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 (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 \begin{alignat}{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 0.693 a_{FCC} \end{alignat} }

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