CaB6 ($D2_{1}$) Structure: A6B_cP7_221_f_a

Picture of Structure; Click for Big Picture
Prototype : CaB6
AFLOW prototype label : A6B_cP7_221_f_a
Strukturbericht designation : $D2_{1}$
Pearson symbol : cP7
Space group number : 221
Space group symbol : $\mbox{Pm}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A6B_cP7_221_f_a
--params=
$a$,$x_{2}$


Simple Cubic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Ca} \\ \mathbf{B}_{2} & = &x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{3} & = &- x_{2} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \mathbf{B}_{7} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(6f\right) & \mbox{B} \\ \end{array} \]

References

  • Z. Yahia, S. Turrell, G. Turrell, and J. P. Mercurio, Infrared and Raman spectra of hexaborides: force–field calculations, and isotopic effects, J. Mol. Struct. 224, 303–312 (1990), doi:10.1016/0022-2860(90)87025-S.

Geometry files


Prototype Generator

aflow --proto=A6B_cP7_221_f_a --params=

Species:

Running:

Output: