Size-dependent melting of gold nanotube: Phase field model and simulations and thermodynamic analytical solution

Abstract

In this paper, a phase field (PF) model is used to investigate the melting of Au nanotubes. The coupled Ginzburg-Landau and elasticity equations are solved to capture the melting process. With size independent surface energy, PF model shows a nonlinear reduction of the melting temperature (θm) by reducing the thickness, in good agreement with a previous thermodynamic model above a specific thickness. A nonlinear reduction of θm is also found as the length reduces. The variable surface energy at the nanotube end is revealed as the key parameter responsible for length dependence ofθm. The radius dependence of melting temperature from PF simulations is validated with that of existing molecular dynamics data for Au nanowires. A thermodynamic model for θm of Au nanotubes is derived in terms of the length and thickness. With size independent surface energy, our PF and thermodynamic models show a similar nonlinear increase vs. the thickness to a previous thermodynamic model for long nanotubes. The new model also shows a length dependence of θm, in good correspondence with the PF results. With radius dependent surface energy, our PF and modified thermodynamic models show a similar nonlinear increase vs. the thickness to a previous thermodynamic model and their correspondence is analyzed. For very small radii, superheating is resolved where, in contrast to larger radii, θm increases by reducing the thickness. The superheating threshold radius from our PF simulations is found in good agreement with that of the previous model.