The Phase-Field-Crystal Model at Large and Small Scales

Speaker: Rustum Choksi

Date: 2021

Location: UBC, Online

Conference: PIMS Workshop on New Trends in Localized Patterns in PDES

Subject: Mathematics

Class: Scientific

Abstract:

The Phase-Field-Crystal (PFC) model is a simple yet surprisingly useful model for successfully capturing the phenomenology of grain growth in polycrystalline materials. PFC models are variational with a free energy functional which is very similar (in some cases, identical) to the well-known Swift-Hohenberg free energy. In this talk, we will discuss the simplest PFC functional and its gradient flow.

The first part of the talk will focus on large scales and address the model’s uncanny ability to o capture certain features of grain growth. We introduce a novel atom-based grain extraction and measurement method, and then use it to provide a comparison of multiple statistical grain metrics between (i) PFC simulations, (ii) experimental thin film data for aluminum, and (iii) simulations from the Mullins model.

In the second part of the talk, we investigate the PFC energy landscape at small scales (the local arrangement of atoms). We address patterns which are numerically observed as steady states via the framework of the modern theory of rigorous computations. In doing so, we make rigorous conclusions on the existence of similar states. In particular, we show that localized patterns and grain boundaries are critical and not simply metastable states. Finally, we present preliminary work on connections and parameter continuation in the PFC system. This talk consists of work from the PhD thesis of Gabriel Martine La Boissoniere at McGill. Parts of the talk also involve joint work with S. Esedoglu (Michigan), K. Barmak (Columbia) and J.-P. Lessard (McGill).