Oscillations of a layer of a crystal with cubic symmetry under the action of harmonic electric field
- PDF / 145,333 Bytes
- 11 Pages / 594 x 792 pts Page_size
- 77 Downloads / 156 Views
OSCILLATIONS OF A LAYER OF A CRYSTAL WITH CUBIC SYMMETRY UNDER THE ACTION OF HARMONIC ELECTRIC FIELD O. R. Hrytsyna The linearized relations of the local gradient theory of nonferromagnetic dielectrics are used for the description of the mechanical vibrations of an infinite layer in a crystal with cubic symmetry that are induced by a time-dependent electric field. It is shown that, contrary to the classical linear theory of piezoelectricity, the local gradient theory describes the piezoelectric effect in highly symmetric crystals. When local mass displacements are taken into account, short waves become dispersive, which does not follow from the linear classical theory of piezoelectricity. The obtained results are compared with previously published results, which are based on Mindlin’s gradient theory of dielectrics. Some model parameters are evaluated. Keywords: local gradient theory of dielectrics, local mass displacement, harmonic oscillations, piezoelectric effect, high-frequency dispersion.
The possibility to deform crystals by the action of an external electric field was theoretically predicted by Lippmann [1]. This phenomenon, called the inverse piezoelectric effect, was experimentally observed in [2] as the vibration of quartz crystals caused by a rapidly varying electric field. It is known that the direct and inverse piezoelectric effects are also inherent in high-symmetry crystals. However, the classical theory of piezoelectrics cannot describe these effects [3, 4]. This disagreement between theory and experiment is overcome by nonlocal theories of dielectrics, which are constructed in the following two ways [3–6]: by postulating a functional relationship between the parameters of a state [7] and by introducing the gradients of certain quantities (e.g., vector of polarization, electric field strength, and strain tensor) in the space of parameters of a state [8–12] or taking into account the dependence of the local state of a physically small element of the body on the higher-order electric multipole moments [13]. Another approach to the construction of nonlocal theories of dielectrics was proposed in [14–16] and generalized in [17]. It is based on the consideration of local mass displacements in a model description. The theories that involve this process are called local gradient theories [6]. A local gradient theory of dielectrics postulates that the displacements of the center of masses of a physically small element of the body can cause a displacement (convection) of this element and a change of its structure that is not related to diffusive processes. This results in the mass flow J ms of a nonconvective nondiffusive nature. This mass transfer was revealed in the formation of thin films [18]. The consideration of local mass displacements in a model description yields the nonlocal equations of state that include the potential gradient μ ′π = μ π − μ , where μ π is the measure of changes in the internal energy of the system caused by a local mass displacement [17], and μ is the chemical potential. The rel
Data Loading...
