Invariant Plane by Addition of Rigid-Body Rotation

3 Invariant Plane by Addition of Rigid-Body Rotation 

The plane containing a and c in Fig. 24.9 is the plane in the f.c.c. phase that initially contained the vectors a and c . If the b.c.t. phase is now given a rigid-body rotation so that a — a and c — c, the undistorted plane in the b.c.t. phase will be returned to its original inclination in the f.c.c.-axis system and will therefore be an invariant plane of the overall deformation. In the present case, this can be achieved by a rotation around the axis indicated by u in Fig. 24.9 (see Exercise 24.3). The solution of the problem is now complete. The invariant plane is known, and the orientation relationship between the two phases and total shape change can be determined from the combined effects of the known lattice-invariant deformation, lattice deformation, and rigid-body rotation. 

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