Mg$_{6}$Si$_{7}$Cu$_{16}$ Structure: A16B6C7_cF116_225_2f_e_ad-001
| Prototype | Cu$_{16}$Mg$_{6}$Si$_{7}$ |
| AFLOW prototype label | A16B6C7_cF116_225_2f_e_ad-001 |
| ICSD | 16624 |
| Pearson symbol | cF116 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A16B6C7_cF116_225_2f_e_ad-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}$ |
Other compounds with this structure
Hf$_{6}$Ge$_{7}$Co$_{16}$, Hf$_{6}$Ge$_{7}$Ni$_{16}$, Hf$_{6}$Si$_{7}$Co$_{16}$, Hf$_{6}$Si$_{7}$Ni$_{16}$, Mg$_{6}$Ge$_{7}$Ni$_{16}$, Mg$_{6}$Si$_{7}$Co$_{16}$, Mg$_{6}$Si$_{7}$Cu$_{16}$, Mg$_{6}$Si$_{7}$Ni$_{16}$, Mn$_{6}$Ge$_{7}$Ni$_{16}$, Mn$_{6}$Si$_{7}$Ni$_{16}$, Nb$_{6}$Ge$_{7}$Co$_{16}$, Nb$_{6}$Ge$_{7}$Ni$_{16}$, Nb$_{6}$Si$_{7}$Co$_{16}$, Nb$_{6}$Si$_{7}$Ni$_{16}$, Sc$_{6}$Ge$_{7}$Ni$_{16}$, Sc$_{6}$Si$_{7}$Co$_{16}$, Sc$_{6}$Si$_{7}$Ni$_{16}$, Ta$_{6}$Ge$_{7}$Co$_{16}$, Ta$_{6}$Ge$_{7}$Ni$_{16}$, Ta$_{6}$Si$_{7}$Co$_{16}$, Ta$_{6}$Si$_{7}$Ni$_{16}$, Ti$_{6}$Ge$_{7}$Ni$_{16}$, Ti$_{6}$Si$_{7}$Co$_{16}$, Ti$_{6}$Si$_{7}$Ni$_{16}$, V$_{6}$Si$_{7}$Ni$_{16}$, Zr$_{6}$Ge$_{7}$Co$_{16}$, Zr$_{6}$Ge$_{7}$Ni$_{16}$, Zr$_{6}$Si$_{7}$Co$_{16}$, Zr$_{6}$Si$_{7}$Ni$_{16}$
- This is the ternary version of Th$_{6}$Mn$_{23}$ ($D8_{a}$).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Si 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) | Si 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) | Si 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) | Si 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) | Si 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) | Si 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) | Si 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) | Mg 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) | Mg 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) | Mg 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) | Mg 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) | Mg 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) | Mg 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) | Cu I |
| $\mathbf{B_{15}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- 3 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{16}}$ | = | $x_{4} \, \mathbf{a}_{1}- 3 x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{17}}$ | = | $- 3 x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+3 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{19}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{20}}$ | = | $- x_{4} \, \mathbf{a}_{1}+3 x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{21}}$ | = | $3 x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (32f) | Cu I |
| $\mathbf{B_{22}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Cu II |
| $\mathbf{B_{23}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- 3 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Cu II |
| $\mathbf{B_{24}}$ | = | $x_{5} \, \mathbf{a}_{1}- 3 x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Cu II |
| $\mathbf{B_{25}}$ | = | $- 3 x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Cu II |
| $\mathbf{B_{26}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+3 x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Cu II |
| $\mathbf{B_{27}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Cu II |
| $\mathbf{B_{28}}$ | = | $- x_{5} \, \mathbf{a}_{1}+3 x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Cu II |
| $\mathbf{B_{29}}$ | = | $3 x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (32f) | Cu II |
References
- G. Bergman and J. L. T. Waugh, The crystal structure of the intermetallic compound Mg$_{6}$Si$_{7}$Cu$_{16}$, Acta Cryst. 9, 214–217 (1956), doi:10.1107/S0365110X56000632.
Found in
- K. L. Holman, E. Morosan, P. A. Casey, L. Li, N. P. Ong, T. Klimczuk, C. Felser, and R. J. Cava, Crystal structure and physical properties of Mg$_{6}$Cu$_{16}$Si$_{7}$-type M$_{6}$Ni$_{16}$Si$_{7}$, for M = Mg, Sc, Ti, Nb, and Ta, Mater. Res. Bull. 43, 9–15 (2008), doi:10.1016/j.materresbull.2007.09.023.
Prototype Generator
aflow --proto=A16B6C7_cF116_225_2f_e_ad --params=$a,x_{3},x_{4},x_{5}$