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Specific heat of BaTiO3
Volume 40A, number 3
PHYSICS LETTERS
17 July 1972
SPECIFIC HEAT OF BaTiO 3 I. HATTA Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan and A. IKUSHIMA The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
Received 7 June 1972
The temperature dependence of the specific heat in BaTiO3 has been obtained near TC by the use of an AC calorimetry technique. Its behavior agrees well with that predicted by the free-energy function. Measurement of the specific heat of BaTiO3, near its ferroelectric-to-paraelectric transition point is very important to elucidate the mechanism of the phase transition. BaTiO 3 has been thought to be a displacement ferroelectric. However, the soft modes in one of the transverse optical branches behave like an overdamped-oscillator [ 1, 2]. The dielectric dispersion of this sort o f the oscillator may also appear in the case of an order-disorder phase transition, which is regarded as the opposite to the displacement phase transition [ 1]. From the temperature dependence of the specific heat, one can expect to get new information about these situations.
The specific heat of BaTiO 3 crystal was measured by an AC calorimetry technique in the temperature range from room temperature to about 450 K. Fig. 1 shows curves of the specific heat as a function of temperature for a crystal grown by a top-seeded solution technique and for a crystal grown by a flux method using KF. The transition point T C, is 408.33 K for the former crystal, and is 397.72 K for the latter crystal. The absolute value of the present specific heat was determined by using the data given by Todd and Lorenson for the polycrystalline sample at 301.23 K [4]. Although the T C are different in these two crystals, the results show a quite similar
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20 300
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400
350 TEMPERATURE
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450
( K )
Fig. 1. Temperature dependence of the specific heat in BaTiO3. o, a sample grown by a top-seeded solution technique [3]; ©, a sample grown by a flux method using KF. 235
Volume 40A, number 3
PHYSICS LETTERS
temperature-dependence as a whole except for the temperature range of T ~> T c + 20 K. In b o t h results in fig. 1, a broad hump appears above TC, though the detailed shape is different from each other. The origin of these humps is not clear yet. A large latent heat appeared at T C in each sample, but its magnitude could not be estimated due to the restriction of the present method. Such a remarkable latent heat has never been observed [5]. Using the free-energy function for a stress-free crystal of BaTiO 3 given by Drougard and Huibregtse [6], we can obtain the temperature dependence of the specific heat. The feature of this result is quite similar to both o f the present experimental values below about T C + 20 K, and furthermore the calculated magnitude of the difference in the specific heat between the both sides of the first-order transition point TC, ACp Cp(T C - O) - Cp(TC + 0), well agrees with the experimental values. The thing of the most importance is the jump of the specific heat at the second-order transition point. In the BaTiO 3 crystal, it is well-known that the stressclamped crystal shows a second-order phase transition,
236
17 July 1972
and then the j u m p in the specific heat in this case is estimated to be about 1.46 k B per unit cell. From recent theories for displacement ferroelectrics [7, 8], such a large value of the jump in the specific heat seems to show that the anharmonic parts of the optical phonons are remarkable in the optical-phonon Hamiltonian, A full paper will be published elsewhere in the near future.
References [1] Y. Yamada, G. Shirane and A. Linz, Phys Rev. 177 (1969) 848. [2] J. Harada. J.D. Axe and G. Shirane, Phys. Rev. B4 (1971) 155. [3] This crystal was grown by A. Linz. We are indebted to him for providing the excellent crystal. [41 S.S. Todd and R.E. Lorenson, J. Am. Chem. Soc. 74 (1952) 2043. [5] G. Shirane and A. Takeda, J. Phys. Soc. Japan 7 (1952) 1. [6] M.E. Drougard and E.J. Huibregtse, IBM J. Res. Developm. 1 (1957) 318. [71 M.E. Lines, Phys. Rev. 177 (1969) 812. [81 Y. Onodera, Progr. theor. Phys. 45 (1971) 986.
PHYSICS LETTERS
17 July 1972
SPECIFIC HEAT OF BaTiO 3 I. HATTA Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan and A. IKUSHIMA The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
Received 7 June 1972
The temperature dependence of the specific heat in BaTiO3 has been obtained near TC by the use of an AC calorimetry technique. Its behavior agrees well with that predicted by the free-energy function. Measurement of the specific heat of BaTiO3, near its ferroelectric-to-paraelectric transition point is very important to elucidate the mechanism of the phase transition. BaTiO 3 has been thought to be a displacement ferroelectric. However, the soft modes in one of the transverse optical branches behave like an overdamped-oscillator [ 1, 2]. The dielectric dispersion of this sort o f the oscillator may also appear in the case of an order-disorder phase transition, which is regarded as the opposite to the displacement phase transition [ 1]. From the temperature dependence of the specific heat, one can expect to get new information about these situations.
The specific heat of BaTiO 3 crystal was measured by an AC calorimetry technique in the temperature range from room temperature to about 450 K. Fig. 1 shows curves of the specific heat as a function of temperature for a crystal grown by a top-seeded solution technique and for a crystal grown by a flux method using KF. The transition point T C, is 408.33 K for the former crystal, and is 397.72 K for the latter crystal. The absolute value of the present specific heat was determined by using the data given by Todd and Lorenson for the polycrystalline sample at 301.23 K [4]. Although the T C are different in these two crystals, the results show a quite similar
35
LI
"U
E .
30
.
.
.
.
oo
..... °:22.. oooOO ~ ° Q ° o l 25 t,3
,
oOO o °
oooO QO o ~ 4 o l D J ~ e o o o e
oOO ooooeo ooo
oooo °
UJ I
20 300
I
l
I
i
l
t
I
l
I
400
350 TEMPERATURE
l
l
I
I
450
( K )
Fig. 1. Temperature dependence of the specific heat in BaTiO3. o, a sample grown by a top-seeded solution technique [3]; ©, a sample grown by a flux method using KF. 235
Volume 40A, number 3
PHYSICS LETTERS
temperature-dependence as a whole except for the temperature range of T ~> T c + 20 K. In b o t h results in fig. 1, a broad hump appears above TC, though the detailed shape is different from each other. The origin of these humps is not clear yet. A large latent heat appeared at T C in each sample, but its magnitude could not be estimated due to the restriction of the present method. Such a remarkable latent heat has never been observed [5]. Using the free-energy function for a stress-free crystal of BaTiO 3 given by Drougard and Huibregtse [6], we can obtain the temperature dependence of the specific heat. The feature of this result is quite similar to both o f the present experimental values below about T C + 20 K, and furthermore the calculated magnitude of the difference in the specific heat between the both sides of the first-order transition point TC, ACp Cp(T C - O) - Cp(TC + 0), well agrees with the experimental values. The thing of the most importance is the jump of the specific heat at the second-order transition point. In the BaTiO 3 crystal, it is well-known that the stressclamped crystal shows a second-order phase transition,
236
17 July 1972
and then the j u m p in the specific heat in this case is estimated to be about 1.46 k B per unit cell. From recent theories for displacement ferroelectrics [7, 8], such a large value of the jump in the specific heat seems to show that the anharmonic parts of the optical phonons are remarkable in the optical-phonon Hamiltonian, A full paper will be published elsewhere in the near future.
References [1] Y. Yamada, G. Shirane and A. Linz, Phys Rev. 177 (1969) 848. [2] J. Harada. J.D. Axe and G. Shirane, Phys. Rev. B4 (1971) 155. [3] This crystal was grown by A. Linz. We are indebted to him for providing the excellent crystal. [41 S.S. Todd and R.E. Lorenson, J. Am. Chem. Soc. 74 (1952) 2043. [5] G. Shirane and A. Takeda, J. Phys. Soc. Japan 7 (1952) 1. [6] M.E. Drougard and E.J. Huibregtse, IBM J. Res. Developm. 1 (1957) 318. [71 M.E. Lines, Phys. Rev. 177 (1969) 812. [81 Y. Onodera, Progr. theor. Phys. 45 (1971) 986.