Orthorhombic Bi$_{3}$NbTiO$_{9}$ $m = 2$ Aurivillius Structure: A3B2C9_oF56_69_ag_g_bfgl-001
| Prototype | Bi$_{3}$Nb$_{2}$O$_{9}$ |
| AFLOW prototype label | A3B2C9_oF56_69_ag_g_bfgl-001 |
| ICSD | 24734 |
| Pearson symbol | oF56 |
| Space group number | 69 |
| Space group symbol | $Fmmm$ |
| AFLOW prototype command |
aflow --proto=A3B2C9_oF56_69_ag_g_bfgl-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}$ |
Other compounds with this structure
BaBi$_{2}$Nb$_{2}$O$_{9}$, CaBi$_{2}$Nb$_{2}$O$_{9}$, KBi$_{2}$Nb$_{2}$O$_{9}$, NaBi$_{2}$Nb$_{2}$O$_{9}$, PbBi$_{2}$Nb$_{2}$O$_{9}$, SrBi$_{2}$Nb$_{2}$O$_{9}$
- Aurivillius phases are layered tetragonal materials with composition (Me$'_{2}$O$_{2}$)$^{2+}$(Me$_{m-1}$R$_{m}$O$_{3m+1}$)$^{2-}$ (Me$_{m-1}$Me$'_{2}$R$_{m}$O$_{3(m+1)}$), where Me and Me' are metals and R is a transition metal with a charge of +4 or +5. (Subbaro, 1962)
- This is the original structural determination by (Aurivillius, 1949). The niobium and titanium atoms equally occupy the same (8g) site. We have arbitrarily labeled this as
Nb.
- Crystals such as BaBi$_{2}$Nb$_{2}$O$_{9}$ put the non-bismuth atom on the (4a) site, and the niobium site can be occupied by niobium, tantalum, and/or titanium. (Aurivillius, 1949)
- We have swapped Aurivillius's $x$- and $z$-axes.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Bi I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4b) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{5}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}$ | (8g) | Bi II |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}$ | (8g) | Bi II |
| $\mathbf{B_{7}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}$ | (8g) | Nb I |
| $\mathbf{B_{8}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}$ | (8g) | Nb I |
| $\mathbf{B_{9}}$ | = | $- x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}$ | (8g) | O III |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}$ | (8g) | O III |
| $\mathbf{B_{11}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | O IV |
| $\mathbf{B_{12}}$ | = | $x_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | O IV |
| $\mathbf{B_{13}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | O IV |
| $\mathbf{B_{14}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16l) | O IV |
References
- B. Aurivillius, Mixed bismuth oxides with layer lattices I. The structure type CaNb$_{2}$Bi$_{2}$O$_{9}$, Arkiv för Kemi 1, 463–479 (1949).
- E. C. Subbarao, A family of ferroelectric bismuth compounds, J. Phys.: Conf. Ser. 23, 665–676 (1962), doi:10.1016/0022-3697(62)90526-7.
Prototype Generator
aflow --proto=A3B2C9_oF56_69_ag_g_bfgl --params=$a,b/a,c/a,x_{4},x_{5},x_{6},x_{7}$