Martensitic transformations lattice invariant deformation

These operations do not occur separately and in any particular sequence but are simply a convenient way to conceptualize the transformation as a series of operations, each of which can be analyzed separately, but which working together produce a martensitic structure containing an invariant plane. As such, they can be imagined to occur in any sequence. For purposes of analysis, it is convenient to imagine that the lattice-invariant deformation occurs first, followed by the lattice deformation, followed finally by the rigid-body rotation. We now show that a lattice-invariant shear by slip followed by the lattice deformation analyzed above can produce an undistorted plane. 

Figure 24.21 shows a two-dimensional martensitic transformation in which a parent phase, P, is transformed into a martensitic phase, M, by a lattice deformation, B. Note that there is no invariant line in this two-dimensional transformation. Find a lattice-invariant deformation, S, and a rigid rotation, R, that together with the lattice deformation, B, produce an overall deformation given by... 

The input data for the model consist of the description of the lattice deformation and the choice of the slip system in the lattice-invariant shear. The model has successfully predicted the observed geometrical features of many martensitic transformations. The observed and calculated habit planes generally have high indices that result from the condition that they be macroscopically invariant. 

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