First-principles Study On The Surface Properties Of Nanofilms

The understanding of the surface properties of solids has an important influence on the physical properties of nanosystems and their size dependence.So far,academia has carried out research on solid surface structure,surface energy and surface stress,scale effect of surface energy,surface elastic modulus,surface multi-field coupling properties and their influence on the force,magnetic and electrical properties of nano-systems,etc.Extensive research has formed a certain theoretical understanding,and at the same time there are several issues to be clarified.Among many problems,the definition of the elastic modulus of the film and the elastic coefficient of the film surface and the calculation scheme have not been well solved.In this paper,considering the lack of crystal symmetry of nano-films,the elastic energy of cubic crystals（001）and（111）films is derived using symmetrical independent strains,and the first principle is used to calculate the elastic modulus of nano-films based on the elastic energy.And the specific scheme of surface elastic modulus.Taking six elemental materials such as elemental Al as an example,the relationship between the surface energy,surface stress,film elasticity coefficient and surface elasticity coefficient of the film thickness and surface relaxation was calculated and studied.The results show that the surface energy and surface stress are related to the scale of the film,the surface energy of the metal changes oscillating with the thickness,and the thickness of 20 layers cannot eliminate the coupling between the two surfaces of the slab model.The value of the new elastic coefficient₂₁c^?introduced by the lack of symmetry is non-zero and positive,proving that there is a coupling between the bulk expansion and vertical relaxation of the film.The surface relaxation makes the elastic coefficient of the film and the surface elastic coefficient decrease significantly,the surface elastic coefficientsc^?₁₁,^sandc^?₂₂,^sare both negative values,the order of magnitude is the same as the previous calculation results.The calculation method of the surface elastic coefficient given in this paper can be combined with the density functional theory calculation to accurately give the elastic coefficient and surface elastic coefficient of the nano-film system,which is helpful to understand the scale effect of the mechanical properties of the nanostructure.