AFLOW Prototype: A3B5_oC32_38_abce_abcdf
Prototype | : | Ta3Ti5 |
AFLOW prototype label | : | A3B5_oC32_38_abce_abcdf |
Strukturbericht designation | : | None |
Pearson symbol | : | oC32 |
Space group number | : | 38 |
Space group symbol | : | $Amm2$ |
AFLOW prototype command | : | aflow --proto=A3B5_oC32_38_abce_abcdf --params=$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$y_{7}$,$z_{7}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & -z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ta I} \\ \mathbf{B}_{2} & = & -z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Ti I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Ta II} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{4}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Ti II} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Ta III} \\ \mathbf{B}_{6} & = & -x_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Ta III} \\ \mathbf{B}_{7} & = & x_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Ti III} \\ \mathbf{B}_{8} & = & -x_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Ti III} \\ \mathbf{B}_{9} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Ti IV} \\ \mathbf{B}_{10} & = & \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Ti IV} \\ \mathbf{B}_{11} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{Ta IV} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(-y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{Ta IV} \\ \mathbf{B}_{13} & = & x_{9} \, \mathbf{a}_{1} + \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{Ti V} \\ \mathbf{B}_{14} & = & -x_{9} \, \mathbf{a}_{1} + \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{Ti V} \\ \mathbf{B}_{15} & = & x_{9} \, \mathbf{a}_{1} + \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{Ti V} \\ \mathbf{B}_{16} & = & -x_{9} \, \mathbf{a}_{1} + \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8f\right) & \text{Ti V} \\ \end{array} \]