Statistical Mechanics of the Dislocation System in a Crystal

抄録

The statistical mechanics of the assembly of the dislocation lines in a three dimensional crystal is developed. Using the transfer matrix method, the statistical mechanics of the dislocations is transformed into the ground state problem of the two dimensional Fermion-Boson system. This approach gives a convincing proof for the free energy expression:
f(ρ)=−F₁ρ ln Cρ+F₂ρ+F₃ρ²,
where ρ is the dislocation density, F₁ and F₃ are positive constants, and C is a constant of the order a² (a being the lattice spacing). The constant F₂ is positive at low temperatures but is negative at high temperatures.