Size- and shape-dependent phase diagram of Ga-Sb nanoparticles

Abstract

It is well known that the phase diagrams calculated using bulk Gibbs energy alone is insufficient when the dimensions of alloy particles are less than 100 nm. This is due to the surface energy contribution to the Gibbs energy, which increases as surface-to-volume ratio of alloy particles increases. In this work, we have used the CALPHAD approach to calculate the phase diagram of the Ga-Sb system taking into account of the size and shape of alloy particles. To accomplish this, we have added size-dependent surface energy terms and optimized the Gibbs energy expressions of various phases in the Ga-Sb system using surface tension information. The surface tension of the liquid phase is calculated using the Butler equation. The surface energy contribution to the Gibbs energy of the terminal phases is approximated using the surface tension expressions of the elements. The surface energy of the line compound GaSb is computed using the slab model within the framework of Density Functional Theory (DFT). The calculations show that there is lowering of liquidus and eutectic temperatures when size decreases. Among the two shapes considered, the depression is more prominent in the nano-spheres than the nano-rods.