Modeling Dynamic Ferroelectric Behavior with the Analytical Landau Theory

Analytic theory of hydrostatic stress effect on switching dynamics in ferroelectrics

“…In a previous study [24,25] we have established that this linear-like trend of polarization switching time under high electric field is due to the e 2 3 effect. In this work, it is shown that when ferroelectric materials are subjected to hydrostatic stress at high electric field the reciprocal switching time still obey the linear-like behaviour due to the e 2 3 effect derived in equation (25). In addition, figure 1 shows that the application of hydrostatic stress causes the shortening of the polarization switching time for barium titanate.…”

“…However, for convenience in analysis this study uses a rescaled form of equation (6) given by [32], 2 . The effect of hydrostatic stress on the behaviour of ferroelectric material is incorporated through the scaled electrostriction factor By the inclusion of hydrostatic stress into our previous work [24,25] we extend the range of ferroelectric behaviour that can be studied using the analytical formulation of the Landau theory of phase transition. Equation ( 11) is solved exactly for the case of complete polarization reversal and the resulting expression for equilibrium polarization p e attained by the ferroelectric material at hydrostatic stress x, temperature t and electric field = e ke M (whereby k > 1) is given by the expression,…”

“…Following the solution of equation ( 16) exactly [24,25], the switching time for complete polarization reversal is determined as an explicit function of t, e and x as shown below, where C is a constant. Compared to our previous result [24,25] for switching time, equation (17) shows that the application of hydrostatic stress x in addition to temperature t and electric field e produces a complex expression for switching time dependent on factors such as − ( )…”

“…In an earlier work [24,25], analytical arguments and simulations were used to show that high electric field and temperature produce important consequences on the dynamic properties of ferroelectric switching behaviour. In this work we investigate the changes to equilibrium polarization and reciprocal switching time at high electric field when hydrostatic stress is applied during switching of ferroelectric material.…”

“…As such explicit functional dependence between ferroelectric properties on factors such as stress, temperature and electric field were not established analytically based on a common theoretical framework. This study develops the explicit functional dependence of ferroelectric properties on stress, electric field and temperature by extending our previous work [24,25] on an analytical form of the Landau theory of phase transitions for second order ferroelectrics by incorporating the effect of hydrostatic stress. The major advantage gained through the analytical approach adopted in this paper is that it enables the changes to the dynamic properties of ferroelectrics caused by the introduction of stress to be explored analytically supported by numerical results.…”