Yb$_{3}$Rh$_{4}$Sn$_{13}$ Structure: A4B13C3_cP40_223_e_ak_c-001
| Prototype | Rh$_{4}$Sn$_{13}$Yb$_{3}$ |
| AFLOW prototype label | A4B13C3_cP40_223_e_ak_c-001 |
| ICSD | 105936 |
| Pearson symbol | cP40 |
| Space group number | 223 |
| Space group symbol | $Pm\overline{3}n$ |
| AFLOW prototype command |
aflow --proto=A4B13C3_cP40_223_e_ak_c-001
--params=$a, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
Ca$_{3}$Co$_{4}$Ge$_{13}$, Ca$_{3}$Ir$_{4}$Ge$_{13}$, Ca$_{3}$Os$_{4}$Ge$_{13}$, Ca$_{3}$Rh$_{4}$Ge$_{13}$, Ca$_{3}$Ru$_{4}$Ge$_{13}$, Ce$_{3}$Rh$_{4}$Sn$_{13}$, Gd$_{3}$Co$_{4}$Ge$_{13}$, Gd$_{3}$Ir$_{4}$Ge$_{13}$, Gd$_{3}$Os$_{4}$Ge$_{13}$, Gd$_{3}$Rh$_{4}$Ge$_{13}$, Gd$_{3}$Ru$_{4}$Ge$_{13}$, La$_{3}$Rh$_{4}$Sn$_{13}$, Pr$_{3}$Rh$_{4}$Sn$_{13}$, Sn$_{3}$Rh$_{4}$Sn$_{13}$, U$_{3}$Co$_{4}$Ge$_{13}$, U$_{3}$Ir$_{4}$Ge$_{13}$, U$_{3}$Os$_{4}$Ge$_{13}$, U$_{3}$Rh$_{4}$Ge$_{13}$, U$_{3}$Ru$_{4}$Ge$_{13}$, Y$_{3}$Co$_{4}$Ge$_{13}$, Y$_{3}$Ir$_{4}$Ge$_{13}$, Y$_{3}$Os$_{4}$Ge$_{13}$, Y$_{3}$Rh$_{4}$Ge$_{13}$, Y$_{3}$Ru$_{4}$Ge$_{13}$, Yb$_{3}$Co$_{4}$Ge$_{13}$, Yb$_{3}$Ir$_{4}$Ge$_{13}$, Yb$_{3}$Os$_{4}$Ge$_{13}$, Yb$_{3}$Rh$_{4}$Ge$_{13}$, Yb$_{3}$Ru$_{4}$Ge$_{13}$
- (Bordet, 1991) refers to this as
phase $I$
of structures with the formula M$_{3}$Rh$_{4}$Sn$_{13}$, with thephase $I'$
structure represented by the non-centrosymmetric La$_{3}$Rh$_{4}$Sn$_{13}$ phase.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Sn I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (2a) | Sn I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | Yb I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | Yb I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (6c) | Yb I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}$ | (6c) | Yb I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6c) | Yb I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6c) | Yb I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8e) | Rh I |
| $\mathbf{B_{10}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8e) | Rh I |
| $\mathbf{B_{11}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8e) | Rh I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8e) | Rh I |
| $\mathbf{B_{13}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8e) | Rh I |
| $\mathbf{B_{14}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8e) | Rh I |
| $\mathbf{B_{15}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8e) | Rh I |
| $\mathbf{B_{16}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8e) | Rh I |
| $\mathbf{B_{17}}$ | = | $y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{18}}$ | = | $- y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{19}}$ | = | $y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{20}}$ | = | $- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{21}}$ | = | $z_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{22}}$ | = | $z_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{23}}$ | = | $- z_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{24}}$ | = | $- z_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{25}}$ | = | $y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}$ | (24k) | Sn II |
| $\mathbf{B_{26}}$ | = | $- y_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}$ | (24k) | Sn II |
| $\mathbf{B_{27}}$ | = | $y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}$ | (24k) | Sn II |
| $\mathbf{B_{28}}$ | = | $- y_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}$ | (24k) | Sn II |
| $\mathbf{B_{29}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{30}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{31}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{32}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{33}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{34}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{35}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{36}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{37}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{38}}$ | = | $\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{39}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Sn II |
| $\mathbf{B_{40}}$ | = | $- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (24k) | Sn II |
References
- J. L. Hodeau, J. Chenavas, and M. Marezio, The crystal structure of SnYb$_{3}$Rh$_{4}$Sn$_{12}$, a new ternary superconducting stannide, Solid State Commun. 36, 839–845 (1980), doi:10.1016/0038-1098(80)90125-8.
- P. Bordet, D. E. Cox, G. P. Espinosa, J. L. Hodeau, and M. Marezio, Synchrotron X-ray powder diffraction study of the phase I' compound: SnLa$_{3}$Rh$_{4}$Sn$_{12}$, Solid State Commun. 78, 359–366 (1991), doi:10.1016/0038-1098(91)90684-N.
Found in
- R. Gumeniuk, M. Schöneich, K. O. Kvashnina, L. Akselrud, A. A. Tsirlin, M. Nicklas, W. Schnelle, O. Janson, Q. Zheng, C. Curfs, U. Burkhardt, U. Schwarz, and A. Leithe-Jasper, Intermetallic germanides with non-centrosymmetric structures derived from the Yb$_{3}$Rh$_{4}$Sn$_{13}$ type, Dalton Trans. 44, 5638–5651 (2015), doi:10.1039/C4DT03155E.
Prototype Generator
aflow --proto=A4B13C3_cP40_223_e_ak_c --params=$a,y_{4},z_{4}$