A generalized Landau-Ginzburg model is constructed and used to develop a methodology for analyzing graded ferroic materials. Material system inhomogeneities are assumed to arise from compositional, temperature, or stress gradients. These spatial nonuniformities are shown to give rise to local order parameters having corresponding spatial variation. Functionally graded ferroic systems are thus found to result in nonuniform free energies with attendant internal potentials, the latter of which are evidenced by displacements of the materials’s stimulus-response hysteresis plots along the response axis (e.g., polarization, magnetization, or strain axis).

• Received 22 October 2002

DOI:https://doi.org/10.1103/PhysRevB.67.184104