Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB4C8_hR13_160_a_ab_2a2b-001

This structure originally had the label AB4C8_hR13_160_a_ab_2a2b. Calls to that address will be redirected here.

If you are using this page, please cite:
D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

Links to this page

https://aflow.org/p/5V5H
or https://aflow.org/p/AB4C8_hR13_160_a_ab_2a2b-001
or PDF Version

Low Temperature GaMo$_{4}$S$_{8}$ Structure: AB4C8_hR13_160_a_ab_2a2b-001

Picture of Structure; Click for Big Picture
Prototype GaMo$_{4}$S$_{8}$
AFLOW prototype label AB4C8_hR13_160_a_ab_2a2b-001
ICSD 33995
Pearson symbol hR13
Space group number 160
Space group symbol $R3m$
AFLOW prototype command aflow --proto=AB4C8_hR13_160_a_ab_2a2b-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}$

Other compounds with this structure

GaV$_{4}$S$_{8}$


  • At temperatures below 45K GaMo$_{4}$S$_{8}$ transforms from its high-temperature cubic structure to this rhombohedral structure.
  • We use the data from (François, 1991) at 8K.
  • Space group $R3m$ #160 allows a arbitrary choice of the zero of the $z$-axis. Here we use this freedom to place the gallium atom at the origin ($z_{1} = 0$).

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ = $c x_{1} \,\mathbf{\hat{z}}$ (1a) Ga I
$\mathbf{B_{2}}$ = $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ = $c x_{2} \,\mathbf{\hat{z}}$ (1a) Mo I
$\mathbf{B_{3}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $c x_{3} \,\mathbf{\hat{z}}$ (1a) Si I
$\mathbf{B_{4}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ = $c x_{4} \,\mathbf{\hat{z}}$ (1a) Si II
$\mathbf{B_{5}}$ = $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (3b) Mo II
$\mathbf{B_{6}}$ = $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (3b) Mo II
$\mathbf{B_{7}}$ = $x_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ = $- \frac{1}{\sqrt{3}}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ (3b) Mo II
$\mathbf{B_{8}}$ = $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (3b) Si III
$\mathbf{B_{9}}$ = $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (3b) Si III
$\mathbf{B_{10}}$ = $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ = $- \frac{1}{\sqrt{3}}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ (3b) Si III
$\mathbf{B_{11}}$ = $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (3b) Si IV
$\mathbf{B_{12}}$ = $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ = $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (3b) Si IV
$\mathbf{B_{13}}$ = $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ = $- \frac{1}{\sqrt{3}}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ (3b) Si IV

References

  • M. François, W. Lengauer, K. Yvon, M. Sergent, M. Potel, P. Gougeon, and H. B. Yaich-Aerrache, Structural phase transition in GaMo$_{4}$S$_{8}$ by X-ray powder diffraction, Z. Kristallogr. 196, 111–120 (1991), doi:10.1524/zkri.1991.196.14.111.

Prototype Generator

aflow --proto=AB4C8_hR13_160_a_ab_2a2b --params=$a,c/a,x_{1},x_{2},x_{3},x_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7}$

Species:

Running:

Output: