Displacive phase transformations

Diffusionless transformations are a class of phase changes that do not occur by the long-range diffusion of atoms but rather by some form of cooperative, homogeneous movement of many atoms that results in a change in crystal structure. These movements are small, usually less than the interatomic distances, and the atoms maintain their relative relationships. The ordered movement of large numbers of atoms lead some to refer to these as military transformations in contrast to civilian diffusion-based phase changes [ref].

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The most commonly encountered transformation of this type is the martensitic transformation which, while being the best known, is actually only one subset of non-diffusional transformations. The marentitic transformation in steel represents the most economically important example of this category of phase transformations but an increasing number of alternatives, such as shape-memory alloys, are leaving the bounds of pure scientific interest and having significant impact on day-to-day life [examples and ref].

Classification and definitions

When a structural change occurs by the coordinated movement of atoms (or groups of atoms) relative to their neighours then the change is termed displacive. This covers a broad range of transformations and so further classifications have been developed [Cohen 1979].

The first distinction can be drawn between transformations dominated by lattice-distortive strains and those where shuffles are of greater importance.

Homogeneous lattice-distortive strains, also known as Bain strains, are strains that transform one Bravais lattice into a different one. This can be represented by a strain matrix S which transforms one vector, y, into a new vector, x:

y = Sx

This is homogeneous as straight lines are transformed to new straight lines. Examples of such transformations include a cubic lattice increasing in size on all three axes (dilation) or shearing into a monoclinic structure.

Shuffles, as the name suggests, involve the small movement of atoms within the unit cell. As a result pure shuffles do not normally result in a shape change of the unit cell - only its symmetry and structure.

Phase transformations normally result in the creation of an interface between the transformed and parent material. The energy required to generate this new interface will depend on its nature - essentially how well the two structures fit together. An additional energy term occurs if the transformation includes a shape change since, if new phase is constrained by surrounding material, this may give rise to elastic or plastic deformation and hence a strain energy term. The ratio of these interfacial and strain energy terms has a notable effect on the kinetics of the transformation and the morphology of the new phase. Thus, shuffle transformations, where distortions are small, are dominated by interfacial energies and can be usefully separated from lattice-distortive transformations where the strain energy tends to have a greater effect.

A subclassification of lattice-distortive dispalcements can be made by considering the dilational and shear components of the distortion. In transformations dominated by the shear component it is possible to find a line in the new phase that is undistorted from the parent phase while all lines are distorted when the dilation is predominant. Shear dominated transformations can be further classified according to the magnitude of the strain energies involved compared to the innate vibrations of the atoms in the lattice and hence whether the strain energies have a notable influence on the kinetics of the transformation and the morpholgy of the resulting phase. If the strain energy is a significant factor then the transformations are dubbed martensitic and if it is not the transformation is referred to as quasi-martensitic.