Physical Realization of the Order Parameters at a Microscopic Level of Description

Abstract

The phase transition from the initial phase of the crystal gives rise to a state which at the microscopic level may be specified by the occurrence of some spontaneous property on each atom. This property is described by a scalar, a vector or a tensor. Thus, for example, a static magnetic moment arises on the atom in a magnetic phase transition and each atom may therefore be specified by an appropriate pseudovector. In the case of a structural phase transition by displacement (displacive transition) it is possible to assign to an atom in a dissymmetric phase a polar displacement vector with respect to its position in the symmetric phase; the assignment of the polar displacement vector on each wholly characterizes this phase. If the magnetic ordering is accompanied by some structural distortions, two vectors should be specified for each atom in the dissymmetric phase: the magnetic moment pseudovector and the polar atomic displacement vector. It is better in such a situation to ascribe to the atom some tensor of rank two. For an ordering-type phase transition each atom is characterized by a scalar quantity that represents the relative probability of occupying determinate positions in the crystal.