Thermodynamics, formation dynamics and structural correlations in the bulk amorphous phase of the phase-field crystal model

TL;DR

This study explores the thermodynamic and structural properties of amorphous solids within the phase-field crystal model, revealing formation history dependence, a first-order liquid-to-amorphous transition, and multiple nucleation pathways.

Contribution

It provides new insights into the formation dynamics, free energy distribution, and structural correlations of amorphous phases in the PFC model, including nucleation mechanisms.

Findings

Free energy density tends to a state-dependent value in the thermodynamic limit.

The liquid to amorphous transition is first order with a finite free energy barrier.

Multiple nucleation pathways, including precursor-mediated nucleation, are observed.

Abstract

We investigate bulk thermodynamic and microscopic structural properties of amorphous solids in the framework of the phase-field crystal (PFC) model. These are metastable states with a non-uniform density distribution having no long-range order. From extensive numerical simulations we determine the distribution of free energy density values in varying size amorphous systems and also the point-to-set correlation length, which is the radius of the largest volume of amorphous one can take while still having the particle arrangements within the volume determined by the particle ordering at the surface of the chosen volume. We find that in the thermodynamic limit, the free energy density of the amorphous tends to a value that has a slight dependence on the initial state from which it was formed -- i.e.\ it has a formation history dependence. The amorphous phase is observed to form on both sides of the liquid linear-stability limit, showing that the liquid to amorphous transition is first order, with an associated finite free energy barrier when the liquid is metastable. In our simulations this is demonstrated when noise in the initial density distribution is used to induce nucleation events from the metastable liquid. Depending on the strength of the initial noise, we observe a variety of nucleation pathways, in agreement with previous results for the PFC model, and which show that amorphous precursor mediated multi-step crystal nucleation can occur in colloidal systems.