Dependence of the Elastic Modulus on the Size and Shape of an Argon Nanocrystal

Abstract

The isothermal dependences of the lattice properties of a nanocrystal on its the size and shape are investigated using the nanocrystal RP model which contains both lattice vacancies and delocalized (diffusing) atoms. A Gibbs surface model is proposed in which a part of the cells is vacant and a part of the atoms are in the delocalized state. The model takes into account that a part of the atoms on the Gibbs surface are delocalized in the bulk manner and the others, on the surface manner. The calculations are performed for argon atoms, which interact by means of the Mie‒Lennard‒Jones pairwise potential. The state equation (P) and the isothermal elastic modulus (B) for argon macro- and nanocrystals along the isotherm T = 10 K are calculated. The calculated data for the macrocrystal are shown to agree well with the experimental data. The isochoric and isobaric dependences of the Debye temperature Θ, the first (γ) and second (q) Grüneisen parameters, the specific surface energy σ, and the functions B and B'(P) = (∂B/∂P)_T on the nanocrystal size and shape are studied. It is shown that the Θ, q, σ, B, and B '(P) functions decrease with an isomorphic-isobaric decrease in the nanocrystal size, while the γ value increases. However, in the case of an isomorphic-isochoric decrease in the nanocrystal size, the modulus of elasticity of argon increases. Upon a deviation of the nanocrystal shape from the energy-optimal shape (for the RP(vac) model it is cube), the size dependences of these functions are enhanced.