Continuous atomic displacements and lattice distortion during fcc-bcc martensitic transformation

The continuous matrices of atomic displacements and lattice distortion from face-centered-cubic (fcc) to body-centered-cubic (bcc) phases compatible with the hard-sphere geometry of iron atoms are calculated for different possible final orientation relationships (ORs), such as Bain, Pitsch and Kurdjumov-Sachs (KS). The angular distortion introduced in the calculations appears as a natural order parameter of the fcc-bcc transitions. The average atomic displacement is lower with Pitsch and KS ORs than for Bain; one of these two distortions probably constitutes the natural mechanism for stress-free isolated small crystals. For matrix-embedded transformations that occur in bulk steels, the distortion associated with KS OR seems very appropriate: it has special mathematical properties and can explain the {2 2 5} habit planes with a simple O-lattice criterion. From these calculations, the fcc-bcc martensitic transformation appears to be “angular distortive”, and not of “shear” type as usually assumed.