Dielectric and electro-mechanic nonlinearities in perovskite oxide ferroelectrics, relaxors, and relaxor ferroelectrics

The polarization and strain response of ferroelectric materials at fields below the macroscopic coercive field is a paramount importance for operation many electronic devices. real related in general complex difficult to interpret. reason this that processes material contribute its properties, often concurrently. Examples include motion ferroelastic domains, presence domains within dynamics different types polar nano-entities, interaction nano-entities (e.g., nanoregions relaxors) with defects rearrangement defect clusters their strain. One signature these nonlinearity polarization. Most ferroelectrics exhibit nonlinear all practical levels meaning apparent coefficients depend on amplitude driving excitation. In paper we show an investigation behavior sensitive way study various mechanisms operating dielectric piezoelectric materials. We review basic formalism description strain, give physical interpretation terms illustrate approach numerous examples relaxors, relaxor ferroelectrics, hard soft morphotropic phase boundary compositions. An experimental based lock-in technique well-suited such studies also discussed.