Ce$_{2}$O$_{2}$S Structure: A2B2C_hP5_164_d_d_a-002
| Prototype | Ce$_{2}$O$_{2}$S |
| AFLOW prototype label | A2B2C_hP5_164_d_d_a-002 |
| ICSD | 31639 |
| Pearson symbol | hP5 |
| Space group number | 164 |
| Space group symbol | $P\overline{3}m1$ |
| AFLOW prototype command |
aflow --proto=A2B2C_hP5_164_d_d_a-002
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}$ |
Other compounds with this structure
BaCd$_{2}$As$_{2}$, CaAl$_{2}$Si$_{2}$, CaAs$_{2}$Bi$_{2}$, CaAs$_{2}$Mn$_{2}$, CaAs$_{2}$P$_{2}$, CaAs$_{2}$Sb$_{2}$, CaBi$_{2}$Mg$_{2}$, CaBi$_{2}$Mn$_{2}$, CaCd$_{2}$As$_{2}$, CaCd$_{2}$P$_{2}$, CaMg$_{2}$Bi$_{2}$, CaMg$_{2}$Sb$_{2}$, CaZn$_{2}$As$_{2}$, CaZn$_{2}$P$_{2}$, CaZn$_{2}$Sb$_{2}$, CeCuZnP$_{2}$, DyCuZnP$_{2}$, ErCuZnP$_{2}$, EuAs$_{2}$Cd$_{2}$, EuBi$_{2}$Mg$_{2}$, EuCd$_{2}$P$_{2}$, GdCuZnP$_{2}$, HoCuZnP$_{2}$, LaCuZnP$_{2}$, LuCuZnP$_{2}$, NdCuZnP$_{2}$, PrCuZnP$_{2}$, SCe$_{2}$O$_{2}$, SCe$_{2}$Se$_{2}$, SLa$_{2}$O$_{2}$, SO$_{2}$Pu$_{2}$, ScCuZnP$_{2}$, SmCuZnP$_{2}$, SrAs$_{2}$Mn$_{2}$, SrAs$_{2}$P$_{2}$, SrAs$_{2}$Sb$_{2}$, SrCd$_{2}$As$_{2}$, SrCd$_{2}$P$_{2}$, TbCuZnP$_{2}$, TmCuZnP$_{2}$, YCuZnP$_{2}$, YbCuZnP$_{2}$, YbMg$_{2}$Bi$_{2}$, YbMnCuP$_{2}$
- This is the ternary form of the $D5_{2}$ La$_{2}$O$_{3}$ and the $D5_{13}$ Al$_{3}$Ni$_{2}$ structures. We have separated it from the parents because of the large number of compounds involved.
- Authors after (Zachariasen, 1949) often use CaAl$_{2}$Si$_{2}$ as the prototype for this structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | S I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2d) | Ce I |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2d) | Ce I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2d) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2d) | O I |
References
- W. H. Zachariasen, Crystal chemical studies of the 5f-series of elements. VII. The crystal structure of Ce$_{2}$O$_{2}$S, La$_{2}$O$_{2}$S and Pu$_{2}$O$_{2}$S, Acta Cryst. 2, 60–62 (1949), doi:10.1107/S0365110X49000138.
Prototype Generator
aflow --proto=A2B2C_hP5_164_d_d_a --params=$a,c/a,z_{2},z_{3}$