The concentration dependence of CD diffusivity enhancement in dilute PBCD alloys

Scripta METALLURGICA

Vol. 13, pp. 355-358, 1979 Printed in the U.S.A.

Pergamon Press Ltd. All rights reserved.

THE CONCENTRATION DEPENDENCE OF CD DIFFUSIVITY ENHANCEMENT IN DILUTE PB-CD ALLOYS* P. T. Carlson and R. A. Padgett, Jr. Metals and Ceramics Division Oak Ridge National Laboratory Oak Ridge, Tennessee 37830 (Received

March 2, 1979)

Introduction There has been considerable interest in recent years in the anomalously fast diffusion of noble and Group II-B solutes in lead. I t is reasonably well established that self and impurity diffusion in most fcc metals occurs by vacancy mechanisms. In addition, impurity diffusion coefficients in such systems seldom d i f f e r appreciably from the s e l f - d i f f u s i v i t i e s . The early work of Seith et al. (1,2), however, on the d i f f u s i v i t i e s of Hg, Cd, Mg, Ag and Au in Pb demonstrated that these solutes have quite large d i f f u s i v i t i e s , ranging from two to five orders of magnitude greater than lead self-diffusion. Since the results of Seith et al. are not readily explicable in terms of a purely substitutional mechanism, a number of investigations have been undertaken since that time to c l a r i f y the diffusion mechanism responsible for the rapid d i f f u sion of solutes in lead. The dissociative mechanism was postulated by Frank and Turnbull (3) in their study of the very rapid diffusion of copper in germanium. The dissociative mechanism is operative when a substitutionally dissolved solute atom is thermally activated to an i n t e r s t i t i a l site. In the original model (3,8), equilibria are established between free i n t e r s t i t i a l s , substitutionals, interstitial-vacancy pairs and vacancies. Miller (4) investigated the dissociative mechanism in his study of lead d i f f u s i v i t y enhancement by small additions of cadmium. He found that the enhancement was less than the minimum enhancement attributable to a purely substitutional mechanism; however, the existence of a positive enhancement precludes the operation of a pure i n t e r s t i t i a l mechanism. In a later work, Miller and Edelstein (5) explained the except i o n a l l y small isotope effect for cadmium diffusion in lead as due to a predominant fraction of cadmium atoms in the interstitial-vacancy pair configuration. Subsequent theoretical work by McKee (6) suggests, in addition, the formation of i n t e r s t i t i a l - s u b s t i t u t i o n a l solute pairs i f the solute atoms are predominantly on substitutional sites in the alloy. I f this type of solute-solute pairing occurs, i t is expected that the solute d i f f u s i v i t y would decrease with increasing solute concentration in dilute regions. There is some evidence (7) for the formation of such pairs for gold diffusion in lead-gold alloys in which the gold d i f f u s i v i t y decreased markedly at low concentrations. The present work uses solute d i f f u s i v i t y enhancement techniques to provide experimental evidence for the existence of i n t e r s t i t i a l - s u b s t i t u t i o n a l solute pairs. I t is thought that the diffusion of cadmium in lead-cadmium alloys represents the substitutional extreme of the dissociative equilibrium. Experimental Procedure Lead and lead-cadmium alloy single crystals were grown from 99.9999% pure lead and cadmium by a modified Bridgman technique. The alloy compositions, determined by atomic absorption spectroscopy, are given in Table I. Cylindrical samples were cut from the single crystals with

*Research sponsored by the Division of Materials Sciences,U.S. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.

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a wire saw and t h e i r faces microtomed to ensure f l a t surfaces. Each sample was electroplated with a thin layer of carrier-free Cd-lO9 isotope, wrapped in aluminum f o i l and encapsulated under helium. To ensure identical thermal histories, a l l ampoules were placed in a wire basket and immersed in a w e l l - s t i r r e d salt bath at 197.7°C for 27 d. The temperature, measured with a pair of Pt/Pt-lO% Rh thermocouples, varied less than O.l°C during the anneal. The samples were air-quenched following the anneal, reduced in diameter to eliminate edge effects and s e r i a l l y sectioned on a microtome. The sections were i n d i v i d u a l l y dissolved in a 75% acetic acid-25% H202 solution and analyzed for Cd-109 in a well-type s c i n t i l l a t i o n detector by appropriate integration of the 0.088 MeV gamma energy peak. A minimum of IO4 counts was taken for each section. The results were plotted as log a c t i v i t y versus x2 in accordance with the t h i n - f i l m solution for radiotracer diffusion. Discussion of Results The penetration p r o f i l e shown in Fig. l for the diffusion of cadmium in a Pb-O.7 at. % Cd alloy is typical of the profiles obtained in this investigation. All profiles were Gaussian ORNL-DWG

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FIG. l Penetration Profile for Diffusion of Cadmium in Pb-O.70 at. % Cd Alloy at 197.7°C for 27 d. over nearly three orders of magnitude drop in specific a c t i v i t y . In some profiles a s l i g h t upward curvature near the o r i g i n , indicative of oxide holdup problems, was observed; however, calculations showed that this effect was negligible on the determination of tracer d i f f u s i v i t i e s providing tracer penetration into the host was s u f f i c i e n t l y deep. Furthermore, s h o r t - c i r c u i t diffusion was apparent in a few runs with an upward curvature of the p r o f i l e at large penetrations. All such points were excluded in the determination of D*. The diffusion coefficients were determined by a least-squares f i t of the linear region of each p r o f i l e and are given in Table I . I t might be noted here that the d i f f u s i v i t y for cadmium in pure lead of this investigation (5.69 x lO-11 cm2/s) is in agreement with M i l l e r ' s (4) value of 5.68 x lO-11 cm2/s. At the 95% confidence level, the uncertainties in D* and D*/D*(O) are ±0.02 x IO-11 cm2/s and ±0.007, respectively.

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TABLE I . D i f f u s i v i t i e s of Cadmium in Lead-Cadmium A11oys at 197.7°C Composition (at. % Cd)

D* (cm2/s) x I0 Iz

0.00475 0.00997 0.0222 0.0982 0.296 0,65 0.904 Pb

D*/D*.(O)

5.33 5.0 4.85 5.2 5.51 6,01 6.42 5.69

The standard expression for solute d i f f u s i v i t y

0.937 0.879 0.852 0.914 0.968 1.056 1.128 1.000 enhancement is

(1)

D*(X) = D*(O) [1 + b21x + b22x2 + . . . ]

where D*(x) is the cadmium d i f f u s i v i t y in a lead-cadmium a l l o y containing x at. f r . Cd, D*(O) is the cadmium d i f f u s i v i t y in pure lead and the b's are the solute d i f f u s i v i t y enhancement c o e f f i c i e n t s . To f i r s t order in concentration, only the b21 term is considered. The d i f f u s i v i t i e s , plotted as D*/D*(O) versus a l l o y composition, are shown in Fig. 2. The most i n t e r e s t i n g feature of t h i s curve is the pronounced decrease in the cadmium d i f f u s i v i t y with increasing cadmium concentration in the d i l u t e region. This behavior is in q u a l i t a t i v e agreement with theoretical predictions (6) for systems in which the formation of i n t e r s t i t i a l s u b s t i t u t i o n a l solute pairs is favored. Such a decrease occurs since the motion of the pair is O R N L - D W G 78-166

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ATOM PERCENT CADMIUM

FIG. 2 Solute D i f f u s i v i t y Enhancement Curve f o r Cd D i f f u s i o n in Pb-Cd Alloys at 197.7°C.

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highly restricted by the fact that one of the atoms occupies a substitutional site. The rate of motion of the solute pair thus depends on the arrival of a fresh l a t t i c e vacancy. The total cadmium d i f f u s i v i t y can be shown to be a summation of the jump characteristics of the solute atoms in the various defect complexes; consequently, a strong tendency for such pair formation results in a decrease in solute diffusion with increasing solute concentration. A least-squares f i t of the linear region at very dilute concentrations yields a value of approximately-1200 for b21. For concentrations above approximately 0.022 at. % Cd, the d i f f u s i v i t y of cadmium in the alloy increases with increasing solute concentration in accordance with normal solute d i f f u s i v i t y enhancement. The formation of i n t e r s t i t i a l - s u b s t i t u t i o n a l solute pairs is thought to be rather strongly temperature dependent. There is some recent evidence (7) to show that pairs of solute atoms are energetically favored at low temperatures. In addition, the measurement of solute d i f f u s i v i t y enhancement coefficients over a range of temperatures w i l l provide information on solute-solute binding energies. To this end, additional experiments are being performed at various temperatures in the lead-cadmium system, and the results w i l l be presented in a subsequent paper. Acknowledgments The authors would like to express their appreciation to R. A. McKee for many f r u i t f u l discussions during the course of this work. Also, we are grateful to L.C.Manley, Jr. for his assistance in the early stages of the investigation. References I. 2. 3. 4. 5. 6. 7. 8.

W. W. F. J. J. R. W. J.

Seith, E. Hofer and H. Etzold, Z. Elektrochem., 40, 322 (1934). Seith and A. Keil, Z. Physik. Chem., B22, 350 (1933). C. Frank and D. Turnbull, Phys. Review, I04, 617 (1956). W. M i l l e r , Phys. Review, 181, I095 (1969). W. Miller and W. A. Edelstein, Phys. Review, 188, 1081 (1969). A. McKee and A. D. LeClaire, to be submitted to Physical Review B. K. Warburton, Phys. Review B, I I , 4945 (1975). W. M i l l e r , Phys. Review, 188, I074 (1969).