Distribution of cracks in a chain of atoms at low temperature

TL;DR

This paper analyzes crack distribution in a low-temperature one-dimensional atomic chain, revealing how defects form alternating crystalline and void domains, with the number of domains depending on temperature and surface energy.

Contribution

It introduces a novel effective lattice gas model for defects in a 1D atomic chain at low temperature, providing detailed crack distribution analysis.

Findings

Cracks form alternating crystalline and void domains.

Number of domains scales with system size and temperature.

Verified conditions for defect interactions in next-nearest neighbor models.

Abstract

We consider a one-dimensional classical many-body system with interaction potential of Lennard-Jones type in the thermodynamic limit at low temperature $1/\beta\in(0,\infty)$. The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with $N$ particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of $N\exp(- \beta e_\mathrm{surf}/2)$ with $e_\mathrm{surf}>0$ a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.