Can nano-particle melt below the melting temperature of its free surface partner?

TL;DR

This paper investigates how quantum phonon effects influence the melting temperature of nano-particles, revealing size-dependent bounds and proposing a simplified estimation method that considers zero-mode contributions.

Contribution

It introduces a detailed analysis of phonon energy levels and boundary conditions, highlighting the importance of zero-mode effects on nano-particle melting temperatures and providing a practical estimation procedure.

Findings

Melting temperature increases with finite size effects.

A lower melting temperature bound exists for nano-particles.

Zero-mode contributions significantly affect melting temperature calculations.

Abstract

The phonon thermal contribution to the melting temperature of nano-particles is inspected. The discrete summation of phonon states and its corresponding integration form as an approximation for a nano-particle or for a bulk system have been analyzed. The discrete phonon energy levels of pure size effect and the wave-vector shifts of boundary conditions were investigated in detail. Unlike in macroscopic thermodynamics, the integration volume of zero-mode of phonon for a nano-particle is not zero, and it plays an important role in pure size effect and boundary condition effect. We found that a nano-particle will have a rising melting temperature due to purely finite size effect; a lower melting temperature bound exists for a nano-particle in various environments, and the melting temperature of a nano-particle with free boundary condition reaches this lower bound. We suggest an easy procedure to estimation the melting temperature, in which the zero-mode contribution will be excluded, and only several bulk quantities will be used as input. We would like to emphasize that the quantum effect of discrete energy levels in nano-particles, which was not present in early thermodynamic studies on finite size corrections to melting temperature in small systems, should be included in future researches.