AFLOW Prototype: A_tI16_142_f
Prototype | : | S |
AFLOW prototype label | : | A_tI16_142_f |
Strukturbericht designation | : | None |
Pearson symbol | : | tI16 |
Space group number | : | 142 |
Space group symbol | : | $I4_{1}/acd$ |
AFLOW prototype command | : | aflow --proto=A_tI16_142_f --params=$a$,$c/a$,$x_{1}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \left(\frac{3}{8} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} +x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +2x_{1}\right) \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{S} \\ \mathbf{B}_{2} & = & \left(\frac{3}{8} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{8} - x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - 2x_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{S} \\ \mathbf{B}_{3} & = & \left(\frac{1}{8} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} - x_{1}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}}- \frac{1}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{S} \\ \mathbf{B}_{4} & = & \left(\frac{1}{8} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{3}{8} +x_{1}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{7}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{S} \\ \mathbf{B}_{5} & = & \left(\frac{5}{8} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{7}{8} - x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - 2x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{S} \\ \mathbf{B}_{6} & = & \left(\frac{5}{8} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{7}{8} +x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +2x_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{S} \\ \mathbf{B}_{7} & = & \left(\frac{7}{8} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{5}{8} +x_{1}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{1}\right)a \, \mathbf{\hat{y}} + \frac{5}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{S} \\ \mathbf{B}_{8} & = & \left(\frac{7}{8} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{5}{8} - x_{1}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{5}{8}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{S} \\ \end{array} \]