 Bain path

A continuous tetragonal deformation connecting FCC and BCC geometries. In a simple uniaxial version, retain basal conventional edges $a,a$ while reducing the third edge to $a/\sqrt{2}$. The alternate vectors ${\mathbf{b}}_1=(a/2)(1,1,0)$, ${\mathbf{b}}_2=(a/2)(-1,1,0)$ and ${\mathbf{b}}_3=(0,0,a/\sqrt{2})$ form a BCC conventional cube, of half the volume of the deformed face-centered tetragonal cell. The name refers to Edgar Bain. Real metallurgical transformations can also change the other edges; this geometric path alone does not specify the energetic or kinetic transformation mechanism.