β-Ta$_{2}$O$_{5}$ Structure: A5B2_oP14_49_cehq_ab-001
| Prototype | O$_{5}$Ta$_{2}$ |
| AFLOW prototype label | A5B2_oP14_49_cehq_ab-001 |
| ICSD | 95462 |
| Pearson symbol | oP14 |
| Space group number | 49 |
| Space group symbol | $Pccm$ |
| AFLOW prototype command |
aflow --proto=A5B2_oP14_49_cehq_ab-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{6}, \allowbreak y_{6}$ |
- (Aleshina, 2002) place this structure in space group $Pccm$ #49, while AFLOW's (and VASP's) default tolerance halves the size of the $c$-axis and places the system in space group $Pmmm$ #47. The reported structure can be recovered using
- aflow --proto=A5B2_oP14_49_cehq_ab:O:Ta --params=a,b/a,c/a,x$_{6}$,y$_{6}$ --tolerance=0.001 .
- It is likely that first-principles calculations starting from this point will relax produce a structure equivalent to the smaller $Pmmm$ unit cell.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ta I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | Ta I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2b) | Ta II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Ta II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2c) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2c) | O I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2e) | O II |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2e) | O II |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2h) | O III |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2h) | O III |
| $\mathbf{B_{11}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}$ | = | $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}$ | (4q) | O IV |
| $\mathbf{B_{12}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}$ | (4q) | O IV |
| $\mathbf{B_{13}}$ | = | $- x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4q) | O IV |
| $\mathbf{B_{14}}$ | = | $x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4q) | O IV |
References
- L. A. Aleshina and S. V. Loginova, Rietveld analysis of X-ray diffraction pattern from $\\beta$-Ta$_{2}$O$_{5}$ oxide}, Crystallogr. Rep. 47, 415–419 (2002), doi:10.1134/1.1481927. Translated from Kristallografiya {\bf 47, 460-464 (2002).
- H. T. Stokes and D. M. Hatch, {\em FINDSYM}: program for identifying the space-group symmetry of a crystal, Appl. Crystallogr. 38, 237–238 (2005), doi:10.1107/S0021889804031528.
- D. Hicks, C. Oses, E. Gossett, G. Gomez, R. H. Taylor, C. Toher, M. J. Mehl, O. Levy, and S. Curtarolo, AFLOW-SYM: platform for the complete, automatic and self-consistent symmetry analysis of crystals, Acta Crystallogr. Sect. A 74, 184–203 (2018), doi:10.1107/S2053273318003066.
- A. L. Speck, Single-crystal structure validation with the program PLATON, Appl. Crystallogr. 36, 7–13 (2003), doi:10.1107/S0021889802022112.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A5B2_oP14_49_cehq_ab --params=$a,b/a,c/a,x_{6},y_{6}$