Orthorhombic BaTiO$_{3}$ Structure: AB3C_oC10_38_a_ae_b-002
| Prototype | BaO$_{3}$Ti |
| AFLOW prototype label | AB3C_oC10_38_a_ae_b-002 |
| ICSD | 31155 |
| Pearson symbol | oC10 |
| Space group number | 38 |
| Space group symbol | $Amm2$ |
| AFLOW prototype command |
aflow --proto=AB3C_oC10_38_a_ae_b-002
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak z_{4}$ |
- The perovskite BaTiO$_{3}$ undergoes a variety of temperature driven phase transitions. (Shirane, 1957)
- The first three structures are ferroelectric:
- Below 193K the structure is rhombohedral.
- Between 193K and 278K the structure is orthorhombic. (This structure)
- Between 278K and 393K the structure is tetragonal. This is the room-temperature form of the material.
- Above 393K the compound is a cubic perovskite ($E2_{1}$).
- Hexagonal BaTiO$_{3}$ can be stabilized by alloying the titanium sites with other transition metals. (Dickson, 1961) The pure structure has been grown at 1853K and cooled to room temperature. (Akimo, 1994)
- The data for this structure was taken 263K.
- Space group $Amm2$ #38 does not specify the origin of the $z$-axis. We set it by taking $z_{1} = 0$, putting the barium atom at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- z_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Ba I |
| $\mathbf{B_{2}}$ | = | $- z_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (2b) | Ti I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O II |
References
- G. Shirane, H. Danner, and R. Pepinsky, Neutron Diffraction Study of Orthorhombic BaTiO$_{3}$, Phys. Rev. 105, 856–860 (1957), doi:10.1103/PhysRev.105.856.
- J. G. Dickson, L. Katz, and R. Ward, Compounds with the Hexagonal Barium Titanate Structure, J. Am. Chem. Soc. 83, 3026–3029 (1961), doi:10.1021/ja01475a012.
- A. W. Hewat, Structure of rhombohedral ferroelectric barium titanate, Ferroelectrics 6, 215–218 (1974), doi:10.1080/00150197408243970.
- J. Akimoto, Y. Gotoh, and Y. Oosawa, Refinement of Hexagonal BaTiO$_{3}$, Acta Crystallogr. Sect. C 50, 160–161 (1994), doi:10.1107/S0108270193008637.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=AB3C_oC10_38_a_ae_b --params=$a,b/a,c/a,z_{1},z_{2},z_{3},y_{4},z_{4}$