substantially during quenching, especially for slow quenches from high temper- atures. If the number of vacancies present in the form of clusters becomes a significant fraction of the total, then their presence may affect the experimental results obtained. For example, if the resistivity of a vacancy pair (di-vacancy) differs from the sum of the resistiv— ities of two isolated vacancies, then the total resis- tivity will not accurately reflect the total vacancy concentration. Also, if small vacancy clusters are more mobile than single vacancies, then vaCancy loss during the quench will be increased. These effects cannot be taken into account without detailed knowledge of the properties of small vacancy Clusters. 2) quenching strains: If a specimen is strained during the quench, three effects can result: 1) the geometry of the specimen will change, leading to a change in its electrical resistance (a change which has no rela- tion to the presence of vacancies); 2) new defects can be created: and 3) new sinks (annihilation centers for 11 vacancies) can be created. The occurrence of any of these three effects during the quench would Change the resis- tance of the quenched specimen relative to the value it would have had if no strain had occurred. Unless the magnitude and the effect of any such strain were known, it would be impossible to relate the experimental data to the vacancy concentration at the quench temperature Tq' Fortunately, it appears to be possible, with care and proper experimental design, to keep the effects of quenching strain small. The same cannot be easily said about the problems of vacancy loss and vacancy Clustering, both of which are intrinsic to the quenching process. However, if one has a metal in which vacancy Clustering should be negligible (e.g. if the interaction between vacancies is small, so that few clusters form), then one can deal with the prob- lem of vacancy loss. We will discuss how in the section devoted to the Flynn, Bass, Lazarus theory. Before doing this, we digress slightly, to discuss two types of exper- iments of importance for our later discussion. 12 D. The Relation of Quenching to Annealing and Self—diffusion Experiments Thus far, we have discussed only one of the important quantities associated with the presence of vacancies in a metal, namely the vacancy formation energy, E Two other f. quantities of equal significance are the vacancy motion energy, Em, which is the energy required for vacancy migra- tion through the crystal: and the activation energy for self-diffusion, Q, which is the energy required for atomic migration through the crystal. Atomic diffusion in the fcc metals is known to occur by means of vacancies. Therefore, if only single vacancies contribute to diffu- sion, the activation energy for self—diffusion, Q, should equal the sum of the single vacancy formation and migra- tion energies (4) Q=E+E. [5] Thus, if one knows any two of the above quantities, one can use eqn 5 to determine the third. Since our primary concern in this thesis is with the determination of Ef, we shall discuss only briefly the methods used for 13 determining Em and O. For more detailed discussions we refer the reader to articles by Seeger and Mehrer (4) and by Chik (ll). Estimates of the vacancy motion energy Em are usually deduced from annealing experiments on quenched samples. In these experiments, one introduces a concen- tration of vacancies into a metal by quenching, and then raises the temperature of the sample to a region where vacancies become mobile. By studying the manner in which the quenched-in vacancies anneal away, one can determine the activation energy for the annealing process (12, 13, 14). The major difficulty with these experiments is one of interpretation: substantial vacancy clustering is likely to occur during the relatively low temperature anneals. Thus the activation energy determined for such a process will represent an average value for all the mobile entities involved-~single vacancies, di-vacancies, etc.,--which, in general, will have different motion energies. Values for Q are usually obtained from measure— ments of the diffusion of radioactive tracer atoms through 14 a sample of the same chemical species (tracer self- diffusion). The interpretation of such experiments in terms of eqn 5 may not be straightforward if other me— chanisms besides the diffusion of single vacancies through bulk material contribute to the diffusion pro- cess. For example, Seeger and Mehrer (4) point out that contributions from di-vacancies or diffusion "short cir- cuits” can lead to values for Q which differ appreciably from Ef + Em. In addition, they suggest that both Ef and Em may be functions of temperature. In this case, even if diffusion takes place solely by means of single va- cancies, eqn 5 would hold only if all quantities were measured at the same temperature. By proper care and experimental design, the problem of "short circuits" can be avoided. Because of the high temperatures at which diffusion experiments are performed, the contribution due to di-vacancies and larger Clusters is usually not substantial. The variation of Ef and Em with tempera— ture has yet to be conclusively demonstrated. For these reasons, it is very likely that eqn 5 will represent at least an excellent approximation to reality for most 15 metals. It should therefore be very useful as a means of correlating the results of quenching experiments (which attempt to measure Ef) with those of annealing and self-diffusion experiments (which attempt to measure E. and Q, respectively). In the following discussion we shall assume eqn 5 to be valid. E. The Theory of Flynn, Bass, and Lazarus While the usual aim of quenching experiments is to trap in the maximum number of vacancies by using the fastest obtainable quenching rates, the possibility of deliberately varying the quench speed in order to obtain further information was originally suggested by Bauerle and Koehler (12). This procedure was later carried out by Mori, Meshii and Kauffman (15), who, using a semi- emmdrical extrapolatation technique, attempted to compensate for vacancy losses during the quench and thereby obtain a better estimate for the vacancy formation energy Ef. A more rigorous approach to this problem was developed by Flynn, Bass, and Lazarus (3), who solved the vacancy 16 diffusion equation for the case of single vacancies mi- grating to fixed sinks during a quence in which the spe- Cimen temperature decreases linearly with time (linear quench). They found the fractional loss of vacancies during the quench to depend only upon the product DqTqTq' where Dq is the vacancy diffusion coefficient at the quench temperature Tq' and Tq is the time for the sample temperature to fall linearly to 0 Kelvin. The importance of this result is that it establishes a relationship be- tween the two quantities Em and Ef in terms of the ex- perimental data. Given the experimental data and a known value for E , the theory determines a unique value for f Em' In this case the sum Ef + Em can be compared to Q, and agreement would constitute a strong argument for the validity of the theory. This is the test we would like to apply in this thesis. If, on the other hand, neither Ef nor Em is known, the theory can still be combined with the experimental data and with eqn 5 to yield values for both quantities. However, the assumption of the validity Of eqn 5 at the beginning of the process precludes its later use as a test of the Flynn et a1. theory. It is 17 this second procedure which has been used in previous applications of the theory to Au, A1, and W. The method of application is as follows. Experimental data are obtained by quenching the sample over a range of quench temperatures for a series of quench times. For each quench time, the data consist of a series of points lying on a curve extending from the lowest quench temperature to the highest. Figure 1 shows such data for Au (16). Here, the vacancy resis- tance quenched into the specimen, divided by the speci- men's resistance at room temperature, is plotted against the inverse Kelvin quench temperature. The quenching speed was varied by quenching the specimen into four different liquids and in air. The analysis begins with the empirically veri- fiable assertion that the smallest vacancy losses should occur for rapid quenches from low temperatures. This can be easily seen in Figure l, where the three fastest quench speeds yield nearly indistinguishable data for quench temperatures below 600°C. Thus it appears that at these temperatures essentially the equilibrium 18 TI°CI l050 [IOOO 900 300 700 600 500 450 5 r T T T F T I I r- --I _. v _09| O ICED BRINE _ ' ' o ‘ o 20 0 WATER I“ "‘ . ' GLYCOL 7 ° A ACETONE I __ v AIR _ I. .. I—- -—4 e -I a _. 3" _. I a? 9 3 d a: _. IO :- A i - A -I _ 4 v v ' V I'- V V -1 v V -— v -—I -2 I0 _— -_j C i —- 4 I— -« “'53 l 1 1 1 1 1 0.70 0.80 0.90 [00 I I0 I20 130 L40 I 103 T(°KI FIG. l.—IESISTPNCE GENOIED INTO 0.016" DINETER (11D WIRES AS A HMKN (F GIENGI TEI‘FERATUIE MD QENCHING SPEED. 19 concentration of vacancies is being trapped in during the quench. From eqns 1 and 4 we see that an assumed value for Ef will then specify a straight line in figure 1, which passes through the low temperature, fast-quench data. For each such line, the data determine a series of quench temperatures Tq, one for each quench time Tq, at which a given fraction of the vacancies are lost during the quench. For quenches characterized by linear cooling curves, the theory leads to the equation D T T = Z = Constant [6a] or D=ZT q /( qTq) [6b] Since for the motion of single vacancies (4) Dq = Doesp(-Em/kTq), we obtain, D e (-E /kT I = Z/(T T ). (7) 0 xp m q q q Thus a plot of ln(thq)-1 against l/Tq should yield a straight line whose slope is -Em/k. If a straight line is indeed obtained, the theory passes its first test. In this manner a value for Em is associated with each 20 assumed value for Ef. The "best value" for each quantity is obtained by requiring that their sum equal Q (see eqn 5). Once these values are obtained, the theory can be subjected to its final test by plotting the fractional vacancy loss for all quench times and quench temperatures against the product DqTqrq. The result should be a single curve containing all of the experimental data. In the three experiments on Au, Al, and W, the theory passed both the first test and this final test. In its initial application, to gold (3), the theory yielded the values Ef = 0.98:0.02 eV and Em = 0.83:0.04 eV, for Q = 1.81 eV. The present consensus is that these are still reasonable values, although the true value for Ef may be slightly smaller, and for Em slightly larger (17, 18, 19). However, Seeger and Mehrer (20) recently Challenged this consensus with a reanalysis of Simmons-Balluffi and Self-Diffusion Experiments. They obtained the values Ef = 0.87 eV and Em = 0.89 eV, with Q = 1.76 eV. In order to rationalize the disagreement with the results obtained using the Flynn et a1. theory, they suggested that the extrapolation might have suffered 21 from a systematic error associated with increasing quenching strain as the quench speed increased. In its application to aluminum (21), the theory yielded the values E = 0.71 eV and Em = 0.77 eV for f Q = 1.48 eV. Subsequently, the accepted value for Q was lowered to about 1.35 eV (22), a value too low to be reconciled with both the theory and the experimental data. In its application to tungsten (23), the theory yielded the values Ef = 3.6 I 0.2 eV and Em = 2.5 i 0.5 eV. There presently exist no alternatives to these values. The most serious deficiency of the Flynn et a1. theory is that it does not take into account vacancy Clustering during the quench. Recent calculations sug- gest that such clustering can be very important in metals in which the binding between vacancies is large if small vacancy complexes are substantially more mobile than single vacancies. For example, Perry (24) shows that if the binding energy between two vacancies Eiv is as large as Ef/4, and Riv/E; = 0.7, then for a quench from 500°C and a sink density of 108 lines/cmz, the vacancy 22 loss is about 10% greater for a quenching rate of 104K/sec, and 40% greater for a quenching rate of 103K/sec than if there were no binding between vacancies. These are certainly significant effects, and may be the reason for the failure of the Flynn et a1. theory to yield satisfactory results for aluminum. F. Previous Studies on Quenched Platinum The study of vacancies quenched into platinum has been the subject of a number of investigations over the last 15 years. Only two other metals, gold and aluminum, have been studied more extensively. As with gold and aluminum, platinum has several advantages for quenching studies: it does not oxidize appreciably except at temperatures very near the melting point: it is not a strong absorber of gases; and it can be refined to high purity. In addition, because of its rather high melting point (1774°C), a measurable concentration of vacancies can be quenched into.it over a larger.range Of tempera- tures than with either gold or aluminum. 23 In the following we shall briefly review the re- sults of previous studies of vacancies in platinum, in order to show the status of the field at the time the present study was begun. In this section we shall take reported results at face value. A more critical and extensive review of these results is given in Appendix C. Table I summarizes previous work on platinum. Between 1955 and 1961 there were seven studies. The six quenching studies all yielded values for Ef between 1.2 and 1.4 eV. The one study of high temperature electrical resistance and specific heat yielded a value in the vicinity of 1.6 eV.* The quenching and annealing studies yielded values for Em varying from 1.1 to 1.5 eV. Al- though the sum of the maximum values obtained for Ef and Em is approximately equal to the activation energy for self-diffusion, Q = 2.9 eV, it is interesting, and per- haps significant, that no single investigator obtained values for E and Em whose sum was this large. Then, in f 1964, Misek (30) reported obtaining the values Ef = 1.24 eV *As suggested in section B, these experiments are usually unreliable. For a discussion of their pros and cons see refs (4) and (41). 24 TABLE I REVIEW OF PREVIOUS WORK ON PLATINUM Bf 8V E E+E m f m ev 8V Investigators Ref. A. Quenching and annealing experiments using electrical resistance measure- 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) Rants .' 1.2 l.4i;l 1.23 1.21.04 1.24 1.42 1.511.04 1.46:.02 Other Mbthods Er ev 1.4 1.6 1.1 2.3 1.2i.1 2.6 1.42 2.65 1.48i.08 2.68 1.13 1.7 2.94 1.38:.05 2.89 1.38:.05 2.84 1.50 1.33:.05 1.35:.05 Property Measured Thermoelectric force High-temperature electrical resis- tance and specific heat Selfhniffusion experiments Q ev 2.96:.06 2.89:.04 Lazarev and OvCharenko (1955) Bradshaw and Pearson (1956) Ascoli 9551;. (1958) Bacchella gt 9.1: (1959) Piercy (1960) MiSek (1964) Kopan (1965) Jackson (1965) Baumgarten gt_al, (1968) Polék (1968) Schumacher _e_t‘;§_l_. (1968) Rattke 31-; 91. (1969) Gerstriken and Novikov (1961) Kraftmaker (1965) and Lanina Kidson and Ross (1957) Cattaneo 213. g. (1962) 25 26 27 28 29 3O 31 32 33 34 35 36 37 38 39 4O 25 and Em = 1.7 eV, whose sum is 2.94 eV. A year later, Jackson (32) obtained the substantially different values Ef = 1.51 eV and Em = 1.38 eV. He proposed a consistent interpretation of nearly all the existing data based upon the propositions that the value Em = 1.1 eV (usually ob- tained from anneals after quenches from high tempera— tures) corresponded to the motion energy for di-vaoancies Eiv, and that the value Em = 1.4 eV (usually obtained from anneals after quences from lower temperatures) corresponded to the motion energy for single vacancies. He argued that earlier investigators had obtained values for Ef less than 1.5 eV because of systematic errors associated with the experimental conditions under which their data were obtained (see section IV-D for further discussion of this point). Jackson interpreted his data in terms of a vacancy-vacancy binding energy Egv of 0.4 eV, approximately 25% of Ef. Subsequent experiments tended to confirm Jackson's values for Ef and Em' and they became the accepted values for platinum. Only his . 2v . estimate for Eb was challenged: the most recent estimate being E2 bv = 0.1 eV, as proposed by Schumacher et a1. (35). 26 Qualitative support for this lower binding energy comes from a number of studies which suggest that fewer large vacancy clusters form in platinum than in Al, Cu, or Au. Quenching studies indicate that only a very small frac- tion of the original quenched-in resistance remains after high temperature quenches and subsequent low temperature anneals. This probably means that the vacancies are annihilating, rather than forming clusters. Also the number of jumps made by a typical vacancy during anneal- ing appears to be much greater than those made in other fcc metals (32). This suggests that the vacancies are traveling all the way to fixed sinks. More directly, electron microscope studies of quenched platinum reveal much smaller clusters formed after quenches from high temperatures and subsequent annealing than in the metals Cu and Al (42, 43). Finally, preliminary results of a Field-ion-microscope study of quenched platinum (44) seem to show few di-vacancies in the quenched material. At the time the present study began, it thus appeared that the value for E lay between 1.45 and f 1.55 eV; that the value for Em lay in the vicinity of 27 1.4 eV: and that Egv was only a small fraction of E f. From Jackson's results, it appeared that a reasonably accurate value for Ef could be obtained from low temper- ature quenching studies without resort to extrapolation, since he reported that for quenching temperatures below 1000°C he was able to trap in essentially all of the vacancies initially present in thermal equilibrium. Platinum thus appeared to be an ideal metal in which to test the Flynn, Bass, and Lazarus model of vacancy loss during a quench, and thereby to obtain a still more accurate value for Bf (and thus also for Em). G. The Present Experiment The present experiment was designed to provide a more rigorous test of the Flynn, Bass, and Lazarus model than had heretofore been made. The experiment was envisioned as follows: 1) Reproduce Jackson's low temperature quenching data, and thus his best estimate for Ef, using the fastest obtainable quenching speeds. 2) 3) 4) 28 Vary the quench speed by quenching wires of dif- ferent diameters in various liquids, in helium gas, and in air. Agreement between data obtained under these different conditions would tend to refute Seeger's objection that the method of ex- trapolation was invalidated by quenching strains, since the quenching strains are different for the different quenching methods. Use the value of Ef determined at low temperatures in conjUnctiOn with the Flynn et a1. theory to determine a value for Em. Test whether these two values yield results in agreement with the pre- diction that the data should be a unique function of the product D T T . q q q See whether Em + Ef = Q. Agreement with this re- sult in addition to all the previous requirements would demonstrate that Perry's objection was not important for platinum--that the effects of va- cancy clustering were small. 29 If all of these conditions were satisfied, we would take it as evidence that the Flynn et a1. theory was adequate to describe Pt, and that it was thus worth applying to any metal in which vacancy-vacancy binding was not large. Unfortunately, despite hard and sustained ef- fort, we were never able to reproduce Jackson's low temperature quenching data. All of our data suggested a value for Ef considerably smaller than 1.5 eV. There- fore in steps 3 and 4 we have used both Jackson's value, E = 1.5 eV, and our own value E = 1.24 eV to test the f f theory. We describe the results obtained below. II. SPECIMEN PREPARATION AND QUENCHING PROCEDURE A. Specimen Preparation All specimens used were hard-drawn 99.999% pure platinum, obtained from the Sigmund Cohn Corporation. The specimens were mounted in holders described in sec- tion III and platinum potential leads of the same nom- inal purity were spot-welded onto them. For specimen diameters of 0.016", 0.010”, and 0.004", the potential leads were respectively chosen to be 0.002", 0.002" or 0.0006”, and 0.0006" in diameter. The overall length of the specimen varied from 3 to 5 inches, and the gauge length, determined by the separation of the potential leads, varied from 1 to 2 inches. The potential leads were placed as far apart as possible, consistent with good temperature uniformity along the gauge length. After mounting on the holder, the specimens were resistance-heated in air and given an initial anneal to 30 31 promote grain growth, to minimize the dislocation den- sity, and to generally remove the effects of drawing. For the 16 mil (0.016“) specimens, this originally con- sisted of one half to one hour at 1600°C, 10 hrs. at 1400°C, and 10 hrs. at 800°C, followed by half hour steps of 100°C each down to 500°C. This anneal produced a re- sidual resistance ratio, eratio (the specimen's resis- tance at 20°C divided by its resistance at 4.2K) of 5000 or greater. It was later found that the high tempera- ture annealing times could be reduced by more than one half with little or no change in the resulting R-ratio. A similar annealing procedure was initially used for the 10 mil (0.010") specimens and produced Rrratios of about 9000. However, as the long anneal at high temperature produced substantial stretching and thinning of the specimens, a shorter anneal was later adopted. It consisted of a few minutes at 1400°C and a few hours at 900°C, followed by slow cooling. This produced Rrratios in the vicinity of 4000. An even more restricted annealing procedure had to be used for the 4 mil (0.004") wires. It was discovered 32 that annealing at temperatures greater than about 1250° for more than a few minutes produced quite low R—ratios-- in the vicinity of 250. However, anneals consisting of a few minutes at 1200 to 1000°C, and then a few hours at 800°C, produced R-ratios greater than 3000. (This phe- nomenon is discussed further in Appendix A.) In addition to these initial anneals, all spe- cimens were periodically given a cleansing anneal to produce a vacancy-free state. (The resistance in this state is called the "vacancy-free base resistance.") For the larger wires this anneal usually consisted of about 1 hour at 800°C, followed by slow cooling. For 4 mil wires the anneal consisted of about 1/2 hour at 800°C, followed by slow cooling. Longer anneals at temperatures above 1000°C were sometimes necessary-for 16 and 10 mil specimens which had been liquid-quenched from high temperatures. Especially in the latter case, it was not always possible to exactly reproduce the pre- quench vacancy-free base resistance, which usually showed a small increase. 33 B. .Quenching Procedure 1. Room Temperature Measurements Prior to quenching one must accurately determine the specimen's resistance at room temperature and at liquid helium temperature (4.2K). For the room tempera- ture measurements the specimen was placed in a large, draft-free plexiglass box and a known current (small enough to avoid heating) was passed through it. The voltage drop across the gauge length was measured on a precision potentiometer. Simultaneously, the air tem- perature in the box was measured with a mercury ther- mometer. The resistance at 20°C was then determined from the formula R R(T) 20 l+aAT where R(T) is the resistance at room temperature T; AT is the difference between room temperature and 20°C, and a is the temperature coefficient of resistance for plat- inum (3.9 x 10-3/°C). 34 2. Liquid Helium Measurements Before and after quenching, the specimen was im- mersed in liquid helium, and a known measuring current (usually 1 ampere) passed through it. The value of the measuring current was accurately determined by measuring the voltage drop across a 19 standard resistor in series with the specimen. This voltage, and that across the specimen gauge length, were simultaneously measured on precision potentiometers. The measuring currents were chosen to cause no measurable heating of the specimen in liquid helium. To eliminate the effects of slowly varying thermal voltages, reversing procedures were used for both the room temperature and liquid helium measure- ments. 3. Quench-Temperature Determination All specimens were resistance heated, and their temperatures just prior to quenching were determined from the ratio R(Tq)/R20, where R(Tq) is the resistance at quench temperature Tq. R(Tq) was determined by 3S simultaneously measuring the voltage across the specimen gauge length and across a standard resistor (either 0.01 or 0.0019) in series with the specimen. The quench temp- erature-Tq was then calculated from the National Bureau of Standards values for the resistance of platinum as a function of temperature (45). Before quenching, all wires were examined for temperature uniformity along the gauge length. Since the specimens were visibly glowing at all but the very lowest quench temperatures, any large temperature variations along the gauge length could be easily detected. If such temperature variations were observed, the specimen was either discarded or the positions of the potential leads were changed until a gauge length with satisfactory tem- perature uniformity was obtained. 4. Quenching Procedure a. The Vacancy-free Base After the initial anneal, the resistance of the specimen was measured at room temperature and at 4.2K. 36 The specimen was then given a few, short, low-temperature anneals and air-quenched several times from 500°C (where the equilibrium concentration of vacancies is too small to be measured). After each series of anneals and/or air quenches, the resistance at 4.2K was measured. Only after a sufficiently stable resistance at 4.2K had been obtained, was the specimen ready to be quenched. The stabilized resistance at 4.2K was used as the "vacancy-free base re- sistance,“ RB' b. Liquid Quenches For liquid quenches (water or kerosene) the spe- cimen was mounted in one of the two holders shown in figures 2 and 3, and placed with the axis of the wire parallel to the surface of the liquid and from l/4 to 1 inch above it. The specimen was resistance heated with direct current and the quench temperature determined from its resistance as described above. With the heating current maintained constant, the specimen was plunged well into the liquid using one of the quenching systems shown in figures 2 and 3. Simultaneously, the voltage 37 .5 zwauwn 8.53 2 ~ 555 an 283....N é...— magna cziozmao 1.20 :uzwao 2.2. zwgowdm 02.02.; con. man.— >>zoo 5:224 M Fzmmmao 0 A2 04 We 5.24.5200 «Eu: 8 o s 04 m WEE 50> 44.50. 0 50 .555 4958 65.5 m2 Edie 6E v\||.:30~:u m>w133a OZ_P_ 0.5 SEC/CM cr .fij<1 EEt: " 83 c9 41ML 33 3 SLOW AIR QUENCH U) 5) Tq=III6°C IIIllIllIL 1 SEC/CM TIME (CM) FIG. 11). —-OI].IIGC1R\£SRR A) MAIRGBCHHIlI-IAIDNIL 513151211911“) B)ASLOIIAIRQBGIHTTHAIIMILSIICIIEN. 1' A1R QUENCH _ SPEEDS +_ 4MIL 10 MIL 10° :- I. . 16 MIL h 0 LL.) I" Q 9 V 01-— _ 2 1 1_ 1 fiL_ 1 '0 L—‘S‘éff 1100 1300 7500 Tel (°C) F16. 15. ~WIKTIOHFTI£1NITIAQBOISEEDTHDHQBDIMTOHRAIRWB HITHQ.ID.N016HILSFECIFB1S. 84 taking the tangent to the initial part of the original quench curve. A typical cooling curve for a slow air quench of a 4 mil wire is shown in figure 14b. These quench curves could be well represented by a straight line extending for about one half of the total temperature drop. This essentially linear behavior characterized all five slowed- air quench settings used with the 10 mil and 4 mil spe- cimens. The dependence of the initial quench speed upon quench temperature for five separate slow-quench settings with a 10 mil specimen is shown in figure 16. A similar temperature dependence was observed for slow air quenches with 4 mil specimens. B. Quenched-in Resistance 1. 16 mil Data--Slowed Liquid and.Gas Quenches In figure 17 we present data for a single 16 mil specimen quenched into water and kerosene, and in He gas and air. The liquid quenches were with QSII and the gas 85 L SLOW AIR QUENCH f‘\ SPEEDS f3 " 10 MIL SPECIMEN Q .SREED 5 8 _ 0 II 4 0|—— . 1| 3 D II 2 600” A II I T o 400* e 200’— M W W " n a __,-. Cl F—a-D’ I I I J I I 800 1000 1200 TCC) FIG. 16. -- VARIATIIN If TIE INITIAL 0.301 SPEED 1' 111111 ([301 WINE Tn HR 8.01 AIR DENIES 111111 A 10 MIL SPECII‘EN. IO"2 I 0":5 AB R 20 10'"4 I05 86 T C°C> _.--_I_600 _-I800._.I?.QQ- - 100.0, _ ._---.,8_00__ _. L I 1 1 I F : 16 MIL SPECIMEN E§"= 1.18 cv _. D . __ - WATER _ DKEROSENE *- 0 He GAS - o A I R I" \ . o “A _. O ' O ‘ I I”. n I T I I I ..... I 1 -1 - - 5.0 6,0 7. O 8.0 9,0 I 0.0 I 4 -1 F16.17. -I£SISTNEQBD£D1NTOA16HILS’E£IIBH6ARICTIGIWCIBDIW MIGHOISFED. 87 quenches were done by abruptly shutting off the heating current and allowing the specimen to cool in the surround- ing gas atmosphere. 2. Air and Slowed-Air;Quenches-- 4 and 10 mil Wires Air and slowed air quenches were performed on 4 and 10 mil specimens using the apparatus described in section III. In figure 18 we present data for a single 10 mil specimen obtained with direct air quenches and five slowed-air quench settings. Also included are water-quench data from the same specimen. In order to avoid the effects of liquid quenching strains on the air- quench data, the water quenches were done after nearly all the air and slowed-air quench data had been taken. Similar data, supplemented with flowing-air quenches, were obtained with two other 10 mil specimens and are shown in figure 19. Air and slowed-air quench data for a 4 mil specimen are presented in figure 20. The data obtained from direct air quenches with the 4 mil spe- eff _ cimen yield an effective formation energy of Ef 1.30 i 0.05 eV. 88 T (°C) IO‘Z __..-_..-_-I_6.Q'Q...I€IOO IIZOO _IQQL 8830 I 10 MIL SPECIMEN IO'3 :' .4111 ; 1 R20 ._ I I .. '0'“:- . SPEED 1 \ E D 11 2 \\ “ - ~ cs \. _ o 11 4 . 9 I1 5 . A AIR 0 WATER IO‘F' J 5:0 610 7.10 810 9.0 10.0 __I__ 4 -1 TiXIO CK) FIG. 18. - IESISTMI 1180311110 A 10 MIL SIECIPBI 15116 INTER. A1R. no FM 8“ AIR um SETS. IO-2 10'4 ~ I(I'-"' IIIITI I I -1 .1609 - V1.00 _ @011 _-I_(.I)Q.O._--. _ 89C). 89 T (°C) IO MIL SPECIMENS E;”= I.29 ev .\ \x :I. \z \ . SPEED 3 ° o I' 4 ‘ o 11 5 ‘ A AIR V FLOWING AIR I -__.--.... . 1.---.. -.__... 1-.-- - 5.0 610 7.0 8.0 9.0 10.0 __L 4 —1 TiXIO (K) F16. 1.9. -- IESISTMI OBOED INTO 110 10 MIL SPECII‘ENS 15116 AIR. name A1R. RI) 3WAIRQBOI§3EHE 90 T (°C) 10-2 1600 1400 1'200 1001) 800 : 4 MIL SPECIMEN f. E;#=1.50ev T D SPEED 2 *‘ I I' 3 o 11 4 F o '1 5 A 11 6 A AIR 10'"s :" C .118 Z ' R20 __ I- IO‘4 :— ‘5 I I It 1 '0 5:0 65 7.0 8? 9.0 10.0 —.'f— x I04 C K)" ‘1 F16. 211. -|£SISTMIQBH£DINIOA4HILSFECIIBHBIIGAIRNDSSNAIR mm. ‘ 91 The major limitations on the accuracy of the quench data presented above are: l) the same sources of uncertainty discussed in detail in section IV-C (which will not be discussed further here), and 2) variations in the quench speeds. Variations in the water quench speeds were usu- ally no larger than about 20% for a given specimen, and variations in the quench speeds for all gas and kerosene quenches were about 10% or less. The resultant varia- tions in the quenched-in.resistance produced by these variations in quench speed will increase systematically with increasing quench temperature. As is shown in section VI, a variation of 10% in the quench time will produce variations of l, 4, and 10% in the quenched-in resistance for fractional vacancy losses in the vicinity of 10, 50, and 90%, respectively. For a 20% variation in the quench speed, the corresponding variations in the quenched-in resistance are 2, 10, and 25% respectively. VI. ANALYSIS AND CONCLUSIONS In sections IV and V, we showed that despite re- peated efforts we could not reproduce Jackson's value of 1.51 eV for the vacancy formation energy in platinum. On eff the contrary, we obtained values of Ef ranging from 1.2 eV for 16 mil diam wires to 1.3 eV for 4 mil diam wires. Because of both the disagreement between our data and Jackson's and the lack of internal consistency in our own data, we cannot follow through unambiguously with the original intent of the thesis--to test the Flynn et a1. theory in a metal in which the value of Ef was reasonably well established. In such a case, we cannot pursue a test of the validity of the theory ESE g2; or, in turn, use the theory to demonstrate the validity of either our data or Jackson's. However, we can still determine whether our complete data are consistent with the theory of Flynn et a1., and if they are, whether the formation energy obtained is closer to our values or to Jackson's. 92 93 In the following, then, we apply the three tests for con- sistency with the Flynn 25 31. theory as discussed in section I. A. The First Test We first test whether the data of figures 17 to 20 are consistent with eqn 7. To do this, we assume values for Ef which then specify lines passing through the low temperature fast-quench data points. Each such line determines a series of quench temperatures Tq at which a given fraction of vacancies is lost during the quench, one for each quench time Tq. According to eqn 7, a plot of ln(1/TqTq) versus (l/Tq) should yield a straight line with slope -Em/k. Figures 21, 22, and 23 contain such plots for the data of figures 17, 18, and 20, using values for Tq at which 50% of the assumed vacancy concen- tration was lost during the quench. Similar analyses using percent losses other than 50% showed no systematic differences from the results shown in figures 17, 18, and 20. Within the indicated uncertainties, the data are in 94 10"_ 3 16 MIL SPECIMEN E? (ev) Em(e\/) " o |.20 I.4O " I 1.25 105' _ A 1.52 2.03 10'2 1 o LIJ “1’ X V I87 10'3 -4 1 i L '0 6.0 7.0 8.0 —'-x 104(10“ T1 FIG. 21. - [ETERNMTIOI (F RJR m VAJES (I: E,: FIR A 16 MIL SIECIPEN 15116 TIE FLY)“ l. MYSIS. 95 I 0’3 IO MIL SPECIMEN I 0‘4 T 8 LLJ ((7 _ E;(ev) Em(ev) ff . 1.25 1.67 a. _ - 1.28 1.75 “IS" A I.32 I.95 [0‘5 I 1 I I J 7.0 7.5 8.0 1 TI Lx IO4CK) T3 F1112. —IETEMIMTIOIG‘ENRR$SIEDW£SGEFFTRAIOHILSECIIEN. 96 IO'Z" 4 MIL SPECIMEN _ Ef§.osm§fis SSSSeggégsgémie Emiegg swan... See.fi.e.§.¢gs§§.fi:§ Sang as.§§s.fiooe§1§sm $.22: Eétmas semen. ~10. n10. «10. To. 2.10. 12:... .22.... No «.0 0.0 old 0.. zw2.0maw 1...). v 106 Flynn g£_31. theory. In figure 25 the data from figure 17 have first been corrected for a possible "temperature shift" as discussed in section IV. The uncorrected data fit well to spherical sinks only for Ef = 1.18 eV. The shift of the 10 mil water quench points has been discussed above and is consistent with an increase in the specimen sink density. In addition to showing that the vacancy loss is. a function of DqTqTq only, one can now attempt to see whether the function f' corresponds to either of those predicted by the Flynn 32 21. theory for a specific geo- metric sink structure. That is, if the dominant sinks in the specimen are uniformly spaced dislocations, approxi- mated as the core of a cylinder, the predicted vacancy- loss curve will be given by the curve labeled C in fig- ures 25, 26, and 27. However, if the dominant sinks are uniformly spaced grain boundaries, approximated as the surface of a sphere, the predicted vacancy-loss curve will be given by the curve labeled S in figures 25, 26, and 27. As is seen in these three figures, the data are approxi- mated quite well by the curve for spherical sinks for the 107 values of Ef and Em obtained for the analysis in part B. Further, for no reasonable choices of Ef or Em are the data approximated well by the curve for cylindrical sinks. Once again, we see that for each specimen diameter the data are consistent with the predictions of the theory. Also, when one attempts to fit the vacancy-loss data with values of Ef as high as 1.50 eV, the resulting curves are extremely flat and resemble neither the curves for cylin- drical or spherical sinks. D. Summary and Discussion Having obtained estimates for Ef and Em in the preceding sections, we note that the value of Ef so ob- tained is not in agreement with that obtained by Jackson, nor is the value of Em so obtained in agreement with that commonly found from low-temperature annealing studies (see Table I). We will now analyze our results for in- ternal consistency and for possible explanations for their lack of agreement with those of other studies. We begin with a summary of our estimates for E by two dif- f ferent methods. 108 1. Determination of Ef from Fast, Low-temperature Quenches From low-temperature water quenches of 16 and 10 mil specimens, and direct air quenches of 4 mil specimens, we obtained the following results: TABLE IV VALUES OF ngf OBTAINED FROM FAST-QUENCH DATA FOR ALL THREE SPECIMEN DIAMETERS Specimen diameter ngf (mil) (eV) 1° 1.20 1 .04 1° 1.26 11.04 4 1.30 i .05 Since-in part I of the results, we have discussed exten- sively our water-quench data vis a vis Jackson's results, we shall not go into further discussion of it here. 109 2. Determination of E; from Flynn et a1. Analysis In parts A, B, C, of the Analysis we applied the Flynn et al. analysis to the raw data given in part II of the results, and found that for any given specimen diam- eter the data passed all tests for consistency with the theory. For Q = 2.90 eV (the value obtained from self- diffusion experiments), the analysis selected a pair of values (Bf, Em) consistent with the requirement Ef + Em = Q. These results are presented in Table III. By comparison of Tables III and IV, we see that the values of Ef deter- mined by method 2)are in satisfactory agreement—-for each specimen diameter--with those obtained from method 1). However, all of these values are considerably smaller than the value of 1.51 eV obtained by Jackson (33). Faced with such an obvious disagreement, we will examine the two possibilities: l) Jackson's results are wrong, or 2) our results are wrong. Let us first consider the possibility of error in Jackson's results. First, we note that there does not yet exist adequate independent confirmation of Jackson's 110 value for Ef. The only subsequent quenching study ob- tained the value Ef = 1.46 i 0.02 eV. However, this value was obtained using only three data points, and we believe that its uncertainty is likely to be consider- ably greater than quoted. In any case, the value is as consistent with Ef = 1.40 eV as it is with 1.51 eV, and therefore represents at best only modest support for Jackson's result. Second, the fact that Jackson's values for Ef and Em add up to Q is not adequate proof that his results are correct. Misek's quite different results also satisfied this criterion. Third, Jackson's value for Em was obtained from low temperature annealing studies, which are known to be subject to substantial errors asso- ciated with vacancy-vacancy and vacancy-impurity interac- tions (4, 11). The difficulties involved are adequately illustrated by the range of values for Em quoted in Table I, when it is realized that some investigators found these values to vary with quench temperature and some did not. Thus, it is not difficult to conceive of future experiments using still lower quenching temperatures and - . . ff still more pure spec1mens produCing values for E: 0.1 111 or 0.2 eV higher than those now available. Finally, al- though Jackson clearly performed a comprehensive and careful study of quenched platinum, the possibility of a systematic error cannot be completely precluded. We now consider the possibility of error in our own results. In section IV we analyzed our data for a series of random and systematic errors, and concluded that these were not large enough to reconcile the differences between our low temperature fast-quench data and Jackson's. At the same time, we observed that none of the "systematic errors” proposed by Jackson to dispose of earlier data appeared to be present in our low temperature fast-quench data. In Appendix A we discuss a difficulty in the study of quenched platinum which might have affected both our data and Jackson's, and whose effects are not yet clear. We now consider those effects which have not yet been discussed in detail which might possibly have produced the necessary systematic errors in our data. There are three such effects: 1) vacancy-vacancy clustering into small mobile defects (Perry's objection (24) to the Flynn et al. extrapolation procedure): 2) quenching 112 strain (Seeger and Mehrer's objection (4) to the extrap- olation procedure): and 3) the possibility that the va- cancies anneal to other than fixed sinks (e.g. to nucleii established during the quench). l) Vacancy-vacancy clustering: If vacancies cluster together during the quench to form small highly mobile di-vacancies, then we would expect to find greater vacancy loss under conditions where more di-vacancies form. Fast quenches from low temperatures should show the smallest effect of such clustering. Slow quenches, particularly those from high temperatures, should show the largest effect. Thus we would expect our low temper- ature fast quench data to be little changed, and our high temperature slow quench data to be reduced in magnitude from what it would have been in the absence of cluster formation. Examination of the data of figure 20 shows that this would lead to lower values for Em for a chosen value of E , and thus to higher estimates for the value f of Ef necessary to satisfy the condition Ef + Em = O. This is just the opposite of what we find. Our values for Ef are considerably smaller than Jackson's value. 113 2) Seeger and Mehrer (4) suggested that in gold quenching strains might be the source of an incorrectly high value for E obtained from the Flynn et al. extrapo- f lation. This is also the opposite of what we find in platinum. Thus, if we are to understand the difference between our results and Jackson's in terms of quenching strain, we cannot use Seeger and Mehrer's arguments. Rather, we must use Jackson's argument that quenching strain is largest for quenches from higher temperatures, and in this case leads to less vacancy retention, because of an increase in sink density produced by the strain. Qualitatively, this mechanism describes what happened, since greater vacancy loss at high temperatures would produce smaller estimates for E (see argument in section f 1 just above). While we cannot completely rule out this possibility, our tests for quenching strain strongly sug- gest that they are too small to explain the total differ- ence between our values for Ef and Jackson's. 3) Annealing to other than fixed sinks: We note first that just as in previous studies of gold (3), aluminum (20), and tungsten (23), our data are consistent 114 in form with what would be expected for annealing of single vacancies to uniformly spaced spherical sinks, such as grain boundaries. However, this is not a proof that such annealing is actually occurring. A better argument comes from the available electron microscope studies of quenched platinum (43, 44), in which it was found that only few, small clusters formed in quenched platinum. We conclude that while the possibility for sys- tematic error in our experimental data exists, we cannot identify either a single source or combination of sources which obviously explain the difference between our values for Ef and Jackson's. E. Conclusion The differences between our values for Ef and Jackson's are real, and difficult to understand. We cannot say for sure which of us is correct. We would like to see one more, careful study of quenched 16 mil dram wires using low temperature fast quenches, in order to see whether our data or Jackson's is reproduced. 115 Otherwise we see no advantage in further quenching studies of platinum using only measurements of electrical resis- tance. We badly need either quenching studies combined with direct observation of vacancies using the Field-ion- microscope, or the application of the Simmons-Balluffi technique to platinum. We are bothered by the failure of the data ob- tained with different specimen sizes to be the same. The explanation may lie in the effects of impurities, of quenching strain, or vacancy-vacancy clustering. In any case, this disagreement means that the Flynn, Bass, and Lazarus theory must be applied with care, and that it must be tested upon samples having substantially different diameters if extremely accurate results are to be obtained. Only if there is agreement for data taken on different wire sizes can the data be accepted as accurate. To see whether one final explanation could be the answer to our problems, we used Takamura's suggestion (49), and extrapolated our data to "infinitely thin" sample diameter. The resulting E lay between 1.30 and 1.35 eV, f on the upper end of the results previously obtained, and still in disagreement with Jackson's results. BIBLIOGRAPHY 8. 10. 11. 12. BIBLIOGRAPHY L. A. Girifulco, Atomic Migration in Crystals, Blais- dell Publishing Co., New York (1964). R. 0. Simmons and R. W. Balluffi, Phys. Rev., 11 , 52 (1960). C. P. Flynn, J. Bass and D. Lazarus, Phil. Mag.,‘1l, 521 (1965). A. Seeger and H. Mehrer, Vacancies and Interstitials in Metals, North Holland Publ. Co., Amsterdam (1970) p. 1. R. 0. Simmons and R. W. Balluffi, Phys. Rev., 119, 600 (1960). R. Feder and A. S. Nowick, Phil. Mag., 15, 805 (1967). G. A. Sullivan and J. W. Weymouth, Phys. Rev., 2, 89 (1964). R. 0. Simmons and R. W. Balluffi, Phys. Rev., 125, 862 (1962). V. G. Weizer and L. A. Girafalco, Phys. Rev., g2.- 848 (1968). M. de Jong and J. S. Koehler, Phys. Rev., 129, 40 (1963). K. P. Chik, Vacancigs and Interstitials in Metals, North Holland Publ. Co., Amsterdam (1970). P. 183. J. E. Bauerle and J. S. Koehler, Phys. Rev., 107, 1493 (1957). 116 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 117 C. J. Meechan and J. A. Brinkman, Phys. Rev.,-103, 1193 (1956). P. Simson and R. Sizmann, Z. Naturf., 174, 596 (1962). J. Mori, M. Meshii, and J. W. Kauffman, J. Appl. Phys., 32, 1671 (1962). J. Bass, Thesis, Univ. of Illinois (1964). T. Kino and J. S. Koehler, Phys. Rev., 162, 632 (1967). R. W. Balluffi, R. W. Siegel, K. H. Lie and D. N. Siedman, Vacancies and Interstitials in Metals, North Holland Publ. Co., Amsterdam (1970), p. 125. C. B. Wang, D. N. Seidman and R. W. Balluffi, Phys. Rev., 169, 553 (1968). A. Seeger and H. Mehrer, Phys. Stat. Sol., 22, 231 (1968). J. Bass, Phil. Mag., _1_§. 136 (1967). N. L. Peterson and S. J. Rothman, Phys. Rev., 1, 3264 (1970). R. J. Gripshover, M. Khoshnevisan, J. Zetts, and J. Bass, Phil Mag., 22, 178 (1970). A. J. Perry, Phil. Mag., 21, 743 (1970). B. G. Lazarev and O. N. Ovcharenko, Dokl. Akad. Nauk., S.S.R., 100, 5 (1955). F. J. Bradshaw and S. Pearson, Phil. Mag., 1, 812 (1956). A. Ascoli, M. Asdente, E. Germagnoli, and A. Manara, J. Phys. Chem. Solids, g, 59 (1958). 28. 29. 3o. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 118 G. L. Bacchella, E. Germagnoli, and S. Granata, J. Appl. Phys., 32, 748 (1959). G. R. Piercy, Phil. Mag., 2, 201 (1960). K. Misek, Phys and Tech. of Low Temp_. Publ. House Czech. Acad. Sci., Prague, 1964, p. 110. V. S. Kopan, Fiz. Metal. Metallovod, 12, 569 (1965). J. J. Jackson, Lattice Defects in Quenched Metals, Academic Press, New York (1965), p. 467. J. Baumgarten, F. Heigl and R. Sizmann, KFA Report, International Conf. on Vacancies and Interstials in Metals, Jfilich, 1968, vol. 1, p. 124. J. PolSk, Phys. Stat. Sol., 28, 773 (1968). D. Schumacher, A. Seeger and O. Harlin, Phys. Stat. Sol., 25, 359 (1968). R. Rattke, O. Hauser and J. Wieting, Phys. Stat. Sol.. 21, 167 (1969). S. D. Gerstriken, and N. N. Novikov, Phys. Metals Mettalog. (USSR) (English Trans.), 11, 78 (1961). Ya. A. Kraftmakher, and E. B. Lanina, Sov. Phys. Sol. State, 1, 92 (1965). C. V. Kidson, and R. Ross, Proc. Intern. Conf. Radio- isotopes Sci. Res., Paris, 1, 185 (1957). F. Cattaneo, E. Germagnoli, and F. Grasso, Phil. Mag., ‘1, 1373 (1962). M. Hoch, Vacancies and Interstials in Metals, North Holland Publ. Co., Amsterdam (1970). p. 81. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 119 E. Ruedl, P. Delavignette, and S. Amelinckx,-Radiation Damage in Solids, Vol. I, p. 363, International Atomic~ Energy Agency, Vienna, 1962. R. W. Newman, Thesis, Univ. of Florida (1967). D. Seidman--Personal Communication. Temperature, Its Measurement and Control in Science and Industry, Reinhold Publ. Co., New York (1941), p. 1312. R. J. Gripshover, Thesis, Mich. St. Univ. (1969). J. J. Jackson, Personal Communication. J. J. Jackson, Lattice Defects in Quenched Metals, Academic Press, New York (1965), p. 479. J. Takamura, Lattice Defects in Quenched Metals, Academic Press, New York (1965), p. 521. A. B. Lidiard, Phil. Mag., 2, 1171 (1960). R. H. Freeman, F. J. Blatt, and J. Bass, Phys. Kondens. Materie, 271, 282 (1969). M. Doyama, Phys. Rev., 148, 681 (1966). K. P. Cizek, Czech, J. Phys., 1317: 186 (1967). R. Gripshover, J. Zetts, and J. Bass, KFA Report, International Conf. on Vacancies and Interstitials in Metals, Jfilich, 1968, Vol. I, p. 228. K. Misek, Czech. J. Phys., 1317, 647 (1967). J. Bass, Phys. Rev., 137, A765 (1965). R. M. Emrick, Phys. Rev., 122, 1720 (1961). 120 . 58. R. R. Conte and J. Dural, Phys. Lett., 27A, 368 (1968). 59. R. J. Berry and J. L. G. Lamarche, Phys. Lett., 31A, 319 (1970). APPENDICES APPENDIX A DATA SHIFTS In figures 10 and 12 we compared the resistance quenched into various 16 mil diameter wires and noted that all data obtained with specimens given the shorter, high temperature. anneals are shifted to the right of those ob- tained with specimens given the longer anneals. Also, the further the data are shifted to the right, the lower, in general, is its slope. In addition to these inter- specimen data shifts, intra-specimen data shifts were ob- served in specimens of all three sizes. The shifts were found most often in specimens which had been quenched at least 25 times and, especially, from temperatures above 1200°C. In these cases, the new low-temperature data line was shifted to the right of the original line, and had an equal or slightly smaller slope. The shift was usually accompanied by a substantial drop in the specimen's re- sistance ratio (in one case by a factor of 3-1/2). The 121 122 new high temperature data would gradually approach the original data and, occasionally, cross over it. In two cases, the new data were shifted by the equivalent of as much as 35K° from the old. Since it is not necessarily true that both the inter- and intra-specimen data shifts are associated with a single phenomenon, we have considered in some detail two possible causes for each: 1) a shift in the specimen’s resistance versus temperature curve from the N.B.S. curve (resulting primarily in a change in the effective quench temperature, but no change in the quenched-in resistance from the “true" quench temperature); and 2) a change in the specimen's impurity content or distribution, which produces at any temperature a change in quenched-in resis- tance from what would have been obtained with a "pure" specimen. (In this case we assume that the impurity con- tent is not large enough to measurably affect the resis- tance versus temperature curve). Such a distinction be- tween a temperature shift and the effects of impurities is somewhat artificial, since a temperature shift must necessarily be due to some physical change in the specimen. 123 However, as we shall see below, the distinction can be useful in analyzing the data. A shift in a specimen's resistance-temperature curve would result in an error in the determination of the quench temperature. Equation 4 would only correctly describe the quench data if the data were explicitly cor- rected for this temperature shift (i.e., one had an inde- pendent means for measuring the temperature). If such a temperature shift exists, the data are described by the equation E f 1 AR.Q - Ro exp [- K ( my”. (9) where A(T) is the difference between T, the temperature determined from the specimen's resistance ratio, and the true temperature, T + A(T). For the simplest case, A(T) independent of T over the entire quench-temperature range, the logarithmic plot of AR.Q versus %'will be nearly linear and will for A positive (negative) have a smaller (larger) slope than that of equation 4 . The data will also be shifted from that of equation 4 , and, because i is a non-linear function of T, the shift will be largest at the 124 lowest temperatures. For A = +40°C, and the sameEE, the slope given by equation 9; is about 7% (0.08 eV) lower than that given by equation 4 for Ef = 1.23 eV. The presence of impurities could affect the quench data in a number of ways, depending upon the type of im- purities involved and their concentration. For an impurity concentration much larger than the concentration of va- cancies in the pure metal (Cv approximately 10-4), an excess number of vacancies can be quenched into the spe- cimen in the form of vacancy-impurity complexes. If no vacancies are lost during the quench, the excess resis- I . . . . . tance RV(T) quenched into the impure spec1men is given by (50) B/KT P\];(T) = R:(T) [(1-12CI) + C15 6 ], [10] P . . where RV(T) = vacancy res1stance 1n the pure metal at temp. '1'. B = vacancy-impurity binding energy C = impurity concentration 6 = correction factor for the effective resis- tance of a vacancy-impurity pair. 125 For positive B, the logarithmic plot of the quenched-in. resistance versus i-will be shifted to the right of the. pure-specimen data, and will have a lower slope. The shift will again be largest at the lowest quench tempera- tures. In addition, for high quench temperatures and slow quenching rates, vacancy-impurity complexing might retard the migration of vacancies to sinks during the course of a quench, thus, producing a larger quenched-in resistance than would have occurred in the pure specimen. Finally, the impurities themselves might move in and out of solution during quenching and annealing, causing fur- ther perturbations in the quenched-in resistances. Before proceeding further, it should be noted that, in the absence of reliable chemical or spectro- scopic analysis of the specimens, the specimen's residual resistance ratio (Rrratio) is the only available measure of its impurity content. However, there are several problems involved in using the resistance ratio as a unique measure of specimen purity. For one, the base resistance in liquid helium, RB' is also sensitive to the specimen's internal structure (grain and sub-grain size, 126 dislocation density, etc.). Thus, it is difficult to de- termine whether changes in a specimen's resistance ratio, caused primarily by changes in RB' are due to changes in its impurity content or internal structure. (Simple geometry changes should cause no change in the R—ratio.) A second, and possibly more fundamental problem, is whether greater impurity concentrations always produce lower resistance ratios and whether the same impurity con- tent always produces the same ratio (e.g. for a given im- purity concentration the ratio could change significantly depending upon whether the impurities were distributed uniformly throughout the lattice, collected at grain boun- daries, or relegated to a few atomic layers at the spe- cimen surface). Phenomena possibly associated with such problems were observed in 4 mil specimens and are dis- cussed below. Returning to the data of figure 12, we see that both equation .9 (a temperature shift) and equation 10 (the presence of impurities) have the qualitative form necessary to describe the observed data shifts. We now consider whether either equation can explain the magnitude of the shifts in detail. We begin with equation 9. 127 The initial purity of all specimens used was given as 99.999% by the supplier, Sigmund Cohn Inc. Subsequent spectroscopic analysis (51) performed by Cominco Inc. of 16, 10, and 2 mil platinum wires taken from the same rolls as several specimens used in this study yielded impurity concentrations in good agreement with the purity claimed by the supplier. The largest single contaminant common to all three wire sizes was silicon, whose concentration was about 1 part per million (Ppm) in the 16 and 10 mil wires and 5 ppm in the 2 mil wires. (No 4 mil wires were submitted for analysis.) Thus it seems unlikely that impurity concentrations greater than a few ppm were ini- tially present in the wires used in this study. Now, returning to the data shifts of figure 12, we see that the highest data line F gives quenched-in resistances approximately two times larger than the lowest data line A for $1: 10 x 10-4 (Tq = 1000°K). Assuming that this increase in quenched-in resistance is caused by an impurity concentration of no larger than 10 ppm, equation 10 requires an associated binding energy of nearly 0.8 eV to describe the observed data. 128 Such a binding energy is significantly greater than those reported for any impurities in fee metals (52). While larger impurity concentrations could be obtained if the specimens had been contaminated during the initial anneal- ing and quenching, all but one of the specimens had R- ratios of 4000 to 5700 after the initial anneal and low- temperature quenches (see Table II). These resistance ratios are consistent with a total impurity concentration of less than 10 ppm. In addition, from the spectrographic analysis mentioned above, no significant difference in the impurity concentrations were observed when 16 or 10 mil wires were annealed at high or low temperatures, or not annealed at all. Finally, the positions and slope of the various data lines of figure 12 show no obvious systematic dependence upon Rrratio for the full range of ratios studied (800-5700). Thus it seems unlikely that the simple impurity effects associated with equation 10 are responsible for the shifts in the data. It is worth noting that several previous experi-v menters have observed effects in quenched or annealed- platinum wires which appear to be associated with 129 impurities. Jackson (32) quenched 16 mil wires into water and found that the data for an impure specimen (R—ratio = 500) had a lower slope and were shifted to the right of the pure specimen data (R-ratio = 5000). He attributed the shift to vacancy—impurity complexing, which retarded the migration of vacancies to sinks during the quench. While it is not clear that such a mechanism is responsible for the observed data shift, this shift is qualitatively consistent with the predictions of equations 9 and 10. Cizek (53) studied the irreversible increase in the re- sistance of thin platinum wires quenched into air and water, and concluded that only 80% of this increase was associated with geometry changes in the specimens; the remaining 20% he ascribed to the formation of stable vacancy-impurity complexes, with oxygen being the most likely contaminant. Other "contamination" effects have been observed by the author in a separate study of the quenching of 2 mil platinum wires in superfluid helium (54) (here neither the specific contaminant nor the con- tamination mechanism involved was identified), and by Misek (55), whose results are discussed below in 130 connection with specific contamination effects we observed in the annealing of 4 mil specimens in air. Considering the data of figure 12 from the point of view of a temperature shift, we see that the data is quantitatively consistent with the prediction of equation 9: the further the line is shifted to the right, the lower, in general, is its slope. Since lines E and F are shifted from line A by nearly a constant temperature dif- ference A, we can further attempt to determine if their respective slopes E and shifts A are quantitatively con- f sistent with equation 9. Using line A as a reference line and the values of A obtained from figure 12, we find that the slopes of lines E and F agree to within experi- mental error with those predicted by equation 9. The actual values are about 0.03 eV higher than the predicted ones, but this disagreement might be associated with the faster quench speeds obtained with a QSII (lines E and F), which might raise the slopes of these lines over that of A, independent of a possible temperature shift. In the absence of an independent means of measur- ing the specimen temperature directly, the occurrence of a temperature shift can only be inferred from the data. 131 However, an indirect means of estimating whether tempera- ture shifts might have taken place can be obtained by plotting the current (i.e., power) used for heating a specimen against its nominal temperature. The reasoning employed is this: if all specimens are nearly identical (i.e., they have the same diameter and are not greatly contaminated with impurities) and are heated in the same environment, then the power necessary to maintain them at a certain temperature T (all specimens normalized to a standard gauge length) depends only on I2, where I is the heating current. Thus, if two nominally identical specimens require different heating currents to obtain the same nominal temperature, they are either not at the same temperature, or are not identical. When the heating currents are plotted against the nominal quench temperatures for the 16 mil specimens whose data is presented in figure 12, a positive correlation is seen between the two sets of data: those specimens which show the largest quenched-in resistance for the same nominal quench temperature also require the largest cur— rent to maintain that temperature: i.e., the current 132 versus temperature curves are shifted, using line A as a reference line, by approximately the same number of de- grees as are their quench data curves. In addition, spe- cimens which yield nearly identical quench data, also yield nearly identical current-versus-temperature curves. Hence, as explained above, the existence of such an anomaly indicates either that a temperature shift has occurred or that the specimens are not identical. Since we had no independent means for measuring the tempera- ture, let us examine in more detail the second possibility. To what extent can the specimens be said to be "identical'I in composition and geometry? With regard to the first criterion, we note that all eight 16 mil spe- cimens were initially 99.999% pure and all but one had an initial Rrratio of 4000 or better, independent of whether it was given the longer or shorter high tempera- ture anneal. With regard to the second criterion, we note that the heating current curves of those specimens given the longer high temperature anneals are shifted in a direction consistent with a thinning of these specimens produced by the annealing. However, changes in the 133 diameters of these specimens obtained from actual measure- ments with a microscope and calculated from observed changes in the room temperature-resistance before and after the anneals are too small to account for the ob- served shifts in their heating current curves. Thus, to within our ability to detect differences in specimen composition or geometry, the specimens appear to be identical and the hypothesis of a temperature shift ap- pears more likely to be correct. We shall now show that the same conclusion does not apply to the intra-specimen data shifts discussed above. For one, although these data shifts are compat- ible with equation '9, a temperature shift, the heating current curves are nearly identical for the original and shifted data. Thus, it seems unlikely that these data shifts are caused by temperature shifts. On the other hand, as previously noted, these specimens always showed a significant decrease in their resistance ratios between the original and shifted data. Such a decrease in the resistance ratio may indeed correspond to an increase in the specimen's impurity content. However, a single 134 explanation (e.g., equation 10) for all of the intra- specimen data shifts is not completely satisfactory when one attempts to explain with it the data obtained with the 4 mil specimens. In section II, we reported that 4 mil specimens annealed at temperatures greater than 1250°C yielded quite low resistance ratios--in the vicinity of 250--while an- neals at lower temperatures produced R-ratios of 3000 or better (see Table II). To further investigate this phe- nomenon, a previously unannealed 4 mil specimen was given an isochronal anneal (using 10 minute holding times and temperature intervals of 100°C) at increasing temperatures between 100° and 1000°C. The specimen's resistance ratio was observed to increase after each annealing step to a value of 2800, until a slight decrease was observed after an anneal at 950°C. Further annealing at higher tempera- tures slowly decreased the Rrratio to 2650 until anneals of less than 5 minutes at l400° and 1500°C lowered the R-ratios to 1000 and 800, respectively. Longer anneals at temperatures less than 950°C were able to restore the respective ratios from 1000 to 1400 and from 800 to 880. 135 Thus, it seems that the high-temperature air anneals are "contaminating” these specimens and lower temperature anneals are “purifying” them. (Similar phenomena have been reported by Misek (55), who also reported the "con- tamination" of ”pure" 4 mil air-annealed specimens by annealing in vacuum.) However, the 4 mil specimens were initially of the same nominal purity (99.999%) as the 16 and 10 mil specimens which had R-ratios of 3000 to 9000 when annealed in air at temperatures of 1500°C or greater. In addition (see Table II), 10 mil specimens given the longer high temperature anneals showed R—ratios between two and three times greater than those given much shorter high temperature anneals: and the Rrratios of the 16 mil specimens showed no dependence on the initial air-annealing treatment. One is therefore left to con- clude that (1) if annealing in air either purifies or contaminates the wires, the relation between specimen purity and resistance ratio is by no means a simple one, or (2) some interaction occurs between the specimen and its annealing atmosphere, and the interaction depends strongly upon the wire diameter (possibly associated with 136 the larger surface area to volume ratio of the thinner specimens). An attempt to isolate a single explanation for the above phenomena and for the observed data shifts is further frustrated when one considers the quenching data from var- ious 4 mil specimens. Intra-specimen data shifts (i.e., shifts to the right) were frequently observed in initially "pure” (R-ratio Z 2000) 4 mil specimens. However, inter- specimen data shifts were also observed among the several 4 mil specimens used, but in one case, the initially “con- taminated" specimens (R—ratio = 250) yielded data shifted slightly to the left of the original "pure“ specimen data and with a slightly lower slope. A possible explanation for this inconsistency may lie in the fact that the heating current-temperature curve for the "contaminated" specimen was shifted from that of the “pure“ specimens in a direction consistent with a temperature shift of nearly 50°C to the left of the "pure" specimen, thereby resulting in a much smaller net shift in the data. Thus, it seems possible in some cases that both a temperature shift and impurity ef- fects are responsible for the shifts in the data. 137 In summary, it appears that the 16 mil inter- specimen data shifts are fairly consistent with the hy- pothesis of a temperature shift, while most of_the intra- specimen shifts are more likely to be associated with im- purity effects. However, the sources of either phenomenon are obscure, and until they are investigated directly (i.e., an alternate means of temperature measurement and an explicit analysis of specimen impurity content), we feel that a positive conclusion as to the cause of these shifts is unwarranted. APPENDIX B CHANGES IN SPECIMEN PARAMETERS AND THE MAGNITUDE OF LIQUID QUENCHING STRAINS Throughout a specimen's lifetime its room tempera- ture resistance in the annealed state, R20, and its vacancy-free base resistance in liquid helium, R , were B periodically measured. Small changes in both values were often observed and were used to make corrections to the previously obtained data. For the 16 and 10 mil specimens, the changes in R were both positive and negative and were 20 usually smaller than a few tenths of a percent over a speci- men's lifetime. However, for specimens that were repeatedly liquid-quenched from high temperatures, R20 tended to in- crease. The 4 mil specimen whose data is presented in figure 20 showed an increase in R20 of about 5% during its lifetime. Long-term changes in a specimen's vacancy-free base RB were nearly always positive and were generally larger for the smaller wire diameters. For most of the 16 mil specimens, the increase in R B over a specimen's 138 139 lifetime was less than Zufl or, equivalently, ARE/R20 = 5 x 10-5. However, increases in RB as large as ARE/R20 = 2 x 10'.4 were observed in some water-quenched 10 mil spec- imens and gas-quenched 4 mil specimens. In most cases, the increases in RB could not be directly associated with geometry changes in the specimen, since no comparable in- crease was observed in R and the resulting resistance 20' ration RZO/RB was seen to decrease significantly. In addition to the periodic measurements of R20 and RB discussed above, more precise measurements of R20 were made in order to determine the magnitude of strains produced in liquid quenches. For, if a specimen is plas- tically strained during a liquid quench, the resulting strain, a, can be detected by the change in its geometry and, therefore, its resistance. In particular, if the strain is characterized by a uniform lengthening and thin- ning of the specimen after the quench (with no change in the specimen volume), then the strain is given by e = l/2‘%§, where R is the specimen's (vacancy-free) resistance at some fixed temperature. Since a is likely to be quite small (10”3 or less), a more sensitive method for detecting 140 changes in the specimen's resistance than those employed so far had to be used. Also, since changes in the resis- tance associated with geometry changes in the specimen increase with increasing measuring temperature, it is ad- vantageous to choose a reasonably high measuring tempera- ture: e.g., room temperature or higher. Both of these conditions were reasonably satisfied by the use of the constant temperature bath employed in the.Mattheissen's rule experiments described in appendix D. With this apparatus, fractional changes in the specimen's resistance at 30.5°C could be detected with an accuracy of better than 1 x 10-4. The procedure employed was to quench a 16 mil specimen into water from temperatures between 20 and 700°C (where no measureable vacancy resistance should be quenched in) and to measure its resistance in the bath at 30.5°C before and after the quench. The resultant changes in R for any single quench were found to be less than or equal to the measuring accuracy, 1 x 10-4. 30.5 Cumulative increases in R30 5 for 13 consecutive water quenches in this same temperature range amounted to less -4 _ than 4 x 10 , or approximately 3 x 10 5 per quench. 141 Higher temperature quenches appeared to produce larger increases, however. Sixteen mil specimens quenched from between 1200 and l700°C and given a short cleansing anneal showed increases in R30.5 ranging from 1 to 5 x 10'.4 per quench. In either case, the magnitude of the induced strain is small enough to avoid significant vacancy losses as determined by Jackson (49), who argued that the pres- ence of strains during a quench will, at all but the lowest quench temperatures, decrease the number of vacancies quenched into the lattice. Finally, in order to ascertain the effects of quenching strains on the quenched—in resistance itself, we quenched other 16 and 10 mil wires into water from quench temperatures between 20 and 650°C, and measured the base resistance RB in liquid helium before and after each quench. Again, in this temperature range, the equi- librium vacancy resistance is too small to be detected by our measuring apparatus. Thus, any changes observed in Rb must be due to changes in the wire's geometry or defect structure induced by liquid quenching (e.g. the production of "strain vacancies”). The observed 142 fractional changes in RB after quenching were found to be less than 1%, the limit of our measuring accuracy.' Since one does not expect strain effects to increase appreciably with temperature (49), it appears that the effects of liquid quenching strains on our low-temperature data should be minimal. APPENDIX C REVIEW OF PREVIOUS QUENCHING EXPERIMENTS ON PLATINUM In section IV we presented data for water quenches of 16 and 10 mil wires which yield a value of 1.23 i .07 ev for the vacancy formation energy in platinum. Such a value agrees well with that of several of the earliest studies on quenched platinum (see Table I). It is considerably lower- however than the value of 1.50 ev obtained by Jackson (32), who concluded that the previous quenching studies could have obtained such low values for Ef because of inherent systematic errors. Specifically, the thin specimens used in the earliest studies may have been contaminated with impurities, or had been strained considerably by rapid quenching into water. Also the temperature range investi- gated in these studies is one in which the loss of vacancies due to insufficient quenching rates can be significant. Since, in the present study, we have attempted to follow 143 144 Jackson's procedure, but have obtained results consistent with those of the earliest studies, we feel it is useful to review the results of previous quenching studies-- especially with respect to the possibility of systematic errors as discussed above. In Table V we have listed the pertinent data for several previous quenching studies, including that of Jackson, and will now review them according to Jackson's criteria, starting with that of specimen purity. All of the studies previous to Jackson‘s reported using 99.999% pure platinum--the same as that of Jackson-- except study A, which reported only that the residual re- sistance ratio of its wires was 560. Thus, the most likely source of any contamination of the specimens must have occurred during preparation, annealing or quenching. The occurrence of such contamination would have been most easily detected by changes in the specimenfs residual re— However, in studies / R sistance ratio, R273 K 4.2 K ' B, C, and D, measurements of the specimen's vacancy-free resistance were made at temperatures no lower than 77 K, a temperature too high for sensitive measurement of small 145 >000.“ 000... on; -088 an. 0 000.mv I . H0 .03 .6 000 8 u. 8 .300 so.“ 000.? 8500.303 84 «.0 88-08 08.8 H32. 3 .830 0883 .m 8.“ 000 III 800: mm 004 E 82:08 80.8 0.3on 0 .1 no 880053 .0 00.“ 000.00 mm 3.4 «.0 82-08 1000.3 ~32. 3 3003891000 .0 000.0H 0... 84 «.0 000 -000 08.0 new 8 $0030.08: .0 00.“ 10 an. 04 .II. 300: 8 84 08 000708 08.0 noun: 0 .1 um 030603 .0 H0 .30 04 0.8.38.0 .. 08 .II. 800: 8 84 M85. 0000.80 80.380 “30.. 0 Am um :83 .o a? H 88.0 .. m 8 . a . 0000 . 0 .. 0 300: 8803 8 04 2. 087000 80.0 000.8 ~32. 0 05 308030 .0 n 3003828385 8 «4 NJ. 087.08. 30 0 05 >888a .0 3: 8c 603 8008.0 :05 omcdm . voomm coma . m ousumuomsoa «Baa Houoaufio mom m ucwusmmoz onsumwogaoa mcwHoou ”MOB cococa msflcocosa smfiwoomm Amvuoummflummch 6800 12.355 no more > HAQSB SDZHBéAm ZO mMHQDBm UZHQUZNDO mDOH>mmm mom mmHBHBz¢§O AdBZMZHmmmxm BZWZHHmmm Admm>mm ho BmHA 4 146 or moderate contamination effects. Thus, while each of these three studies reports changes in the specimen's vacancy-free resistance after a number of quenches they do not provide a sensitive means for discriminating be- tween resistance changes associated with geometry changes or with impurity effects. As noted in Appendix A, Misek (56), Cizek (54), and Jackson (32) have observed effects in quenched or annealed platinum wires which are accompanied by significant changes in the R-ratio of the specimens. However, the exact mechanism behind such "im- purity effects" and their influence on the values of Ef determined from such studies have yet to be determined. The quench speeds or quench times reported for water quenches in studies B, C, and D, appear to be equal to or greater than those reported by Jackson in his study--presumably a consequence of the thinner wires used in all of the above experiments--but, without direct knowledge of the sink densities of the specimens used, one cannot make a direct comparison of the respective quench data for specimens of different diameters. How- ever, according to the findings of Jackson and of the 147 present study, it is possible that these studies could still be adversely affected by insufficient quenching rates, because of the relatively high temperature range (qui 1000°C) in which the bulk of the quenches were done. Specifically, as both Jackson (32) and the present study have shown, the quenched-in resistance appears to be rela- tively insensitive to the quenching rate for quench temr peratures lower than about 1000°C. At higher temperatures, however, the quenched-in resistance begins to fall off more rapidly with temperature for even the faster quench- ing rates. Such behavior is reflected in the curvature (i.e. the departure from linearity) in the logarithmic plot of AR.Q versus 1/‘1‘q at the higher quench temperatures. Such curvature is evident throughout nearly the whole temperature range of the Bradshaw and Pearson data (study B). Because of this and because of the larger scatter in their data, we believe that their lower esti— mate of Ef (1.30 eV) to be the most justified by the data. In this regard, the data of studies C and D are rather surprising in that they report nearly linear quench data over an even larger temperature range than that of 148 Bradshaw and Pearson, despite the slightly longer quench times reported in the former studies. However, the values of Ef obtained in studies C and D (1.23 and 1.20 t .04 eV respectively) do not disagree substantially with Bradshaw and Pearson's lower estimate, and agree quite closely with the value of 1.24 eV determined by Misek, and the 1.2 eV of Lazarev and Ovcharenko. In particular, these latter two studies (A and E in the table) are not- able in that (a) they quenched either 2 or 4 mil wires in air, eliminating the possibility of liquid quenching strains; (b) the bulk of the quenches were done below 1000°C, reducing the possibility of vacancy losses caused by insufficient quenching rates; (c) their resistance measurements were made at 4.2K, insuring adequate measur- ing sensitivity. The major deficiency of both of these two studies is their limited amount of data. The same deficiency is present in study G, which gives data for the quenched-in resistance at only 3 quench temperatures. The effects of liquid quenching strains on the quenched-in vacancy concentration would be most signifi- cant in studies B, C, and D, where rather thin wires were 149 quenched into water, and these studies do report phenomena likely to be produced by significant quenching strains: increases in the quenched-in resistance independent of quench temperature (study C), and increases in the resid- ual resistance of the wires after a number of quenches, attributed to changes in their dimensions (studies B and C). However, these studies give little or no quantitative data from which the magnitude of liquid quenching strains can be deduced. On the other hand, all three studies in- clude complementary air quench data that agrees well with that of the water quenches. Also, the values of Ef ob- tained from the studies B, C, and D are in good agreement with those of studies A and E, despite the different quenching methods employed in both groups of studies. In summary, it appears that all of the platinum quenching experiments done before that of Jackson could have been affected to some extent by the systematic errors produced by impurities, insufficient quenching rates, or liquid quenching strains. In most cases, it is not pos- sible to determine the extent to which any of these were operative in these five early studies because of the lack 150 of data related directly to them. Considering, however, the amount of diversity included among these studies (wire diameters ranging from 1 to 8 mil, both air and water quenches, and quench data for both the high and low- temperature ranges) and the relatively good agreement in the values of E obtained in studies A, C, D, and E, it f is not obvious that the differences in the values of Ef obtained from them (1.20-1.24 eV) and from Jackson's study (1.50 i .04 eV) are due solely to the occurrence of the above-mentioned systematic errors as proposed by Jackson. From our discussion in Appendix A, it appears that the annealing treatment used in any platinum quenching study may be a criterion of equal or greater importance than those listed above. Again, there is little quantitative information regarding the annealing treatments used in any of the published studies (except E and F) listed in Table V from which meaningful comparisons can be made. APPENDIX D VACANCIES AND MATTHEISSEN'S RULE IN GOLD AND PLATINUM When electrical resistance measurements are used in conjunction with quenching experiments, two basic assumptions related to the vacancy resistivity are usu- ally made. The first is that quenched-in resistivity is directly proportional to Cv' the quenched-in monovacancy concentration: i.e. o = 0.0 [3] where p is the resistivity per unit concentration of i single vacancies. This assumption is the more crucial one since it directly affects the interpretation of quenching experiments. Thusfar, very little has been done to investigate the validity of equation 3 directly, but it is believed to be a good approximation except in the case of extensive vacancy clustering (18). 151 152 The second assumption-~Mattheissen's rule--is that pv is independent of the temperature at which the quenched- in vacancy concentration is measured; i.e. T = T + o( ) oL( ) av [11] Here, p(T) is the resistivity of the specimen at absolute temperature T, and pL(T) is the normal, temperature- dependent, lattice resistivity of a pure, vacancy-free specimen. The assumption of the validity of equation 11 should, however, pose no serious problems for quenching experiments, since, in practice, all measurements of pv are made at the same highly-reproducible temperature (e.g. in liquid helium at 4.2 K). And, since resistivity measurements give Cv only to within a constant, the de- termination of Ef via equation 4 should not be affected by a temperature dependence in pv. Nevertheless, very little is known about the validity of Mattheissen's rule for vacancies in quenched metals. And what information is available is not internally consistent. In 1965 Bass (56) showed that there was good agreement between his measurements at 4.2°K of the 153 resistivity quenched into 0.016" diameter gold wires and similar measurements by Bauerle and Koehler (12) at 77°K and by Emrick (57) at 273°K. He concluded that there appeared to be little deviation from Matthiessen‘s rule F‘ in the resistivity of vacancies in gold. Recently, how- 1 ever, Conte and Dural (58) reported observing an increase by a factor of four in the resistivity quenched into a H 0.004“ diameter gold wire as the temperature of the wire was raised from 4.2°K to 303°K. In View of this disagree- ment we decided to investigate deviations from Matthiessen's rule in gold and platinum by measuring at 4.2°K and 303°K the excess resistivity retained in 0.016“ diameter gold and platinum wires and 0.008" diameter gold wires quenched into water from a series of temperatures. The high temperature measurements were made in a well-stirred bath of either kerosene or distilled water (with similar results), which served to maintain the rela- tive resistance of the wires constant to within GR/R > 1 x 10-4 over a period of many hours. Here 20°C“ GR is the maximum resistance variation, and R20°C is the resistance of the well annealed wire at 20°C. For most 154 of the data, the cleansed (vacancy-free) resistances were measured at 4.2 and 303°K before and after each quench. However, in some cases two or three quenches were made between measurements of the cleansed resistance. In these cases, suitable averages of the pre- and post-quench cleansed resistances were subtracted from the resistance of the quenched wire to obtain the quenched-in resistance. Originally,-only 0.016” diameter platinum and 0.008" diameter gold wires were quenched. However, quench- ing stresses often produced substantial changes in the geometry of the 0.008" diameter wires, making it difficult to obtain precise data at 303°K. Therefore, additional quenches were made with a 0.016" diameter gold wire, in which smaller geometry changes were expected, and, in fact, observed. The quench data for three independent platinum wires and one 0.016" and two 0.008" diameter gold wires are shown in figure 28. (To remove the effects of dif- fering specimen geometries, the measured resistances have been divided by the resistance of the same wire at 20°C.) The precision of the helium temperature measurements was | I r \ I I \ \ \ \ \\ i \\ \ 8 5xl0—3L \\\\ \\ .. A89 .4‘ZOK \\ 9% Rzo'c °303°K \\ \ \\ \ \ .\ \\ \ ZXIO-a" , \ i \\ J PLATINw—OOIS DIAM.1 \ 9 4 5 6 7 I04/T(°K) we I I I U T \ \ \ \ \ A I . \ .3 \ E x . 5"0 IPRESENT DATA & \ \ \ ' l4.2°K \ \ ABA o 303°K ‘ ‘ \ RZO'C \\\ CONTE 3: DURAL DATA \ . 0004 DIAMGOLD \ % A4?K 2on r A 273°K . ‘ 60.0-0008 DIAM. 7.5 8.0 85 9.0 9.5 DC 104/ TM FIG. 28. - TIE IESISIPNCE WED INTO (11D PM) HATIMM HIIES AS A 155 WHEN (I: BOTH 1H5 WINS TEI‘PERATURE MD INVERSE KELVIN GEM}! TB'PERAIUIE. TI£ WED LINES INDICATE ME ME (I: WED-IN IESISTMI PIEVIUJSLY (BTAIIED BY BASS (1%!) CI 6le PM) IN THE PRESENT STUDY (SECTIUI IV) (N PLATIMN. 156 better than the size of the symbols shown in the figure. For the data at 303°K, the error bars indicate the pos- sible maximum and minimum values of the quenched-in re- sistances associated with changes in the cleansed resis- tances produced by changes in specimen geometry. These error bars are generally large for the 0.008" diameter wires, but usually no larger than the symbols for the 0.016" diameter wires. The remaining sources of error lead to an additional uncertainty of about (SR/R20°C = 2 x 10.4 for each 303°K data point. To test for vacancy annealing at 303°K, repeated measurements at 4.2 and 303°K were made. Corresponding decreases in the resistances measured at both temperatures confirmed the existance of minor annealing in gold quenched from high temperatures. No annealing was ob- served in platinum. To further test the effects of va- cancy annealing on deviations form Matthiessen's rule, isochronal anneals were performed on a platinum wire quenched from 1300°C and on a 0.008" diameter gold wire quenched from 870°C. Measurements at 4.2 and 303°K of the fractional resistance losses during the anneals 157 indicated no large deviations from Matthiessen's rule in either gold or platinum. As can be seen from figure 1, we do not reproduce the large deviations from Matthiessen's rule reported by Conte and Dural. To within our experimental uncertainty, we find no increase in quenched-in resistance with in- creasing measuring temperature for either gold or platinum. It may be that the large deviation seen by Conte and Dural was due to geometry changes associated with quenching strain in their thin specimen.