AFLOW Prototype: A2BC4_oP28_50_ij_ac_ijm
Prototype | : | La2NiO4 |
AFLOW prototype label | : | A2BC4_oP28_50_ij_ac_ijm |
Strukturbericht designation | : | None |
Pearson symbol | : | oP28 |
Space group number | : | 50 |
Space group symbol | : | $Pban$ |
AFLOW prototype command | : | aflow --proto=A2BC4_oP28_50_ij_ac_ijm --params=$a$,$b/a$,$c/a$,$y_{3}$,$y_{4}$,$y_{5}$,$y_{6}$,$x_{7}$,$y_{7}$,$z_{7}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} & \left(2a\right) & \text{Ni I} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} & \left(2a\right) & \text{Ni I} \\ \mathbf{B}_{3} & = & \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}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Ni II} \\ \mathbf{B}_{4} & = & \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}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Ni II} \\ \mathbf{B}_{5} & = & \frac{1}{4} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} & \left(4i\right) & \text{La I} \\ \mathbf{B}_{6} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{3}\right)b \, \mathbf{\hat{y}} & \left(4i\right) & \text{La I} \\ \mathbf{B}_{7} & = & \frac{3}{4} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} & \left(4i\right) & \text{La I} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3}\right) \, \mathbf{a}_{2} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)b \, \mathbf{\hat{y}} & \left(4i\right) & \text{La I} \\ \mathbf{B}_{9} & = & \frac{1}{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} & \left(4i\right) & \text{O I} \\ \mathbf{B}_{10} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{4}\right) \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{4}\right)b \, \mathbf{\hat{y}} & \left(4i\right) & \text{O I} \\ \mathbf{B}_{11} & = & \frac{3}{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} & \left(4i\right) & \text{O I} \\ \mathbf{B}_{12} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{4}\right) \, \mathbf{a}_{2} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)b \, \mathbf{\hat{y}} & \left(4i\right) & \text{O I} \\ \mathbf{B}_{13} & = & \frac{1}{4} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4j\right) & \text{La II} \\ \mathbf{B}_{14} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{5}\right)b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4j\right) & \text{La II} \\ \mathbf{B}_{15} & = & \frac{3}{4} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4j\right) & \text{La II} \\ \mathbf{B}_{16} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{5}\right)b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4j\right) & \text{La II} \\ \mathbf{B}_{17} & = & \frac{1}{4} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4j\right) & \text{O II} \\ \mathbf{B}_{18} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{6}\right)b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4j\right) & \text{O II} \\ \mathbf{B}_{19} & = & \frac{3}{4} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4j\right) & \text{O II} \\ \mathbf{B}_{20} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4j\right) & \text{O II} \\ \mathbf{B}_{21} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{O III} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{7}\right)b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{O III} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{7}\right)a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{O III} \\ \mathbf{B}_{24} & = & x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{7}\right)b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{O III} \\ \mathbf{B}_{25} & = & -x_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{O III} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{7}\right)b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{O III} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{O III} \\ \mathbf{B}_{28} & = & -x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{7}\right)b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8m\right) & \text{O III} \\ \end{array} \]