Thenardite [Na$_{2}$SO$_{4}$ (V), $H1_{7}$] Structure: A2B4C_oF56_70_e_h_a-001
| Prototype | Na$_{2}$O$_{4}$S |
| AFLOW prototype label | A2B4C_oF56_70_e_h_a-001 |
| Strukturbericht designation | $H1_{7}$ |
| Mineral name | thenardite |
| ICSD | 2895 |
| Pearson symbol | oF56 |
| Space group number | 70 |
| Space group symbol | $Fddd$ |
| AFLOW prototype command |
aflow --proto=A2B4C_oF56_70_e_h_a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
Ag$_{2}$SO$_{4}$, Cr$_{2}$SO$_{4}$
- Na$_{2}$SO$_{4}$ has eight known anhydrous phases. The thenardite phase is
reported to be stable between 32$^\circ$C and about 180$^\circ$C
(Nord, 1973), however the data reported here was taken on synthetic thenardite at 25$^\circ$C.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8a) | S I |
| $\mathbf{B_{2}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{7}{8}a \,\mathbf{\hat{x}}+\frac{7}{8}b \,\mathbf{\hat{y}}+\frac{7}{8}c \,\mathbf{\hat{z}}$ | (8a) | S I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16e) | Na I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{8}b \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16e) | Na I |
| $\mathbf{B_{5}}$ | = | $\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{3}{8}b \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16e) | Na I |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}b \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16e) | Na I |
| $\mathbf{B_{7}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (32h) | O I |
| $\mathbf{B_{8}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (32h) | O I |
| $\mathbf{B_{9}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | O I |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} + y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | O I |
| $\mathbf{B_{11}}$ | = | $\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (32h) | O I |
| $\mathbf{B_{12}}$ | = | $- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (32h) | O I |
| $\mathbf{B_{13}}$ | = | $- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | O I |
| $\mathbf{B_{14}}$ | = | $\left(x_{3} + y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32h) | O I |
References
- A. C. Nord, Refinement of the Crystal Structure of Thenardite Na$_{2}$SO$_{4}$ (V), Acta Chem. Scand. 27, 814–822 (1973).
Prototype Generator
aflow --proto=A2B4C_oF56_70_e_h_a --params=$a,b/a,c/a,x_{2},x_{3},y_{3},z_{3}$