Stress distribution and the fragility of supercooled melts

TL;DR

This paper develops a microscopic framework to understand stress distribution and fragility in supercooled melts, linking metastable phases, configurational entropy, and material properties like Poisson ratio.

Contribution

It introduces a minimal ansatz for local stress in solids, revealing a metastable phase with frozen-in stress and mapping transitions to a classical Heisenberg model.

Findings

Identification of a broken-symmetry metastable phase with aperiodic stress distribution

Establishment of an order parameter for the glass-to-crystal transition

Demonstration that fragility depends non-monotonically on Poisson ratio

Abstract

We formulate a minimal ansatz for local stress distribution in a solid that includes the possibility of strongly anharmonic short-length motions. We discover a broken-symmetry metastable phase that exhibits an aperiodic, frozen-in stress distribution. This aperiodic metastable phase is characterized by many distinct, nearly degenerate configurations. The activated transitions between the configurations are mapped onto the dynamics of a long range classical Heisenberg model with 6-component spins and anisotropic couplings. We argue the metastable phase corresponds to a deeply supercooled non-polymeric, non-metallic liquid, and further establish an order parameter for the glass-to-crystal transition. The spin model itself exhibits a continuous range of behaviors between two limits corresponding to frozen-in shear and uniform compression/dilation respectively. The two regimes are separated by a continuous transition controlled by the anisotropy in the spin-spin interaction, which is directly related to the Poisson ratio $\sigma$ of the material. The latter ratio and the ultra-violet cutoff of the theory determine the liquid configurational entropy. Our results suggest that liquid's fragility depends on the Poisson ratio in a non-monotonic way. The present ansatz provides a microscopic framework for computing the configurational entropy and relaxational spectrum of specific substances.