Orthorhombic B$_{2}$O$_{3}$ Structure: A2B3_oC20_36_b_ab-001
| Prototype | B$_{2}$O$_{3}$ |
| AFLOW prototype label | A2B3_oC20_36_b_ab-001 |
| ICSD | 34685 |
| Pearson symbol | oC20 |
| Space group number | 36 |
| Space group symbol | $Cmc2_1$ |
| AFLOW prototype command |
aflow --proto=A2B3_oC20_36_b_ab-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- This is the high-pressure structure of B$_{2}$O$_{3}$, stable above $≈ 2$\,GPa. The ground state is trigonal.
- Data was taken a 6.5 GPa. (Prewitt, 1968) give the structure in the $Ccm2_{1}$ setting of space group #36. We used FINDSYM to transform it to the standard $Cmc2_{1}$ setting. This space group allows for an arbitrary placement of the origin of the $z$-axis, which we fixed by setting $z_{1} = 0$ for the O-I (2a) Wyckoff position.
- The ICSD 34685 website entry for this structure states that it was refined at ambient pressure, but the data is consistent with the high-pressure structure shown here.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{3}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | B I |
| $\mathbf{B_{4}}$ | = | $- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B I |
| $\mathbf{B_{5}}$ | = | $\left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8b) | B I |
| $\mathbf{B_{7}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{8}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{9}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | O II |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | O II |
References
- C. T. Prewitt and R. D. Shannon, Crystal Structure of a High-Pressure Form of B$_{2}$O$_{3}$, Acta Crystallogr. Sect. B 24, 869–874 (1968), doi:10.1107/S0567740868003304.
Found in
- H. Effenberger, C. L. Lengauer, and E. Parthé, Trigonal B$_{2}$O$_{3}$ with Higher Space-Group Symmetry: Results of a Reevaluation, Monatsh. Chem. 132, 1515–1517 (2001), doi:10.1007/s007060170008.
Prototype Generator
aflow --proto=A2B3_oC20_36_b_ab --params=$a,b/a,c/a,y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$