Diamond ($A4$) Structure: A_cF8_227_a

Picture of Structure; Click for Big Picture
Prototype : C
AFLOW prototype label : A_cF8_227_a
Strukturbericht designation : $A4$
Pearson symbol : cF8
Space group number : 227
Space group symbol : $\mbox{Fd}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A_cF8_227_a
--params=
$a$


Other elements with this structure

  • Si, Ge, Sn

  • This is the first crystal structure to be determined by X-ray diffraction.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &\frac18 \, \mathbf{a}_{1}+ \frac18 \, \mathbf{a}_{2}+ \frac18 \, \mathbf{a}_{3}& = &\frac18 \, a \, \mathbf{\hat{x}}+ \frac18 \, a \, \mathbf{\hat{y}}+ \frac18 \, a \, \mathbf{\hat{z}}& \left(8a\right) & \mbox{C} \\ \mathbf{B}_{2} & = &\frac78 \, \mathbf{a}_{1}+ \frac78 \, \mathbf{a}_{2}+ \frac78 \, \mathbf{a}_{3}& = &\frac78 \, a \, \mathbf{\hat{x}}+ \frac78 \, a \, \mathbf{\hat{y}}+ \frac78 \, a \, \mathbf{\hat{z}}& \left(8a\right) & \mbox{C} \\ \end{array} \]

References

  • W. H. Bragg and W. L. Bragg, The Structure of Diamond, Proc. R. Soc. A Math. Phys. Eng. Sci. 89, 277–291 (1913), doi:10.1098/rspa.1913.0084.

Geometry files


Prototype Generator

aflow --proto=A_cF8_227_a --params=

Species:

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