A generalised lattice correspondence for phase transformation.

Abstract

Each atom in a given position of the matrix phase is assigned a certain probability that it will occupy, upon transformation, a given site in the product phase. This probabilistic view of the atomic movements permitsa to define a vector which is a weighted average of all the sites in the parent phase the atoms at which have a finite probability of occupying a given position in the transformad phase. For transformations generating a macroscopic homogeneous deformation, a generalised correspondence is defined that incorporate the possibility of a certain degree of independence of atomic movements. This approach is used to explain the crystallography of the Widmänastatten ferrite. Out of this example it is concluded that if a generalised correspondence is assumed for transformations producing a martensitic type of shape change, 1 ) a microstructure may be not necessary for describing the total atomic displacements , and 2) the hypothesis of additional distortions in the habit plane is unnecessary.