Gd$_{4}$RhIn Structure: A4BC_cF96_216_efg_e_e-001
| Prototype | Gd$_{4}$InRh |
| AFLOW prototype label | A4BC_cF96_216_efg_e_e-001 |
| ICSD | 417515 |
| Pearson symbol | cF96 |
| Space group number | 216 |
| Space group symbol | $F\overline{4}3m$ |
| AFLOW prototype command |
aflow --proto=A4BC_cF96_216_efg_e_e-001
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}$ |
Other compounds with this structure
Ca$_{4}$AgMg, Ca$_{4}$AuMg, Ca$_{4}$PdMg, Ce$_{4}$RuMg, Dy$_{4}$CoCd, Dy$_{4}$CoMg, Dy$_{4}$PdAl, Dy$_{4}$PdMg, Dy$_{4}$PtAl, Dy$_{4}$PtMg, Dy$_{4}$RhCd, Dy$_{4}$RhIn, Er$_{4}$CoMg, Er$_{4}$PdAl, Er$_{4}$PdMg, Er$_{4}$PtAl, Er$_{4}$PtMg, Er$_{4}$RhAl, Er$_{4}$RhIn, Eu$_{4}$AuMg, Eu$_{4}$PdMg, Eu$_{4}$PtMg, Gd$_{4}$CoMg, Gd$_{4}$PdAl, Gd$_{4}$PtAl, Gd$_{4}$RhAl, Gd$_{4}$RhIn, Ho$_{4}$CoCd, Ho$_{4}$CoMg, Ho$_{4}$PdAl, Ho$_{4}$PdMg, Ho$_{4}$PtAl, Ho$_{4}$PtMg, Ho$_{4}$RhAl, Ho$_{4}$RhCd, Ho$_{4}$RhIn, La$_{4}$CoMg, Lu$_{4}$PdAl, Lu$_{4}$PdMg, Lu$_{4}$PtAl, Lu$_{4}$PtMg, Lu$_{4}$RhIn, Nd$_{4}$CdIr, Nd$_{4}$CoMg, Pr$_{4}$CoMg, Sm$_{4}$CoMg, Sm$_{4}$PdAl, Sm$_{4}$PdMg, Sm$_{4}$PtAl, Tb$_{4}$CoCd, Tb$_{4}$CoMg, Tb$_{4}$PdAl, Tb$_{4}$PtAl, Tb$_{4}$PtMg, Tb$_{4}$RhAl, Tb$_{4}$RhCd, Tb$_{4}$RhIn, Tm$_{4}$CoMg, Tm$_{4}$PdAl, Tm$_{4}$PdMg, Tm$_{4}$PtAl, Tm$_{4}$PtMg, Tm$_{4}$RhIn, Y$_{4}$CoMg, Y$_{4}$PdAl, Y$_{4}$PtAl, Yb$_{4}$AgMg, Yb$_{4}$AuMg, Yb$_{4}$PdMg, Yb$_{4}$PtMg
- The ICSD gives Dy$_{4}$CoCd as the prototype for this structure, but even (Doǧan, 2007), which defines that structure, designates Gd$_{4}$RhIn as the prototype, so we use that compound.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (16e) | Gd I |
| $\mathbf{B_{2}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}- 3 x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (16e) | Gd I |
| $\mathbf{B_{3}}$ | = | $x_{1} \, \mathbf{a}_{1}- 3 x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (16e) | Gd I |
| $\mathbf{B_{4}}$ | = | $- 3 x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (16e) | Gd I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16e) | In I |
| $\mathbf{B_{6}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- 3 x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16e) | In I |
| $\mathbf{B_{7}}$ | = | $x_{2} \, \mathbf{a}_{1}- 3 x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16e) | In I |
| $\mathbf{B_{8}}$ | = | $- 3 x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16e) | In I |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Rh I |
| $\mathbf{B_{10}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- 3 x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Rh I |
| $\mathbf{B_{11}}$ | = | $x_{3} \, \mathbf{a}_{1}- 3 x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Rh I |
| $\mathbf{B_{12}}$ | = | $- 3 x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (16e) | Rh I |
| $\mathbf{B_{13}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}$ | (24f) | Gd II |
| $\mathbf{B_{14}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}$ | (24f) | Gd II |
| $\mathbf{B_{15}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{y}}$ | (24f) | Gd II |
| $\mathbf{B_{16}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{y}}$ | (24f) | Gd II |
| $\mathbf{B_{17}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{z}}$ | (24f) | Gd II |
| $\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{z}}$ | (24f) | Gd II |
| $\mathbf{B_{19}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Gd III |
| $\mathbf{B_{20}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Gd III |
| $\mathbf{B_{21}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Gd III |
| $\mathbf{B_{22}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Gd III |
| $\mathbf{B_{23}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24g) | Gd III |
| $\mathbf{B_{24}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Gd III |
References
- R. Zaremba, U. C. Rodewald, R.-D. Hoffmann, and R. Pöttgen, The Rare Earth Metal-Rich Indides RE$_{4}$RhIn (RE = Gd–Tm, Lu), Monatsh. Chem. 138, 523–528 (2007), doi:10.1007/s00706-007-0663-9.
- A. Doǧan, S. Rayaprol, and R. Pöttgen, Structure and magnetic properties of RE$_{4}$CoCd and RE$_{4}$RhCd (RE = Tb, Dy, Ho), J. Phys.: Condens. Matter 19, 076213 (2007), doi:10.1088/0953-8984/19/7/076213.
Prototype Generator
aflow --proto=A4BC_cF96_216_efg_e_e --params=$a,x_{1},x_{2},x_{3},x_{4},x_{5}$