AlPS4 Structure: ABC4_oP12_16_ag_cd_2u

Picture of Structure; Click for Big Picture
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.

Geometry files


Prototype Generator

aflow --proto=ABC4_oP12_16_ag_cd_2u --params=

Species:

Running:

Output: