TY - JOUR
TI - Continuum and atomistic models of surface elasticity and applications
DO - https://doi.org/doi:10.7282/T361121Z
PY - 2015
AB - We present an analysis of surface elasticity from the Born-Oppenheimer approximation for monatomic crystals. The analysis shows that the relaxations of crystal planes parallel to a free surface can be sufficiently determined by a low-rank algebraic Riccati equation instead of a full-scale molecular dynamic (MD) simulation, and gives new restrictions on physically reasonable atomistic models and simple criteria for surface reconstructions. In the case of surface relaxations, we calculate surface elasticity properties from atomistic models, which are compared with experimental data and prior simulation results. This fundamental research is useful in a variety of applications. First, with the help of the proposed algorithm we quickly calculate the surface tension and determine the equilibrium shape of crystals. Secondly, in previous studies of wave propagation the impact of surface elasticity was not noticed. We find that when the surface/interface gains its own elasticity, the inhomogeneities between the bulk and the surface/interface result in nonlinearity for both interfacial and bulk wave propagation aspects. We study the interfacial wave between two half-spaces with surface elasticity taken into account. ii A sufficient condition for the existence and uniqueness of a subsonic interfacial wave is obtained for general anisotropic materials. In addition, from explicitly calculated dispersion relations of interfacial waves for interfaces between two solids and solid & fluid, we observe that the dispersion relations of interfacial waves are nonlinear at the presence of surface elasticity and depend on surface elasticity parameters. Further, we analyze the wave reflection and refraction with surface elasticity. We find that both the amplitude ratios and energy rates of reflected and refracted waves become dependent on the incident wave frequency. Also, the analysis of the existence of reflected and refracted waves shows that when the incident angle is above some critical angle, the corresponding reflected or refracted waves become typical interfacial waves. Finally, from Landau phenomenological theory we propose a model for size dependence of phase transformation temperature of ferroelectric nano-particles. We postulate that the surface effect plays an important role of such size effect. Our model shows the size dependence and predicts the critical size for certain ferroelectric particles.
KW - Mechanical and Aerospace Engineering
KW - Elasticity
KW - Surface energy
KW - Surface chemistry
LA - eng
ER -