Numerical simulations of nonlinear and chaotic order parameter responses in bulk antiferroelectrics using ammonium dihydrogen phosphate parameter

Authors

DOI:

https://doi.org/10.33910/2687-153X-2022-3-3-122-136

Keywords:

antiferroelectrics, ammonium dihydrogen phosphate, chaos, Landau free energy density, nonlinear, Poincare Sections

Abstract

In this paper, the nonlinear and chaotic responses of bulk antiferroelectrics are elaborated phenomenologically and numerically. The first ordered phase of bulk antiferroelectrics is formulated by applying calculus of variations to Landau free energy density expansions of bulk antiferroelectrics. With applied time-dependent electric field, the antiferroelectrics dynamic responses are obtained by Landau–Khalatnikov equation of motion. The resulting dynamical equations are two nonlinearly-coupled second order differential equations corresponding to two inter-penetrating sub-lattices of antiferroelectrics, and these are solved numerically using forth-order Runge–Kutta methods and ammonium dihydrogen phosphate parameters in its first ordered phase. These calculated results are presented graphically for various frequencies and amplitudes in the applied electric fields.

References

Chan, T. Y. (2010) Study of chaotic dynamics and hysteresis in bulk antiferromagnet and Antiferromagnetic Film. MSc Thesis (Antiferromagnetism). George Town, Universiti Sains Malaysia, 125 p. (In English)

Diestelhorst, M. (2003) What can we learn about ferroelectrics using methods of nonlinear dynamics? Condensed Matter Physics, 6 (2), 189–196. https://doi.org/10.5488/CMP.6.2.189 (In English)

Goldstone, J. A., Garmire, E. (1984) Intrinsic optical bistability in nonlinear media. Physical Review Letter, 53 (9), 910–913. https://doi.org/10.1103/PhysRevLett.53.910 (In English)

Ledzion, R., Bondarczuk, K., Kucharczyk, W. (2004) Temperature dependence of the quadratic electrooptic effect andestimation of antipolarization of ADP. Crystal Research and Technology, 39 (2), 161–164. https://doi.org/10.1002/crat.200310165 (In English)

Lines, M. E., Glass, A. M. (1977) Principles and applications of ferroelectrics and related materials. Oxford: Clarendon Press, 664 p. (In English)

Milek, J. T., Neuberger, M. (1972) Handbook of Electronic Materials. Vol.8. Linear electrooptic modular materials. New York: IFI/Plenum Publ., 264 p. (In English)

Murgan, R., Tilley, D. R., Ishibashi, Y. et al. (2002) Calculation of nonlinear-susceptibility tensor components in ferroelectrics: Сubic, tetragonal, and rhombohedral symmetries. Journal of the Optical Society of America B, 19 (9), 2007–2021. https://doi.org/10.1364/JOSAB.19.002007 (In English)

Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P. (1996) Numerical recipes in C: The art of scientific computing. 2nd ed. Cambridge: Cambridge University Press, 537 p. (In English)

Strogatz, S. H. (2018) Nonlinear dynamics and chaos with applications to Physics, Biology, Chemistry, and Engineering. New York: CRC Press, 532 p. https://doi.org/10.1201/9780429492563 (In English)

Tan, E. K. (2001) Static and dynamic properties of ferroelectric materials. MSc Thesis (Ferroelectricity). George Town, Universiti Sains Malaysia, 164 p. (In English)

Toh, P. L. (2009) Study of chaotic dynamics and hysteresis in bulk ferromagnet and ferromagnetic film based on yttrium iron garnet. MSc Thesis (Ferromagnetic Materials). George Town, Universiti Sains Malaysia, 76 p. (In English)

Downloads

Published

30.09.2022

Issue

Section

Theoretical Physics