FCC to BCC

The FCC lattice can be distorted to become a BCC. An expansion along the x- and y-directions, with corresponding contraction along the z-direction, can continuously distort the FCC into an BCC structure.

Note that in the FCC state, with unit cell:

$a_{FCC}\times a_{FCC}\times a_{FCC}=a_{FCC}^{3}$

there is a "distorted" BCC lattice with a tetragonal (square cuboid) unit cell:

${\frac {{\sqrt {2}}a_{FCC}}{2}}\times {\frac {{\sqrt {2}}a_{FCC}}{2}}\times a_{FCC}={\frac {a_{FCC}^{3}}{2}}$

In the final BCC state, we instead have unit cell:

$a_{BCC}\times a_{BCC}\times a_{BCC}=a_{BCC}^{3}$

and the FCC lattice has been distorted into a tetragonal cell:

${\sqrt {2}}a_{BCC}\times {\sqrt {2}}a_{BCC}\times a_{BCC}=2a_{BCC}^{3}$

Note that in general $a_{FCC}\neq a_{BCC}$. To conserve volume during the transformation would require that:

${\begin{alignedat}{2}a_{BCC}^{3}&={\frac {a_{FCC}^{3}}{2}}\\{\sqrt[{3}]{a_{BCC}^{3}}}&={\sqrt[{3}]{\frac {a_{FCC}^{3}}{2}}}\\a_{BCC}&={\frac {1}{\sqrt[{3}]{2}}}a_{FCC}\\a_{BCC}&\approx 0.693a_{FCC}\end{alignedat}}$

Experimental conversion factors may deviate from this. (E.g. Fe conversion has a BCC lattice parameter is 0.776 that of the FCC lattice.)

See Also

• Cemal Engin and Herbert M. Urbassek Molecular-dynamics investigation of the fcc → bcc phase transformation in Fe Computational Materials Science, Volume 41, Issue 3, January 2008, Pages 297-304 doi: 10.1016/j.commatsci.2007.04.019

• Negative supracrystals inducing a FCC-BCC transition in gold nanocrystal superlattices doi: 10.1007/s12274-013-0384-9

• The Bain versus Nishiyama–Wassermann path in the martensitic transformation of Fe doi: 10.1088/1367-2630/11/10/103027

• Thermoreversible, Epitaxial fcc↔bcc Transitions in Block Copolymer Solutions doi: 10.1103/PhysRevLett.89.215505