Abstract
We consider the problem of determining the permittivity and the electrocaloric effect in the model of a ferroelectric ceramics grain. We assume that a grain consists of a spherical ferroelectric core coated with a dielectric shell and placed into a dielectric matrix. The transition layer thickness is assumed small as compared to the grain size. The dependence of the polarization on the electric field in the core is given by the nonlinear Ginzburg–Landau equation. The polarization reversal is induced by a change in the electric field that is considered uniform at large distance from the grain. The electrostriction effect in the core–shell–matrix three-phase system produces an elastic field described by linear equations. To take into account the effect of domain walls on the physical characteristics of the ceramics in the given model, we propose that the Kittel–Mitsui–Furuichi approach be used. The proposed computational algorithm makes it possible to refine the dependence of the number of domains on the spherical grain size. The electrocaloric effect in the grain is represented by the combination of the primary and secondary effects that appear due to ordering of dipole moments of the ferroelectric with the perovskite structure; by way of example, we consider the barium titanate ceramics. For this material, we report on the results of calculations of the dependences of the permittivity and individual electrocaloric effect components on the grain size.
REFERENCES
A. Starkov, O. Pakhomov, and I. Starkov, Ferroelectrics 14, 108 (2014).
G. Suchaneck, O. Pakhomov, and G. Gerlach, Electrocaloric Cooling (InTechOpen, London, 2017).
A. Greco, C. Aprea, A. Maiorino, and C. Masselli, Int. J. Refrig. 106, 66 (2019).
Y. V. Sinyavsky and V. M. Brodyansky, Ferroelectrics 131, 321 (1992).
B. C. Kim, K. W. Chae, and C. I. Cheon, J. Korean Phys. Soc. 76, 226 (2020).
I. A. Starkov, A. S. Anokhin, I. L. Myl’nikov, M. A. Mishnev, and A. S. Starkov, Fiz. Tverd. Tela 64, 443 (2022).
J. H. Qiu and Q. Jiang, J. Appl. Phys. 105, 034110 (2009).
J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford Univ. Press, Oxford, 1985).
A. S. Starkov and I. A. Starkov, J. Exp. Theor. Phys. 119, 258 (2014).
A. L. Kholkin, V. A. Trepakov, and G. A. Smolenskii, JETP Lett. 35, 124 (1982).
E. P. Smirnova, G. Yu. Sotnikova, N. V. Zaitseva, A. A. Kapralov, and G. A. Gavrilov, Tech. Phys. Lett. 44, 60 (2018).
N. A. Pertsev, A. G. Zembilgotov, and A. K. Tagantsev, Phys. Rev. Lett. 80, 1988 (1998).
M. Vrabelj, H. Uršič, Z. Kutnjak, B. Rožič, S. Drnovšek, A. Benčan, V. Bobnar, L. Fulanovič, and B. Malič, J. Eur. Ceram. Soc. 36, 75 (2016).
T. Hoshina, S. Wada, Y. Kuroiwa, and T. Tsurumi, Appl. Phys. Lett. 93, 192914 (2008).
A. Y. Emelyanov, N. A. Pertsev, S. Hoffmann-Eifert, U. Böttger, and R. Waser, J. Electroceram. 9, 5 (2002).
A. S. Starkov, O. V. Pakhomov, and I. A. Starkov, J. Exp. Theor. Phys. 116, 987 (2013).
B. A. Strukov, S. T. Davitadze, S. G. Shulman, B. V. Goltzman, and V. V. Lemanov, Ferroelectrics 301, 157 (2004).
T. Hoshina, J. Ceram. Soc. Jpn. 121, 156 (2013).
I. A. Starkov and A. S. Starkov, J. Nanophoton. 10, 033503 (2016).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Nauka, Moscow, 1992; Pergamon, New York, 1984).
V. I. Aleshin, Sov. Phys. Crystallogr. 36, 766 (1991).
O. G. Vendik, N. Yu. Medvedeva, and S. P. Zubko, Tech. Phys. Lett. 34, 323 (2008).
A. S. Starkov, I. A. Starkov, A. I. Dedyk, G. Suchaneck, and G. Gerlach, Phys. Status Solidi B 255, 1700245 (2018).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 7: Theory of Elasticity (Nauka, Moscow, 1987; Pergamon Press, New York, 1986).
A. S. Starkov and I. A. Starkov, J. Exp. Theor. Phys. 119, 861 (2014).
V. G. Edvabnik, Sovrem. Probl. Nauki Obrazov., Nos. 1–2, 76 (2015).
L. A. Apresyan, T. V. Vlasova, V. I. Krasovskii, V. I. Kryshtob, and S. I. Rasmagin, Tech. Phys. 65, 1130 (2020).
L. D. Landau and E. M. Lifshits, Phys. Z. Sowjet. 8, 153 (1935).
C. Kittel, Phys. Rev. 70, 965 (1946).
T. Mitsui and J. Furuichi, Phys. Rev. 90, 193 (1953).
A. K. Tagantsev, J. Fousek, and L. E. Cross, Domains in Ferroic Crystals and Thin Films (Springer, New York, 2010).
G. Arlt, D. Hennings, and G. de With, J. Appl. Phys. 58, 1619 (1985).
A. M. Bratkovsky and A. P. Levanyuk, AIP Conf. Proc. 535, 218 (2000).
Y. Huan, X. Wang, J. Fang, and L. Li, J. Eur. Ceram. Soc. 34, 1445 (2014).
Y. Tan, J. Zhang, Y. Wu, Ch. Wang, V. Koval, B. Shi, H. Ye, R. McKinnon, G. Viola, and H. Yan, Sci. Rep. 5, 1 (2015).
B. Dai, X. Hu, R. Yin, W. Bai, F. Wen, J. Deng, L. Zheng, J. Du, P. Zheng, and H. Qin, J. Mater. Sci.: Mater. Electron. 28, 7928 (2017).
N. A. Pertsev and A. G. Zembilgotov, J. Appl. Phys. 78, 6170 (1995).
Z. Zhao, V. Buscaglia, M. Viviani, M. T. Buscaglia, L. Mitoseriu, A. Testino, M. Nygren, M. Johnsson, and P. Nanni, Phys. Rev. B 70, 024107 (2004).
Y. L. Li, L. E. Cross, and L. Q. Chen, J. Appl. Phys. 98, 064101 (2005).
P. Marton, I. Rychetsky, and J. Hlinka, Phys. Rev. B 81, 144125 (2010).
M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Oxford Univ. Press, Oxford, 1977).
V. A. Lukacs, M. Airimioaei, L. Padurariu, L. P. Curecheriu, C. E. Ciomaga, A. Bencan,G. Drazic, M. Avakian, J. L. Jones, G. Stoian, M. Deluca, R. Brunner, A. Rotaru, and L. Mitoseriu, J. Eur. Ceram. Soc. 42, 2230 (2022).
V. I. Smirnov, Course of Higher Mathematics (Nauka, Moscow, 1974), Vol. 2 [in Russian].
A. S. Starkov, O. V. Pakhomov, and I. A. Starkov, JETP Lett. 91, 507 (2010).
G. G. Wiseman and J. K. Kuebler, Phys. Rev. 131, 2023 (1963).
D. L. Shan, C. H. Lei, Y. C. Cai, K. Pan, and Y. Y. Liu, Int. J. Solids Struct. 216, 59 (2021).
R. P. S. M. Lobo, N. D. Mohallem, and R. L. Moreira, J. Am. Ceram. Soc. 78, 1343 (1995).
Funding
This study was supported by the Russian Foundation for Basic Research (project no. 20-58-26015).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Translated by N. Wadhwa
Rights and permissions
About this article
Cite this article
Starkov, A.S., Starkov, I.A. Dependence of the Permittivity and of the Electrocaloric Effect on the Ferroelectric Ceramics Grain Size. J. Exp. Theor. Phys. 136, 605–619 (2023). https://doi.org/10.1134/S1063776123050126
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776123050126