LuNi$_{2}$B$_{2}$C Structure: A2BCD2_tI12_139_e_a_b_d-001
Other compounds with this structure
GdN$_{2}$B$_{2}$C, LaIr$_{2}$B$_{2}$C, LaN$_{2}$B$_{2}$C, LaPt$_{2}$B$_{2}$C, LaRh$_{2}$B$_{2}$C
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | C I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Lu I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Nd I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Nd I |
| $\mathbf{B_{5}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | B I |
| $\mathbf{B_{6}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | B I |
References
- T. Siegrist, R. J. Cava, J. J. Krajewski, and W. F. P. Jr., Crystal chemistry of the series LnT$_{2}$B$_{2}$C (Ln = rare earth, T = transition element), J. Alloys Compd. 216, 135–139 (1994), doi:10.1016/0925-8388(94)91055-3.
Found in
- M. W. Pohlkamp and W. Jeitschko, Preparation, Properties, and Crystal Structure of Quaternary Silicide Carbides RCr$_{2}$Si$_{2}$C (R = Y, La-Nd, Sm, Gd-Ho), Z. Naturforsch. B 56, 1143–1148 (2001), doi:10.1515/znb-2001-1108.
First cited in
- H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters, X. Campilongo, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4, Comp. Mat. Sci. 240, 112988 (2024). (doi=10.1016/j.commatsci.2021.110450)
Geometry files
Prototype Generator
aflow --proto=A2BCD2_tI12_139_e_a_b_d --params=$a,c/a,z_{4}$