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Self-diffusion and impurity diffusion of fee metals using the five-frequency model and the Embedded Atom Method

Published online by Cambridge University Press:  31 January 2011

J. B. Adams ,
S. M. Foiles  and
W. G. Wolfer
J. B. Adams
Affiliation:
Theoretical Division, Sandia National Laboratories, Livermore, California 94550
S. M. Foiles
Affiliation:
Theoretical Division, Sandia National Laboratories, Livermore, California 94550
W. G. Wolfer
Affiliation:
Theoretical Division, Sandia National Laboratories, Livermore, California 94550
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Abstract

The activation energies for self-diffusion of transition metals (Au, Ag, Cu, Ni, Pd, Pt) have been calculated with the Embedded Atom Method (EAM); the results agree well with available experimental data for both mono-vacancy and di-vacancy mechanisms. The EAM was also used to calculate activation energies for vacancy migration near dilute impurities. These energies determine the atomic jump frequencies of the classic “five-frequency formula,” which yields the diffusion rates of impurities by a mono-vacancy mechanism. These calculations were found to agree fairly well with experiment and with Neumann and Hirschwald's “Tm” model.

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Articles
Information
Journal of Materials Research , Volume 4 , Issue 1 , February 1989 , pp. 102 - 112
Copyright
Copyright © Materials Research Society 1989

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References

REFERENCES

1Butrymowicz, D.B., Manning, J.R., and Read, M.E., J. Phys. Chem. Ref. Data V2 (3), 643 (1973).CrossRefGoogle Scholar
2Butrymowicz, D.B., Manning, J.R., and Read, M.E., J. Phys. Chem. Ref. Data V3 (2), 527 (1974).CrossRefGoogle Scholar
3Butrymowicz, D.B., Manning, J.R., and Read, M.E., J. Phys. Chem. Ref. Data V4 (1), 177 (1975).Google Scholar
4Butrymowicz, D.B., Manning, J.R., and Read, M.E., J. Phys. Chem. Ref. Data V5 (1), 103 (1976).CrossRefGoogle Scholar
5Dorner, P., Gust, W., Hintz, M.B., Lodding, A., Odelius, H., and Predel, B., Acta Metall. 28, 291 (1980).CrossRefGoogle Scholar
6Treheux, D., Heurtel, A., and Guiraldenq, P., C. R. Acad. Sc. Paris t280, 1191 (1975).Google Scholar
7Ladet, J., Bernadini, J., and F. Cabane-Brouty, Scripta Metall. 10, 195 (1976).Google Scholar
8Eguchi, T., Iijima, Y., and Hirano, K., Acta Crystall. A28, S161 (1972).Google Scholar
9Hoffman, R. E. and Turnbull, D., J. Appl. Phys. 22, 634 (1951).CrossRefGoogle Scholar
10Herzig, C. and Wolter, D., Z. Metallkunde H4, 273 (1974).Google Scholar
11Million, B. and Kucera, B., Kovove Mater. 11, 300 (1973).Google Scholar
12Fogel'son, R.L., Ugay, Y. A. A., and Akimova, I. A., Fiz. Met. Metalloved. 41 (3), 653 (1976).Google Scholar
13Sen, S.K., Dutt, M.B., and Barua, A. K., Phys. Stat. Sol. (a) 45, 657 (1978).CrossRefGoogle Scholar
14Rothman, S.J., Peterson, N.L., and Robinson, J.J., Phys. Stat. Sol. 39, 635 (1970).CrossRefGoogle Scholar
15Fogel'son, R.L., Voronina, I.M., and Somova, T.I., Phys. Met. Metall. V46 (1), 163 (1979).Google Scholar
16Fogel'son, R.L., Ugay, Y. A. A., and Akimova, I. A., Fiz. Met. Metalloved. 39 (2), 447 (1975).Google Scholar
17Rein, G., Mehrer, H., and Maier, K., Phys. Stat. Sol. (a) 45, 253 (1978).CrossRefGoogle Scholar
18Nowak, W. B. and Dyer, R. N., J. Vac. Sci. Technol. 9, 279 (1971).CrossRefGoogle Scholar
19Fogel'son, R.L., Ugay, Y. A. A., and Pokoyev, A. V., Fiz. Metal. Metalloved. 33 (5), 1102 (1972).Google Scholar
20Neumann, G., Pfundstein, M., and Reimerrs, P., Phil. Mag. A45, 499 (1982).Google Scholar
21Taguchi, O., Iijima, Y., and Hirano, K., J. Jap. Inst. Met. 48 (1), 20 (1984).CrossRefGoogle Scholar
22Dayananda, M. A. and Kim, C. W., Metall. Trans. A10 (9), 1333 (1979).CrossRefGoogle Scholar
23Bergner, D. and Schwartz, K., Neue Hutte, 23 (6), 210 (1978).Google Scholar
24Macht, M.P., Naundorf, V., and Dohl, R., Proceedings of Int. Conf. on Diffusion in Metals and Alloys at Tihany, Hungary, edited by Kedves, F. J. and Beke, D. L., Diffusion and Defect Monograph Series No. 7 (1983), Trans. Tech. Pub., Switzerland.Google Scholar
25Peterson, N.L., Phys. Rev. 132, 2471 (1963).Google Scholar
26Mallard, W. C., Gardner, A.B., Bass, R. F., and Slifkin, L. M., Phys. Rev. 129, 617 (1963).CrossRefGoogle Scholar
27Duhl, D., Hirano, K., and Cohen, M., Acta Metall. 11, 1 (1963).Google Scholar
28Monma, K., Suto, H., and Oikawa, H., J. Jap. Inst. Met. 28, 188 (1964).CrossRefGoogle Scholar
29Johnson, R.D. and Faulkenberry, B.H., ASD-TDR-63-625 (July 1963).Google Scholar
30Kurtz, A.D., Averbach, B.L., and Cohen, M., Acta Metall. 3, 442 (1955).CrossRefGoogle Scholar
31Vladmirov, A. B., Kaigorodov, V. N., Klotsman, SM, and Trachtenberg, I. Sh., Proceeding of Int. Conf. on Diffusion in Metals and Alloys at Tihany, Hungary, edited by Kedves, F. J. and Beke, D. L., Diffusion and Defect Monograph Series No. 7 (1983), Trans. Tech. Pub., Switzerland.Google Scholar
32Peterson, N. L., Phys. Rev. 136, A568 (1964).CrossRefGoogle Scholar
33Fujikawa, S., Werner, M., Mehrer, H., and Seeger, A., Mat. Sci. Forum V.15-18, 431 (1987).CrossRefGoogle Scholar
34Meinel, K. and Klaua, M., Sitzungsberichte der AdW der DDR, No. 17N, 57 (1978).Google Scholar
35Kubaschewski, O., Trans. Faraday Soc. 46, 713 (1950).CrossRefGoogle Scholar
36Neumann, G. M., in Diffusion Processes, edited by Sherwood, J. N., Chadwick, A. V., Muir, W. M., and Swinton, F. L. (Gordon and Breach Science Publishers, New York), p. 329.Google Scholar
37Archbold, T. F. and King, W. H., Trans. Met. Soc. AIME 233, 839 (1965).Google Scholar
38Anusavice, K.J., Pinayan, J.J., Oikawa, H., and T. De Hoff, Trans. AIME 242, 2 (1968).Google Scholar
39Gorbacher, V. A., Klotsman, S.M., Ya. A. Rabovski, V. K. Talinski, and A.N. Timofeev, Fiz. Met. I. Metalloved 34, 879 (1972).Google Scholar
40Sippel, R.R., Phys. Rev. 115, 1141 (1959).CrossRefGoogle Scholar
41Tomizuka, C.T., Bull. Am. Phys. Soc. 2, 123 (1957).Google Scholar
42Renouf, T. J., Phil. Mag. 22, 359 (1970).CrossRefGoogle Scholar
43Martin, A.B. and Asaro, F., Phys. Rev. 80, 123 (1950). A.B. Martin, R. D. Johnson, and F. Asaro, J. Appl. Phys. 25, 364 (1954).Google Scholar
44Machliet, C. A., Phys. Rev. 109 (6), 1964 (1958).Google Scholar
45Ikushima, A., J. Phys. Soc. Japan 14 (11), 1636(1959).CrossRefGoogle Scholar
46Monma, K., Suto, H., and Oikawa, H., Nippon Kinsoku Gakkaishi 28, 192 (1964).Google Scholar
47Jaumot, F. D. and Sawatskii, A., J. Appl. Phys. 27, 1186 (1956).CrossRefGoogle Scholar
48Mead, H. W. and Birchenall, C. E., Trans. Met. Soc. AIME 209 (7), 874 (1957).Google Scholar
49Hirone, T., Miura, S., and Suzuoka, T., J. Phys. Soc. Japan 16 (12), 2456 (1961).CrossRefGoogle Scholar
50Sawatskii, A. and Jaumot, F. E., Trans. AIME 209, 1207 (1957).Google Scholar
51Klotsman, S.M., Arkhipova, N.K., Timofeyev, A.N., and Trakhtenberg, L.S., Fiz. Metal, i Metalloved. 20 (3), 390 (1965).Google Scholar
52Reynolds, J.E., Averbach, B.L., and Cohen, M., Acta Metall. 5, 29 (1957).Google Scholar
53Kurtz, A.D., Averbach, B.L., and Cohen, M., Acta Metall. 3, 442 (1955).CrossRefGoogle Scholar
54Mercer, M. L., “Atom Movements in Alloys, Ph.D. Thesis, Univ. Leeds (1955).Google Scholar
55(a) Tomizuka, C.T., private communication cited by Morrison, H. M., Phil. Mag. 12, 985 (1965). (b) N.H. Nachtrieb, C.T. Tomizuka, and L.G. Schulz: Report AFOSR-TR-60-23, The University of Chicago (1960).Google Scholar
56Vignes, A. and Haeussler, J. P., Mem. Sci. Rev. Metall. 63, 1091 (1966) (translation available from NTIS as TT 70-57660).Google Scholar
57Anand, M.S., Muraka, S.P., and Agarwala, R.Pl., J. Appl. Phys. V36 (12), 3860 (1965).Google Scholar
58Brunei, G., Cizeron, G., and Lacombe, P., C. R. Acad. Sc. Paris t270, Serie C, 393 (1970).Google Scholar
59Claire, A. D. Le and Neumann, G., Chapter 3 in Diffusion in Metals and Alloys, Landolt-Bornstein, New Series, edited by Madelung, O., vol. edited by Mehrer, H. (Springer, Heidelberg) (in press).Google Scholar
60Neumann, G. and Tolle, V., Phil. Mag. A V54 (5), 619 (1986).CrossRefGoogle Scholar
61Peterson, N.L., J. Nucl. Mater. 69/70, 3 (1978).CrossRefGoogle Scholar
62Schule, W., Point Defects and Defect Interactions in Metals, edited by Takamura, J. I., Doyama, M., and Kiritani, M. (Univ. of Tokyo Press, 1982), p. 551.Google Scholar
63Neumann, G. and Tolle, V., Phil. Mag. A57 (4), 621 (1988).Google Scholar
64Claire, A. D. Le, J. Nucl. Mater. 69/70, 70 (1978).CrossRefGoogle Scholar
65Mehrer, H., J. Phys. F. 2, Lll (1972).Google Scholar
66Claire, A. D. Le, Phil. Mag. 7, 141 (1962); A. D. Le Claire, Phil. Mag. 10, 641 (1964).Google Scholar
67Neumann, G. and Hirschwald, W., Z. Phys. Chem. Neue Folge, Bd. 89, 309 (1974); G. Neumann and W. Hirschwald, Phys. Stat. Sol. (b) 55, 99 (1973).CrossRefGoogle Scholar
68Neumann, G., Materials Science Forum V 15-18, 413 (1987); G. Neumann, Phys. Stat. Sol. (b) 144, 329 (1987).CrossRefGoogle Scholar
69Adams, J.B. and Wolfer, W.G., J. Nucl. Mater. 158, 25 (1988).Google Scholar
70Daw, M.S. and Baskes, M.I., Phys. Rev. Lett. 50, 1285 (1983).Google Scholar
71Foiles, S.M., Baskes, M.I., and Daw, M.S., Phys. Rev. B 33, 7983 (1986); Errata: to be published.CrossRefGoogle Scholar
72Daw, M. S. and Hatcher, R. D., Sol. St. Comm. 56, 697 (1985).Google Scholar
73Foiles, S. M., Phys. Rev. B32, 3409 (1985).CrossRefGoogle Scholar
74Foiles, S. M., Surf. Sci. 191, L779 (1987); M. S. Daw and S. M. Foiles, Phys. Rev. Lett. 59, 2756 (1987).Google Scholar
75Daw, M. S., Baskes, M. I., Bisson, C. L., and Wolfer, W. G., in Modelling Environmental Effects on Crack Growth Processes, edited by Jones, R. H. and Gerberich, W. W. (Metallurgical Society of AIME, New York, 1986).Google Scholar
76Foiles, S.M., Phys. Rev. B 32, 7685 (1985).Google Scholar
77Foiles, S. M. and Daw, M. S., J. Mater. Res. 2, 5 (1987); S. M. Foiles, in High Temperature Ordered Intermetallic Alloys II, edited by N. S. Stoloff, C.C. Koch, C.T. Liu, and O. Izumi (Materials Research Society, Pittsburgh, PA, 1987).CrossRefGoogle Scholar
78Wycisk, W. and Feller-Kniepmeier, M., J. Nucl. Mater. 69/70, 616 (1978).CrossRefGoogle Scholar
79Smedskjaer, L.C., Fluss, M.J., Legnini, D.G., Chason, M. K., and Siegel, R.W., J. Phys. F: Metal Phys. 11, 2221 (1981).CrossRefGoogle Scholar
80Kraftmakher, Y. A. and Strelkov, P. G., in Vacancies and Interstitials in Metals, edited by Seeger, A., Schumacher, D., Schilling, W., and Diehl, J. (North-Holland, Amsterdam, 1970), p. 59.Google Scholar
81Kuribayashi, K., D. Eng. Thesis, University of Tokyo (1975), quoted by Doyama, M. and Koehler, J.S., Acta Metall. 24, 871 (1976).Google Scholar
82Balluffi, R. W., J. Nucl. Mater. 69/70, 240 (1978).CrossRefGoogle Scholar
83Ashcroft, N. W. and Mermin, N. D., Solid State Physics (Holt, Rinehart, and Winston, New York, 1976).Google Scholar
84Metal Reference Book, 5th ed., edited by Smith, C. J. (Butterworth's, London, 1976), p. 186.Google Scholar
85Simmons, G. and Wang, H., Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook (MIT Press, Cambridge, MA, 1971).Google Scholar
86Seeger, A. and Mehrer, H., in Vacancies and Interstitials in Metals, Ref. 74, p. 1.Google Scholar
87Koehler, J. S., in Vacancies and Interstitials in Metals, Ref. 74, p. 169.Google Scholar
88Kronmuller, H., in Vacancies and Interstitials in Metals, Ref. 74, p. 183.Google Scholar