α-S ($A16$) Structure: A_oF128_70_4h-001
| Prototype | S |
| AFLOW prototype label | A_oF128_70_4h-001 |
| Strukturbericht designation | $A16$ |
| ICSD | 63082 |
| Pearson symbol | oF128 |
| Space group number | 70 |
| Space group symbol | $Fddd$ |
| AFLOW prototype command |
aflow --proto=A_oF128_70_4h-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(- x_{1} + y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} - y_{1} + z_{1}\right) \, \mathbf{a}_{2}+\left(x_{1} + y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (32h) | S I |
| $\mathbf{B_{2}}$ | = | $\left(x_{1} - y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(- x_{1} + y_{1} + z_{1}\right) \, \mathbf{a}_{2}- \left(x_{1} + y_{1} + z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (32h) | S I |
| $\mathbf{B_{3}}$ | = | $\left(x_{1} + y_{1} - z_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} + y_{1} + z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{1} + y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S I |
| $\mathbf{B_{4}}$ | = | $- \left(x_{1} + y_{1} + z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + y_{1} - z_{1}\right) \, \mathbf{a}_{2}+\left(x_{1} - y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}- b \left(y_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S I |
| $\mathbf{B_{5}}$ | = | $\left(x_{1} - y_{1} - z_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} - y_{1} + z_{1}\right) \, \mathbf{a}_{2}- \left(x_{1} + y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (32h) | S I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{1} - y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} - y_{1} - z_{1}\right) \, \mathbf{a}_{2}+\left(x_{1} + y_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (32h) | S I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{1} + y_{1} - z_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} + y_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{1} - y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S I |
| $\mathbf{B_{8}}$ | = | $\left(x_{1} + y_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} + y_{1} - z_{1}\right) \, \mathbf{a}_{2}- \left(x_{1} - y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+b \left(y_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S I |
| $\mathbf{B_{9}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{10}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{2} + y_{2} + z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{13}}$ | = | $\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{14}}$ | = | $- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{15}}$ | = | $- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{16}}$ | = | $\left(x_{2} + y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S II |
| $\mathbf{B_{17}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (32h) | S III |
| $\mathbf{B_{18}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (32h) | S III |
| $\mathbf{B_{19}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S III |
| $\mathbf{B_{20}}$ | = | $- \left(x_{3} + y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S III |
| $\mathbf{B_{21}}$ | = | $\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (32h) | S III |
| $\mathbf{B_{22}}$ | = | $- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (32h) | S III |
| $\mathbf{B_{23}}$ | = | $- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S III |
| $\mathbf{B_{24}}$ | = | $\left(x_{3} + y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S III |
| $\mathbf{B_{25}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (32h) | S IV |
| $\mathbf{B_{26}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (32h) | S IV |
| $\mathbf{B_{27}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S IV |
| $\mathbf{B_{28}}$ | = | $- \left(x_{4} + y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S IV |
| $\mathbf{B_{29}}$ | = | $\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (32h) | S IV |
| $\mathbf{B_{30}}$ | = | $- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (32h) | S IV |
| $\mathbf{B_{31}}$ | = | $- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S IV |
| $\mathbf{B_{32}}$ | = | $\left(x_{4} + y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | S IV |
References
- S. J. Rettig and J. Trotter, Refinement of the structure of orthorhombic sulfur, α-S$_8$, Acta Crystallogr. Sect. C 43, 2260–2262 (1987), doi:10.1107/S0108270187088152.
Prototype Generator
aflow --proto=A_oF128_70_4h --params=$a,b/a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4}$