Modification of Butler equation for nanoparticles

Abstract

Compared to the conventional use of the Butler equation applied for the calculation of surface energy of a binary alloy, we considered limited size nanoparticles with a large surface to volume ratio and applied additional mass balances to calculate the nanoparticles surface and core composition. Due to limited source of the component with a lower surface energy, its segregation on the surface is less pronounced compared to the unlimited bulk source. Thus, the core is depleted from the surface-preferred component and enriched by the higher surface energy one. The different behaviour of bulk and nanoparticles was demonstrated on the Al-Ti liquid alloy using the Redlich-Kister equation for excess Gibbs energy for the melt. As the depletion effect is size-dependent our approach thus predicts size-dependent surface energy of binary alloy nanoparticles.