Low–Temperature GaMo4S8 Structure : AB4C8_hR13_160_a_ab_2a2b

Picture of Structure; Click for Big Picture
Prototype : GaMo4S8
AFLOW prototype label : AB4C8_hR13_160_a_ab_2a2b
Strukturbericht designation : None
Pearson symbol : hR13
Space group number : 160
Space group symbol : $R3m$
AFLOW prototype command : aflow --proto=AB4C8_hR13_160_a_ab_2a2b
--params=
$a$,$c/a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$


  • At temperatures below 45 K GaMo4S8 transforms from its high–temperature cubic structure to this rhombohedral structure.
  • We use the data from (François, 1991) at 8 K.
  • Space group $R3m$ #160 allows an arbitrary choice of the zero of the $z$–axis. Here this use used to place the gallium atom at the origin ($z_{1} = 0$).

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Ga} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Mo I} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Si I} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}c \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Si II} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Mo II} \\ \mathbf{B}_{6} & = & z_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{5}+z_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{5}-z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Mo II} \\ \mathbf{B}_{7} & = & x_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{5}+z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{5}+\frac{1}{3}z_{5}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Mo II} \\ \mathbf{B}_{8} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{6}-z_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{6}-z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{6}+\frac{1}{3}z_{6}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Si III} \\ \mathbf{B}_{9} & = & z_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{6}+z_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{6}-z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{6}+\frac{1}{3}z_{6}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Si III} \\ \mathbf{B}_{10} & = & x_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{6}+z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{6}+\frac{1}{3}z_{6}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Si III} \\ \mathbf{B}_{11} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Si IV} \\ \mathbf{B}_{12} & = & z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}\left(x_{7}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Si IV} \\ \mathbf{B}_{13} & = & x_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \frac{1}{\sqrt{3}}\left(-x_{7}+z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{2}{3}x_{7}+\frac{1}{3}z_{7}\right)c \, \mathbf{\hat{z}} & \left(3b\right) & \mbox{Si IV} \\ \end{array} \]

References

  • M. François, W. Lengauer, K. Yvon, M. Sergent, M. Potel, P. Gougeon, and H. Ben Yaich–Aerrache, Structural phase transition in GaMo4S8 by X–ray powder diffraction, Zeitschrift für Kristallographie – Crystalline Materials 196, 111–128 (1991), doi:10.1524/zkri.1991.196.14.111.

Geometry files


Prototype Generator

aflow --proto=AB4C8_hR13_160_a_ab_2a2b --params=

Species:

Running:

Output: