Theory of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi><mi></mi><mo>−</mo><mi></mi><mi>γ</mi></math></span> Phase Transition in Metallic Cerium

Ricardo Ramirez; L. M. Falicov

doi:10.1103/PhysRevB.3.2425

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Theory of the $α - γ$ Phase Transition in Metallic Cerium

Ricardo Ramirez^*,† and L. M. Falicov^†

Department of Physics, University of California, Berkeley, California 94720

^*Chile-California Cooperative Program Fellow (supported by the Ford Foundation); present address: Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Casilla 5487, Santiago, Chile.
^†Work supported in part by the National Science Foundation, through Grant No. GP13889.

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Phys. Rev. B 3, 2425 – Published 15 April, 1971

DOI: https://doi.org/10.1103/PhysRevB.3.2425

Abstract

A simple model for the $α - γ$ phase transition in Ce is presented. It is based on the change of occupation number of the $f$ levels, which are assumed to be atomiclike in character, i.e., highly correlated and with a very narrow bandwidth. The change in occupation number is, as a function of temperature, caused by the short-range part of the electron-electron interaction. The theory allows for the existence of a critical point. With the assumption of a linear relationship between $f$ -level occupation numbers and lattice constant, pressure-latticeconstant isotherms are calculated. Curves for the paramagnetic susceptibility as a function of pressure and temperature are also presented.

References (26)

E. King, J. A. Lee, I. R. Harris, and T. F. Smith, Phys. Rev. B 1, 1380 (1970)
E. Franceschi and G. L. Olcese, Phys. Rev. Letters 22, 1299 (1969)
D. B. McWhan, Phys. Rev. B 1, 2826 (1970)
A. Blandin, B. Coqblin, and J. Friedel, in Physics of Solids at High Pressures, edited by C. T. Tomizuka and R. M. Emrick (Academic, New York, 1965), p. 233
B. Coqblin and A. Blandin, Advan. Phys. 17, 281 (1968)
C. F. Ratto, B. Coqblin, and E. Galleani D'Agliano, Advan. Phys. 18, 489 (1969)
K. A. Gschneider, Jr., R. O. Elliott, and R. R. McDonald, J. Phys. Chem. Solids 23, 555 (1962)
Y. A. Rocher, Advan. Phys. 11, 233 (1962)
H. Tracy Hall, J. Dean Barnett, and L. Merrill, Science 139, 111 (1963)
K. A. Gschneider, Jr. and R. Smoluchowski, J. Less-Common Metals 5, 374 (1963)
R. I. Beecroft and C. A. Swenson, J. Phys. Chem. Solids 15, 234 (1960)
E. Ponyatovskii, Dokl. Akad. Nauk SSSR 120, 1021 (1958) [Soviet Phys. Doklady 3, 498 (1958)]
A. Jayaraman, Phys. Rev. 137, A179 (1965)
W. H. Zachariasen, Phys. Rev. 76, 301 (1949)
L. Pauling, J. Chem. Phys. 18, 145 (1950)
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H. W. Myron and S. H. Liu (private communication)
Omitted endnote
N. F. Mott, Rev. Mod. Phys. 40, 677 (1968)
L. M. Falicov and J. C. Kimball, Phys. Rev. Letters 22, 997 (1969)
R. Ramirez, L. M. Falicov, and J. C. Kimball, Phys. Rev. B 2, 3383 (1970)
D. L. Johnson and D. K. Finnemore, Phys. Rev. 158, 376 (1967)
Omitted endnote
, p. 436
M. R. MacPherson, D. Wohlleben, M. B. Maple, and G. E. Everett, Phys. Rev. Letters 26, 20 (1971)

[c1] E. King, J. A. Lee, I. R. Harris, and T. F. Smith, Phys. Rev. B 1, 1380 (1970)

[c2] E. Franceschi and G. L. Olcese, Phys. Rev. Letters 22, 1299 (1969)

[c3] D. B. McWhan, Phys. Rev. B 1, 2826 (1970)

[c4] A. Blandin, B. Coqblin, and J. Friedel, in Physics of Solids at High Pressures, edited by C. T. Tomizuka and R. M. Emrick (Academic, New York, 1965), p. 233

[c5] B. Coqblin and A. Blandin, Advan. Phys. 17, 281 (1968)

[c6] C. F. Ratto, B. Coqblin, and E. Galleani D'Agliano, Advan. Phys. 18, 489 (1969)

[c7] K. A. Gschneider, Jr., R. O. Elliott, and R. R. McDonald, J. Phys. Chem. Solids 23, 555 (1962)

[c8] Y. A. Rocher, Advan. Phys. 11, 233 (1962)

[c9] H. Tracy Hall, J. Dean Barnett, and L. Merrill, Science 139, 111 (1963)

[c10] K. A. Gschneider, Jr. and R. Smoluchowski, J. Less-Common Metals 5, 374 (1963)

[c11] R. I. Beecroft and C. A. Swenson, J. Phys. Chem. Solids 15, 234 (1960)

[c12] E. Ponyatovskii, Dokl. Akad. Nauk SSSR 120, 1021 (1958) [Soviet Phys. Doklady 3, 498 (1958)]

[c13] A. Jayaraman, Phys. Rev. 137, A179 (1965)

[c14] W. H. Zachariasen, Phys. Rev. 76, 301 (1949)

[c15] L. Pauling, J. Chem. Phys. 18, 145 (1950)

[c16] C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1966), p. 437

[c17] S. C. Keeton and T. L. Loucks, Phys. Rev. 168, 672 (1968) O. K. Andersen and T. L. Loucks, ibid. 167, 551 (1968)

[c18] H. W. Myron and S. H. Liu (private communication)

[c19] Omitted endnote

[c20] N. F. Mott, Rev. Mod. Phys. 40, 677 (1968)

[c21] L. M. Falicov and J. C. Kimball, Phys. Rev. Letters 22, 997 (1969)

[c22] R. Ramirez, L. M. Falicov, and J. C. Kimball, Phys. Rev. B 2, 3383 (1970)

[c23] D. L. Johnson and D. K. Finnemore, Phys. Rev. 158, 376 (1967)

[c24] Omitted endnote

[c25] , p. 436

[c26] M. R. MacPherson, D. Wohlleben, M. B. Maple, and G. E. Everett, Phys. Rev. Letters 26, 20 (1971)

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Theory of the $α - γ$ Phase Transition in Metallic Cerium

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Theory of the α−γ Phase Transition in Metallic Cerium

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Theory of the $α - γ$ Phase Transition in Metallic Cerium