ThBC Structure: ABC_tP24_91_d_d_d

Picture of Structure; Click for Big Picture
Prototype : ThBC
AFLOW prototype label : ABC_tP24_91_d_d_d
Strukturbericht designation : None
Pearson symbol : tP24
Space group number : 91
Space group symbol : $P4_{1}22$
AFLOW prototype command : aflow --proto=ABC_tP24_91_d_d_d
--params=
$a$,$c/a$,$x_{1}$,$y_{1}$,$z_{1}$,$x_{2}$,$y_{2}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$


Simple Tetragonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + y_{1}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{B} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}}-y_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{B} \\ \mathbf{B}_{3} & = & -y_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \left(\frac{1}{4} +z_{1}\right) \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{B} \\ \mathbf{B}_{4} & = & y_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{1}\right) \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{B} \\ \mathbf{B}_{5} & = & -x_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + y_{1}a \, \mathbf{\hat{y}}-z_{1}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{B} \\ \mathbf{B}_{6} & = & x_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{1}\right) \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}}-y_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{1}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{B} \\ \mathbf{B}_{7} & = & y_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \left(\frac{3}{4} - z_{1}\right) \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} - z_{1}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{B} \\ \mathbf{B}_{8} & = & -y_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \left(\frac{1}{4} - z_{1}\right) \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{1}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{B} \\ \mathbf{B}_{9} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{C} \\ \mathbf{B}_{10} & = & -x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{C} \\ \mathbf{B}_{11} & = & -y_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{C} \\ \mathbf{B}_{12} & = & y_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{C} \\ \mathbf{B}_{13} & = & -x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{C} \\ \mathbf{B}_{14} & = & x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{C} \\ \mathbf{B}_{15} & = & y_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} - z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{C} \\ \mathbf{B}_{16} & = & -y_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{4} - z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{C} \\ \mathbf{B}_{17} & = & x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Th} \\ \mathbf{B}_{18} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Th} \\ \mathbf{B}_{19} & = & -y_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{4} +z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Th} \\ \mathbf{B}_{20} & = & y_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Th} \\ \mathbf{B}_{21} & = & -x_{3} \, \mathbf{a}_{1} + y_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Th} \\ \mathbf{B}_{22} & = & x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{3}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Th} \\ \mathbf{B}_{23} & = & y_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{3}{4} - z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} - z_{3}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Th} \\ \mathbf{B}_{24} & = & -y_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{4} - z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{3}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{Th} \\ \end{array} \]

References

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=ABC_tP24_91_d_d_d --params=

Species:

Running:

Output: