AFLOW Prototype: A5B6C2_hP13_157_2ac_2c_b
Prototype | : | Ag5Pb2O6 |
AFLOW prototype label | : | A5B6C2_hP13_157_2ac_2c_b |
Strukturbericht designation | : | None |
Pearson symbol | : | hP13 |
Space group number | : | 157 |
Space group symbol | : | $P31m$ |
AFLOW prototype command | : | aflow --proto=A5B6C2_hP13_157_2ac_2c_b --params=$a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(1a\right) & \text{Ag I} \\ \mathbf{B}_{2} & = & z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(1a\right) & \text{Ag II} \\ \mathbf{B}_{3} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Pb} \\ \mathbf{B}_{4} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Pb} \\ \mathbf{B}_{5} & = & x_{4} \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{Ag III} \\ \mathbf{B}_{6} & = & x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{Ag III} \\ \mathbf{B}_{7} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + z_{4}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{Ag III} \\ \mathbf{B}_{8} & = & x_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{5}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{O I} \\ \mathbf{B}_{9} & = & x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{5}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{O I} \\ \mathbf{B}_{10} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{O I} \\ \mathbf{B}_{11} & = & x_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{6}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{O II} \\ \mathbf{B}_{12} & = & x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}x_{6}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{O II} \\ \mathbf{B}_{13} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(3c\right) & \text{O II} \\ \end{array} \]