Quaternary Heusler (LiMgAuSn) Structure: ABCD_cF16_216_a_b_c_d-001
| Prototype | AuLiMgSn |
| AFLOW prototype label | ABCD_cF16_216_a_b_c_d-001 |
| ICSD | 16477 |
| Pearson symbol | cF16 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=ABCD_cF16_216_a_b_c_d-001
--params=$a$ |
Other compounds with this structure
AuLiMgSn, LiMgPdSn, LiMgPtSn, CuMg$_{2}$Ti, AuBiLi$_{2}$, AgLi$_{2}$Sn, AuLi$_{2}$Sn, CuHfHg$_{2}$, MnPd$_{2}$Sn
- This
quaternary-Heusler
structure can be considered as the parent of a wide variety of structures, depending on the occupancy of the (4a), (4b), (4c), and (4d) Wyckoff positions. Consider atoms of type A, B, C, D, distributed in this structure. We can get:
Structure Strukturbericht AFLOW Label (4a) (4b) (4c) (4d) simple cubic A$_h$ A_cP1_221_a A A - - fcc A1 A_cF4_225_a A - - - bcc A2 A_cI2_229_a A A - - bcc A2 A_cI2_229_a A A A A diamond A4 A_cF8_227_a A - A - NaCl B1 AB_cF8_225_a_b A B - - CsCl B2 AB_cP2_221_a_b A A B B ZnS (zincblende) B3 AB_cF8_216_c_a A - B - BiF$_{3}$ D0$_3$ AB3_cF16_225_a_bc A B B B NaTl B32 AB_cF16_227_a_b A B A B Fluorite C1 AB2_cF12_225_a_c A - B B half-Heusler C1$_{b}$ ABC_cF12_216_a_b_c A B C - Heusler L2$_1$ AB2C_cF16_225_a_c_b A C B B Inverse-Heusler AB2C_cF16_216_a_bc_d A B B C
- The ordering of this structure is somewhat arbitary. We will get the same structure if Sn and Mg are on either the (4a)/(4b) or (4c)/(4d) sites with Au and Li on the opposite sites.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Au 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) | Li 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) | Mg I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (4d) | Sn I |
References
- U. Eberz, W. Seelentag, and H.-U. Schuster, Zur Kenntnis farbiger ternärer und quaternärer Zintl-Phasen Coloured Ternary and Quaternary Zintl-Phases, Z. Naturforsch. B 35, 1341–1343 (1980), doi:10.1515/znb-1980-1103.
Found in
- P. Villars, ed., PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database) (Springer Materials, Heigelberg, 2016), chap. LiMgPdSn Crystal Structure.
Prototype Generator
aflow --proto=ABCD_cF16_216_a_b_c_d --params=$a$