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Edgar Bain was an American materials scientist who studied transformations in steel. His 1924 paper The Nature of Martensite by Edgar Bain examined how the structure of martensite relates to its parent austenite, connecting the mechanical behaviour of hardened steel with changes in crystal structure.^[ref]

The Bain path expresses a geometric connection between face-centered cubic and body-centred cubic structures through a tetragonal deformation. It helps make a structural transformation concrete: changing the relative lengths along different axes can map one lattice geometry to another. Such a geometric path by itself does not specify the complete chemical kinetics or every observed feature of a transformation in real steel; those also depend on chemical composition and microstructural constraints.

In the tetragonal crystal system, physical squared distances use $a^2(\Delta x^2+\Delta y^2)+c^2\Delta z^2$. Two Ti–O distances from the corner Ti have length $\sqrt{2}ua$; the other four have length $\sqrt{2a^2(1/2-u{)}^2+c^2/4}$. Equating both to $r$ givesThus, within the equal-bond model,The rutile structure remains tetragonal and its octahedral angles remain distorted; these numbers are not a claim about measured ambient-pressure lattice parameters.