Heusler (Cu$_{2}$AlMn, $L2_{1}$) Structure: AB2C_cF16_225_a_c_b-001
| Prototype | AlCu$_{2}$Mn |
| AFLOW prototype label | AB2C_cF16_225_a_c_b-001 |
| Strukturbericht designation | $L2_{1}$ |
| Mineral name | heusler |
| ICSD | 607008 |
| Pearson symbol | cF16 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB2C_cF16_225_a_c_b-001
--params=$a$ |
Other compounds with this structure
Ag$_{2}$AlMn, Cd$_{2}$AgAu, Co$_{2}$AlHf, Co$_{2}$AlMn, Co$_{2}$AlNb, Co$_{2}$AlTa, Co$_{2}$AlZr, Co$_{2}$FeGe, Co$_{2}$GaMn, Co$_{2}$GaMn, Co$_{2}$GaNb, Co$_{2}$GaTa, Co$_{2}$GaTi, Co$_{2}$MnSi, Co$_{2}$MnSn, Co$_{2}$SiV, Co$_{2}$SnTi, Co$_{2}$SnV, Cu$_{2}$AlMn, Cu$_{2}$AlZr, Cu$_{2}$CoSn, Cu$_{2}$FeSn, Cu$_{2}$GaMn, Cu$_{2}$InMn, Cu$_{2}$InTi, Cu$_{2}$MnSb, Cu$_{2}$MnSn, Cu$_{2}$NiSn, Fe$_{2}$AlV, Fe$_{2}$AlCo, Fe$_{2}$GaTi, Fe$_{2}$GaV, Fe$_{2}$SnTi, K$_{2}$CsSb, Li$_{2}$AuSn, Li$_{2}$NaSb, Mg$_{2}$LiTl, Na$_{2}$KSb, Ni$_{2}$AlHf, Ni$_{2}$AlNb, Ni$_{2}$AlTa, Ni$_{2}$AlTi, Ni$_{2}$AlZr, Ni$_{2}$GaHf, Ni$_{2}$GaMn, Ni$_{2}$GaNb, Ni$_{2}$GaTa, Ni$_{2}$GaV, Ni$_{2}$GeMn, Ni$_{2}$InMg, Ni$_{2}$InMn, Ni$_{2}$InTi, Ni$_{2}$MgSb, Ni$_{2}$MgSn, Ni$_{2}$MnGa, Ni$_{2}$MnSb, Ni$_{2}$MnSn, Ni$_{2}$SnTi, Ni$_{2}$SnV, Pd$_{2}$AlMn, Pd$_{2}$InMn, Pd$_{2}$MnSb, Pd$_{2}$MnSn, Zn$_{2}$AgAu, $\beta$-Zn$_{2}$AuCu
- All of the atoms are located on the sites of a body-centered cubic lattice. If we replace the Mn atom by another copper atom, the structure reduces to the crystallographically equivalent $D0_{3}$ (BiF$_{3}$) structure.
- If we replace one of the copper atoms by an fourth species we get the the
quaternary-Heusler,
LiMgAuSn. - Also see the $C1_{b}$ (AsAgMg)
half–Heusler
structure. - The ICSD entry is from (Heusler, 1934). It is identical to the structure describe by (Bradley, 1934) except for a small change in the lattice constant.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Mn I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | Cu I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8c) | Cu I |
References
- A. J. Bradley and J. W. Rodgers, The Crystal Structure of Heusler Alloys, Proc. R. Soc. A Math. Phys. Eng. Sci. 144, 340–359 (1934), doi:10.1098/rspa.1934.0053.
- O. Heusler, Kristallstruktur und Ferromagnetismus der Mangan-Aluminium-Kupferlegierungen, Ann. Phys. 411, 155–201 (1934). Originally referenced as
5.Folge. Band 19.
.
Prototype Generator
aflow --proto=AB2C_cF16_225_a_c_b --params=$a$