Na$_{2}$CrO$_{4}$ ($H1_{8}$) Structure: AB2C4_oC28_63_c_ac_fg-001
| Prototype | CrNa$_{2}$O$_{4}$ |
| AFLOW prototype label | AB2C4_oC28_63_c_ac_fg-001 |
| Strukturbericht designation | $H1_{8}$ |
| ICSD | 76001 |
| Pearson symbol | oC28 |
| Space group number | 63 |
| Space group symbol | $Cmcm$ |
| AFLOW prototype command |
aflow --proto=AB2C4_oC28_63_c_ac_fg-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
Li$_{2}$SO$_{4}$, LiFeP$_{4}$, Na$_{2}$FeO$_{4}$, Na$_{2}$SO$_{4}$ (III), NaCaVO$_{4}$, NaMnPO$_{4}$, NaVCdO$_{4}$, Tl$_{2}$SeO$_{4}$
- This structure was originally determined by (Miller, 1936), who placed it in space group $Pnna$ #52, and (Gottfried, 1938) uses this data for Strukturbericht $H1_{8}$. Subsequently (Niggli, 1954) rather acerbically pointed out that Miller's coordinates were consistent with the more compact $Cmcm$ #63 space group. This does not change the positions of the atoms in the conventional cell, so we use the compact structure as our prototype for Strukturbericht designation $H1_{8}$.
- This structure is stable up to 413°C. (Amirathanlingam, 1982)
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
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) | Cr I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Cr I |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Na II |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Na II |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (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
- A. Niggli, Die Raumgruppe von Na$_{2}$CrO$_{4}$, Acta Cryst. 7, 776 (1954), doi:10.1107/S0365110X54002368.
- J. J. Miller, The Crystal Structure of Anhydrous Sodium Chromate, Na$_{2}$CrO$_{4}$, Z. Kristallogr. 94, 131–136 (1936), doi:10.1524/zkri.1936.94.1.131.
- C. Gottfried, ed., Strukturbericht Band IV 1936 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1938).
- V. Amirathanlingam and K. S. Venkateswarlu, Te Thermal Expansion and Crystallographic Phase Transformation of Na$_{2}$CrO$_{4}$, Thermochimica Acat 58, 107–109 (1982), doi:10.1016/0040-6031(82)87145-1.
Prototype Generator
aflow --proto=AB2C4_oC28_63_c_ac_fg --params=$a,b/a,c/a,y_{2},y_{3},y_{4},z_{4},x_{5},y_{5}$