WIAS Preprint No. 2789, (2020)
Distribution of cracks in a chain of atoms at low temperature
Authors
- Jansen, Sabine
- König, Wolfgang
ORCID: 0000-0002-7673-4364 - Schmidt, Bernd
- Theil, Florian
2010 Mathematics Subject Classification
- 82B21 74B20 74G65 60F10
Keywords
- Equilibrium statistical mechanics, atomistic models of elasticity, fracture, lattice gas of defects
DOI
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/β ∈ (0, ∞). 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(-β e surf /2) with e surf > 0 a surface energy.
Appeared in
- Ann. Henri Poincare, published online on 24.06.2021, DOI 10.1007/s00023-021-01076-7 .
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