Fe$_{3}$PO$_{7}$ Structure: A3B7C_hR11_160_b_a2b_a-001
| Prototype | Fe$_{3}$O$_{7}$P |
| AFLOW prototype label | A3B7C_hR11_160_b_a2b_a-001 |
| ICSD | 36207 |
| Pearson symbol | hR11 |
| Space group number | 160 |
| Space group symbol | $R3m$ |
| AFLOW prototype command |
aflow --proto=A3B7C_hR11_160_b_a2b_a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}$ |
- Space group $R3m$ #160 allows an arbitary definition of the zero of the $z$-axis. Here we select $z_{1} = 0$, putting the phosphorous atom at the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $c x_{1} \,\mathbf{\hat{z}}$ | (1a) | O I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (1a) | P I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | Fe I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | Fe I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (3b) | Fe I |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (3b) | O II |
| $\mathbf{B_{7}}$ | = | $z_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (3b) | O II |
| $\mathbf{B_{8}}$ | = | $x_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (3b) | O II |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | O III |
| $\mathbf{B_{10}}$ | = | $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | O III |
| $\mathbf{B_{11}}$ | = | $x_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (3b) | O III |
References
- A. Modaressi, A. Courtois, R. Gerardin, B. Malaman, and C. Gleitzer, Fe$_{3}$PO$_{7}$, Un cas de coordinence 5 du fer trivalent, etude structurale et magnetique, J. Solid State Chem. 47, 245–255 (1983), doi:10.1016/0022-4596(83)90016-6.
Found in
- C. L. Sarkis, M. J. Tarne, J. R. Neilson, H. B. Cao, E. Coldren, M. P. Gelfand, and K. A. Ross, Partial Antiferromagnetic Helical Order in Single Crystal Fe$_{3}$PO$_{4}$O$_{3}$, Phys. Rev. B 101, 184417 (2020), doi:10.1103/PhysRevB.101.184417.
Prototype Generator
aflow --proto=A3B7C_hR11_160_b_a2b_a --params=$a,c/a,x_{1},x_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5}$