Gananite (BiF$_{3}$, $D0_{3}$) Structure: AB3_cF16_225_a_bc-001
| Prototype | BiF$_{3}$ |
| AFLOW prototype label | AB3_cF16_225_a_bc-001 |
| Strukturbericht designation | $D0_{3}$ |
| Mineral name | gananite |
| ICSD | 25567 |
| CCDC | 1601221 |
| Pearson symbol | cF16 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=AB3_cF16_225_a_bc-001
--params=$a$ |
Other compounds with this structure
AgLi$_{3}$, AlCu$_{3}$, AlFe$_{3}$, AmBa$_{3}$, AsLi$_{3}$, AsNa$_{3}$, AsPd$_{3}$, AuLi$_{3}$, BiCs$_{3}$, BiFe$_{3}$, β-BiK$_{3}$ (HT), BiLi$_{3}$, BiO$_{3}$, BiPd$_{3}$, BiRb$_{3}$, CaH$_{3}$, CdLi$_{3}$, CeCd$_{3}$, CeH$_{3}$, CeO$_{3}$, CeMg$_{3}$, DyMg$_{3}$, ErH$_{3}$, FeH$_{3}$, GaFe$_{3}$, GaMn$_{3}$, GdH$_{3}$, GdMg$_{3}$, GeCo$_{3}$, GeCu$_{3}$, GeFe$_{3}$, GeLi$_{3}$, GeMg$_{3}$, GeMn$_{3}$, HoH$_{3}$, HgLi$_{3}$, IAg$_{3}$, InCa$_{3}$, InSr$_{3}$, LaH$_{3}$, LaMg$_{3}$, LaO$_{3}$, LuH$_{3}$, MgAg$_{3}$, MgCe$_{3}$, MgH$_{3}$, MnFe$_{3}$, NNa$_{3}$, NbO$_{3}$, NbSr$_{3}$, NdCd$_{3}$, NdH$_{3}$, NdMg$_{3}$, NpBa$_{3}$, OAl$_{3}$, OFe$_{3}$, OMo$_{3}$, PLi$_{3}$, PbF$_{3}$, PbLi$_{3}$, PrCd$_{3}$, PrH$_{3}$, PrMg$_{3}$, PuH$_{3}$, RbBi$_{3}$, RuK$_{3}$, SAg$_{3}$, SLi$_{3}$, SPd$_{3}$, β-SbCu$_{3}$ (HT), SbK$_{3}$, SbLi$_{3}$, SbNi$_{3}$ (HT), ScH$_{3}$, SePd$_{3}$, SiCo$_{3}$, SiFe$_{3}$, SiMg$_{3}$, SiMn$_{3}$, SiNa$_{3}$, SmCd$_{3}$, SmMg$_{3}$, SmO$_{3}$, γ-SnCu$_{3}$ (HT), SnLi$_{3}$, SnNi$_{3}$ (HT), SrCl$_{3}$, TaO$_{3}$, TbH$_{3}$, TbMg$_{3}$, TiH$_{3}$, TlCa$_{3}$, TlLi$_{3}$, UO$_{3}$, VH$_{3}$, YCd$_{3}$, YH$_{3}$, YMg$_{3}$, YbH$_{3}$, YbO$_{3}$
- (Villars, 1991) corrects (Hund, 1949), changing the positions of one third of the fluorine atoms so that the space group becomes $Fm\overline{3}m$ #225, as is accepted for $D0_{3}$, and in agreement with (Hassel, 1929). This structure is crystallographically equivalent to the Heusler ($L2_{1}$) structure and a derivative of the
quaternary-Heusler,
LiMgAuSn.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Bi 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) | F 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) | F II |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8c) | F II |
References
- O. Hassel and S. Nilssen, Der Kristallbau des BiF$_3$, Z. Anorganische und Allgemeine Chemie 181, 172–176 (1929), doi:10.1002/zaac.19291810117.
- F. Hund and R. Fricke, Der Kristallbau von α-BiF$_3$, Z. Anorganische und Allgemeine Chemie 258, 198–204 (1949), doi:10.1002/zaac.19492580310.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=AB3_cF16_225_a_bc --params=$a$