$\alpha$–PbO Structure: AB_oC8_67_a_g
| Prototype | : | PbO |
| AFLOW prototype label | : | AB_oC8_67_a_g |
| Strukturbericht designation | : | None |
| Pearson symbol | : | oC8 |
| Space group number | : | 67 |
| Space group symbol | : | $Cmma$ |
| AFLOW prototype command | : | aflow --proto=AB_oC8_67_a_g --params=$a,b/a,c/a,z_{2}$ |
- FINDSYM identifies space group #67 for this structure (consistent with the reference); however, since $b/a \approx 1$, AFLOW–SYM and Platon identify #129. Lowering the tolerance value for AFLOW–SYM resolves the expected space group #67. Space groups #67 and #129 are both reasonable classifications since they are commensurate with subgroup relations. $\alpha$–FeSe and $\alpha$–PbO have the same AFLOW prototype label. They are generated by the same symmetry operations with different sets of parameters (––params) specified in their corresponding CIF files.
Base-centered Orthorhombic primitive vectors:
\[
\begin{array}{ccc}
\mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\
\mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\
\mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\
\end{array}
\]
Basis vectors:
\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} & \left(4a\right) & \mbox{O} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} & = & \frac{3}{4}a \, \mathbf{\hat{x}} & \left(4a\right) & \mbox{O} \\ \mathbf{B}_{3} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{4}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4g\right) & \mbox{Pb} \\ \mathbf{B}_{4} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(4g\right) & \mbox{Pb} \\ \end{array} \]References
- P. Boher, P. Garnier, J. R. Gavarri, and A. W. Hewat, Monoxyde quadratique PbOα (I): Description de la transition structurale ferroélastique, J. Solid State Chem. 57, 343–350 (1985), doi:10.1016/0022-4596(85)90197-5.
- H. T. Stokes and D. M. Hatch, FINDSYM: Program for identifying the space group symmetry of a crystal, J. 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, it 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. Spek, Single–crystal structure validation with the program PLATON, J. 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, ASM International (2013).