Surface stress calculations for nanoparticles and cavities in aluminum, silicon, and iron: influence of pressure and validity of the Young-Laplace equation

This study is dedicated to the determination of the surface energy and stress of nanoparticles and cavities in presence of pressure, and to the evaluation of the accuracy of the Young-Laplace equation for these systems. Procedures are proposed to extract those quantities from classical interatomic potentials calculations, carried out for three distinct materials: aluminum, silicon, and iron. Our investigations first reveal the increase of surface energy and stress of nanoparticles as a function of pressure. On the contrary we find a significant decrease for cavities, which can be correlated to the initiation of plastic deformation at high pressure. We show that the Young-Laplace equation should not be used for quantitative predictions when the Laplace pressure is computed with a constant surface energy value, as usually done in the literature. Instead, a significant improvement is obtained by using the diameter and pressure-dependent surface stress. In that case, the Young-Laplace equation can be used with a reasonable accuracy at low pressures for nanoparticles with diameters as low as 4 nm, and 2 nm for cavities. At lower sizes, or high pressures, a severely limiting factor is the challenge of extracting meaningful surface stress values.