Order-Disorder Behavior in KNbO3 and KNbO3/KTaO3 Solid Solutions and Superlattices by Molecular-Dynamics Simulations

We use molecular-dynamics simulation to examine the order-disorder behavior in pure ferroelectric KNbO3 and in KNbO3-KTaO3 ferroelectric-paraelectric solid solutions and superlattices. We find that the order-disorder behavior is remarkably robust and plays an important role in both the polarization rotation associated with switching of the perfect crystal and in the dynamical behavior of the solid solutions and superlattices. INTRODUCTION Potassium niobate (KNbO3) is a perovskite ferroelectric displaying transitions from the cubic to tetragonal to orthorhombic to rhombohedral phases with decreasing temperature. It is well-known that KNbO3 displays order-disorder behavior, characterized by the Nb and O ions hardly ever being at their crystallographically assigned positions even in the cubic phase. As a consequence, even in the cubic phase every unit cell is polarized at almost every instant of time: only the time-average macroscopic polarization is actually zero. In this paper, we illustrate how this order-disorder behavior is manifested in a number of different scenarios. In each case, KNbO3 is in an environment very far from that which it usually experiences in an equilibrium perfect crystal. In particular, we examine the dynamical behavior associated with polarization rotation during the switching of a perfect crystal and the coupling of order-disorder behavior with the displacive dynamics of paraelectric KTaO3 in solid solutions and superlattices. POLARIZATION ROTATION IN A PERFECT CRYSTAL We have previously developed and validated an atomic-level simulation method for KNbO3 based on a traditional shell-model description[1] of the ionic interactions in the system[2]; we use this interatomic description here. Our model of KNbO3 displays the order-disorder type behavior seen experimentally.[3] This is illustrated by Fig. 1, which shows the distribution of the Cartesian components of polarization in a KNbO3 perfect crystal in the cubic phase and in the orthorhombic phase. In the cubic phase the distribution functions for all three components of polarization are essentially identical, each showing a double-peaked structure with peaks at ±30 μC/cm and a minimum at P=0; this is order-disorder behavior. Similar order-disorder behavior is seen in the tetragonal phase. In the orthorhombic phase by contrast, the system is polarized along the <110> direction, as characterized by the large components of polarization in the y-z plane. The polarization in the x-direction is zero on average; however, the distribution function consists of an extremely broad single peak. While such a unimodal distribution is characteristic of displacive behavior, the extremely broad flat top is atypical and suggests the presence of some order-disorder behavior also. It has been seen experimentally that the orthorhombic phase, indeed, has a more displacive character.[4] To address the question of how this order-disorder behavior plays out in the switching behavior, we have simulated polarization switching in a surface-free, singledomain material.[5] We simulated a 3-d periodically repeated perfect crystal in the tetragonal phase with the initial polarization parallel to the [001] direction in the +z direction, i.e., Pz>0. In the tetragonal phase, the polarization of any unit cell at any time is equally likely to be directed along any one of four equivalent crystallographic directions: [111], [ 1 11], [1 1 1] and [ 1 1 1]. To force the polarization reversal, an external electric field, Ez = 5x10 5 V/cm, was applied along the [00 1 ] direction; we found that this electric field is large enough to reverse the polarization, while an electric field of 10 V/cm cannot reverse the polarization on molecular-dynamics time scales. In order to allow full coupling between strain and polarization, all of our simulations were performed at zero pressure by the imposition of a Parinello-Rahman constant-pressure scheme.[6] FIGURE 1. Distribution functions for the component of polarization in the cubic phase (left) and the orthorhombic phase of KNbO3 (right) exemplify order-disorder and displacive dynamics respectively 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 -60 -40 -20 0 20 40 60 P ro ba bi lit y Polarization ( C/cm2) py = pz