Four-dimensional structural description of phase transformations in titanium alloys

Abstract

Titanium alloys display formation of $$\beta$$ , $$\alpha$$ , and $$\omega$$ phases under different processing conditions. Understanding structural transformations involving these phases on a unified basis and identifying a possible path of transformation seem to be interesting from the point of view of studies on phase transformations. An alternative and unified description pertaining to these is being presented here. This is accomplished by making an appeal to four dimensional structural description. It will be shown that such a model requires an angular distortion ( $$\theta$$ ) around the threefold axis. Such a distortion helps one define a scalar order parameter ( $$\eta$$ ) with values lying between 0 and 1. The two terminal values recover all the symmetrical characteristics of $$\beta$$ phase corresponding to $$\eta =0$$ and that of $$\omega$$ phase pertaining to $$\eta =1$$ . $$\alpha$$ phase formation in this model takes place for $$\theta = \cos ^{-1} (\frac{1}{4})$$ and $$\eta =\frac{13}{16}$$ . It is important to point out here that all structures related to choice of $$\eta$$ always preserve a minimal threefold symmetry. This led us to conclude that formation of trigonal phases may be taking place during the paths of transformation. In addition to all these advantages, the model also provides a general possibility of understanding commensurate and incommensurate modulations along threefold axis.