Na$_{2}$SO$_{4}$ (III) Structure: A2B4C_oC28_63_ac_fg_c-001
| Prototype | Na$_{2}$O$_{4}$S |
| AFLOW prototype label | A2B4C_oC28_63_ac_fg_c-001 |
| ICSD | 31687 |
| CCDC | 1605685 |
| Pearson symbol | oC28 |
| Space group number | 63 |
| Space group symbol | $Cmcm$ |
| AFLOW prototype command |
aflow --proto=A2B4C_oC28_63_ac_fg_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}$ |
Other compounds with this structure
Na$_{2}$CrO$_{4}$
- Na$_{2}$SO$_{4}$ forms in many anhydroous phases (Nord, 1973), which we will reference as we update this site. For now we have
- Na$_{2}$SO$_{4}$ III (this structure) and
- Thenardite (Na$_{2}$SO$_{4}$ V, $H1_{7}$).
- (Frevel, 1940) put this structure in the $Pbnn$ setting of space group #52, but AFLOW shows that the positions of the atoms are consistent with the higher symmetry $Cmcm$ #63 space group. Transforming from $Pbnn$ to $Cmcm$ halves the size of the unit cell.
- The date for this structure was taken at room temperature.
- The lattice constants in the ICSD differ slightly (less than 1%) from the published values in (Frevel, 1940). Ordinarily we would use the published values, but since there is a space group shift here we decided to use the ICSD values to avoid confusion.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Na I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | Na I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Na II |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Na II |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | S I |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | S I |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{8}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{9}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{10}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8f) | O I |
| $\mathbf{B_{11}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | O II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | O II |
| $\mathbf{B_{13}}$ | = | $- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | O II |
| $\mathbf{B_{14}}$ | = | $\left(x_{5} + y_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | O II |
References
- L. F. Frevel, The Crystal Structure of Sodium Sulfate III, J. Chem. Phys. 8, 290 (1940), doi:10.1063/1.1750647.
- A. C. Nord, Refinement of the Crystal Structure of Thenardite Na$_{2}$SO$_{4}$ (V), Acta Chem. Scand. 27, 814–822 (1973).
Found in
- Inorganic Crystal Structure Database. Entry 31687 [Na2SO4 (III)].
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A2B4C_oC28_63_ac_fg_c --params=$a,b/a,c/a,y_{2},y_{3},y_{4},z_{4},x_{5},y_{5}$