$\alpha$–PbO Structure: AB_oC8_67_a_g

Picture of Structure; Click for Big Picture
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).

Geometry files


Prototype Generator

aflow --proto=AB_oC8_67_a_g --params=

Species:

Running:

Output: