Hg$_{2}$TiCu Inverse Heusler Structure: AB2C_cF16_216_a_bc_d-001
| Prototype | CuHg$_{2}$Ti |
| AFLOW prototype label | AB2C_cF16_216_a_bc_d-001 |
| Mineral name | Inverse Heusler |
| ICSD | 102972 |
| Pearson symbol | cF16 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=AB2C_cF16_216_a_bc_d-001
--params=$a$ |
Other compounds with this structure
Mn$_{2}$CoAl, Mn$_{2}$CoGa, Mn$_{2}$CoIn, Li$_{2}$AgSb, Li$_{2}$CuSn, Li$_{2}$CuSb, Li$_{2}$AgAl, Li$_{2}$AgIn, Li$_{2}$AgSb, Li$_{2}$AgSn, Li$_{2}$AgPb, Li$_{2}$AgBi, Li$_{2}$AuGa, Li$_{2}$AuIn, Li$_{2}$AuSb, Li$_{2}$AuSn, Li$_{2}$AuPb, Li$_{2}$AuTl
- Most of the literature on inverse Heusler compounds identifies Hg$_{2}$TiCu as the prototype structure, however (Villars, 2016) and (Villars, 2016a) use the Li$_{2}$AgSb structure found in (Pauly, 1968) as the prototype.
- Although it is tempting to use the older paper, we follow the majority and use Hg$_{2}$TiCu as the prototype.
- The inverse Heusler structure is a variation of the quaternary Heusler structure, where the mercury atoms are on adjacent face-centered cubic sublattices, forming a diamond structure.
- Contrast this with the standard Heusler ($L1_{2}$) structure, where the like atoms are at second-neighbor positions in the fcc lattice.
- This structure is also referred to as the XA or X$_\mathrm{a}$ 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) | Cu 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) | Hg 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) | Hg II |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (4d) | Ti I |
References
- M. Pušelj and Z. Ban, The Crystal Structure of TiCuHg$_{2}$, Croatica Chemica Acta 41, 79–83 (1969).
- H. Pauly, A. Weiss, and H. Witte, The Crystal Structure of the Ternary Intermetallic Phases Li$_{2}$EX (E=Cu,Ag,Au; X=Al,Ga,In,Tl,Si,Ge,Sn,Pb,Sb,Bi), Z. Metallkd. 59, 47–58 (1968).
- P. Villars, Li$_{2}$AgSb Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.).
Found in
- P. Villars, TiCuHg$_{2}$ (CuHg$_{2}$Ti) Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.).
Prototype Generator
aflow --proto=AB2C_cF16_216_a_bc_d --params=$a$