Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezo-magnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.
Thermodynamic models formulated based on the Landau free-energy expansion are popular and well suited to studies involving properties of the ferro/para-electric transition,or near it.Indeed,the general nature of thermodynamics,from which the strength of the model is derived,allows a valid model to be constructed based on simple functional forms with parameters fitted to experiments,by passing the mechanistic complexity.Despite inaccuracy due to the neglect of fluctuations,this approach has been proven effective and powerful for recent research development of ferroelectrics in nanoscale.Efforts in some important works have recently faced much challenge,when free-energy contributions have to be incorporated to account for the presence of depolarization fields,surfaces and other defects.To minimize the problems with mechanistic obscurity,it is of paramount importance that the electromagnetics,mechanics and thermodynamics involved are accounted for explicitly and with full self-consistency.It is important that the free-energy functional of nanoscale ferroelectric systems,such as ferroelectric thin films(FTF),bilayers(FB),superlattices(FS),nanowires(FNW),nanotubes(FNT) and tunneling junctions(FTJ) etc.,must be derived thermodynamically from first principles.
