**Classification and Definitions**

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

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**:

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 displacements 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 morphology 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*.

Read more about this topic: Diffusionless Transformation

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