Surface and interfacial waves in ionic crystals

Abstract

The continuum linear theory of ionic crystals is applied to develop a two-dimensional eigenvalue problem in the Stroh formalism. An integral approach is exploited to study the occurrence of surface waves along a free boundary of the crystal. Dispersion relations are obtained by separating real and imaginary parts of the governing system and various boundary conditions are examined. The problem of interfacial waves along the separation boundary between two different crystals is also outlined. Numerical computations are performed for a centrosymmetric crystal (KCl) in order to evaluate bulk wave speeds, limiting speed of surface waves and solutions to the dispersion equations for different boundary conditions.

Dynamic eigenvector problem in thermoelectroelasticity of dissipative ionic crystals

“…It is worth remarking that, to this aim, we have used a slight modification of the governing equations with respect to the usual linear theory (see Mindlin 1968, Maugin 1988, bringing the intrinsic "polarization traction" in a boundary datum, instead of considering it as an inhomogeneous term in the constitutive equation for E. A detailed comment on this point can be found in Romeo (2008). Another relevant feature of the present work is that we have taken into account dissipative effects via suitable internal variables subjected to evolution equations compatible with the second law of thermodynamics (see Romeo 2007).…”

“…t (n) , q n and d n represent, respectively, the mechanical traction acting at the boundary, the heat flux across ∂B t and the normal component of the electric displacement at ∂B t , while π π π (s) , −b (0) are, respectively, the surface density of (possible) electric dipoles and the intrinsic "polarization traction" on ∂B t (cf. Romeo 2008). The last quantity is a constitutive parameter of the polarizable continuum, which depends on the microscopic structure of the crystal lattice (Askar and Lee 1974).…”