A Theoretical Investigation of Orientation Relationships and   Transformation Strains in Steels
  The identification of orientation relationships (ORs) plays a crucial r\^ole in the understanding of solid phase transformations. In steels, the most common models of ORs are the ones by Nishiyama-Wassermann (NW) and Kurdjumov-Sachs (KS). The defining feature of these and other OR models is the matching of directions and planes in the parent face-centred cubic $\gamma$-phase to ones in the product body-centred cubic/tetragonal $\alpha/\alpha'$-phase.   In this paper a novel method that identifies transformation strains with ORs is introduced and used to develop a new strain-based approach to phase transformation models in steels. Using this approach, it is shown that the transformation strains that leave a close packed plane in the $\gamma$-phase and a close packed direction within that plane unrotated are precisely those giving rise to the NW and KS ORs when a cubic product phase is considered. Further, it is outlined how, by choosing different pairs of unrotated planes and directions, other common ORs such as the ones by Pitsch (PT) and Greninger-Troiano (GT) can be derived.   One of the advantages of our approach is that it leads to a natural generalisation of the NW, KS and other ORs for different ratios of tetragonality $r$ of the product bct $\alpha'$-phase. These generalised ORs predict a sharpening of the transformation textures with increasing tetragonality and are thus in qualitative agreement with experiments on steels with varying alloy concentration. 
Anton Muehlemann and Konstantinos Koumatos
cond-mat.mtrl-sci math-ph math.MP