Dielectric properties of material with random off-center defects: Monte Carlo simulation of relaxor ferroelectrics

Abstract

A Ginzburg–Landau type theory of interaction of randomly distributed local dipoles in a paraelectric crystal is developed. The interaction is caused by the polarization of the host lattice generated by these dipoles. The obtained effective Hamiltonian of the dipole–dipole interaction is employed for the Monte Carlo simulation of ferroelectric properties of a system with off-center dopant ions producing local dipoles. The computer simulation shows that at low dopant ion concentration the paraelectric state transforms into a macroscopically paraelectric state consisting of randomly oriented polar clusters. These clusters amplify the effective dipole moment and dramatically increase the dielectric constant. The interaction between the clusters results in a spectrum of relaxation time and transition to the relaxor state. The real and imaginary parts of the susceptibility of this state are calculated. At intermediate dopant concentration, the material undergoes a diffuse phase transition into a ferroelectric state smeared within a temperature range. A further increase in the dopant concentration makes the transition sharper and closer to the conventional ferroelectric transition. The results obtained are compared with the behavior of the K1−xLixTaO3 relaxor ferroelectric.

Monte Carlo simulation on dielectric and ferroelectric behaviors of relaxor ferroelectrics

“…Here in this article we give our attention to the configuration of electric dipoles in RFs. Although there is no quantitative comparison between our simulation and the 3D simulation, 19 a qualitative consistence between them will be revealed.…”

“…Structurally, it is believed that RFs are disordered electric-dipole media in which nanosized dipole ordered clusters are randomly embedded in the matrix of nonpolar phase ͑paraelectric phase, PE͒ below a certain temperature ͑typically 10 2 K). [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] A number of experimental and theoretical studies on the mechanism responsible for the abnormal polarization characteristics in RFs have been performed in the last several decades since the compositional inhomogeneity model proposed by Smolensky,4 although a widely accepted physical portrait has not yet been available. The micromacro domain transition model, 3 the superparaelectric model, 5 the dipole-glass model, 6 the order-disorder model 7,8 and random-bondrandom-field model, [9][10][11] among some other models are commonly employed to explain those experimentally observed effects for various RFs.…”

“…Recently, this idea was once more adopted by Semenovskaya and Khachaturyan 20 in the GinzburgLandau thermodynamic description of the FE lattice with impurity-induced defects and subsequently by the same group in the coarse-grain description of the GinzburgLandau theory. 19 They included the effect of local dipole fluctuations induced by impurity ions and dopants in the Landau free energy. In addition, these models represent a realistic description of multi-domained FE lattice in which the dipole-dipole interaction, domain wall energy, and even long-range elastic energy are taken into account, [21][22][23][24] while these interactions have been less considered in other models.…”

“…For example, in the compositional inhomogeneity model, the defects may be impurity atom or dopant ion. 19 For the former, the impurity atoms in the lattice are viewed as disordered ͑random͒ static defects coupled locally with the transformational mode which is responsible for a stable dipole. Therefore, the defects may suppress the magnitude of local dipoles from site to site.…”

“…The micromacro domain transition model, 3 the superparaelectric model, 5 the dipole-glass model, 6 the order-disorder model 7,8 and random-bondrandom-field model, [9][10][11] among some other models are commonly employed to explain those experimentally observed effects for various RFs. [12][13][14][15][16][17][18][19] In the comprehensive understanding of the microscopic characteristics of RFs, the concept of defect is basically important. It can also be viewed as a kind of compositional or structural inhomogeneity.…”