Etude théorique de la stabilité mécanique et de l'evolution thermodynamique d'un cristal. Application au krypton

An analysis of the potential energy has shown that a cubic lattice cannot be mechanically stable unless the lattice parameter a remains inside relatively narrow limits. The stability field so defined depends on the kind of lattice, face-centred, body-centred or simple cubic, the interatomic potential being the same. In the case of the face-centred cubic lattice, which is the real lattice of krypton, a computation of the free energy F(T,a), made at the quasiharmonic approximation shows that at T = 0°K F(0, a) reaches a minimum at a value a(0) of the lattice parameter, and a(0) is inside the field of mechanical stability. But for body-centred and simple cubic lattices, no field of mechanical stability has been found. As the temperature increases, the equilibrium value a(T) of the face-centred lattice increases too and the shape of the curve F(T,a) changes as function of a. The thermodynamical equilibrium which is stable at low temperatures becomes metastable and disappears from the field of mechanical stability.