Half–Heusler (AgAsMg, $C1_{b}$) Structure: ABC_cF12_216_a_c_b-001
| Prototype | AgAsMg |
| AFLOW prototype label | ABC_cF12_216_a_c_b-001 |
| Strukturbericht designation | $C1_{b}$ |
| Mineral name | half-heusler |
| ICSD | 43819 |
| Pearson symbol | cF12 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=ABC_cF12_216_a_c_b-001
--params=$a$ |
Other compounds with this structure
AlBBe, AuMgSn, AuScSn, BiCoZr, BiCuMg, BiLiMg, BiMgNi, BiPdTe, BiPtY, CdCuSb, CdLiP, CoSbTi, CoSbV, CoSbZr, CuMgSb, CuMgSn, CuMnSb, CuSbV, FeSbTi, FeSbV, LiMgSb, LiNZn, LiPZn, MgNiSb, MgPtSn, MnNiSb, NiSbTi, NiSbV, PtScSn, RhSnTi
- All of the atoms are located on the sites of a body-centered cubic lattice. This is sometimes called the
half–Heusler
structure because it is identical to the $L2_{1}$ (Heusler) structure, Cu$_{2}$AlMn with half of the copper atoms missing. The Mg and Ag atoms form a rock salt ($B1$) structure, while the As and either the Mg or Ag atoms form a zincblende ($B3$) structure. If the atoms on the (4a) and (4c) sites are identical, this reduces to the fluorite ($C1$) structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Ag 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) | Mg I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (4c) | As I |
References
- H. Nowotny and W. Sibert, Ternäre Valenzverbindungen in den Systemen Kupfer(Silber)-Arsen(Antimon,Wismut)-Magnesium, Z. Metallkd. 33, 391–394 (1941).
Found in
- W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley Interscience, New York, London, Sydney, Tornoto, 1972).
Prototype Generator
aflow --proto=ABC_cF12_216_a_c_b --params=$a$