Scaling of Nanoalloy Phase Transitions: Elucidating the Distinct Role of Surface Sites

Abstract

Abstract

Nano-size-induced shifts in alloy phase-separation critical temperatures (TCnano) are explored by introducing an atomistic concept concerning site-specific contributions to the shift (SSCS) associated with several types of coordination in cuboctahedral and truncated-octahedral nanoparticles (NPs). TCnano computed before by the Free-energy Concentration Expansion Method (FCEM) for the transformation of three small quasi-Janus Pd-Ir NPs to mixed nanophases is expanded to a much wider range of 22 sizes (147-49,049 atoms), forming a database for the modeling. The main goal of the study is to unravel the deviations of the critical temperature shifts in small NPs from the finite-size-scaling (FSS) inverse-size power law (n-1), previously proposed in thermodynamic non-atomistic modeling. In the framework of the present SSCS approach, this is done in terms of face, edge, and vertex contributions, which are proportional to the relative fraction of each type of these surface sites and are also approximated by n-1, n-2, and n-3, respectively. The introduced SSCS can be applied also to other transitions in nanoparticles with diverse shapes and sizes.