PrMn$_{7}$O$_{12}$ Structure: A7B12C_mC40_12_abcef_2i2j_d-001
| Prototype | Mn$_{7}$O$_{12}$Pr |
| AFLOW prototype label | A7B12C_mC40_12_abcef_2i2j_d-001 |
| ICSD | 163258 |
| CCDC | 1679425 |
| Pearson symbol | mC40 |
| Space group number | 12 |
| Space group symbol | $C2/m$ |
| AFLOW prototype command |
aflow --proto=A7B12C_mC40_12_abcef_2i2j_d-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}$ |
Other compounds with this structure
BiMn$_{7}$O$_{12}$, CeMn$_{7}$O$_{12}$, EuMn$_{7}$O$_{12}$, LaMn$_{7}$O$_{12}$, NaMn$_{7}$O$_{12}$, NdMn$_{7}$O$_{12}$, SmMn$_{7}$O$_{12}$, SmMn$_{7}$O$_{12}$, YMn$_{7}$O$_{12}$
- The rare-earth quadruple perovskite manganites, RMn$_{7}$O$_{12}$ undergo a variety of transformations as they cool from the high temperature cubic NaMn$_{7}$O$_{12}$ form. This PrMn$_{7}$O$_{12}$ structure is often the first phase transition after cooling. (Mezzadri, 2009; Okamoto, 2010; Johnson 2018; Behr, 2023).
- (Mezzadri, 2009) found two slightly different structures for this phase depending
on the synthesis conditions.
We use their monoclinic (I) structure here. - This structure is exclusively reported in the base-centered monoclinic $I2/m$ setting of space group #12, as this results in a conventional unit cell that is nearly cubic. AFLOW translates this into the standard body-centered monoclinic $C2/m$ setting.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (2b) | Mn II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (2c) | Mn III |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}\left(a + c \cos{\beta}\right) \,\mathbf{\hat{x}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (2d) | Pr I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}$ | (4e) | Mn IV |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{1}{4}b \,\mathbf{\hat{y}}$ | (4e) | Mn IV |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\left(\frac{a}{4} + \frac{c \cos{\beta}}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4f) | Mn V |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\left(\frac{a}{4} + \frac{c \cos{\beta}}{2}\right) \,\mathbf{\hat{x}}- \frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (4f) | Mn V |
| $\mathbf{B_{9}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O I |
| $\mathbf{B_{10}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + c z_{7} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{7} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O I |
| $\mathbf{B_{11}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}+c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O II |
| $\mathbf{B_{12}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + c z_{8} \cos{\beta}\right) \,\mathbf{\hat{x}}- c z_{8} \sin{\beta} \,\mathbf{\hat{z}}$ | (4i) | O II |
| $\mathbf{B_{13}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O III |
| $\mathbf{B_{14}}$ | = | $- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}- c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O III |
| $\mathbf{B_{15}}$ | = | $- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O III |
| $\mathbf{B_{16}}$ | = | $\left(x_{9} + y_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + c z_{9} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O III |
| $\mathbf{B_{17}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O IV |
| $\mathbf{B_{18}}$ | = | $- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}- c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O IV |
| $\mathbf{B_{19}}$ | = | $- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O IV |
| $\mathbf{B_{20}}$ | = | $\left(x_{10} + y_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + c z_{10} \cos{\beta}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c z_{10} \sin{\beta} \,\mathbf{\hat{z}}$ | (8j) | O IV |
References
- F. Mezzadri, M. Calicchio, E. Gilioli, R. Cabassi, F. Bolzoni, G. Calestani, and F. Bissoli, High-pressure synthesis and characterization of PrMn$_{7}$O$_{12}$ polymorphs, Phys. Rev. B 79, 014420 (2009), doi:10.1103/PhysRevB.79.014420.
- H. Okamoto, N. Imamura, M. Karppinen, H. Yamauchi, and H. Fjellvåg, Crystal structure of the monoclinic and cubic polymorphs of BiMn$_{7}$O$_{12}$, J. Solid State Chem. 183, 186–191 (2010), doi:10.1016/j.jssc.2009.10.013.
- D. Behr, A. A. Belik, D. D. Khalyavin, and R. D. Johnson, BiMn$_{7}$O$_{12}$: Polar antiferromagnetism by inverse exchange striction, Phys. Rev. B 107, L140402 (2023), doi:10.1103/PhysRevB.107.L140402.
Found in
- R. D. Johnson, D. D. Khalyavin, P. Manuel, L. Zhang, K. Yamaura, and A. A. Belik, Magnetic structures of the rare-earth quadruple perovskite manganites {\em R}Mn$_{7}$O$_{12}$, Phys. Rev. B 98, 104423 (2018), doi:10.1103/PhysRevB.98.104423.
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=A7B12C_mC40_12_abcef_2i2j_d --params=$a,b/a,c/a,\beta,x_{7},z_{7},x_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10}$