AFLOW Prototype: A10B3C4_oC68_64_2dfg_ad_2d
Prototype | : | O10Ru3Sr4 |
AFLOW prototype label | : | A10B3C4_oC68_64_2dfg_ad_2d |
Strukturbericht designation | : | None |
Pearson symbol | : | oC68 |
Space group number | : | 64 |
Space group symbol | : | $Cmca$ |
AFLOW prototype command | : | aflow --proto=A10B3C4_oC68_64_2dfg_ad_2d --params=$a$,$b/a$,$c/a$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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) & \text{Ru I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Ru I} \\ \mathbf{B}_{3} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} & = & x_{2}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{O I} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{O I} \\ \mathbf{B}_{5} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} & = & -x_{2}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{O I} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{O I} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{O II} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{O II} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{O II} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{O II} \\ \mathbf{B}_{11} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} & = & x_{4}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{Ru II} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{Ru II} \\ \mathbf{B}_{13} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} & = & -x_{4}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{Ru II} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{Ru II} \\ \mathbf{B}_{15} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} & = & x_{5}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{Sr I} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{Sr I} \\ \mathbf{B}_{17} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} & = & -x_{5}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{Sr I} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{Sr I} \\ \mathbf{B}_{19} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} & = & x_{6}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{Sr II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{Sr II} \\ \mathbf{B}_{21} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} & = & -x_{6}a \, \mathbf{\hat{x}} & \left(8d\right) & \text{Sr II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{Sr II} \\ \mathbf{B}_{23} & = & -y_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O III} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O III} \\ \mathbf{B}_{25} & = & \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O III} \\ \mathbf{B}_{26} & = & y_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -y_{7}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{O III} \\ \mathbf{B}_{27} & = & \left(x_{8}-y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(16g\right) & \text{O IV} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - x_{8} + y_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8} - y_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(16g\right) & \text{O IV} \\ \mathbf{B}_{29} & = & \left(\frac{1}{2} - x_{8} - y_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8} + y_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{8}\right)c \, \mathbf{\hat{z}} & \left(16g\right) & \text{O IV} \\ \mathbf{B}_{30} & = & \left(x_{8}+y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(16g\right) & \text{O IV} \\ \mathbf{B}_{31} & = & \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(16g\right) & \text{O IV} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} +x_{8} - y_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8} + y_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{8}\right)c \, \mathbf{\hat{z}} & \left(16g\right) & \text{O IV} \\ \mathbf{B}_{33} & = & \left(\frac{1}{2} +x_{8} + y_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8} - y_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(16g\right) & \text{O IV} \\ \mathbf{B}_{34} & = & \left(-x_{8}-y_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(16g\right) & \text{O IV} \\ \end{array} \]