Melting of micro/nanoparticles considering anisotropy of surface energy

C. M. Yang,Z. D. Wang,G. J. Zheng,M. W. Chen

doi:10.1038/s41598-021-98704-3

C. M. Yang, Z. D. Wang + Show 2 more

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https://doi.org/10.1038/s41598-021-98704-3

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Abstract

The effect of surface energy on the melting of micro/nanoparticles is studied using the asymptotic method. The asymptotic solution of the dynamic model for micro/nanoparticle melting reveals the dependence of the particle melting temperature on the particle size and the anisotropy of surface energy. Specifically, as the particle radius decreases, the isotropic surface energy reduces the melting temperature and accelerates the interface melting of the particle. Along certain crystal orientations, the anisotropy of surface energy enhances the melting temperature of the micro/nanoparticles, whereas depresses the melting temperature of the micro/nanoparticle along other crystal orientations. The anisotropy of surface energy enhances the melting speed of the micro/nanoparticles along certain crystal orientations, whereas reduces the melting speed of the micro/nanoparticles along other crystal orientations. The result of the asymptotic solution is in good agreement with the experimental data.

Highlights

The effect of surface energy on the melting of micro/nanoparticles is studied using the asymptotic method
By using the asymptotic method, we find the asymptotic solution of the temperature and interface speed of the micro/nanoparticles and reveal the dependence of the melting temperature on size, crystal orientation and interface speed of the micro/nanoparticles
When surface energy is considered the predictions of the asymptotic solution agree very well with the experimental d ata[7], only exhibiting a slight deviation for 20 < R < 40 nm. This suggests that the deviation of the size dependence of the melting temperature reduction is caused by the anisotropic effect of surface energy

Summary

Introduction

The effect of surface energy on the melting of micro/nanoparticles is studied using the asymptotic method. The asymptotic solution of the dynamic model for micro/nanoparticle melting reveals the dependence of the particle melting temperature on the particle size and the anisotropy of surface energy. The anisotropy of surface energy enhances the melting speed of the micro/nanoparticles along certain crystal orientations, whereas reduces the melting speed of the micro/nanoparticles along other crystal orientations. McCue et al.[21] and Back et al.[22,23] investigated the melting of a spherical particle by solving a two-phase Stefan problem with the Gibbs–Thomson condition They found that surface energy reduces the melting temperature of solid nanoparticles with decreasing particle radius. We include the anisotropy of surface energy in the Gibbs–Thomson condition of the dynamic model for melting a micro/nanoparticle. By using the asymptotic method, we find the asymptotic solution of the temperature and interface speed of the micro/nanoparticles and reveal the dependence of the melting temperature on size, crystal orientation and interface speed of the micro/nanoparticles

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