AFLOW Prototype: ABCD3_oI48_73_d_e_e_ef
Prototype | : | KAg[CO3] |
AFLOW prototype label | : | ABCD3_oI48_73_d_e_e_ef |
Strukturbericht designation | : | None |
Pearson symbol | : | oI48 |
Space group number | : | 73 |
Space group symbol | : | $Ibca$ |
AFLOW prototype command | : | aflow --proto=ABCD3_oI48_73_d_e_e_ef --params=$a$,$b/a$,$c/a$,$y_{1}$,$z_{2}$,$z_{3}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & y_{1} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{1}b \, \mathbf{\hat{y}} & \left(8d\right) & \text{Ag} \\ \mathbf{B}_{2} & = & \left(\frac{1}{2} - y_{1}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}}-y_{1}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{Ag} \\ \mathbf{B}_{3} & = & -y_{1} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} - y_{1}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}}-y_{1}b \, \mathbf{\hat{y}} & \left(8d\right) & \text{Ag} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} +y_{1}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} +y_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{1}\right)b \, \mathbf{\hat{y}} & \left(8d\right) & \text{Ag} \\ \mathbf{B}_{5} & = & \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{C} \\ \mathbf{B}_{6} & = & \left(\frac{1}{4} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{C} \\ \mathbf{B}_{7} & = & \left(\frac{3}{4} - z_{2}\right) \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{C} \\ \mathbf{B}_{8} & = & \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8e\right) & \text{C} \\ \mathbf{B}_{9} & = & \left(\frac{1}{4} +z_{3}\right) \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{K} \\ \mathbf{B}_{10} & = & \left(\frac{1}{4} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{K} \\ \mathbf{B}_{11} & = & \left(\frac{3}{4} - z_{3}\right) \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{K} \\ \mathbf{B}_{12} & = & \left(\frac{3}{4} +z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(8e\right) & \text{K} \\ \mathbf{B}_{13} & = & \left(\frac{1}{4} +z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{14} & = & \left(\frac{1}{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{15} & = & \left(\frac{3}{4} - z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{16} & = & \left(\frac{3}{4} +z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(8e\right) & \text{O I} \\ \mathbf{B}_{17} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{O II} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} - y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{5}\right)b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{O II} \\ \mathbf{B}_{19} & = & \left(y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5} + y_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{5}\right)a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{O II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{5}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \text{O II} \\ \mathbf{B}_{21} & = & \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{O II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +y_{5} - z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} + y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{5}\right)b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{O II} \\ \mathbf{B}_{23} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5} - y_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16f\right) & \text{O II} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} +y_{5} + z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5} + z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \text{O II} \\ \end{array} \]