Mavlyanovite (Mn$_{5}$Si$_{3}$, $D8_{8}$) Structure: A5B3_hP16_193_dg_g-001
| Prototype | Mn$_{5}$Si$_{3}$ |
| AFLOW prototype label | A5B3_hP16_193_dg_g-001 |
| Strukturbericht designation | $D8_{8}$ |
| Mineral name | mavlyanovite |
| ICSD | 24359 |
| Pearson symbol | hP16 |
| Space group number | 193 |
| Space group symbol | $P6_3/mcm$ |
| AFLOW prototype command |
aflow --proto=A5B3_hP16_193_dg_g-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}$ |
Other compounds with this structure
Ce$_{5}$Ge$_{3}$, Ce$_{5}$Pb$_{3}$, Ce$_{5}$Sb$_{3}$, Dy$_{5}$Ge$_{3}$, Dy$_{5}$Sb$_{3}$, Er$_{5}$Si$_{3}$, Fe$_{5}$Si$_{3}$ (HT), Gd$_{5}$Ge$_{3}$, Gd$_{5}$Sb$_{3}$, Hf$_{5}$Ga$_{3}$, Hf$_{5}$Ge$_{3}$, Hf$_{5}$Si$_{3}$, Hf$_{5}$Sn$_{3}$, Ho$_{5}$Sb$_{3}$, Ho$_{5}$Sn$_{3}$, La$_{5}$Ge$_{3}$, La$_{5}$Pb$_{3}$, La$_{5}$Sb$_{3}$, Lu$_{5}$Si$_{3}$, Mg$_{5}$Hg$_{3}$, Mn$_{5}$Ge$_{3}$, Mn$_{5}$Si$_{3}$, Mo$_{5}$Si$_{3}$, Nb$_{5}$Ge$_{3}$, Nb$_{5}$Si$_{3}$, Nd$_{5}$Sb$_{3}$, Pr$_{5}$Sb$_{3}$, Sc$_{5}$Ga$_{3}$, Sc$_{5}$Ge$_{3}$, Sc$_{5}$Pb$_{3}$, Sc$_{5}$Si$_{3}$, Sc$_{5}$Sn$_{3}$, Ta$_{5}$Si$_{3}$, Tb$_{5}$Sb$_{3}$, Ti$_{5}$Ga$_{3}$, Ti$_{5}$Ge$_{3}$, Ti$_{5}$P$_{3}$, Ti$_{5}$Si$_{3}$, Ti$_{5}$Sn$_{3}$, U$_{5}$Ge$_{3}$, V$_{5}$Ga$_{3}$, V$_{5}$Ge$_{3}$, V$_{5}$Si$_{3}$, W$_{5}$Si$_{3}$, Y$_{5}$Ga$_{3}$, Y$_{5}$Ge$_{3}$, Y$_{5}$Pb$_{3}$, Y$_{5}$Si$_{3}$, Y$_{5}$Sn$_{3}$, Yb$_{5}$Sb$_{3}$, Zr$_{5}$Al$_{3}$, Zr$_{5}$Ga$_{3}$, Zr$_{5}$Ge$_{3}$, Zr$_{5}$Pb$_{3}$, Zr$_{5}$Pt$_{3}$, Zr$_{5}$Sb$_{3}$, Zr$_{5}$Si$_{3}$, Zr$_{5}$Sn$_{3}$, Cr$_{5-x-y}$Fe$_{x}$Nb$_{y}$Si$_{3}$, Mn$_{5-x}$Fe$_{x}$Si$_{3}$, Ti$_{5}$Ga$_{1.5}$Ge$_{1.5}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (4d) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4d) | Mn I |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (4d) | Mn I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4d) | Mn I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Mn II |
| $\mathbf{B_{6}}$ | = | $x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Mn II |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Mn II |
| $\mathbf{B_{8}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{2} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Mn II |
| $\mathbf{B_{9}}$ | = | $- x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{2} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Mn II |
| $\mathbf{B_{10}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Mn II |
| $\mathbf{B_{11}}$ | = | $x_{3} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Si I |
| $\mathbf{B_{12}}$ | = | $x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Si I |
| $\mathbf{B_{13}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6g) | Si I |
| $\mathbf{B_{14}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Si I |
| $\mathbf{B_{15}}$ | = | $- x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Si I |
| $\mathbf{B_{16}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6g) | Si I |
References
- B. Aronson, A Note on the Compositions and Crystal Structures of MnB$_{2}$, Mn$_{3}$Si, Mn$_5$Si$_{3}$, and FeSi$_{2}$, Acta Chem. Scand. 14, 1414–1418 (1960), doi:10.3891/acta.chem.scand.14-1414.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A5B3_hP16_193_dg_g --params=$a,c/a,x_{2},x_{3}$