Studies of Phase Transitions in Order-Disorder Ferroelectrics. II. Calorimetric Investigations of K<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>P<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span>

W. Reese; L. F. May

doi:10.1103/PhysRev.167.504

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Studies of Phase Transitions in Order-Disorder Ferroelectrics. II. Calorimetric Investigations of K $D_{2}$ P $O_{4}$

W. Reese and L. F. May

Department of Physics, Naval Postgraduate School, Monterey, California

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Phys. Rev. 167, 504 – Published 10 March, 1968

DOI: https://doi.org/10.1103/PhysRev.167.504

Abstract

Calorimetric measurements on K $D_{2}$ P $O_{4}$ have been conducted, and the transition is found to be first order with an entropy change at $T_{c}$ of $(0.2407 \pm 0.0016) R$ . The entropy change associated with destruction of the polarization from 0°K to $T_{c}$ is found to be $(0.4234 \pm 0.0071) R$ . It is shown that a mean-field theory of the type proposed by Silsbee, Uehling, and Schmidt can give a good account of the heat capacity and polarization to within about 1°K of $T_{c}$ , although the latent heat and entropy are not predicted satisfactorily, presumably because of the breakdown of the mean-field approximation close to the transition. Below $T_{c}$ the divergence in the heat capacity may be argued to be logarithmic in the region closer than 1° to $T_{c}$ , or to be as $\frac{1}{{(T_{c} - T)}^{\frac{1}{2}}}$ in the region $T_{c} - 2 ° < T < T_{c} - 0.2 °$ . Arguments are offered in favor of the logarithmic divergence.

References (21)

W. Kanzig, in Solid State Physics, edited by F. Sietz and D. Turnbull (Academic Press Inc., New York, 1957), Vol. 4, p. 1
F. Jona and G. Shirane, Ferroelectric Crystals (The Macmillan Co., New York, 1962)
R. M. Hill and S. K. Ichiki, Phys. Rev. 130, 150 (1963)
W. Reese and L. F. May, Phys. Rev. 162, 510 (1967)
J. C. Slater, J. Chem. Phys. 9, 16 (1941)
H. B. Silsbee, E. A. Uehling, and V. H. Schmidt, Phys. Rev. 133, A165 (1964)
S. B. Garret, U.S. Atomic Energy Commission, Oak Ridge National Laboratory Report No. ORNL-1745, 149, 1954 (unpublished)
R. Blinc and S. Svetina, Phys. Rev. 147, 430 (1966)
Y. Takagi, J. Phys. Soc. Japan 3, 271 (1948) ibid.3, 273 (1948)
G. Shirane and T. Oguchi, J. Phys. Soc. Japan 3, 274 (1948)
V. H. Schmidt and E. A. Uehling, Phys. Rev. 126, 477 (1962)
T. Yamamoto, O. Tanimoto, Y. Yasada, and K. Okada, Natl. Bur. Std. (U.S.) Misc. Publ. 273, 86 (1966)
J. L, Bjorkstam, Phys. Rev. 153, 599 (1967)
C. C. Stephenson and J. G. Hooley, J. Am. Chem. Soc. 66, 1397 (1944)
J. F. Nagle and M. E. Fisher (to be published)
W. Bantle, Helv. Phys. Acta 15, 373 (1962)
R. M. Hill and S. K. Ichiki, Phys. Rev. 132, 1603 (1963)
B. Zwicker and P. Scherrer, Helv. Phys. Acta 17, 346 (1944)
D. T. Teaney, Solid State Commun. 5, 207 (1967)
R. Brout, Phase Transitions (W. A. Benjamin, Inc., New York, 1964)
E. H. Lieb, Phys. Rev. Letters 18, 692 (1967) ibid.18, 1046 (1967) ibid.19, 108 (1967) B. Sutherland, ibid. 19, 103 (1967) C. P. Yang, ibid. 19, 586 (1967) B. Sutherland, C. N. Yang, and C. P. Yang, ibid. 19, 588 (1967)

[c1] W. Kanzig, in Solid State Physics, edited by F. Sietz and D. Turnbull (Academic Press Inc., New York, 1957), Vol. 4, p. 1

[c2] F. Jona and G. Shirane, Ferroelectric Crystals (The Macmillan Co., New York, 1962)

[c3] R. M. Hill and S. K. Ichiki, Phys. Rev. 130, 150 (1963)

[c4] W. Reese and L. F. May, Phys. Rev. 162, 510 (1967)

[c5] J. C. Slater, J. Chem. Phys. 9, 16 (1941)

[c6] H. B. Silsbee, E. A. Uehling, and V. H. Schmidt, Phys. Rev. 133, A165 (1964)

[c7] S. B. Garret, U.S. Atomic Energy Commission, Oak Ridge National Laboratory Report No. ORNL-1745, 149, 1954 (unpublished)

[c8] R. Blinc and S. Svetina, Phys. Rev. 147, 430 (1966)

[c9] Y. Takagi, J. Phys. Soc. Japan 3, 271 (1948) ibid.3, 273 (1948)

[c10] G. Shirane and T. Oguchi, J. Phys. Soc. Japan 3, 274 (1948)

[c11] V. H. Schmidt and E. A. Uehling, Phys. Rev. 126, 477 (1962)

[c12] T. Yamamoto, O. Tanimoto, Y. Yasada, and K. Okada, Natl. Bur. Std. (U.S.) Misc. Publ. 273, 86 (1966)

[c13] J. L, Bjorkstam, Phys. Rev. 153, 599 (1967)

[c14] C. C. Stephenson and J. G. Hooley, J. Am. Chem. Soc. 66, 1397 (1944)

[c15] J. F. Nagle and M. E. Fisher (to be published)

[c16] W. Bantle, Helv. Phys. Acta 15, 373 (1962)

[c17] R. M. Hill and S. K. Ichiki, Phys. Rev. 132, 1603 (1963)

[c18] B. Zwicker and P. Scherrer, Helv. Phys. Acta 17, 346 (1944)

[c19] D. T. Teaney, Solid State Commun. 5, 207 (1967)

[c20] R. Brout, Phase Transitions (W. A. Benjamin, Inc., New York, 1964)

[c21] E. H. Lieb, Phys. Rev. Letters 18, 692 (1967) ibid.18, 1046 (1967) ibid.19, 108 (1967) B. Sutherland, ibid. 19, 103 (1967) C. P. Yang, ibid. 19, 586 (1967) B. Sutherland, C. N. Yang, and C. P. Yang, ibid. 19, 588 (1967)

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Studies of Phase Transitions in Order-Disorder Ferroelectrics. II. Calorimetric Investigations of K $D_{2}$ P $O_{4}$

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Studies of Phase Transitions in Order-Disorder Ferroelectrics. II. Calorimetric Investigations of KD2PO4

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Studies of Phase Transitions in Order-Disorder Ferroelectrics. II. Calorimetric Investigations of K $D_{2}$ P $O_{4}$