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 |
| CCDC | 1744490 |
| 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
AuBe$_{5}$, CaAu$_{5}$, CeIr$_{5}$, CoBe$_{5}$, DyCu$_{5}$, ErCu$_{5}$, GdCu$_{5}$, HfNi$_{5}$, HoCu$_{5}$, LuCu$_{5}$, PaPt$_{5}$, PdBe$_{5}$, PtBe$_{5}$, TbCu$_{5}$, TmCu$_{5}$, UCu$_{5}$, UNi$_{5}$, UPt$_{5}$, ZrCo$_{5}$, ZrCu$_{5}$, CaAu$_{5}$, CoBe$_{5}$, HfNi$_{5}$, PdBe$_{5}$, UCu$_{5}$, UNi$_{5}$, UPt$_{5}$, ZrNi$_{5}$
- 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.
- The history of this page is complicated. The original NRL Crystal Lattice Structure Page listed Cu$_{4}$MgSn as the prototype for Strukturbericht symbol $C15_{b}$. Later we used AuBe$_{5}$ as the prototype, but included both binary and ternary compounds on the same page. We have now separated the two.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
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).
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=AB5_cF24_216_a_ce --params=$a,x_{3}$