Symmetry of pretransition structures in alloys with a B2-type superstructure

Abstract

Transformation properties of the order parameters-atomic displacements in the B2 structure related to the wave vectors of the 1/3͗110͘ and 1/3͗111͘ type, which, in particular, are observed in B2 titanium nickelide based alloys, have been studied. Irreducible representations and their basis vectors related to these wave vectors have been determined. Subgroups of the symmetry group of the B2 structure relative to which the order parameters are invariant have been calculated. The feasibility of the realization of these subgroups as symmetry groups of the pretransition structures that arise prior to the B2 → R martensitic transformation in titanium nickelide based alloys has been analyzed.

Model of the B2 → R martensitic transformation in alloys with a B2 superstructure

“…As was already noted in [1], the R 0 structure at the earlier stages of studies of the TiNi based alloys was considered as a structure correspond ing to the R martensite [2]. The later investigations showed that the unit cell of the R phase (SG P3 or ), just as the unit cell of the R 0 structure, is hexago nal, with the area of the base three times as large as that of the unit cell of the R 0 structure.…”

“…For an analysis of the possible symmetry changes caused by atomic displacements with WVs of the type in different SEPs, we will use the same methods as in our previous work [1]. The lattice of a new phase is obtained in a trivial way.…”

“…We construct the representation of displacements using the same induction scheme that was used in [1]. Then, we consider the parts of this representation related to the star As the LUVs multiplied in the SEPs a, b, and d, we use the unit vectors e α , α = 1, 2, 3, of the coordinate system Oe of the crystal.…”

“…In our previous work [1], we have analyzed possible changes in the symmetry of the В2 structure that are caused by atomic displacements with wave vectors (WVs) of the and type. In particular, for the case of the TiNi based В2 alloys (CsCl type structure), we considered the possibility of a recon struction of the В2 structure (space group (SG) ) into the so called R phase (SG or ).…”

“…Let us denote the structure with the SG calcu lated in [1] as R 0 . As was already noted in [1], the R 0 structure at the earlier stages of studies of the TiNi based alloys was considered as a structure correspond ing to the R martensite [2].…”