A domain wall model for relaxor ferroelectrics

Abstract

A domain wall model is proposed for relaxor ferroelectrics typified by Pb(Mg1/3Nb2/3. Under a large applied field or a large internal field, domain walls move over a long distance by overcoming localized barriers. This movement is responsible for the hysteresis loop and depolarization at temperatures below T max. The activation volumes obtained by analyzing the coercive field dependence on temperature and frequency suggest that the barriers encountered by the domain walls are of the size of 1000 unit cells, and they increase as the relaxor becomes more like a normal ferroelectric. Since polarization is usually incomplete in relaxors even under a large polarizing field, depolarization readily occurs without the need of nucleating new domains. Domain walls are also responsible for permittivity peaks at high temperature under a weak field. However, without a strong field, domain walls are partially pinned by barriers and can only oscillate within the unpolarized regions between barriers. The mobility of domain walls can be modified by alloying to vary the spacing between ferroelectrically active ions and the internal field driving the walls. Furthermore, below a certain temperature, polarization domains become increasingly sharp and domain wall oscillation becomes increasingly difficult. This leads to the exhaustion of oscillation at an apparent freezing temperature below T max. Overall, the domain wall model provides a simple framework that can be used to quantitatively analyze relaxor behavior over a broad range of compositions. Its theoretical basis is further justified by analogy to dislocation theory and interface mechanics in phase transformations.