HfFe$_{6}$Ge$_{6}$ Structure: A6B6C_hP13_191_i_cde_a-002
| Prototype | Fe$_{6}$Ge$_{6}$Hf |
| AFLOW prototype label | A6B6C_hP13_191_i_cde_a-002 |
| ICSD | 632038 |
| Pearson symbol | hP13 |
| Space group number | 191 |
| Space group symbol | $P6/mmm$ |
| AFLOW prototype command |
aflow --proto=A6B6C_hP13_191_i_cde_a-002
--params=$a, \allowbreak c/a, \allowbreak z_{4}, \allowbreak z_{5}$ |
Other compounds with this structure
DyCr$_{6}$Ge$_{6}$, DyFe$_{6}$Ge$_{6}$, DyMn$_{6}$Ge$_{6}$, ErCr$_{6}$Ge$_{6}$, GdFe$_{6}$Ge$_{6}$, GdMn$_{6}$Ge$_{6}$, HfFe$_{6}$Ge$_{6}$, HoCr$_{6}$Ge$_{6}$, HoFe$_{6}$Ge$_{6}$, HoMn$_{6}$Ge$_{6}$, LuFe$_{6}$Ge$_{6}$, LuMn$_{6}$Ge$_{6}$, MgCo$_{6}$Ge$_{6}$, MgFe$_{6}$Ge$_{6}$, NbFe$_{6}$Ge$_{6}$, NdMn$_{6}$Ge$_{6}$, ScFe$_{6}$Ge$_{6}$, ScMn$_{6}$Ge$_{6}$, ScMn$_{6}$Sn$_{6}$, TbCr$_{6}$Ge$_{6}$, TbFe$_{6}$Ge$_{6}$, TbMn$_{6}$Ge$_{6}$, TbMn$_{6}$Sn$_{6}$, TiFe$_{6}$Ge$_{6}$, TmFe$_{6}$Ge$_{6}$, TmMn$_{6}$Ge$_{6}$, YCr$_{6}$Ge$_{6}$, YFe$_{6}$Ge$_{6}$, YMn$_{6}$Sn$_{6}$, YbFe$_{6}$Ge$_{6}$, YbMn$_{6}$Ge$_{6}$, ZrFe$_{6}$Ge$_{6}$, DyFe$_{6}$Sn$_{4}$Ge$_{2}$, ErFe$_{6}$Sn$_{4}$Ge$_{2}$, GdFe$_{6}$Sn$_{4}$Ge$_{2}$, HoFe$_{6}$Sn$_{4}$Ge$_{2}$, TbFe$_{6}$Sn$_{4}$Ge$_{2}$, YFe$_{6}$Sn$_{4}$Ge$_{2}$
- (Zyubrik, 1982) originally determined the structure of HfFe$_{6}$Ge$_{6}$. While we do not have a copy of this paper, we were able to extract the data from the ICSD entry.
- This structure is related to the $D2_{a}$ TiBe$_{12}$ structure. That structure, however, is probably not the actual TiBe$_{12}$ structure, so we designate HfFe$_{6}$Ge$_{6}$ as the prototype for the ternary form.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Hf I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (2c) | Ge I |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (2c) | Ge I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Ge II |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Ge II |
| $\mathbf{B_{6}}$ | = | $z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (2e) | Ge III |
| $\mathbf{B_{7}}$ | = | $- z_{4} \, \mathbf{a}_{3}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (2e) | Ge III |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{5} \,\mathbf{\hat{z}}$ | (6i) | Fe I |
References
- A. A. Zyubrik, R. R. Olenych, I. A. Mizak, and Y. P. Yarmolyuk, The (titanium, hafnium)-iron-germanium systems, Dopov. Akad. Nauk Ukr. RSR A 44, 78–81 (1982).
Found in
- T. Mazet, O. Isnard, and B. Malaman, Neutron diffraction and $^{57}$Fe Mössbauer study of the HfFe$_{6}$Ge$_{6}$-type RFe$_{6}$Ge$_{6}$ compounds (R=Sc, Ti, Zr, Hf, Nb), Solid State Commun. 114, 91–96 (2000), doi:10.1016/S0038-1098(00)00003-X.
Prototype Generator
aflow --proto=A6B6C_hP13_191_i_cde_a --params=$a,c/a,z_{4},z_{5}$