AuBe$_{5}$ ($C15_{b}$) Structure: AB5_cF24_216_a_ce-001
| Prototype | AuBe$_{5}$ |
| AFLOW prototype label | AB5_cF24_216_a_ce-001 |
| Strukturbericht designation | $C15_{b}$ |
| ICSD | 611643 |
| Pearson symbol | cF24 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=AB5_cF24_216_a_ce-001
--params=$a, \allowbreak x_{3}$ |
Other compounds with this structure
CaAu$_{5}$, CoBe$_{5}$, HfNi$_{5}$, PdBe$_{5}$, UCu$_{5}$, UNi$_{5}$, UPt$_{5}$, ZrNi$_{5}$, CaNi$_{4}$Mg, CeNi$_{4}$Mg, DyNi$_{4}$Mg, ErNi$_{4}$Mg, HoNi$_{4}$Mg, InCu$_{4}$Mg, LaNi$_{4}$Mg, LuNi$_{4}$Mg, NdNi$_{4}$Mg, PrNi$_{4}$Mg, ScNi$_{4}$Mg, SmNi$_{4}$Mg, SnCu$_{4}$Mg, SnCu$_{4}$Mn, TbNi$_{4}$Mg, TmNi$_{4}$Mg, YNi$_{4}$Mg, YbNi$_{4}$Mg
- The lattice constant for this structure is taken from (Batchelder, 1958), which does not give the internal coordinate for the (16c) site. However, (Baenziger, 1950) assumes that uranium compounds of this type have an internal parameter $x_{3} ≈ 5/8$. (Pearson, 1958) uses this to infer a value of $x_{3} ≈ 5/8$ here as well.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Au I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (4c) | Be I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Be II |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- 3 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Be II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}- 3 x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Be II |
| $\mathbf{B_{6}}$ | = | $- 3 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Be II |
References
- N. C. Baenziger, R. E. Rundle, A. I. Snow, and A. S. Wilson, Compounds of uranium with the transition metals of the first long period, Acta Cryst. 3, 34–40 (1950), doi:10.1107/S0365110X50000082.
- F. W. von Batchelder and R. F. Raeuchle, The tetragonal MBe$_{12}$ structure of silver, palladium, platinum and gold, Acta Cryst. 11, 122 (1958), doi:10.1107/S0365110X58000323.
Found in
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).
Prototype Generator
aflow --proto=AB5_cF24_216_a_ce --params=$a,x_{3}$