The rotation axes and angles involved in the formation of self-accommodating plates of Widmanstätten ferrite

When Widmanstätten ferrite is produced by mechanical activation, it forms in pairs of self-accommodating plates of near-identical orientation. An explanation is proposed for the lack of orientation difference between these pairs. This done by deriving all the possible rotation axes and angles associated with the Kurdjumov-Sachs, Nishiyama-Wassermann, Pitsch, Greninger-Troiano and inverse Greninger-Troiano relationships. It is shown that whereas the misorientations associated with these relationships are conventionally described in terms of minimum angles, in every case an alternative rotation axis is available around which the angle is in the range 90.0-90.12°. Given that the plates form as a result of opposite shears, the misorientations between two plates in a pair formed according to any of the usual orientation relationships all fall in the range 180-180.24°.