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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{FCC}\times a_{FCC}\times a_{FCC} = a_{FCC}^3}

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{BCC}\times a_{BCC}\times a_{BCC} = a_{BCC}^3}

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2} a_{BCC}\times \sqrt{2}a_{BCC}\times a_{BCC} = 2 a_{BCC}^3}

Note that in general Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{FCC}\neq a_{BCC}} . To conserve volume during the transformation would require that:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\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