AFLOW Prototype: A_hP6_178_a
Prototype | : | Sc |
AFLOW prototype label | : | A_hP6_178_a |
Strukturbericht designation | : | None |
Pearson symbol | : | hP6 |
Space group number | : | 178 |
Space group symbol | : | $P6_{1}22$ |
AFLOW prototype command | : | aflow --proto=A_hP6_178_a --params=$a$,$c/a$,$x_{1}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} & \left(6a\right) & \text{Sc} \\ \mathbf{B}_{2} & = & x_{1} \, \mathbf{a}_{2} + \frac{1}{3} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{1}{3}c \, \mathbf{\hat{z}} & \left(6a\right) & \text{Sc} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \frac{2}{3} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{2}{3}c \, \mathbf{\hat{z}} & \left(6a\right) & \text{Sc} \\ \mathbf{B}_{4} & = & -x_{1} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{1}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(6a\right) & \text{Sc} \\ \mathbf{B}_{5} & = & -x_{1} \, \mathbf{a}_{2} + \frac{5}{6} \, \mathbf{a}_{3} & = & -\frac{1}{2}x_{1}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{1}a \, \mathbf{\hat{y}} + \frac{5}{6}c \, \mathbf{\hat{z}} & \left(6a\right) & \text{Sc} \\ \mathbf{B}_{6} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \frac{1}{6} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \frac{1}{6}c \, \mathbf{\hat{z}} & \left(6a\right) & \text{Sc} \\ \end{array} \]