$\beta$–In2S3 Crystal Structure: A2B3_tI80_141_ceh_3h
| Prototype | : | $\beta$–In2S3 |
| AFLOW prototype label | : | A2B3_tI80_141_ceh_3h |
| Strukturbericht designation | : | None |
| Pearson symbol | : | tI80 |
| Space group number | : | 141 |
| Space group symbol | : | $\text{I4}_{1}\text{/amd}$ |
| AFLOW prototype command | : | aflow --proto=A2B3_tI80_141_ceh_3h --params=$a$,$c/a$,$z_{2}$,$y_{3}$,$z_{3}$,$y_{4}$,$z_{4}$,$y_{5}$,$z_{5}$,$y_{6}$,$z_{6}$ |
- This is a spinel structure with ordered defects.
Body-centered Tetragonal primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}}\\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, c \, \mathbf{\hat{z}}\\ \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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(8c\right) & \text{In I} \\ \mathbf{B}_{2} & =&\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{y}}& \left(8c\right) & \text{In I} \\ \mathbf{B}_{3} & =&\frac12 \, \mathbf{a}_{2}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(8c\right) & \text{In I} \\ \mathbf{B}_{4} & =&\frac12 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(8c\right) & \text{In I} \\ \mathbf{B}_{5} & =&\left(\frac14 + z_{2}\right) \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \text{In II} \\ \mathbf{B}_{6} & =&z_{2} \, \mathbf{a}_{1}+ \left(\frac14 + z_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \text{In II} \\ \mathbf{B}_{7} & =&\left(\frac34 - z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(8e\right) & \text{In II} \\ \mathbf{B}_{8} & =&- z_{2} \, \mathbf{a}_{1}+ \left(\frac34 - z_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& =&\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(8e\right) & \text{In II} \\ \mathbf{B}_{9} & =&\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& =&y_{3} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{In III} \\ \mathbf{B}_{10} & =&\left(\frac12 - y_{3} + z_{3}\right)\, \mathbf{a}_{1}+ z_{3} \, \mathbf{a}_{2}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - y_{3}\right) \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{In III} \\ \mathbf{B}_{11} & =&z_{3}\, \mathbf{a}_{1}+ \left(\frac12 - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& =&\left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{In III} \\ \mathbf{B}_{12} & =&z_{3}\, \mathbf{a}_{1}+ \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{In III} \\ \mathbf{B}_{13} & =&\left(\frac12 + y_{3} - z_{3}\right)\, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+ \left(\frac12 + y_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + y_{3}\right) \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{In III} \\ \mathbf{B}_{14} & =&- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& =&- y_{3} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{In III} \\ \mathbf{B}_{15} & =&- z_{3}\, \mathbf{a}_{1}+ \left(\frac12 + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& =&\left(\frac14 + y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{In III} \\ \mathbf{B}_{16} & =&- z_{3}\, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{3}\right) \, \mathbf{a}_{3}& =&\left(\frac14 - y_{3}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{In III} \\ \mathbf{B}_{17} & =&\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+ z_{4} \, \mathbf{a}_{2}+ y_{4} \, \mathbf{a}_{3}& =&y_{4} \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S I} \\ \mathbf{B}_{18} & =&\left(\frac12 - y_{4} + z_{4}\right)\, \mathbf{a}_{1}+ z_{4} \, \mathbf{a}_{2}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - y_{4}\right) \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S I} \\ \mathbf{B}_{19} & =&z_{4}\, \mathbf{a}_{1}+ \left(\frac12 - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}& =&\left(\frac14 - y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S I} \\ \mathbf{B}_{20} & =&z_{4}\, \mathbf{a}_{1}+ \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac14 + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S I} \\ \mathbf{B}_{21} & =&\left(\frac12 + y_{4} - z_{4}\right)\, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+ \left(\frac12 + y_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + y_{4}\right) \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S I} \\ \mathbf{B}_{22} & =&- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}& =&- y_{4} \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S I} \\ \mathbf{B}_{23} & =&- z_{4}\, \mathbf{a}_{1}+ \left(\frac12 + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+ y_{4} \, \mathbf{a}_{3}& =&\left(\frac14 + y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S I} \\ \mathbf{B}_{24} & =&- z_{4}\, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{4}\right) \, \mathbf{a}_{3}& =&\left(\frac14 - y_{4}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S I} \\ \mathbf{B}_{25} & =&\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+ z_{5} \, \mathbf{a}_{2}+ y_{5} \, \mathbf{a}_{3}& =&y_{5} \, a \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S II} \\ \mathbf{B}_{26} & =&\left(\frac12 - y_{5} + z_{5}\right)\, \mathbf{a}_{1}+ z_{5} \, \mathbf{a}_{2}+ \left(\frac12 - y_{5}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - y_{5}\right) \, a \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S II} \\ \mathbf{B}_{27} & =&z_{5}\, \mathbf{a}_{1}+ \left(\frac12 - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}& =&\left(\frac14 - y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S II} \\ \mathbf{B}_{28} & =&z_{5}\, \mathbf{a}_{1}+ \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{5}\right) \, \mathbf{a}_{3}& =&\left(\frac14 + y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S II} \\ \mathbf{B}_{29} & =&\left(\frac12 + y_{5} - z_{5}\right)\, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+ \left(\frac12 + y_{5}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + y_{5}\right) \, a \, \mathbf{\hat{y}}- z_{5} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S II} \\ \mathbf{B}_{30} & =&- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}& =&- y_{5} \, a \, \mathbf{\hat{y}}- z_{5} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S II} \\ \mathbf{B}_{31} & =&- z_{5}\, \mathbf{a}_{1}+ \left(\frac12 + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+ y_{5} \, \mathbf{a}_{3}& =&\left(\frac14 + y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S II} \\ \mathbf{B}_{32} & =&- z_{5}\, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{5}\right) \, \mathbf{a}_{3}& =&\left(\frac14 - y_{5}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 - z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S II} \\ \mathbf{B}_{33} & =&\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+ z_{6} \, \mathbf{a}_{2}+ y_{6} \, \mathbf{a}_{3}& =&y_{6} \, a \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S III} \\ \mathbf{B}_{34} & =&\left(\frac12 - y_{6} + z_{6}\right)\, \mathbf{a}_{1}+ z_{6} \, \mathbf{a}_{2}+ \left(\frac12 - y_{6}\right) \, \mathbf{a}_{3}& =&\left(\frac12 - y_{6}\right) \, a \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S III} \\ \mathbf{B}_{35} & =&z_{6}\, \mathbf{a}_{1}+ \left(\frac12 - y_{6} + z_{6}\right) \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}& =&\left(\frac14 - y_{6}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 + z_{6}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S III} \\ \mathbf{B}_{36} & =&z_{6}\, \mathbf{a}_{1}+ \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+ \left(\frac12 + y_{6}\right) \, \mathbf{a}_{3}& =&\left(\frac14 + y_{6}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 + z_{6}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S III} \\ \mathbf{B}_{37} & =&\left(\frac12 + y_{6} - z_{6}\right)\, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+ \left(\frac12 + y_{6}\right) \, \mathbf{a}_{3}& =&\left(\frac12 + y_{6}\right) \, a \, \mathbf{\hat{y}}- z_{6} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S III} \\ \mathbf{B}_{38} & =&- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}& =&- y_{6} \, a \, \mathbf{\hat{y}}- z_{6} \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S III} \\ \mathbf{B}_{39} & =&- z_{6}\, \mathbf{a}_{1}+ \left(\frac12 + y_{6} - z_{6}\right) \, \mathbf{a}_{2}+ y_{6} \, \mathbf{a}_{3}& =&\left(\frac14 + y_{6}\right) \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - z_{6}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S III} \\ \mathbf{B}_{40} & =&- z_{6}\, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+ \left(\frac12 - y_{6}\right) \, \mathbf{a}_{3}& =&\left(\frac14 - y_{6}\right) \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac34 - z_{6}\right) \, c \, \mathbf{\hat{z}}& \left(16h\right) & \text{S III} \\ \end{array} \]References
- N. S. Rampersadh, A. M. Venter, and D. G. Billing, Rietveld refinement of In2S3 using neutron and X–ray powder diffraction data, Physica B 350, e383–e385 (2004), doi:10.1016/j.physb.2004.03.102.