Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A_cF8_227_a

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

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 : $\text{Fd}\bar{3}\text{m}$
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:

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

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=

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