Athermal fluctuations in three dimensional disordered crystals

TL;DR

This paper investigates the microscopic fluctuations and correlations in three-dimensional jammed disordered crystals, providing exact predictions for force and position changes due to polydispersity and revealing anisotropic fluctuation constraints.

Contribution

It extends a perturbation expansion method to 3D systems, enabling precise predictions of force and displacement responses in disordered crystalline materials.

Findings

Force fluctuations orthogonal to lattice directions are highly constrained.

Displacement correlations exhibit long-range behavior.

The perturbation approach accurately predicts particle response to size variations.

Abstract

We study jammed near-crystalline materials composed of frictionless spheres in three dimensions. We analyze the fluctuations in positions and forces produced by small polydispersity in particle sizes. We generalize a recently developed perturbation expansion about the crystalline ordered state to three dimensional systems. This allows us to exactly predict changes in positions and forces as a response to the changes in particle radii. We show that fluctuations in forces orthogonal to the lattice directions are highly constrained as compared to the fluctuations along lattice directions. Additionally, we analyze the correlations in the displacement fields produced by the microscopic disorder, which we show displays long ranged behaviour.