Statistical Mechanical Model of the Self-Organized Intermediate Phase in Glass-Forming Systems With Adaptable Network Topologies

Katelyn A Kirchner,John C Mauro

doi:10.3389/fmats.2019.00011

Abstract

Nonequilibrium systems continuously evolve toward states with a lower free energy. For glass-forming systems, the most stable structures satisfy the condition of isostaticity, where the number of rigid constraints is exactly equal to the number of atomic degrees of freedom. The rigidity of a system is based on the topology of the glass network, which is affected by atomistic structural rearrangements. In some systems with adaptable network topologies, a perfect isostatic condition can be achieved over a range of compositions, i.e., over a range of different structures, giving rise to the intermediate phase of optimized glass formation. Here we develop a statistical mechanical model to quantify the width of the intermediate phase, accounting for the rearrangement of atomic structure to relax localized stresses and achieve an ideal, isostatic state.

Highlights

Within the field of topological constraint theory, there is growing interest in the ability of a glass network to adapt its topology to achieve isostaticity
The width of the intermediate phase is dependent on the adaptability of the glass network, which is enabled by the distribution of rigidity fluctuations
To account for thermal history effects in a glass, the temperature can be set equal to the fictive temperature of the system. This statistical mechanical approach calculates the probability density of Ni(x), the mole fraction of network-forming species i in composition x, which serves as an input for the distribution of the number of atomistic constraints, given distribution of local constraints, which quantifies the topological fluctuations dictating the width of the intermediate phase (Kirchner et al, 2018)

Summary

Introduction

Within the field of topological constraint theory, there is growing interest in the ability of a glass network to adapt its topology to achieve isostaticity. The current investigation analyzes the degree of self-organization enabled through these structural and topological fluctuations to create a generalized approach for modeling the width of the intermediate phase of an arbitrary glass-forming system.

Results

Conclusion