AFLOW Prototype: AB3_mC32_8_4a_12a
Prototype | : | TaTi3 |
AFLOW prototype label | : | AB3_mC32_8_4a_12a |
Strukturbericht designation | : | None |
Pearson symbol | : | mC32 |
Space group number | : | 8 |
Space group symbol | : | $Cm$ |
AFLOW prototype command | : | aflow --proto=AB3_mC32_8_4a_12a --params=$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$,$x_{12}$,$z_{12}$,$x_{13}$,$z_{13}$,$x_{14}$,$z_{14}$,$x_{15}$,$z_{15}$,$x_{16}$,$z_{16}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ta I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ta II} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ta III} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}a+z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ta IV} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}a+z_{5}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti I} \\ \mathbf{B}_{6} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}a+z_{6}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{6}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti II} \\ \mathbf{B}_{7} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti III} \\ \mathbf{B}_{8} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti IV} \\ \mathbf{B}_{9} & = & x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti V} \\ \mathbf{B}_{10} & = & x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti VI} \\ \mathbf{B}_{11} & = & x_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti VII} \\ \mathbf{B}_{12} & = & x_{12} \, \mathbf{a}_{1} + x_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}a+z_{12}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti VIII} \\ \mathbf{B}_{13} & = & x_{13} \, \mathbf{a}_{1} + x_{13} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & \left(x_{13}a+z_{13}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti IX} \\ \mathbf{B}_{14} & = & x_{14} \, \mathbf{a}_{1} + x_{14} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & \left(x_{14}a+z_{14}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti X} \\ \mathbf{B}_{15} & = & x_{15} \, \mathbf{a}_{1} + x_{15} \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & \left(x_{15}a+z_{15}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti XI} \\ \mathbf{B}_{16} & = & x_{16} \, \mathbf{a}_{1} + x_{16} \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3} & = & \left(x_{16}a+z_{16}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti XII} \\ \end{array} \]