Orthorhombic Sr$_{4}$Ru$_{3}$O$_{10}$ Structure: A10B3C4_oP68_55_2e2fgh2i_adef_2e2f-001
| Prototype | O$_{10}$Ru$_{3}$Sr$_{4}$ |
| AFLOW prototype label | A10B3C4_oP68_55_2e2fgh2i_adef_2e2f-001 |
| ICSD | 96729 |
| Pearson symbol | oP68 |
| Space group number | 55 |
| Space group symbol | $Pbam$ |
| AFLOW prototype command |
aflow --proto=A10B3C4_oP68_55_2e2fgh2i_adef_2e2f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}, \allowbreak z_{9}, \allowbreak z_{10}, \allowbreak z_{11}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}$ |
- This structure consists of triple-layer ruthenate structures separated by 2.37Å from each other. In the $Pbam$ #55 space group shown here there are two inequivalent stacks in the orthorhombic cell.
- This cell is very problematic. (Crawford, 2002) note that the x-ray scattering intensities are pseudo body-centered, but found that refining this structure in a body-centered cell with space group $Bbcm$ ($Cmca$ #64 in our standard orientation) led to non-positive definite thermal parameters. In that case there is only one triple-layer stack in the primitive cell, and the two stacks in the conventional orthorhombic cell are equivalent.
- If we use AFLOW with its default tolerance the structure also resolves into the smaller unit cell. The current cell can be recovered by using a smaller tolerance:
- aflow --proto=A10B3C4_oC68_64_2dfg_ad_2d:O:Ru:Sr --params=a,b/a,c/a,x$_{2}$,z$_{3}$,z$_{4}$,z$_{5}$,z$_{6}$,z$_{7}$,z$_{8}$,z$_{9}$,z$_{10}$,z$_{11}$,z$_{12}$,x$_{13}$,y$_{13}$,x$_{14}$,y$_{14}$,x$_{15}$,y$_{15}$,z$_{15}$,x$_{16}$,y$_{16}$,z$_{16}$ --tolerance=0.001 .
- Note that the lattice constants in the CIF for ICSD 96729 do not agree with the lattice constants in (Crawford, 2002), although the atomic positions are the same.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ru I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2a) | Ru I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Ru II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2d) | Ru II |
| $\mathbf{B_{5}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{7}}$ | = | $- z_{3} \, \mathbf{a}_{3}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{9}}$ | = | $z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O II |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O II |
| $\mathbf{B_{11}}$ | = | $- z_{4} \, \mathbf{a}_{3}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O II |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4e) | O II |
| $\mathbf{B_{13}}$ | = | $z_{5} \, \mathbf{a}_{3}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Ru III |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Ru III |
| $\mathbf{B_{15}}$ | = | $- z_{5} \, \mathbf{a}_{3}$ | = | $- c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Ru III |
| $\mathbf{B_{16}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4e) | Ru III |
| $\mathbf{B_{17}}$ | = | $z_{6} \, \mathbf{a}_{3}$ | = | $c z_{6} \,\mathbf{\hat{z}}$ | (4e) | Sr I |
| $\mathbf{B_{18}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (4e) | Sr I |
| $\mathbf{B_{19}}$ | = | $- z_{6} \, \mathbf{a}_{3}$ | = | $- c z_{6} \,\mathbf{\hat{z}}$ | (4e) | Sr I |
| $\mathbf{B_{20}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4e) | Sr I |
| $\mathbf{B_{21}}$ | = | $z_{7} \, \mathbf{a}_{3}$ | = | $c z_{7} \,\mathbf{\hat{z}}$ | (4e) | Sr II |
| $\mathbf{B_{22}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (4e) | Sr II |
| $\mathbf{B_{23}}$ | = | $- z_{7} \, \mathbf{a}_{3}$ | = | $- c z_{7} \,\mathbf{\hat{z}}$ | (4e) | Sr II |
| $\mathbf{B_{24}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4e) | Sr II |
| $\mathbf{B_{25}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4f) | O III |
| $\mathbf{B_{26}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (4f) | O III |
| $\mathbf{B_{27}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (4f) | O III |
| $\mathbf{B_{28}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (4f) | O III |
| $\mathbf{B_{29}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (4f) | O IV |
| $\mathbf{B_{30}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{9} \,\mathbf{\hat{z}}$ | (4f) | O IV |
| $\mathbf{B_{31}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (4f) | O IV |
| $\mathbf{B_{32}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (4f) | O IV |
| $\mathbf{B_{33}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (4f) | Ru IV |
| $\mathbf{B_{34}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{10} \,\mathbf{\hat{z}}$ | (4f) | Ru IV |
| $\mathbf{B_{35}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (4f) | Ru IV |
| $\mathbf{B_{36}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (4f) | Ru IV |
| $\mathbf{B_{37}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (4f) | Sr III |
| $\mathbf{B_{38}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{11} \,\mathbf{\hat{z}}$ | (4f) | Sr III |
| $\mathbf{B_{39}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (4f) | Sr III |
| $\mathbf{B_{40}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (4f) | Sr III |
| $\mathbf{B_{41}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (4f) | Sr IV |
| $\mathbf{B_{42}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{12} \,\mathbf{\hat{z}}$ | (4f) | Sr IV |
| $\mathbf{B_{43}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (4f) | Sr IV |
| $\mathbf{B_{44}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{12} \,\mathbf{\hat{z}}$ | (4f) | Sr IV |
| $\mathbf{B_{45}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}$ | = | $a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}$ | (4g) | O V |
| $\mathbf{B_{46}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}$ | (4g) | O V |
| $\mathbf{B_{47}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (4g) | O V |
| $\mathbf{B_{48}}$ | = | $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (4g) | O V |
| $\mathbf{B_{49}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O VI |
| $\mathbf{B_{50}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O VI |
| $\mathbf{B_{51}}$ | = | $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O VI |
| $\mathbf{B_{52}}$ | = | $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O VI |
| $\mathbf{B_{53}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{54}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{55}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{56}}$ | = | $\left(x_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{57}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{58}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{59}}$ | = | $\left(x_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{60}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{61}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8i) | O VIII |
| $\mathbf{B_{62}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8i) | O VIII |
| $\mathbf{B_{63}}$ | = | $- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8i) | O VIII |
| $\mathbf{B_{64}}$ | = | $\left(x_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{16} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $a \left(x_{16} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8i) | O VIII |
| $\mathbf{B_{65}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8i) | O VIII |
| $\mathbf{B_{66}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8i) | O VIII |
| $\mathbf{B_{67}}$ | = | $\left(x_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{16} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a \left(x_{16} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8i) | O VIII |
| $\mathbf{B_{68}}$ | = | $- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b \left(y_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8i) | O VIII |
References
- M. K. Crawford, R. L. Harlow, W. Marshall, Z. Li, G. Cao, R. L. Lindstrom, Q. Huang, and J. W. Lynn, Structure and magnetism of single crystal Sr$_{4}$Ru$_{3}$O$_{10}$: A ferromagnetic triple-layer ruthenate, Phys. Rev. B 65, 214412 (2002), doi:10.1103/PhysRevB.65.214412.
Prototype Generator
aflow --proto=A10B3C4_oP68_55_2e2fgh2i_adef_2e2f --params=$a,b/a,c/a,z_{3},z_{4},z_{5},z_{6},z_{7},z_{8},z_{9},z_{10},z_{11},z_{12},x_{13},y_{13},x_{14},y_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16}$