Predictive Gibbs-energy approach to crystalline/amorphous relative stability of nanoparticles: Size-effect calculations and experimental test

Abstract

Ball milling experiments performed in the last decade in various systems opened the question about the stability of crystalline nanoparticles with respect to the same group of atoms but in the amorphous state. The general purpose of the present work is to develop a predictive approach to this problem, and assess its accuracy by confronting thermodynamic calculations with experimental observations on Cu-Zn nanoparticles. The bases of the approach are as follows. First, the present Gibbs energy formalism makes use of the “lattice-stability” concept currently applied in so-called CALPHAD (“Calculation of Phase Diagrams”) modeling work. Second, the enthalpy of formation of the alloy phases is treated in the framework of the Miedema model, with special attention to the parameters for the amorphous phase. Third, the surface contribution to Gibbs energy is accounted for. With the current thermodynamic description, the sizes of the crystalline nanoparticles which are stable with respect to the amorphous are determined by calculation. These predictions are confronted with the minimum size of the nanoparticles generated by subjecting γ-Cu-Zn powders to low-energy milling treatments, which is determined by X-ray diffraction and high-resolution transmission electron microscopy techniques. On this basis, a discussion is reported of the accuracy of the present approach. In particular, the parameters in the Gibbs energy description which crucially affect the agreement between calculations and experiments are highlighted.