High Temperature BaBi$_{4}$Ti$_{4}$O$_{15}$ $m = 4$ Aurivillius Structure: AB4C15D4_tI48_139_a_2e_bd2e2g_2e-001
| Prototype | BaBi$_{4}$O$_{15}$Ti$_{4}$ |
| AFLOW prototype label | AB4C15D4_tI48_139_a_2e_bd2e2g_2e-001 |
| ICSD | 150929 |
| Pearson symbol | tI48 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=AB4C15D4_tI48_139_a_2e_bd2e2g_2e-001
--params=$a, \allowbreak c/a, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}, \allowbreak z_{9}, \allowbreak z_{10}, \allowbreak z_{11}$ |
Other compounds with this structure
PbBi$_{4}$Ti$_{4}$O$_{15}$, Bi$_{5}$Ti$_{3}$GaO$_{15}$
- 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)
- The ICSD entry for this structure states that the actual composition of our Ba I site is Ba$_{0.26}$Bi$_{0.74}$, while the Bi II sites composition is Ba$_{0.37}$Bi$_{0.63}$. We have arbitrarily labeled the first of these sites Ba and the second Bi so that the AFLOW label mimics the composition of the structure. The original work of (Aurivillius, 1950) assumes equal mixing of barium and bismuth on all of the Ba/Bi sites.
- Below 700K this structure transforms into the orthorhombic low temperature BaBi$_{4}$Ti$_{4}$O$_{15}$ structure. (Kennedy, 2003) Data for the illustrated structure was taken at 1000K.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ba I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | O II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | O II |
| $\mathbf{B_{5}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Bi I |
| $\mathbf{B_{6}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Bi I |
| $\mathbf{B_{7}}$ | = | $z_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Bi II |
| $\mathbf{B_{8}}$ | = | $- z_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}$ | = | $- c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Bi II |
| $\mathbf{B_{9}}$ | = | $z_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}$ | = | $c z_{6} \,\mathbf{\hat{z}}$ | (4e) | O III |
| $\mathbf{B_{10}}$ | = | $- z_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}$ | = | $- c z_{6} \,\mathbf{\hat{z}}$ | (4e) | O III |
| $\mathbf{B_{11}}$ | = | $z_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}$ | = | $c z_{7} \,\mathbf{\hat{z}}$ | (4e) | O IV |
| $\mathbf{B_{12}}$ | = | $- z_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}$ | = | $- c z_{7} \,\mathbf{\hat{z}}$ | (4e) | O IV |
| $\mathbf{B_{13}}$ | = | $z_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}$ | = | $c z_{8} \,\mathbf{\hat{z}}$ | (4e) | Ti I |
| $\mathbf{B_{14}}$ | = | $- z_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}$ | = | $- c z_{8} \,\mathbf{\hat{z}}$ | (4e) | Ti I |
| $\mathbf{B_{15}}$ | = | $z_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}$ | = | $c z_{9} \,\mathbf{\hat{z}}$ | (4e) | Ti II |
| $\mathbf{B_{16}}$ | = | $- z_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}$ | = | $- c z_{9} \,\mathbf{\hat{z}}$ | (4e) | Ti II |
| $\mathbf{B_{17}}$ | = | $\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8g) | O V |
| $\mathbf{B_{18}}$ | = | $z_{10} \, \mathbf{a}_{1}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (8g) | O V |
| $\mathbf{B_{19}}$ | = | $- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8g) | O V |
| $\mathbf{B_{20}}$ | = | $- z_{10} \, \mathbf{a}_{1}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{10} \,\mathbf{\hat{z}}$ | (8g) | O V |
| $\mathbf{B_{21}}$ | = | $\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8g) | O VI |
| $\mathbf{B_{22}}$ | = | $z_{11} \, \mathbf{a}_{1}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (8g) | O VI |
| $\mathbf{B_{23}}$ | = | $- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8g) | O VI |
| $\mathbf{B_{24}}$ | = | $- z_{11} \, \mathbf{a}_{1}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{11} \,\mathbf{\hat{z}}$ | (8g) | O VI |
References
- B. J. Kennedy, Y. Kubota, B. A. Hunter, I., and K. Kato, Structural phase transitions in the layered bismuth oxide BaBi$_{4}$Ti$_{4}$O$_{15}$, Solid State Commun. 126, 653–658 (2003), doi:10.1016/S0038-1098(03)00332-6.
- 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.
- B. Aurivillius, Mixed oxides with layer lattice. III. Structure of BaBi$_{4}$Ti$_{4}$O$_{15}$, Arkiv für Kemi 2, 519–527 (1950).
Prototype Generator
aflow --proto=AB4C15D4_tI48_139_a_2e_bd2e2g_2e --params=$a,c/a,z_{4},z_{5},z_{6},z_{7},z_{8},z_{9},z_{10},z_{11}$