Th$_{3}$P$_{4}$ ($D7_{3}$) Structure: A4B3_cI28_220_c_a-001
| Prototype | P$_{4}$Th$_{3}$ |
| AFLOW prototype label | A4B3_cI28_220_c_a-001 |
| Strukturbericht designation | $D7_{3}$ |
| ICSD | 648207 |
| Pearson symbol | cI28 |
| Space group number | 220 |
| Space group symbol | $I\overline{4}3d$ |
| AFLOW prototype command |
aflow --proto=A4B3_cI28_220_c_a-001
--params=$a, \allowbreak x_{2}$ |
Other compounds with this structure
Bi$_{3}$Yb$_{4}$, Ce$_{3}$S$_{4}$, Ce$_{3}$Se$_{4}$, Ce$_{3}$Te$_{4}$, Eu$_{3}$S$_{4}$, La$_{3}$S$_{4}$, La$_{3}$Se$_{4}$, La$_{3}$Te$_{4}$, N$_{3}$P$_{4}$, Nd$_{3}$S$_{4}$, Nd$_{3}$Se$_{4}$, Nd$_{3}$Te$_{4}$, Pa$_{3}$As$_{4}$, Pa$_{3}$P$_{4}$, Pa$_{3}$Sb$_{4}$, Pr$_{3}$S$_{4}$, Pr$_{3}$Se$_{4}$, Pr$_{3}$Te$_{4}$, Sm$_{3}$S$_{4}$, Sm$_{3}$Se$_{4}$, Sm$_{3}$Te$_{4}$, Th$_{3}$As$_{4}$, Th$_{3}$As$_{4}$, Th$_{3}$Bi$_{4}$, Th$_{3}$P$_{4}$, Th$_{3}$Sb$_{4}$, U$_{3}$As$_{4}$, U$_{3}$Bi$_{4}$, U$_{3}$P$_{4}$, U$_{3}$Sb$_{4}$, U$_{3}$Te$_{4}$, BaCe$_{2}$S$_{4}$, BaCe$_{2}$Se$_{4}$, BaLa$_{2}$S$_{4}$, BaLa$_{2}$Se$_{4}$, BaNd$_{2}$S$_{4}$, BaNd$_{2}$Se$_{4}$, BaPr$_{2}$S$_{4}$, BaPr$_{2}$Se$_{4}$, CaCe$_{2}$S$_{4}$, CaDy$_{2}$S$_{4}$, CaGd$_{2}$S$_{4}$, CaLa$_{2}$S$_{4}$, CaNd$_{2}$S$_{4}$, CaPr$_{2}$S$_{4}$, CaSm$_{2}$S$_{4}$, CaTb$_{2}$S$_{4}$, SrCe$_{2}$S$_{4}$, SrCe$_{2}$Se$_{4}$, SrGd$_{2}$S$_{4}$, SrGd$_{2}$Se$_{4}$, SrLa$_{2}$S$_{4}$, SrLa$_{2}$Se$_{4}$, SrNd$_{2}$S$_{4}$, SrNd$_{2}$Se$_{4}$, SrPr$_{2}$S$_{4}$, SrPr$_{2}$Se$_{4}$, SrSm$_{2}$S$_{4}$, SrSm$_{2}$Se$_{4}$, Ac$_{2}$S$_{3}$, Am$_{2}$S$_{3}$, Ce$_{2}$S$_{3}$, Ce$_{2}$Te$_{3}$, Gd$_{2}$S$_{3}$, La$_{2}$S$_{3}$, La$_{2}$Te$_{3}$, Nd$_{2}$S$_{3}$, Nd$_{2}$Te$_{3}$, Pr$_{2}$S$_{3}$, Pr$_{2}$Te$_{3}$, Sm$_{2}$S$_{3}$, Sm$_{2}$Te$_{3}$, Tb$_{2}$S$_{3}$
- The Th$_{3}$P$_{4}$ structure allows a large degree of disorder in the thorium (12a) site. Compounds of the form AB$_{2}$C$_{4}$ have the A and B atoms mixed on the (12a) site (Flahaut, 1965). Compounds of the form A$_{2}$B$_{3}$ should more properly be listed as A$_{3-x}$B$_{4}$, with $x$ in the range [0,1/3] and a corresponding number of vacancies distributed statistically on the (12a) site (Zachariasen, 1949).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12a) | Th I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12a) | Th I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}$ | (12a) | Th I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}$ | (12a) | Th I |
| $\mathbf{B_{5}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (12a) | Th I |
| $\mathbf{B_{6}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (12a) | Th I |
| $\mathbf{B_{7}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16c) | P I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(2 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16c) | P I |
| $\mathbf{B_{9}}$ | = | $- \left(2 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16c) | P I |
| $\mathbf{B_{10}}$ | = | $- \left(2 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16c) | P I |
| $\mathbf{B_{11}}$ | = | $\left(2 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | P I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | P I |
| $\mathbf{B_{13}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | P I |
| $\mathbf{B_{14}}$ | = | $- 2 x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | P I |
References
- K. Meisel, Kristallstrukturen von Thoriumphosphiden, Z. Anorganische und Allgemeine Chemie 240, 300–312 (1939), doi:10.1002/zaac.19392400403.
- J. Flahaut, M. Guittard, M. Patrie, M. P. Pardo, S. M. Golabi, and L. Domange, Phase cubiques type Th$_{3}$P$_{4}$ dans les sulfures, les séléniures et les tellurures L$_{2}$X$_{3}$ et L$_{3}$X$_{4}$ des terres rares, et dans leurs combinaisons ML$_{2}$X$_{4}$ avec les sulfures et séléniures MX de calcium, strontium et baryum. Formation et propriétés cristallines, Acta Cryst. 19, 14–19 (1965), doi:10.1107/S0365110X65002694.
- W. H. Zachariasen, Crystal chemical studies of the 5f-series of elements. VI. The Ce$_{2}$S$_{3}$-Ce$_{3}$S$_{4}$ type of structure, Acta Cryst. 2, 57–60 (1949), doi:10.1107/S0365110X49000126.
Prototype Generator
aflow --proto=A4B3_cI28_220_c_a --params=$a,x_{2}$