Cu$_{4}$SnMg Structure: A4BC_cF24_216_e_a_c-001
| Prototype | Cu$_{4}$MgSn |
| AFLOW prototype label | A4BC_cF24_216_e_a_c-001 |
| ICSD | 103055 |
| CCDC | 1661013 |
| Pearson symbol | cF24 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=A4BC_cF24_216_e_a_c-001
--params=$a, \allowbreak x_{3}$ |
Other compounds with this structure
Co$_{4}$CeMg, Co$_{4}$TbMg, Co$_{4}$USn, Co$_{4}$YMg, Cu$_{4}$AgZr, Cu$_{4}$CaIn, Cu$_{4}$DyAg, Cu$_{4}$DyAu, Cu$_{4}$DyIn, Cu$_{4}$ErAg, Cu$_{4}$ErAu, Cu$_{4}$ErCd, Cu$_{4}$ErPd, Cu$_{4}$GdAg, Cu$_{4}$GdAu, Cu$_{4}$GdIn, Cu$_{4}$GdPd, Cu$_{4}$HoAg, Cu$_{4}$HoAu, Cu$_{4}$HoCd, Cu$_{4}$HoIn, Cu$_{4}$InCa, Cu$_{4}$InMg, Cu$_{4}$InYb, Cu$_{4}$LuAu, Cu$_{4}$MnSn, Cu$_{4}$NdAg, Cu$_{4}$NdAu, Cu$_{4}$NdMg, Cu$_{4}$NdPd, Cu$_{4}$ScIn, Cu$_{4}$ScSn, Cu$_{4}$SmAg, Cu$_{4}$SmPd, Cu$_{4}$TbAg, Cu$_{4}$TbAu, Cu$_{4}$TbIn, Cu$_{4}$TmAg, Cu$_{4}$TmBe, Cu$_{4}$TmCd, Cu$_{4}$UAg, Cu$_{4}$UAu, Cu$_{4}$UPd, Cu$_{4}$YIn, Cu$_{4}$YMg, Cu$_{4}$YbAg, Cu$_{4}$YbAu, Cu$_{4}$YbCd, Cu$_{4}$YbIn, Cu$_{4}$YbNi, Cu$_{4}$YbPd, Ni$_{4}$AlU, Ni$_{4}$CaMg, Ni$_{4}$CeCd, Ni$_{4}$CeMg, Ni$_{4}$CeMn, Ni$_{4}$DyAu, Ni$_{4}$DyCd, Ni$_{4}$ErAu, Ni$_{4}$ErCd, Ni$_{4}$ErMn, Ni$_{4}$GdAu, Ni$_{4}$GdCd, Ni$_{4}$GdIn, Ni$_{4}$GdMg, Ni$_{4}$HoAu, Ni$_{4}$HoCd, Ni$_{4}$InU, Ni$_{4}$InZr, Ni$_{4}$LaMg, Ni$_{4}$LuAu, Ni$_{4}$LuCd, Ni$_{4}$LuSn, Ni$_{4}$NdCd, Ni$_{4}$NdMg, Ni$_{4}$PrCd, Ni$_{4}$PrMg, Ni$_{4}$ScAu, Ni$_{4}$ScCd, Ni$_{4}$ScSn, Ni$_{4}$SmCd, Ni$_{4}$SmMg, Ni$_{4}$SnU, Ni$_{4}$SnZr, Ni$_{4}$TbAu, Ni$_{4}$TbCd, Ni$_{4}$TbMg, Ni$_{4}$TmAu, Ni$_{4}$TmCd, Ni$_{4}$TmIn, Ni$_{4}$UIn, Ni$_{4}$USn, Ni$_{4}$UZn, Ni$_{4}$YAu, Ni$_{4}$YCd, Ni$_{4}$YIn, Ni$_{4}$YMg, Ni$_{4}$YMn, Ni$_{4}$YbAu, Ni$_{4}$YbCd, Ni$_{4}$ZnZr, Pt$_{4}$CeIn, Pt$_{4}$DyIn, Pt$_{4}$ErIn, Pt$_{4}$EuIn, Pt$_{4}$GdIn, Pt$_{4}$HoIn, Pt$_{4}$LaIn, Pt$_{4}$NdIn, Pt$_{4}$PrIn, Pt$_{4}$SmIn, Pt$_{4}$TbIn, Pt$_{4}$UAu, Pt$_{4}$UIr, Cu$_{4}$InMg, Cu$_{4}$SnMg, Cu$_{4}$SnMn, Ni$_{4}$CaMg, Ni$_{4}$CeMg, Ni$_{4}$DyMg, Ni$_{4}$ErMg, Ni$_{4}$HoMg, Ni$_{4}$LaMg, Ni$_{4}$LuMg, Ni$_{4}$NdMg, Ni$_{4}$PrMg, Ni$_{4}$ScMg, Ni$_{4}$SmMg, Ni$_{4}$TbMg, Ni$_{4}$TmMg, Ni$_{4}Y$Mg, Ni$_{4}$YbMg
- This is the ternary form of AuBe$_{5}$, Strukturbericht $C15_{b}$. The original NRL Crystal Lattice Structure Page listed it as the prototype $C15_{b}$. Later we listed both binary and ternary compounds on the same page, but now we have separated them.
- (Osamura, 1978) put the tin atom Sn I on the (4a) site. The AFLOW standard label protocol moves the origin so that the magnesium Mg I atom is on the (4a) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Mg I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (4c) | Sn I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Cu I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- 3 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Cu I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}- 3 x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Cu I |
| $\mathbf{B_{6}}$ | = | $- 3 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Cu I |
References
- K. Osamura and Y. Murakami, Crystal structures of CuSnMg and Cu$_{4}$SnMg ternary compounds, J. Less-Common Met. 60, 311–313 (1978), doi:10.1016/0022-5088(78)90185-6.
Found in
- ICSD, Inorganic Crystal Structure Database [MgSnCu4]. ID 103055.
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=A4BC_cF24_216_e_a_c --params=$a,x_{3}$