Nd$_{3}$Ni$_{29}$Si$_{4}$B$_{10}$: A10B3C29D4_tP92_129_2cij_bd_c3i2jk_i-001
| Prototype | B$_{10}$Nd$_{3}$Ni$_{29}$Si$_{4}$ |
| AFLOW prototype label | A10B3C29D4_tP92_129_2cij_bd_c3i2jk_i-001 |
| ICSD | 86052 |
| CCDC | 1645957 |
| Pearson symbol | tP92 |
| Space group number | 129 |
| Space group symbol | $P4/nmm$ |
| AFLOW prototype command |
aflow --proto=A10B3C29D4_tP92_129_2cij_bd_c3i2jk_i-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}$ |
Other compounds with this structure
Ce$_{3}$Ni$_{30}$B$_{20}$, La$_{3}$Ni$_{30}$B$_{20}$
- In the experimental sample the Si (8i) site contained 4% nickel, and the Ni I (4c) site contained 16.8% silicon.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Nd I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Nd I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2c) | B I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2c) | B I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2c) | B II |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2c) | B II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2c) | Ni I |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2c) | Ni I |
| $\mathbf{B_{9}}$ | = | $0$ | = | $0$ | (4d) | Nd II |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4d) | Nd II |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (4d) | Nd II |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4d) | Nd II |
| $\mathbf{B_{13}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8i) | B III |
| $\mathbf{B_{14}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8i) | B III |
| $\mathbf{B_{15}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8i) | B III |
| $\mathbf{B_{16}}$ | = | $y_{6} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8i) | B III |
| $\mathbf{B_{17}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8i) | B III |
| $\mathbf{B_{18}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8i) | B III |
| $\mathbf{B_{19}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8i) | B III |
| $\mathbf{B_{20}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8i) | B III |
| $\mathbf{B_{21}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8i) | Ni II |
| $\mathbf{B_{22}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8i) | Ni II |
| $\mathbf{B_{23}}$ | = | $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8i) | Ni II |
| $\mathbf{B_{24}}$ | = | $y_{7} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8i) | Ni II |
| $\mathbf{B_{25}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8i) | Ni II |
| $\mathbf{B_{26}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8i) | Ni II |
| $\mathbf{B_{27}}$ | = | $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8i) | Ni II |
| $\mathbf{B_{28}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8i) | Ni II |
| $\mathbf{B_{29}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Ni III |
| $\mathbf{B_{30}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Ni III |
| $\mathbf{B_{31}}$ | = | $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Ni III |
| $\mathbf{B_{32}}$ | = | $y_{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Ni III |
| $\mathbf{B_{33}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Ni III |
| $\mathbf{B_{34}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Ni III |
| $\mathbf{B_{35}}$ | = | $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Ni III |
| $\mathbf{B_{36}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | Ni III |
| $\mathbf{B_{37}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | Ni IV |
| $\mathbf{B_{38}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | Ni IV |
| $\mathbf{B_{39}}$ | = | $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | Ni IV |
| $\mathbf{B_{40}}$ | = | $y_{9} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8i) | Ni IV |
| $\mathbf{B_{41}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | Ni IV |
| $\mathbf{B_{42}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | Ni IV |
| $\mathbf{B_{43}}$ | = | $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | Ni IV |
| $\mathbf{B_{44}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8i) | Ni IV |
| $\mathbf{B_{45}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8i) | Si I |
| $\mathbf{B_{46}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8i) | Si I |
| $\mathbf{B_{47}}$ | = | $- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8i) | Si I |
| $\mathbf{B_{48}}$ | = | $y_{10} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8i) | Si I |
| $\mathbf{B_{49}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8i) | Si I |
| $\mathbf{B_{50}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8i) | Si I |
| $\mathbf{B_{51}}$ | = | $\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8i) | Si I |
| $\mathbf{B_{52}}$ | = | $- y_{10} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8i) | Si I |
| $\mathbf{B_{53}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8j) | B IV |
| $\mathbf{B_{54}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8j) | B IV |
| $\mathbf{B_{55}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8j) | B IV |
| $\mathbf{B_{56}}$ | = | $x_{11} \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8j) | B IV |
| $\mathbf{B_{57}}$ | = | $- x_{11} \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8j) | B IV |
| $\mathbf{B_{58}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8j) | B IV |
| $\mathbf{B_{59}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8j) | B IV |
| $\mathbf{B_{60}}$ | = | $- x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8j) | B IV |
| $\mathbf{B_{61}}$ | = | $x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8j) | Ni V |
| $\mathbf{B_{62}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8j) | Ni V |
| $\mathbf{B_{63}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8j) | Ni V |
| $\mathbf{B_{64}}$ | = | $x_{12} \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8j) | Ni V |
| $\mathbf{B_{65}}$ | = | $- x_{12} \, \mathbf{a}_{1}+\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (8j) | Ni V |
| $\mathbf{B_{66}}$ | = | $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (8j) | Ni V |
| $\mathbf{B_{67}}$ | = | $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (8j) | Ni V |
| $\mathbf{B_{68}}$ | = | $- x_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (8j) | Ni V |
| $\mathbf{B_{69}}$ | = | $x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ni VI |
| $\mathbf{B_{70}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ni VI |
| $\mathbf{B_{71}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ni VI |
| $\mathbf{B_{72}}$ | = | $x_{13} \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ni VI |
| $\mathbf{B_{73}}$ | = | $- x_{13} \, \mathbf{a}_{1}+\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ni VI |
| $\mathbf{B_{74}}$ | = | $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ni VI |
| $\mathbf{B_{75}}$ | = | $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ni VI |
| $\mathbf{B_{76}}$ | = | $- x_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8j) | Ni VI |
| $\mathbf{B_{77}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{78}}$ | = | $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{79}}$ | = | $- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{80}}$ | = | $y_{14} \, \mathbf{a}_{1}- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{81}}$ | = | $- x_{14} \, \mathbf{a}_{1}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{82}}$ | = | $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{83}}$ | = | $\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{84}}$ | = | $- y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{85}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{86}}$ | = | $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{87}}$ | = | $\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{88}}$ | = | $- y_{14} \, \mathbf{a}_{1}+\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}+a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{89}}$ | = | $x_{14} \, \mathbf{a}_{1}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{90}}$ | = | $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{91}}$ | = | $- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
| $\mathbf{B_{92}}$ | = | $y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16k) | Ni VII |
References
- H. Zhang, E. Wu, S. J. Campbell, S. J. Kennedy, H.-S. Li, A. J. Studer, S. R. Bulcock, and A. D. Rae, Structural study of the rare-earth transition-metal intermetallic compound Nd$_{3}$Ni$_{29}$Si$_{4}$B$_{10}$, J. Alloys Compd. 278, 239–245 (1998), doi:10.1016/S0925-8388(98)00596-9.
Found in
- M. F. Debbas, T. Suzuki, and J. G. Checkelsky, Anomalous order in $R_{3}$Ni$_{30}$B$_{10}$, Phys. Rev. B 111, 155102 (2025), doi:10.1103/PhysRevB.111.155102.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A10B3C29D4_tP92_129_2cij_bd_c3i2jk_i --params=$a,c/a,z_{2},z_{3},z_{4},y_{6},z_{6},y_{7},z_{7},y_{8},z_{8},y_{9},z_{9},y_{10},z_{10},x_{11},z_{11},x_{12},z_{12},x_{13},z_{13},x_{14},y_{14},z_{14}$