PHASE TRANSFORMATIONS IN VCP-SPACE

Dmitry M.Mazo

Russia, 121352, Moscow, Slavyansky boulevard, 3-179
dmm@child.ru

Keywords: crystal, structure, phase, transition, database

The group theory methods of the phase transitions analysis in the solid state physics are based on their kind L.D.Landau definition, and operate by the representations, different from ones are connected with the structural analysis and with the problems of new materials development. The analysis on the basis of symmetry-group representations may be carried out in the group-subgroup directions, but not in the external parameters change direction. This is a reason of this method heuristic opportunities narrowing.

We considered opportunities of any structures and, in particular, crystal structures representation by the three lists of parameters:

1. capable to continuous and monotonous to change in connection with continuous and monotonous change of external parameters for given structure, but keeping a constancy in similar conditions for though by one of structures of the multiplicity,
2. keeping a constancy for the given structure, but capable to continuous and monotonous change at least in one of structures from the multiplicity and
3. capable to change after structure transition only by discrete meaning and compose the structure identificators in complex.

The database is intended for structures accommodation in VCP-space cells, where V - the independent variable number in the first list, C - the unequal constants number from the second list and P - designates multiplicity M of Wykoff positions WP: M=1 * 2^P or 3 * 2^P , which are engaged in the crystal structures. The values of P (M) are enter in all structure identificators. A sequence and the kind of transitions are define by mutual vicinity of structures in VCP-space, which is mesure by the minimum number of elementary steps |dV|, |dC|, |dP| from the initial structure VCP-cell to the prospective transformed structure cell, but the direction is define by the sign of dV. The transformation should be fixed by the change of the identificator and of constants number.

The database works on MS Access platform and includes all 1731 WP for 230 three-dimensional symmetry groups and all 72 WP for 17 plane groups. The input information is:

• list of WP which are engaged by the elements of the structure and
• direction of external parameters change - with the increasing or reduction of V, or transformation mode.

The result of search is the list of structures, formed by means of different variants of transformation:

- deformation of a lattice, i.e. change of its parameters a, b, c,,,,
- displacement of structure elements, i.e. WP coordinates x, y, z, or
- ordering-disordering of different structure elements in WP positions, i.e. appropriate probabilities .

with the increasing or reduction of the freedom degrees. This list contains the opportunity indications of the transition realization as the transition of second kind on Landau (dV=+-1), first kind, or first kind, close to the second kind. At the temperature increasing transformations are characterize by dV>0, dC<=0, and on the contrary at the temperature decreasing. In accordance with increase of pressure the transitions are accompanied by changes dV<0, dC>=0. The reduction of pressure is capable to return this result. Thus the dP values may be <0 or >0.

On the specified principles we construct the phase diagrams and investigate the structural transitions in ices and some liquid crystals. Our results don't contradict to the group theory analysis results where the comparison is possible.

Table 1 is the plane representation of VCP diagram for all 73 WPs concerning to 17 symmetry plane groups.

Table 2 consist all variants of the second kind transitions between WPs 17 symmetry plane groups.

The database for three-dimensional WPs. was constructed by analogy to a database for the plane WPs.