UB12 ($D2_{f}$) Structure: A12B_cF52_225_i_a

Picture of Structure; Click for Big Picture
Prototype : UB12
AFLOW prototype label : A12B_cF52_225_i_a
Strukturbericht designation : $D2_{f}$
Pearson symbol : cF52
Space group number : 225
Space group symbol : $\mbox{Fm}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A12B_cF52_225_i_a
--params=
$a$,$y_{2}$


Other compounds with this structure

  • DyB12, ErB12, LuB12, ThB12, TmB12, YB12, YbB12, ZrB12, and (Th0.93Zr0.07)B12

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} & = &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(4a\right) & \mbox{U} \\ \mathbf{B}_{2} & = &\left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{3} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{4} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{5} & = &\left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{6} & = &+ \frac12 \, \mathbf{a}_{1}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{7} & = &\left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{8} & = &\left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{9} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{10} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{11} & = &\left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{12} & = &\left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 + 2 \, y_{2}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 + y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \mathbf{B}_{13} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \left(\frac12 - 2 \, y_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(48i\right) & \mbox{B} \\ \end{array} \]

References

  • P. Blum and F. Bertaut, Contribution ‘a l’Étude des Borures ‘a Teneur Élevée en Bore, Acta Cryst. 7, 81–86 (1954), doi:10.1107/S0365110X54000151.

Found in

  • W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley– Interscience, New York, London, Sydney, Toronto, 1972)., pp. 757-759.

Geometry files


Prototype Generator

aflow --proto=A12B_cF52_225_i_a --params=

Species:

Running:

Output: