Size- and shape-dependent phase diagram of In–Sb nano-alloys

Abstract

Nano-scale alloy systems with at least one dimension below 100 nm have different phase stabilities than those observed in the macro-scale systems due to a large surface to volume ratio. We have used the semi-empirical thermodynamic modelling, i.e. the CALPHAD method, to predict the phase equilibria of the In–Sb nano-scale systems as a function of size and shape. To calculate the size- and shape-dependent phase diagram of the In–Sb system, we have added size-dependent surface energy terms to the Gibbs energy expressions in the In–Sb thermodynamic database. We estimated the surface energies of the solution phases and of the InSb intermetallic phase using the Butler equation and DFT calculations, respectively. A melting point and eutectic point depression were observed for both nanoparticle and nanowire systems. The eutectic composition on the In-rich and Sb-rich sides of the phase diagram shifted towards higher solubility. We believe that the phase diagram of In–Sb nano-alloys is useful for an increased understanding of the growth parameters and mechanisms of InSb nanostructures.