Ferroelectric NaNO$_{2}$ ($F5_{5}$) Structure: ABC2_oI8_44_a_a_c-001
| Prototype | NaNO$_{2}$ |
| AFLOW prototype label | ABC2_oI8_44_a_a_c-001 |
| Strukturbericht designation | $F5_{5}$ |
| Mineral name | sodium nitrite |
| ICSD | 15400 |
| Pearson symbol | oI8 |
| Space group number | 44 |
| Space group symbol | $Imm2$ |
| AFLOW prototype command |
aflow --proto=ABC2_oI8_44_a_a_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
AgNO$_{3}$ ($F5_{12}$)
- This is the low-temperature phase of NaNO$_{2}$, ferroelectric below 158°C.
- (Kay, 1961) gives the structure in the $Im2m$ setting of space group #44. We have used FINDSYM to put it in the standard $Imm2$ setting.
- This structure is very similar to silver nitrite, AgNO$_{2}$, $F5_{12}$. We present both structures as they are listed separately in the Strukturbericht volumes.
- The original publications give Wyckoff positions giving NaNO$_{2}$ the AFLOW prototype label ABC2_oI8_44_a_a_c and AgNO$_{2}$ the label ABC2_oI8_44_a_a_d. When we apply our AFLOW prototype label rules, however, the label for both structures becomes ABC2_oI8_44_a_a_c. The two structures are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files. - The origin of the $z$ coordinate in $Imm2$, or the $y$ coordinate in $Im2m$, is arbitrary. Here $z_{3}$ is set to zero.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | N I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Na I |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (4c) | O I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (4c) | O I |
References
- M. I. Kay and B. C. Frazier, A neutron diffraction refinement of the low temperature phase of NaNO$_{2}$, Acta Cryst. 14, 56–57 (1961), doi:10.1107/S0365110X61000103.
Prototype Generator
aflow --proto=ABC2_oI8_44_a_a_c --params=$a,b/a,c/a,z_{1},z_{2},x_{3},z_{3}$