# Determining phase transition using potential energy distribution and surface energy of Pd nanoparticles

## TL;DR

This study uses molecular dynamics simulations to analyze phase transitions in Pd nanoparticles, highlighting the advantages of potential energy distribution and surface energy as criteria over traditional methods.

## Contribution

The paper introduces potential energy distribution and surface energy as effective criteria for detecting phase transitions in nanoparticles, with a new simple method for estimating surface energy.

## Key findings

- Potential energy distribution distinguishes surface and interior atoms.
- Surface energy and caloric curves better identify allotropic transitions.
- Proposed method accurately predicts size-dependent surface energy trends.

## Abstract

Molecular dynamics simulation is employed to understand the thermodynamic behavior of cuboctahedron (cub) and icosahedron (ico) nanoparticles with 2-20 number of shells (55-28741 atoms). The embedded atom method was used to describe the interatomic potential. Conventional melting criteria such as potential energy and specific heat capacity (C_p) caloric curves as well as structure analysis by radial distribution function (G(r)) and common neighbor analysis (CNA) were utilized simultaneously to provide a comprehensive picture of the melting process. It is shown that the potential energy distribution and surface energy (gamma_p) proposed here are holding several advantages over previous criteria. In particular, potential energy distribution can distinguish between interior and surface atoms and even corner, edge and plane atoms at the surface. While G(r) and CNA are not surface sensitive methods and cannot distinguish between surface melting and an allotropic transition. It is also shown that allotropic change appears more clearly in C_p and gamma_p rather than potential energy. However, determining accurate C_p requires enough sampling to be averaged. Finally, a few issues in the current methods for determining gamma_p were discussed and a simple method based on available models was proposed which, independent of estimation of the surface area, predicts the correct temperature and size-dependent trend in agreement with Guggenheim-Katayama and Tolman's models, respectively.