KevinYager at 22:57, 13 November 2016

2016-11-13T22:57:12Z

KevinYager: Created page with "The FCC lattice can be distorted to become a BCC. An expansion along the x- and y-directions, with corresponding contraction along the z-direct..."

2016-11-13T22:54:01Z

Created page with "The FCC lattice can be distorted to become a BCC. An expansion along the x- and y-directions, with corresponding contraction along the z-direct..."

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The [[Lattice:FCC|FCC]] lattice can be distorted to become a [[Lattice:BCC|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.

[[Image:Fcc to bcc000.png|300px]]

[[Image:Fcc to bcc025.png|300px]]

[[Image:Fcc to bcc050.png|300px]]

[[Image:Fcc to bcc075.png|300px]]

[[Image:Fcc to bcc100.png|300px]]

Note that in the FCC state, with unit cell:
:: <math>a_{FCC}\times a_{FCC}\times a_{FCC} = a_{FCC}^3</math>
there is a "distorted" BCC lattice with a [http://en.wikipedia.org/wiki/Tetragonal_crystal_system tetragonal] (square cuboid) unit cell:
:: <math>\frac{\sqrt{2}a_{FCC}}{2}\times \frac{\sqrt{2}a_{FCC}}{2}\times a_{FCC} = \frac{a_{FCC}^3}{2}</math>
In the final BCC state, we instead have unit cell:
:: <math>a_{BCC}\times a_{BCC}\times a_{BCC} = a_{BCC}^3</math>
and the FCC lattice has been distorted into a tetragonal cell:
:: <math>\sqrt{2} a_{BCC}\times \sqrt{2}a_{BCC}\times a_{BCC} = 2 a_{BCC}^3</math>
Note that in general <math>a_{FCC}\neq a_{BCC}</math>. To conserve volume during the transformation would require that:
::<math>
\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}
</math>
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 [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TWM-4P00RY6-1&_user=2422869&_coverDate=01%2F31%2F2008&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000057228&_version=1&_urlVersion=0&_userid=2422869&md5=5e2860f421f44f243d39031f8c185375&searchtype=a Molecular-dynamics investigation of the fcc → bcc phase transformation in Fe] Computational Materials Science, Volume 41, Issue 3, January '''2008''', Pages 297-304 [http://dx.doi.org/10.1016/j.commatsci.2007.04.019 doi: 10.1016/j.commatsci.2007.04.019]

* Negative supracrystals inducing a FCC-BCC transition in gold nanocrystal superlattices [http://dx.doi.org/10.1007/s12274-013-0384-9 doi: 10.1007/s12274-013-0384-9]

* The Bain versus Nishiyama–Wassermann path in the martensitic transformation of Fe [http://dx.doi.org/10.1088/1367-2630/11/10/103027 doi: 10.1088/1367-2630/11/10/103027]

* Thermoreversible, Epitaxial fcc↔bcc Transitions in Block Copolymer Solutions [http://dx.doi.org/10.1103/PhysRevLett.89.215505 doi: 10.1103/PhysRevLett.89.215505]

@@ Line 1: / Line 1: @@
-The [[Lattice:FCC|FCC]] lattice can be distorted to become a [[Lattice:BCC|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.
+The [[Lattice:FCC|FCC]] [[lattice]] can be distorted to become a [[Lattice:BCC|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.
 [[Image:Fcc to bcc000.png|300px]]
@@ Line 11: / Line 11: @@
 [[Image:Fcc to bcc100.png|300px]]
-Note that in the FCC state, with unit cell:
+Note that in the FCC state, with [[unit cell]]:
 :: <math>a_{FCC}\times a_{FCC}\times a_{FCC} = a_{FCC}^3</math>
 there is a "distorted" BCC lattice with a [http://en.wikipedia.org/wiki/Tetragonal_crystal_system tetragonal] (square cuboid) unit cell:

FCC to BCC - Revision history

KevinYager at 22:57, 13 November 2016

KevinYager: Created page with "The FCC lattice can be distorted to become a BCC. An expansion along the x- and y-directions, with corresponding contraction along the z-direct..."