Thermodynamic Stabilities of PdRuM (M = Cu, Rh, Ir, Au) Alloy Nanoparticles Assessed by Wang–Landau Sampling Combined with DFT Calculations and Multiple Regression Analysis

Abstract

Abstract Unique features of alloy nanoparticles (NPs) originate from the configuration of elements within NPs; solid solution and segregated configurations show different properties even with the same overall composition of elements. The configuration space of an alloy NP is exponentially expanded by an increase of the constituent elements. Besides, the configurational entropy in an alloy NP cannot be analytically estimated due to the heterogeneous surface. Revealing the stable configuration and the corresponding entropy in the extensive configuration space is difficult. Herein, Wang–Landau sampling, combined with density functional theory (DFT) calculations and multiple regression analysis, was used to assess the thermodynamic stabilities of PdRuM (M = Cu, Rh, Ir, Au) ternary alloy NPs. Specifically, the excess energies calculated by DFT were subjected to multiple regression analysis, and the obtained regression equations were used for Wang–Landau sampling. The thus-obtained configurational densities of states allowed us to estimate thermodynamic quantities, and hence, to predict stable configurations at a finite temperature. We conclude that the developed method is well suited to probing the stable configurations of multinary alloy NPs at a finite temperature.