A Theory of the Deviation from Close Packing in Hexagonal Metal Crystals

John B. Goodenough

doi:10.1103/PhysRev.89.282

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A Theory of the Deviation from Close Packing in Hexagonal Metal Crystals

John B. Goodenough^*

Department of Physics, University of Chicago, Chicago, Illinois

^*Now at Massachusetts Institute of Technology Digital Computor Laboratory, Cambridge, Massachusetts.

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Phys. Rev. 89, 282 – Published 1 January, 1953

DOI: https://doi.org/10.1103/PhysRev.89.282

Abstract

A mechanism is proposed to show how the Fermi surface interacts with the Brillouin zone boundaries. The direction and relative magnitude of the variation of the $\frac{c}{a}$ ratio for hexagonal crystals from the ideal value for close packing are predicted as a function of the electron-atom ratio, and these predictions are compared with values of lattice parameters which are reported in the literature.

References (24)

E. Wigner and F. Seitz, Phys. Rev. 43, 804 (1933) ibid.46, 509 (1934) E. Wigner, 46, 1002 (1934)
J. Bardeen, J. Chem. Phys. 6, 367 (1938)
H. Jones, Proc. Roy. Soc. (London) A147, 396 (1934)
C. S. Barrett and O. R. Trautz, Am. Inst. Mining Met. Engrs. 175, 579 (1948)
C. S. Barrett, Phase Transformations in Solids (John Wiley & Sons, Inc., New York, 1951), p. 343. Edited by R. Smoluchowski
E. A. Owen and I. G. Edmunds, J. Inst. Metals 63, 291 (1938)
A. Pabst, Z. physik. Chem., B3, 443 (1929)
S. Stenbeck, Z. anorg. u. allgem. Chem. 214, 16 (1933)
E. A. Owen and L. Pickup, Proc. Roy. Soc. (London) A140, 179 (1933)
W. Hume-Rothery and G. V. Raynor, J. Inst. Metals 66, 191 (1940)
C. Zener, Phys. Rev. 81, 440 (1951)
F. Bloch, Z. Physik 52, 555 (1928)
K. Fuchs, Proc. Roy. Soc. (London) A151, 585 (1935)
L. Brillouin, Quantenstatistik (Julius Springer, Berlin, 1931)
Omitted endnote
Omitted endnote
A. H. Wilson, The Theory of Metals (Cambridge University Press, Cambridge, 1936), p. 78
L. Brillouin, Wave Propagation in Periodic Structures (McGraw-Hill Book Company, Inc., New York, 1946)
F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940)
N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, London, 1936), Chap. V
Richard Jones (private communication)
E. A. Edmunds and Qurashi (private communication to R. Jones by H. Lipsom)
H. Jones, Proc. Roy. Soc. (London) 144, 225 (1934) ibid.147, 396 (1934) N. F. Mott and H. Jones, p. 170 of [20]
W. Hume-Rothery, J. Inst. Metals 35, 295 (1926) The Metallic State (Oxford University Press, London, 1931), p. 328

[c1] E. Wigner and F. Seitz, Phys. Rev. 43, 804 (1933) ibid.46, 509 (1934) E. Wigner, 46, 1002 (1934)

[c2] J. Bardeen, J. Chem. Phys. 6, 367 (1938)

[c3] H. Jones, Proc. Roy. Soc. (London) A147, 396 (1934)

[c4] C. S. Barrett and O. R. Trautz, Am. Inst. Mining Met. Engrs. 175, 579 (1948)

[c5] C. S. Barrett, Phase Transformations in Solids (John Wiley & Sons, Inc., New York, 1951), p. 343. Edited by R. Smoluchowski

[c6] E. A. Owen and I. G. Edmunds, J. Inst. Metals 63, 291 (1938)

[c7] A. Pabst, Z. physik. Chem., B3, 443 (1929)

[c8] S. Stenbeck, Z. anorg. u. allgem. Chem. 214, 16 (1933)

[c9] E. A. Owen and L. Pickup, Proc. Roy. Soc. (London) A140, 179 (1933)

[c10] W. Hume-Rothery and G. V. Raynor, J. Inst. Metals 66, 191 (1940)

[c11] C. Zener, Phys. Rev. 81, 440 (1951)

[c12] F. Bloch, Z. Physik 52, 555 (1928)

[c13] K. Fuchs, Proc. Roy. Soc. (London) A151, 585 (1935)

[c14] L. Brillouin, Quantenstatistik (Julius Springer, Berlin, 1931)

[c15] Omitted endnote

[c16] Omitted endnote

[c17] A. H. Wilson, The Theory of Metals (Cambridge University Press, Cambridge, 1936), p. 78

[c18] L. Brillouin, Wave Propagation in Periodic Structures (McGraw-Hill Book Company, Inc., New York, 1946)

[c19] F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940)

[c20] N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, London, 1936), Chap. V

[c21] Richard Jones (private communication)

[c22] E. A. Edmunds and Qurashi (private communication to R. Jones by H. Lipsom)

[c23] H. Jones, Proc. Roy. Soc. (London) 144, 225 (1934) ibid.147, 396 (1934) N. F. Mott and H. Jones, p. 170 of [20]

[c24] W. Hume-Rothery, J. Inst. Metals 35, 295 (1926) The Metallic State (Oxford University Press, London, 1931), p. 328

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A Theory of the Deviation from Close Packing in Hexagonal Metal Crystals

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