Elastic Compliance and Stiffness Matrix of the FCC Lennard-Jones Thin Films: Influence of Thickness and Temperature

Abstract

The fcc Lennard-Jones crystal is used as a generic model of solid to study the elastic properties of thin films as a function of thickness and temperature. The Monte Carlo algorithm is used to calculate the average deformations along the axes in the isostressisothermal ensemble that mimics a real uniaxial loading experiment. The four independent parameters (tetragonal symmetry without shear) have been calculated for film thicknesses ranging from 4 to 12 atomic layers, and for five reduced temperatures between 0 and 0.5 /k B , where  is the energetic parameter of the Lennard Jones potential and k B is Boltzmann's constant. These parameters (Poisson's ratio and moduli) give the compliance matrix, which is inverted to get the stiffness coefficients. It is shown that the three Poisson's ratios exhibit a good linearity with the inverse of the film thickness, while this is not the case for the moduli and the compliance coefficients. Remarkably, the stiffness coefficients do exhibit a good linearity with the inverse of the film thickness, including the limiting value of infinite thickness (bulk solid) obtained by applying periodic boundary conditions in all directions.This linearity suggests to interpret the results in terms of a bulk+surface decomposition.However, the surface stiffness matrix deduced from the slopes has nonzero components along the out-of-plane direction, an unexpected observation in the framework of the surface stress theory.

Multi-Physics Fields Simulations and Optimization of Solder Joints in Advanced Electronic Packaging

“…Owing to the deformation of the solder joint is very small (approximately 10 −7 ), the stress and strain in the solder joint are directly proportional, described by the generalized Hooke's Law [25]. The equation can be written in the Voigt notation as the following:…”