A diffusionless transformation is a phase change that occurs without the long-range diffusion of atoms but rather by some form of cooperative, homogenous movement of many atoms that results in a change in the crystal structure. These movements are small, usually less than the interatomic distances, and the neighbors of an atom remain close. The systematic movement of large numbers of atoms led to some to refer to these as military transformations in contrast to civilian diffusion-based phase changes, initially by Frederick Charles Frank and John Wyrill Christian. The most commonly encountered transformation of this type is the martensitic transformation which, while probably the most studied, is only one subset of non-diffusional transformations. The martensitic transformation in steel represents the most economically significant example of this category of phase transformations, but an increasing number of alternatives, such as shape memory alloys, are becoming more important as well. 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 a 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 into 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 the new phase is constrained by the surrounding material, this may give rise to elastic or plastic deformation and hence a strain energy term. The ratio of