Landau Theory of the Displacive Phase Transformations in Gold-Cadmium and Titanium-Nickel Alloys

Abstract

On the basis of group theoretical symmetry criteria, the primary and secondary order parameters (OP's) have been identified for the three ferroelastic martensitic transformations that occur in the Au-Cd binary, and in the Ti-Ni-M (M = Fe, At, Cu) pseudo-binary shape-memory alloys, viz (i) from the cubic β 2 austenite parent phase (B2 structure) to the rhombohedral (R) ζ' 2 product phase of P3 symmetry, (ii) from the β 2 to the orthorhombic (γ 2 ) product phase of Pmma symmetry (B19 structure), and (iii) from the B19 to the monoclinic B19'structure of P2 1 /m symmetry. For all three transformations, the Landau free energy and the relations between the primary OP and the atom shuffle displacements are given for the transition to a single product phase variant. For case (i), the 12 experimentally measured structural (shuffle) parameters of the R phase can be accounted for and fitted by only two theoretical model parameters, giving satisfactory agreement with the (only available) room temperature data for Au .505 Cd .495 ; for Ti .4977 Ni .5023 larger discrepancies, but mostly within the relatively large experimental error are found. For the two cases (ii) and (iii), the two shuffle displacements each can be fitted exactly by the two theoretical model parameters required.