Possible Phase III Pb$_{3}$O$_{4}$ Structure: A4B3_oP14_55_gh_ah-001
| Prototype | O$_{4}$Pb$_{3}$ |
| AFLOW prototype label | A4B3_oP14_55_gh_ah-001 |
| ICSD | 97282 |
| CCDC | 1656611 |
| Pearson symbol | oP14 |
| Space group number | 55 |
| Space group symbol | $Pbam$ |
| AFLOW prototype command |
aflow --proto=A4B3_oP14_55_gh_ah-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{4}$ |
- Pb$_{3}$O$_{4}$ has been observed in several structures (Wriedt, 1988; Dinnebier, 2003):
- Below 170K (Wriedt, 1988) it is in the orthorhombic Minium-R structure. (Gavarri, 1978) tracks this structure up to 240K.
- Above 170K it is in the tetragonal Minium-T structure.
- At ambient temperature the Minium-T structure transforms into what is apparently the Minium-R structure at a pressure between 0.11 and 0.3 GPa. (Dinnebier, 2003) call this Phase II.
- If the pressure is increased, between 5.54 and 6.6 GPa the structure transforms into orthorhombic Phase III structure (this structure).
- We use the data taken at 13.3GPa and 295K. (Dinnebier, 2003) give the coordinates of the Pb I atom as (1/2 1/2 0). This is a (4e) Wyckoff position and makes the stoichiometry of the structure Pb$_{4}$O$_{4}$. The ICSD entry corrects this to (0 1/2 0), the (2c) site. We use this, however AFLOW shifts the origin, moving the (2c) atoms to the (2a) site. Unfortunately, the resulting configuration of the lead atoms does not match that shown in Figure 5(c) of the paper. We have no resolution of this, so we have marked the structure as possible.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Pb I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2a) | Pb I |
| $\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}$ | (4g) | O I |
| $\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}$ | (4g) | O I |
| $\mathbf{B_{5}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (4g) | O I |
| $\mathbf{B_{6}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (4g) | O I |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O II |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O II |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O II |
| $\mathbf{B_{11}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Pb II |
| $\mathbf{B_{12}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Pb II |
| $\mathbf{B_{13}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Pb II |
| $\mathbf{B_{14}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Pb II |
References
- R. E. Dinnebier, S. Carlson, M. Hanfland, and M. Jansen, Bulk moduli and high-pressure crystal structures of minium, Pb$_{3}$O$_{4}$, determined by X-ray powder diffraction, Am. Mineral. 88, 996–1002 (2003), doi:10.2138/am-2003-0707.
- H. A. Wriedt, The O-Pb (Oxygen-Lead) System, Bull. Alloy Phase Diag. 9, 106–127 (1988).
- J. R. Gavarri, G. Calvarin, and D. Weigel, Oxydes de plomb. II. Etude structurale a 5 K de la phase orthorhombique de l'oxyde Pb$_{3}$O$_{4}$, J. Solid State Chem. 14, 91–98 (1975), doi:10.1016/0022-4596(75)90365-5.
- J. R. Gavarri, D. Weigel, and A. W. Hewat, Oxydes de plomb. IV. Evolution structurale de l'oxyde Pb$_{3}$O$_{4}$ entre 240 et 5$^\circ$K et mécanisme de la transition, J. Solid State Chem. 23, 327–339 (1978), doi:10.1016/0022-4596(78)90081-6.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A4B3_oP14_55_gh_ah --params=$a,b/a,c/a,x_{2},y_{2},x_{3},y_{3},x_{4},y_{4}$