Th$_{6}$Mn$_{23}$ ($D8_{a}$) Structure: A23B6_cF116_225_ad2f_e-001
| Prototype | Mn$_{23}$Th$_{6}$ |
| AFLOW prototype label | A23B6_cF116_225_ad2f_e-001 |
| Strukturbericht designation | $D8_{a}$ |
| ICSD | 104987 |
| Pearson symbol | cF116 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A23B6_cF116_225_ad2f_e-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}$ |
Other compounds with this structure
Co$_{23}$Zr$_{6}$, Fe$_{23}$Er$_{6}$, Fe$_{23}$Ho$_{6}$, Fe$_{23}$Sm$_{6}$, Fe$_{23}$Tb$_{6}$, Li$_{23}$Sr$_{6}$, Mg$_{23}$Ba$_{6}$, Mg$_{23}$Dy$_{6}$, Mg$_{23}$Er$_{6}$, Mg$_{23}$Gd$_{6}$, Mg$_{23}$Ho$_{6}$, Mg$_{23}$Lu$_{6}$, Mg$_{23}$Nd$_{6}$, Mg$_{23}$Sr$_{6}$, Mg$_{23}$Tb$_{6}$, Mg$_{23}$Th$_{6}$, Mg$_{23}$Tm$_{6}$, Mg$_{23}$Y$_{6}$, Mn$_{23}$Th$_{6-x}$Y$_{x}$, Mn$_{23}$Th$_{6}$, Mn$_{23}$Y$_{6}$, Fe$_{3}$Zn, Ge$_{13}$Fe$_{10}$Ti$_{6}$
- We have moved the ternary compounds with this structure to the Mg$_{6}$Si$_{7}$Cu$_{16}$ page.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mn II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mn II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mn II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24d) | Mn II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (24d) | Mn II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24d) | Mn II |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (24e) | Th I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (24e) | Th I |
| $\mathbf{B_{10}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{y}}$ | (24e) | Th I |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{y}}$ | (24e) | Th I |
| $\mathbf{B_{12}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{z}}$ | (24e) | Th I |
| $\mathbf{B_{13}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{z}}$ | (24e) | Th I |
| $\mathbf{B_{14}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Mn III |
| $\mathbf{B_{15}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- 3 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Mn III |
| $\mathbf{B_{16}}$ | = | $x_{4} \, \mathbf{a}_{1}- 3 x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Mn III |
| $\mathbf{B_{17}}$ | = | $- 3 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Mn III |
| $\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+3 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Mn III |
| $\mathbf{B_{19}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Mn III |
| $\mathbf{B_{20}}$ | = | $- x_{4} \, \mathbf{a}_{1}+3 x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Mn III |
| $\mathbf{B_{21}}$ | = | $3 x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Mn III |
| $\mathbf{B_{22}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Mn IV |
| $\mathbf{B_{23}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- 3 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Mn IV |
| $\mathbf{B_{24}}$ | = | $x_{5} \, \mathbf{a}_{1}- 3 x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Mn IV |
| $\mathbf{B_{25}}$ | = | $- 3 x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Mn IV |
| $\mathbf{B_{26}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+3 x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Mn IV |
| $\mathbf{B_{27}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Mn IV |
| $\mathbf{B_{28}}$ | = | $- x_{5} \, \mathbf{a}_{1}+3 x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Mn IV |
| $\mathbf{B_{29}}$ | = | $3 x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Mn IV |
References
- J. V. Florio, R. E. Rundle, and A. I. Snow, Compounds of thorium with transition metals. I. The thorium-manganese system 5, 445–457 (1952), doi:10.1107/S0365110X52001337.
Found in
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 4 (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfort, 1958), 1964 reprint with corrections edn.
Prototype Generator
aflow --proto=A23B6_cF116_225_ad2f_e --params=$a,x_{3},x_{4},x_{5}$