Ab initio calculation of surface elasticity parameters in cubic crystalline films with surface point defects: Effects on SH wave propagation

Abstract

Elastic material surface and interface properties have non-negligible influences on the behavior of nano-sized elastic objects. Even though the concern and the need for the evaluation of surface properties were raised in 1876 by Gibbs, due to serious experimental and theoretical difficulties their measurements have remained idle till only recently. This paper offers a theoretical approach for an accurate evaluation of free surface energy density, surface layer relaxation, surface elastic constants, surface residual stresses, and surface mass density for the (100) and (111) planes of several non-magnetic cubic metals. Moreover, the analysis is extended to the surfaces where point defects, such as vacancies and substitutional impurity atoms, are present. The interaction of these point defects with surface is in particular important for irradiation and fracture phenomena. The present results are compared with the recent available experimental and theoretical data. For the sake of illustration of the importance of surface effects, the propagation of horizontally polarized shear waves (SH waves) in ultra-thin layers of only a few lattice parameters height will be studied. Utilizing the theoretically calculated surface parameters herein, the surface effects with and without the above-mentioned surface point defects will be examined in some details. Thus, the negative dispersion of SH waves within surface elasticity theory will be showcased quantitatively for various cubic crystals of interest. Moreover, the effects of the crystallographic orientations will also be examined in the presence and absence of surface point defects.