CeRu2B2 Structure: A2BC2_oF40_22_fi_ad_gh

Picture of Structure; Click for Big Picture
Prototype : CeRu2B2
AFLOW prototype label : A2BC2_oF40_22_fi_ad_gh
Strukturbericht designation : None
Pearson symbol : oF40
Space group number : 22
Space group symbol : $F222$
AFLOW prototype command : aflow --proto=A2BC2_oF40_22_fi_ad_gh
--params=
$a$,$b/a$,$c/a$,$y_{3}$,$z_{4}$,$z_{5}$,$y_{6}$


Face-centered Orthorhombic primitive vectors:

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

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{Ce I} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Ce II} \\ \mathbf{B}_{3} & = & y_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + y_{3} \, \mathbf{a}_{3} & = & y_{3}b \, \mathbf{\hat{y}} & \left(8f\right) & \mbox{B I} \\ \mathbf{B}_{4} & = & -y_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2}-y_{3} \, \mathbf{a}_{3} & = & -y_{3}b \, \mathbf{\hat{y}} & \left(8f\right) & \mbox{B I} \\ \mathbf{B}_{5} & = & z_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & z_{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ru I} \\ \mathbf{B}_{6} & = & -z_{4} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -z_{4}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Ru I} \\ \mathbf{B}_{7} & = & z_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Ru II} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Ru II} \\ \mathbf{B}_{9} & = & y_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{2} + y_{6} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{B II} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{6}\right)b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{B II} \\ \end{array} \]

References

  • P. Rogl, Structural chemistry and phase equilibria of ternary rare earth–platinum metal borides, J. Less–Common Met. 110, 283–294 (1985), doi:10.1016/0022-5088(85)90334-0.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=A2BC2_oF40_22_fi_ad_gh --params=

Species:

Running:

Output: