Monte Carlo simulation on dielectric and ferroelectric behaviors of relaxor ferroelectrics

Abstract

The dielectric and ferroelectric behaviors of relaxor ferroelectrics over the ferroelectric transition range are simulated using Monte Carlo simulation. The simulation is based on the GinzburgLandau ferroelectric model lattice in which a random distribution of two types of defects ͑dopants͒ which will suppress and enhance the local polarization, respectively, is assumed. The simulation reveals an evolution of the ferroelectric transitions from a normal first-order mode toward a diffusive mode, with increasing defect concentration. The simulated lattice configuration shows the microdipole ordered clusters embedded in the matrix of paraelectric phase over a wide range of temperature, a characteristic of relaxor ferroelectrics. The relaxor-like behaviors are confirmed by the lattice free energy, dielectric susceptibility, and ferroelectric relaxation evaluated as a function of the defect concentration. Finally, we present a qualitative comparison of our simulated results with the simulation based on the coarse-grain model ͓C. C. Su, B. Vugmeister, and A. G. Khachaturyan, J. Appl. Phys. 90, 6345 ͑2001͔͒.

Antiferroelectric polarization switching and dynamic scaling of energy storage: A Monte Carlo simulation

“…It is noted that for a two-dimensional lattice, this treatment is accurate as long as the truncating distance R is big (R ¼ 8 in our simulation). 41,42 As mentioned earlier, one key problem with the present simulation is that so far neither phenomenological theory other than the above scheme on AFE lattice is available nor physical parameters for those AFE materials have been reported. As a qualitative approximation, all the physical coefficients except the AFE coupling constant J in Eq.…”

“…Considering that the response time of elastic strain is far shorter than that for dipole relaxation, we give ten chances to its strain relaxation every time we relax one electric dipole. 41,42 As a result, the initial dipole configuration of sublattice a is a ferroelectrically ordered state with all the dipoles aligned along the x-axis, while those from sublattice b are oriented in the opposite directions. The annealing process continues for 10 6 mcs with 1 mcs standing for L 2 dipole flip attempts.…”

Monte Carlo simulation on the size effect in ferroelectric nanostructures

“…[15][16][17][18] Subsequently, we look at the elastic energy f u . However, to make the computation tractable, the dipole-dipole interaction is truncated at a preset separation from the central site, and this truncating distance is sufficient for a reliable accounting of this interaction.…”

“…[9][10][11][12] The phenomenological studies mainly deal with phase-field modeling of the time-dependent Ginzburg-Landau ͑TDGL͒ theory, while the Langevin dynamics of polarization evolution is simulated numerically. Despite the Monte Carlo simulation was once employed to investigate the domain structure in ferroelectrics, [15][16][17][18] no comprehensive simulations taking account of the full set of free energy terms has been successfully performed, since no elastic energy and electrostrictive interaction, which play significant roles in the formation of domain patterns, were included in these simulations. It should be addressed that solving the TDGL equation and the mechanical equilibrium equation for a large lattice is extremely time consuming, and these approaches are mainly employed to deal with a small size lattice.…”

Diffuse First Order Phase Transitions

“…They found out that the defects help the system avoiding the hysteretic phenomena by finding passes over metastable states in a random network, which have only comparatively small potential barriers between each other. Further studies of Wang et al within the same approach [11] showed that dielectric permittivity diffuses in such a system, and there appears a number of relaxators, which produce a frequency dependence of dielectric permittivity. Qian and Bursill [12] considered the smoothening of the phase transition in PbMg 1/3 Nb 2/3 O 3 as a result of random fields on the Pb sites produced by Mg and Nb.…”