A diffusionless transformation, commonly known as displacive transformation, denotes solid-state alterations in crystal structures that do not hinge on the diffusion of atoms across extensive distances. Rather, these transformations manifest as a result of synchronized shifts in atomic positions, wherein atoms undergo displacements of distances smaller than the spacing between adjacent atoms, all while preserving their relative arrangement. An example of such a phenomenon is the martensitic transformation, a notable occurrence observed in the context of steel materials.

The term "martensite" was originally coined to describe the rigid and finely dispersed constituent that emerges in steels subjected to rapid cooling. Subsequent investigations revealed that materials beyond ferrous alloys, such as non-ferrous alloys and ceramics, can also undergo diffusionless transformations. Consequently, the term "martensite" has evolved to encompass the resultant product arising from such transformations in a more inclusive manner. In the context of diffusionless transformations, a cooperative and homogeneous movement occurs, leading to a modification in the crystal structure during a phase change. These movements are small, usually less than their interatomic distances, and the neighbors of an atom remain close.

The systematic movement of large numbers of atoms led some to refer to them as military transformations, in contrast to civilian diffusion-based phase changes, initially by Charles Frank and John Wyrill Christian.

The most commonly encountered transformation of this type is the martensitic transformation, which is probably the most studied but 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. However, an increasing number of alternatives, such as shape memory alloys, are becoming more important as well.

The phenomenon in which atoms or groups of atoms coordinate to displace their neighboring counterparts resulting in structural modification is known as a displacive transformation. The scope of displacive transformations is extensive, encompassing a diverse array of structural changes. As a result, additional classifications have been devised to provide a more nuanced understanding of these transformations.

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, 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.