Distribution of cracks in a chain of atoms at low temperature
- Jansen, Sabine
- König, Wolfgang
- Schmidt, Bernd
- Theil, Florian
2010 Mathematics Subject Classification
- 82B21 74B20 74G65 60F10
- Equilibrium statistical mechanics, atomistic models of elasticity, fracture, lattice gas of defects
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.
- Ann. Henri Poincare, published online on 24.06.2021, DOI 10.1007/s00023-021-01076-7 .