Sc$_{2}$S$_{3}$ Structure: A3B2_oF80_70_fh_2e-001
| Prototype | S$_{3}$Sc$_{2}$ |
| AFLOW prototype label | A3B2_oF80_70_fh_2e-001 |
| ICSD | 22236 |
| Pearson symbol | oF80 |
| Space group number | 70 |
| Space group symbol | $Fddd$ |
| AFLOW prototype command |
aflow --proto=A3B2_oF80_70_fh_2e-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
Dy$_{2}$Se$_{3}$, Dy$_{2}$Te$_{3}$, Eu$_{2}$Se$_{3}$, Eu$_{2}$Te$_{3}$, Lu$_{2}$Se$_{3}$, Sc$_{2}$Se$_{3}$, Y$_{2}$Se$_{3}$, Y$_{2}$Te$_{3}$, Yb$_{2}$Se$_{3}$
- This structure has been rotated from the orientation given by (Dismukes, 1964).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16e) | Sc I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16e) | Sc I |
| $\mathbf{B_{3}}$ | = | $\left(x_{1} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+\frac{3}{8}b \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16e) | Sc I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\left(x_{1} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{1} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}b \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16e) | Sc I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16e) | Sc II |
| $\mathbf{B_{6}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16e) | Sc II |
| $\mathbf{B_{7}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{8}b \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16e) | Sc II |
| $\mathbf{B_{8}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}b \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16e) | Sc II |
| $\mathbf{B_{9}}$ | = | $y_{3} \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | S I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | S I |
| $\mathbf{B_{11}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | S I |
| $\mathbf{B_{12}}$ | = | $\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(y_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | S I |
| $\mathbf{B_{13}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{14}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{15}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{4} + y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{17}}$ | = | $\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{18}}$ | = | $- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{19}}$ | = | $- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{20}}$ | = | $\left(x_{4} + y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S II |
References
- J. P. Dismukes and J. G. White, The Preparation, Properties, and Crystal Structures of Some Scandium Sulfides in the Range Sc$_{2}$S$_{3}$-ScS, Inorg. Chem. 3, 1220–1228 (1964), doi:10.1021/ic50019a004.
Prototype Generator
aflow --proto=A3B2_oF80_70_fh_2e --params=$a,b/a,c/a,x_{1},x_{2},y_{3},x_{4},y_{4},z_{4}$