Collective Behavior of Polar Impurities in Ionic Crystals. II

Wolfgang Zernik

doi:10.1103/PhysRev.158.562

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Collective Behavior of Polar Impurities in Ionic Crystals. II

Wolfgang Zernik

RCA Laboratories, Princeton, New Jersey

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Phys. Rev. 158, 562 – Published 10 June, 1967

DOI: https://doi.org/10.1103/PhysRev.158.562

Abstract

The purpose of this work is to construct an improved theory to account for the low-temperature dielectric properties of KCl crystals containing substitutional ${(OH)}^{-}$ impurities. The statistical mechanics of a pair of dipoles is discussed in order to derive a generalized Langevin function giving the mean moment of such a pair along the direction of an applied field. A hybrid approximation is then developed, in which the interaction of a typical pair of ${(OH)}^{-}$ dipoles is treated explicitly while the remaining interactions are treated by means of a modified Onsager-Pirenne approximation. The resulting equations predict a second-order phase transition at $\frac{k T_{c}}{N m^{2}} ≅ 0.53$ , where $N$ is the concentration and $m$ the dipole moment of the ${(OH)}^{-}$ ions. The predicted spontaneous polarization increases continuously below $T_{c}$ to reach a saturation value of ${P_{0}}^{max} ≅ 0.45 N m$ . A thermodynamic analysis indicates that the asymptotic behavior of the model as $T \to 0$ is essentially in agreement with the third law, and also enables one to show that the critical temperature should be independent of the applied field.

References (22)

W. Zernik, Phys. Rev. 139, A1010 (1965)
H. Eyring, D. Henderson, B. J. Stover, and E. M. Eyring, Statistical Mechanics and Dynamics (John Wiley & Sons, Inc., New York, 1964), Chap. 8
H. Eyring et al., Statistical Mechanics and Dynamics (John Wiley & Sons, Inc., New York, 1964), Chap. 10
[1] J. A. Ewing R. M. Bozorth, Ferromagnetism (D. Van Nostrand Company, Inc., New York, 1951), Chap. 10
M. W. Klein, Phys. Rev. 141, 489 (1966)
W. N. Lawless, Physik Kondensierten Materie 5, 100 (1966)
W. N. Lawless, Phys. Rev. Letters 17, 1048 (1966)
A. F. Devonshire, Proc. Roy. Soc. (London) A153, 601 (1936)
M. E. Baur and W. R. Salzman, Phys. Rev. Letters 16, 701 (1966) Phys. Rev. 17, 159 (E) (1966)
H. B. Shore, Phys. Rev. 151, 570 (1966)
P. Sauer, Z. Physik 194, 360 (1966)
P. Kuri and P. Sauer, Z. Physik 194, 478 (1966)
P. Sauer, O. Schirmer, and J. Schneider, Phys. Status Solidi 16, 79 (1966)
M. E. Baur and W. R. Salzman, Phys. Rev. 151, 710 (1966)
H. B. Shore, Phys. Rev. Letters 17, 1142 (1966)
K. F. Niessen, Phys. Rev. 34, 253 (1929)
H. Paus and F. Lüty, Phys. Status Solidi 12, 341 (1965)
I. Shepherd and G. Feher, Phys. Rev. Letters 15, 194 (1965)
C. K. Chau, M. V. Klein, and B. Wedding, Phys. Rev. Letters 17, 521 (1966) D. R. Bosomworth (unpublished)
Omitted endnote
H. Fröhlich, Theory of Dielectrics (Clarendon Press, Oxford, England, 1949), pp. 9-13
H. B. Callen, Thermodynamics (John Wiley & Sons, Inc., New York, 1960), Chap. 9

[c1] W. Zernik, Phys. Rev. 139, A1010 (1965)

[c2] H. Eyring, D. Henderson, B. J. Stover, and E. M. Eyring, Statistical Mechanics and Dynamics (John Wiley & Sons, Inc., New York, 1964), Chap. 8

[c3] H. Eyring et al., Statistical Mechanics and Dynamics (John Wiley & Sons, Inc., New York, 1964), Chap. 10

[c4] [1] J. A. Ewing R. M. Bozorth, Ferromagnetism (D. Van Nostrand Company, Inc., New York, 1951), Chap. 10

[c5] M. W. Klein, Phys. Rev. 141, 489 (1966)

[c6] W. N. Lawless, Physik Kondensierten Materie 5, 100 (1966)

[c7] W. N. Lawless, Phys. Rev. Letters 17, 1048 (1966)

[c8] A. F. Devonshire, Proc. Roy. Soc. (London) A153, 601 (1936)

[c9] M. E. Baur and W. R. Salzman, Phys. Rev. Letters 16, 701 (1966) Phys. Rev. 17, 159 (E) (1966)

[c10] H. B. Shore, Phys. Rev. 151, 570 (1966)

[c11] P. Sauer, Z. Physik 194, 360 (1966)

[c12] P. Kuri and P. Sauer, Z. Physik 194, 478 (1966)

[c13] P. Sauer, O. Schirmer, and J. Schneider, Phys. Status Solidi 16, 79 (1966)

[c14] M. E. Baur and W. R. Salzman, Phys. Rev. 151, 710 (1966)

[c15] H. B. Shore, Phys. Rev. Letters 17, 1142 (1966)

[c16] K. F. Niessen, Phys. Rev. 34, 253 (1929)

[c17] H. Paus and F. Lüty, Phys. Status Solidi 12, 341 (1965)

[c18] I. Shepherd and G. Feher, Phys. Rev. Letters 15, 194 (1965)

[c19] C. K. Chau, M. V. Klein, and B. Wedding, Phys. Rev. Letters 17, 521 (1966) D. R. Bosomworth (unpublished)

[c20] Omitted endnote

[c21] H. Fröhlich, Theory of Dielectrics (Clarendon Press, Oxford, England, 1949), pp. 9-13

[c22] H. B. Callen, Thermodynamics (John Wiley & Sons, Inc., New York, 1960), Chap. 9

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Collective Behavior of Polar Impurities in Ionic Crystals. II

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