Phase-Field Crystal Model with a Vapor Phase

TL;DR

This paper extends the Phase-Field Crystal model to include a vapor phase, enabling realistic simulation of interfacial phenomena, surface energies, and growth processes relevant to materials processing like vapor deposition and nanowire growth.

Contribution

The authors introduce a vapor phase into the PFC model and demonstrate its capability to simulate interfacial phenomena, surface energies, and growth dynamics in vapor-involved processes.

Findings

Density oscillations at liquid-vapor interfaces match experimental and simulation data.

Quantified anisotropic solid-vapor surface energies and step energies.

Reproduced strain fields and growth dynamics consistent with continuum models and experiments.

Abstract

Phase-Field Crystal (PFC) models are able to resolve atomic length scale features of materials during temporal evolution over diffusive time scales. Traditional PFC models contain solid and liquid phases, however many important materials processing phenomena involve a vapor phase as well. In this work, we add a vapor phase to an existing PFC model and show realistic interfacial phenomena near the triple point temperature. For example, the PFC model exhibits density oscillations at liquid-vapor interfaces that compare favorably to data available for interfaces in metallic systems from both experiment and molecular dynamics simulations. We also quantify the anisotropic solid-vapor surface energy for a 2D PFC hexagonal crystal and find well defined step energies from measurements on the faceted interfaces. Additionally, the strain field beneath a stepped interface is characterized and shown to qualitatively reproduce predictions from continuum models, simulations, and experimental data. Finally, we examine the dynamic case of step-flow growth of a crystal into a supersaturated vapor phase. The ability to model such a wide range of surface and bulk defects makes this PFC model a useful tool to study processing techniques such as Chemical Vapor Deposition or Vapor-Liquid-Solid growth of nanowires.