AlPS4 Structure: ABC4_oP12_16_ag_cd_2u
| Prototype | : | AlPS4 |
| AFLOW prototype label | : | ABC4_oP12_16_ag_cd_2u |
| Strukturbericht designation | : | None |
| Pearson symbol | : | oP12 |
| Space group number | : | 16 |
| Space group symbol | : | $\mbox{P222}$ |
| AFLOW prototype command | : | aflow --proto=ABC4_oP12_16_ag_cd_2u --params=$a,b/a,c/a,x_5,y_5,z_5,x_6,y_6,z_6$ |
Simple Orthorhombic primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\
\mathbf{a}_2 & = & b \, \mathbf{\hat{y}} \\
\mathbf{a}_3 & = & c \, \mathbf{\hat{z}}
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Al I} \\ \mathbf{B_2} & =& \frac12 \mathbf{a}_{2}& =& \frac12 \, b \, \mathbf{\hat{y}}& \left(1c\right) & \mbox{P I} \\ \mathbf{B_3} & =& \frac12 \mathbf{a}_{3}& =& \frac12 \, c \, \mathbf{\hat{z}}& \left(1d\right) & \mbox{P II} \\ \mathbf{B_4} & =& \frac12 \mathbf{a}_{2} + \frac12 \mathbf{a}_{3}& =& \frac12 \, b \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}& \left(1g\right) & \mbox{Al II} \\ \mathbf{B_5} & =& x_5 \mathbf{a}_{1} + y_5 \mathbf{a}_{2} + z_5 \mathbf{a}_{3}& =& x_5 \, a \, \mathbf{\hat{x}} + y_5 \, b \, \mathbf{\hat{y}} + z_5 \, c \, \mathbf{\hat{z}}& \left(4u\right) & \mbox{S I} \\ \mathbf{B_6} & =& - x_5 \mathbf{a}_{1} - y_5 \mathbf{a}_{2} + z_5 \mathbf{a}_{3}& =& - x_5 \, a \, \mathbf{\hat{x}} - y_5 \, b \, \mathbf{\hat{y}} + z_5 \, c \, \mathbf{\hat{z}}& \left(4u\right) & \mbox{S I} \\ \mathbf{B_7} & =& - x_5 \mathbf{a}_{1} + y_5 \mathbf{a}_{2} - z_5 \mathbf{a}_{3}& =& - x_5 \, a \, \mathbf{\hat{x}} + y_5 \, b \, \mathbf{\hat{y}} - z_5 \, c \, \mathbf{\hat{z}}& \left(4u\right) & \mbox{S I} \\ \mathbf{B_8} & =& x_5 \mathbf{a}_{1} - y_5 \mathbf{a}_{2} - z_5 \mathbf{a}_{3}& =& x_5 \, a \, \mathbf{\hat{x}} - y_5 \, b \, \mathbf{\hat{y}} - z_5 \, c \, \mathbf{\hat{z}}& \left(4u\right) & \mbox{S I} \\ \mathbf{B_9} & =& x_6 \mathbf{a}_{1} + y_6 \mathbf{a}_{2} + z_6 \mathbf{a}_{3}& =& x_6 \, a \, \mathbf{\hat{x}} + y_6 \, b \, \mathbf{\hat{y}} + z_6 \, c \, \mathbf{\hat{z}}& \left(4u\right) & \mbox{S II} \\ \mathbf{B}_{10} & =& - x_6 \mathbf{a}_{1} - y_6 \mathbf{a}_{2} + z_6 \mathbf{a}_{3}& =& - x_6 \, a \, \mathbf{\hat{x}} - y_6 \, b \, \mathbf{\hat{y}} + z_6 \, c \, \mathbf{\hat{z}}& \left(4u\right) & \mbox{S II} \\ \mathbf{B}_{11} & =& - x_6 \mathbf{a}_{1} + y_6 \mathbf{a}_{2} - z_6 \mathbf{a}_{3}& =& - x_6 \, a \, \mathbf{\hat{x}} + y_6 \, b \, \mathbf{\hat{y}} - z_6 \, c \, \mathbf{\hat{z}}& \left(4u\right) & \mbox{S II} \\ \mathbf{B}_{12} & =& x_6 \mathbf{a}_{1} - y_6 \mathbf{a}_{2} - z_6 \mathbf{a}_{3}& =& x_6 \, a \, \mathbf{\hat{x}} - y_6 \, b \, \mathbf{\hat{y}} - z_6 \, c \, \mathbf{\hat{z}}& \left(4u\right) & \mbox{S II} \\ \end{array} \]References
- A. Weiss and H. Schäfer, Zur Kenntnis von Aluminiumthiophosphat AlPS4, Naturwissenschaften 47, 495 (1960), doi:10.1007/BF00631053.