Statistical Theory of Properties of Solid Solutions

R. Smoluchowski

doi:10.1103/PhysRev.84.511

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Statistical Theory of Properties of Solid Solutions

R. Smoluchowski

Carnegie Institute of Technology, Pittsburgh, Pennsylvania

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Phys. Rev. 84, 511 – Published 1 November, 1951

DOI: https://doi.org/10.1103/PhysRev.84.511

Abstract

Properties of binary solid solutions are considered from the point of view of the fluctuation of local composition in the crystalline lattice. These variations influence the properties of the alloys by varying the corresponding local concentration of electrons. A simple general statistical method is given for calculating properties of random and ordered solid solutions. The theory is applied to saturation magnetization, temperature coefficient of electrical resistivity, thermoelectric power, and to other properties in various alloys. A satisfactory agreement with experiment is obtained.

References (16)

R. Smoluchowski, Intern. Conf. on Magnetism, Grenoble, 1950 J. phys. radium 12, 389 (1951) Phys. Rev. 78, 638 (1950)
R. Smoluchowski and J. E. Goldman, Phys. Rev. 75, 140 (1949)
C. G. Shull, private communication
N. F. Mott and H. Jones, Theory of Properties of Metals and Alloys (Oxford University Press, London, 1936)
A. R. Kaufmann and C. Starr, Phys. Rev. 63, 445 (1943)
N. F. Mott, Proc. Roy. Soc. (London) 153, 699 (1936) ibid.156, 368 (1936) Proc. Phys. Soc. (London) 47, 571 (1935)
B. Svensson, Ann. Physik (5) 25, 263 (1936)
R. Smoluchowski, Metal Progress 41, 363 (1942) Phys. Rev. 61, 390 (1942) R. Smoluchowski and J. S. Koehler, Ann. Rev. Phys. Chem. (1951)
W. F. Meggers, J. Opt. Soc. Am. 31, 39, 605 (1941)
A. Sieverts and G. Zapf, Z. physik. Chem. 172, 314 (1935)
W. Geibel, Z. anorg. u. allgem. Chem. 69, 38 (1910) ibid.70, 240 (1911)
J. E. Goldman, Phys. Rev. 82, 339(A) (1951)
R. Smoluchowski, Intern. Conf. on Metals, Amsterdam, 1948 Physica 15, 179 (1949)
R. Smoluchowski, Nat. Res. Council Conf. on Phase Transformations, Cornell University, 1948, published by John Wiley and Sons, Inc., New York, 1951
W. Hume-Rothery, Atomic Theory for Students of Metallurgy (Institute of Metals, London, 1946)
R. Smoluchowski (to be published)

[c1] R. Smoluchowski, Intern. Conf. on Magnetism, Grenoble, 1950 J. phys. radium 12, 389 (1951) Phys. Rev. 78, 638 (1950)

[c2] R. Smoluchowski and J. E. Goldman, Phys. Rev. 75, 140 (1949)

[c3] C. G. Shull, private communication

[c4] N. F. Mott and H. Jones, Theory of Properties of Metals and Alloys (Oxford University Press, London, 1936)

[c5] A. R. Kaufmann and C. Starr, Phys. Rev. 63, 445 (1943)

[c6] N. F. Mott, Proc. Roy. Soc. (London) 153, 699 (1936) ibid.156, 368 (1936) Proc. Phys. Soc. (London) 47, 571 (1935)

[c7] B. Svensson, Ann. Physik (5) 25, 263 (1936)

[c8] R. Smoluchowski, Metal Progress 41, 363 (1942) Phys. Rev. 61, 390 (1942) R. Smoluchowski and J. S. Koehler, Ann. Rev. Phys. Chem. (1951)

[c9] W. F. Meggers, J. Opt. Soc. Am. 31, 39, 605 (1941)

[c10] A. Sieverts and G. Zapf, Z. physik. Chem. 172, 314 (1935)

[c11] W. Geibel, Z. anorg. u. allgem. Chem. 69, 38 (1910) ibid.70, 240 (1911)

[c12] J. E. Goldman, Phys. Rev. 82, 339(A) (1951)

[c13] R. Smoluchowski, Intern. Conf. on Metals, Amsterdam, 1948 Physica 15, 179 (1949)

[c14] R. Smoluchowski, Nat. Res. Council Conf. on Phase Transformations, Cornell University, 1948, published by John Wiley and Sons, Inc., New York, 1951

[c15] W. Hume-Rothery, Atomic Theory for Students of Metallurgy (Institute of Metals, London, 1946)

[c16] R. Smoluchowski (to be published)

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Statistical Theory of Properties of Solid Solutions

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