ScRh$_{6}$P$_{4}$ Structure: A4B6C_hP11_143_ad_2d_b-001
| Prototype | P$_{4}$Rh$_{6}$Sc |
| AFLOW prototype label | A4B6C_hP11_143_ad_2d_b-001 |
| ICSD | 182778 |
| Pearson symbol | hP11 |
| Space group number | 143 |
| Space group symbol | $P3$ |
| AFLOW prototype command |
aflow --proto=A4B6C_hP11_143_ad_2d_b-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
LuRh$_{6}$P$_{4}$, YbRh$_{6}$P$_{4}$
- (Pfannenschmidt, 2011) place this structure in space group $P3$ #143, but they find the $z$ coordinates of the atoms on the (3d) site all close to 0 or 1/2. As a result, the default tolerance of AFLOW places this structure in space group $P\overline{6}m2$ #187. It is likely that first-principles calculations will converge to the higher-symmetry space group.
- The reported experimental structure may be recovered using
- aflow --proto=A4B6C_hP11_143_ad_2d_b:P:Rh:Sc --params=a,c/a,z$_{1}$,z$_{2}$,x$_{3}$,y$_{3}$,z$_{3}$,x$_{4}$,y$_{4}$,z$_{4}$,x$_{5}$,y$_{5}$,z$_{5}$ --tolerance=0.001.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (1a) | P I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (1b) | Sc I |
| $\mathbf{B_{3}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (3d) | P II |
| $\mathbf{B_{4}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - 2 y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (3d) | P II |
| $\mathbf{B_{5}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (3d) | P II |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (3d) | Rh I |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - 2 y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (3d) | Rh I |
| $\mathbf{B_{8}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (3d) | Rh I |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (3d) | Rh II |
| $\mathbf{B_{10}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (3d) | Rh II |
| $\mathbf{B_{11}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (3d) | Rh II |
References
- U. Pfannenschmidt, U. C. Rodewald, and R. Pöttgen, Bismuth flux crystal growth of RERh$_{6}$P$_{4}$ (RE = Sc, Yb, Lu): new phosphides with a superstructure of the LiCo$_{6}$P$_{4}$ type, Monatsh. Chem. 142, 219–224 (2011), doi:10.1007/s00706-011-0450-5.
- H. T. Stokes and D. M. Hatch, {\em FINDSYM}: program for identifying the space-group symmetry of a crystal, J. Appl. Crystallogr. 38, 237–238 (2005), doi:10.1107/S0021889804031528.
- D. Hicks, C. Oses, E. Gossett, G. Gomez, R. H. Taylor, C. Toher, M. J. Mehl, O. Levy, and S. Curtarolo, AFLOW-SYM: platform for the complete, automatic and self-consistent symmetry analysis of crystals, Acta Crystallogr. Sect. A 74, 184–203 (2018), doi:10.1107/S2053273318003066.
- A. L. Speck, Single-crystal structure validation with the program PLATON, J. Appl. Crystallogr. 36, 7–13 (2003), doi:10.1107/S0021889802022112.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A4B6C_hP11_143_ad_2d_b --params=$a,c/a,z_{1},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5}$