Finding elastic moduli of FCC monocrystals using interatomic interaction potential

In the present paper the connection between parameters of Lennard-Jones potential for central type of interatomic interaction and macroscopic elastic moduli of metals with ideal FCC lattice was studied. For this a monocrystal cube was subject to different types of deformation, components of the stress tensor were expressed using Cauchy relation without supposing stress symmetry. The Taylor series of obtained expressions was taken using deformation parameter (shear magnitude ¥ or stretching degree ­). Representations of series coefficients of terms are calculated. These coefficients are equated with macroscopic elastic moduli. It is shown that the found linear tensor of elastic properties for FCC materials is symmetric. The FCC lattice period was found to be equal to a 1.3918 ∗= £, where ƒ is an equilibrium distance for the pair of atoms. An expression for the second parameter of Lennard-Jones potential was represented using lattice period a∗ and macroscopic shear modulus G. The dependence of elastic moduli on the body size was found. The values of shear modulus for copper specimens of sizes from 10 nm up to 10 centimeters were calculated.