Improved prediction of heat of mixing and segregation in metallic alloys using tunable mixing rule for embedded atom method

Capturing segregation behavior in metal alloy nanoparticles accurately using computer simulations is contingent upon the availability of high-fidelity interatomic potentials. The embedded atom method (EAM) potential is a widely trusted interatomic potential form used with pure metals and their alloys. When limited experimental data is available, the A-B EAM cross-interaction potential for metal alloys A_xB _1-x are often constructed from pure metal A and B potentials by employing a pre-defined 'mixing rule' without any adjustable parameters. While this approach is convenient, we show that for AuPt, NiPt, AgAu, AgPd, AuNi, NiPd, PtPd and AuPd such mixing rules may not even yield the correct alloy properties, e.g., heats of mixing, that are closely related to the segregation behavior. A general theoretical formulation based on scaling invariance arguments is introduced that addresses this issue by tuning the mixing rule to better describe alloy properties. Starting with an existing pure metal EAM potential that is used extensively in literature, we find that the mixing rule fitted to heats of mixing for metal solutions usually provides good estimates of segregation energies, lattice parameters and cohesive energy, as well as equilibrium distribution of metals within a nanoparticle using Monte Carlo simulations. While the tunable mixing rule generally performs better than non-adjustable mixing rules, the use of the tunable mixing rule may still require some caution. For e.g., in Pt-Ni system we find that the segregation behavior can deviate from the experimentally observed one at Ni-rich compositions. Despite this the overall results suggest that the same approach may be useful for developing improved cross-potentials with other existing pure metal EAM potentials as well. As a further test of our approach, mixing rule estimated from binary data is used to calculate heat of mixing in AuPdPt, AuNiPd, AuPtNi, AgAuPd and NiPtPd. Excellent agreement with experiments is observed for AuPdPt.