LiFe$_{6}$Ge$_{6}$ Structure: A6B6C_hP39_191_io_ehjk_ad-001
| Prototype | Fe$_{6}$Ge$_{6}$Li |
| AFLOW prototype label | A6B6C_hP39_191_io_ehjk_ad-001 |
| ICSD | 41384 |
| CCDC | 1611167 |
| Pearson symbol | hP39 |
| Space group number | 191 |
| Space group symbol | $P6/mmm$ |
| AFLOW prototype command |
aflow --proto=A6B6C_hP39_191_io_ehjk_ad-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}, \allowbreak z_{8}$ |
Other compounds with this structure
LiNi$_{6}$Ge$_{6}$, LiNi$_{6}$Si$_{6}$
- All of the LiFe$_{x}$Ge$_{x}$ structures are Kagome compounds with the iron, germanium, and lithium/germanium layers all having trihexagonal tiling.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Li II |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Li II |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Ge I |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{3}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Ge I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4h) | Ge II |
| $\mathbf{B_{7}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4h) | Ge II |
| $\mathbf{B_{8}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (4h) | Ge II |
| $\mathbf{B_{9}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (4h) | Ge II |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{15}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{16}}$ | = | $x_{6} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}$ | (6j) | Ge III |
| $\mathbf{B_{17}}$ | = | $x_{6} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}$ | (6j) | Ge III |
| $\mathbf{B_{18}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}$ | = | $- a x_{6} \,\mathbf{\hat{x}}$ | (6j) | Ge III |
| $\mathbf{B_{19}}$ | = | $- x_{6} \, \mathbf{a}_{1}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}$ | (6j) | Ge III |
| $\mathbf{B_{20}}$ | = | $- x_{6} \, \mathbf{a}_{2}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}$ | (6j) | Ge III |
| $\mathbf{B_{21}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}$ | = | $a x_{6} \,\mathbf{\hat{x}}$ | (6j) | Ge III |
| $\mathbf{B_{22}}$ | = | $x_{7} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{7} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6k) | Ge IV |
| $\mathbf{B_{23}}$ | = | $x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{7} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6k) | Ge IV |
| $\mathbf{B_{24}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6k) | Ge IV |
| $\mathbf{B_{25}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{7} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6k) | Ge IV |
| $\mathbf{B_{26}}$ | = | $- x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{7} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6k) | Ge IV |
| $\mathbf{B_{27}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (6k) | Ge IV |
| $\mathbf{B_{28}}$ | = | $x_{8} \, \mathbf{a}_{1}+2 x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{29}}$ | = | $- 2 x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{30}}$ | = | $x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{31}}$ | = | $- x_{8} \, \mathbf{a}_{1}- 2 x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{32}}$ | = | $2 x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{33}}$ | = | $- x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{34}}$ | = | $2 x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{35}}$ | = | $- x_{8} \, \mathbf{a}_{1}- 2 x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{36}}$ | = | $- x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\sqrt{3}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{37}}$ | = | $- 2 x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{3}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{38}}$ | = | $x_{8} \, \mathbf{a}_{1}+2 x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
| $\mathbf{B_{39}}$ | = | $x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \sqrt{3}a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (12o) | Fe II |
References
- \newcommand{\Ozolins}{Ozoli{ņ}{š}}\begin{thebibliography}{1}\expandafter\ifx\csname urlstyle\endcsname\relax \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup \urlstyle{rm}\Url}\fi\providecommand{\selectlanguage}[1]{\relax}\providecommand{\bibAnnoteFile}[1]{% \IfFileExists{#1}{\begin{quotation}\noindent\textsc{Key:} #1\ \textsc{Annotation:} \input{#1}\end{quotation}}{}}\providecommand{\bibAnnote}[2]{% \begin{quotation}\noindent\textsc{Key:} #1\ \textsc{Annotation:} #2\end{quotation}}\bibitem{LiFe6Ge6/Welk_ZAAC_424_193_1976}E. Welk and H.-U. Schuster, Zur Kenntnis der Phase LiFe$_{6}$Ge$_{6}$}, Z. Anorganische und Allgemeine Chemie 424, 193–197 (1976), doi:10.1002/zaac.19764240302.\bibAnnoteFile{LiFe6Ge6/Welk_ZAAC_424_193_1976
Found in
- A. Mantravadi, R. A. Ribeiro, S. L. Bud'ko, P. C. Canfield, and J. V. Zaikina, Experimental Testing of the Theoretically Predicted Magnetic Properties for Kagomé Compounds in the Li-Fe-Ge System, Inorg. Chem. 63, 24697–24708 (2024), doi:10.1021/acs.inorgchem.4c03925.
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=A6B6C_hP39_191_io_ehjk_ad --params=$a,c/a,z_{3},z_{4},z_{5},x_{6},x_{7},x_{8},z_{8}$