# Multi-Phase-Field Model for Surface/Phase-Boundary Diffusion

## TL;DR

This paper extends the multi-phase-field model to include capillarity-driven diffusion along surfaces and phase boundaries, enabling the study of phenomena like thermal grooving and nano-cluster annealing with new insights into transient surface structures.

## Contribution

The authors develop a generalized multi-phase-field model incorporating capillarity effects for surface and phase-boundary diffusion, applied to thermal grooving and nano-cluster annealing.

## Key findings

- Observation of decaying oscillations in thermal grooving profiles.
- Identification of transient crater-like structures during nano-cluster annealing.
- Model successfully captures capillarity-driven diffusion phenomena.

## Abstract

The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase-boundaries, i.e. the boundaries between a condensed phase and its vapor and the boundaries between two or multiple condensed phases. The effect of capillarity is modeled via curvature-dependence of the chemical potential whose gradient gives rise to diffusion. The model is used to study thermal grooving on the surface of a polycrystalline body. Decaying oscillations of the surface profile during thermal grooving, postulated by Hillert long ago but reported only in few studies so far, are observed and discussed. Furthermore, annealing of multi-nano-clusters on a deformable free surface is investigated using the proposed model. Results of these simulations suggest that the characteristic crater-like structure with an elevated perimeter, observed in recent experiments, is a transient non-equilibrium state during the annealing process.