MgB2C2 Crystal Structure: A2B2C_oC80_64_efg_efg_df

Picture of Structure; Click for Big Picture
Prototype : MgB2C2
AFLOW prototype label : A2B2C_oC80_64_efg_efg_df
Strukturbericht designation : None
Pearson symbol : oC80
Space group number : 64
Space group symbol : $\mbox{Cmca}$
AFLOW prototype command : aflow --proto=A2B2C_oC80_64_efg_efg_df
--params=
$a$,$b/a$,$c/a$,$x_{1}$,$y_{2}$,$y_{3}$,$y_{4}$,$z_{4}$,$y_{5}$,$z_{5}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$


Base-centered Orthorhombic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \end{array} \]

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} + x_{1} \, \mathbf{a}_{2}& =& x_{1} \, a \, \mathbf{\hat{x}}& \left(8d\right) & \mbox{Mg I} \\ \mathbf{B}_{2} & =& \left(\frac12 - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac12 - x_{1}\right) \,\mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}} + \frac12 \,c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{Mg I} \\ \mathbf{B}_{3} & =& - x_{1} \, \mathbf{a}_{1} - x_{1} \, \mathbf{a}_{2}& =& - x_{1} \, a \, \mathbf{\hat{x}}& \left(8d\right) & \mbox{Mg I} \\ \mathbf{B}_{4} & =& \left(\frac12 + x_{1}\right) \, \mathbf{a}_{1} + \left(\frac12 + x_{1}\right) \,\mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \left(\frac12 + x_{1}\right) \, a \, \mathbf{\hat{x}} + \frac12 \,c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{Mg I} \\ \mathbf{B}_{5} & =& \left(\frac14 - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac14 + y_{2}\right) \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} + y_{2} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(8e\right) & \mbox{B I} \\ \mathbf{B}_{6} & =& \left(\frac14 + y_{2}\right) \, \mathbf{a}_{1} + \left(\frac14 - y_{2}\right) \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} - y_{2} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(8e\right) & \mbox{B I} \\ \mathbf{B}_{7} & =& \left(\frac34 + y_{2}\right) \, \mathbf{a}_{1} + \left(\frac34 - y_{2}\right) \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& \frac34 \, a \, \mathbf{\hat{x}} - y_{2} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(8e\right) & \mbox{B I} \\ \mathbf{B}_{8} & =& \left(\frac34 - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac34 + y_{2}\right) \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& \frac34 \, a \, \mathbf{\hat{x}} + y_{2} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(8e\right) & \mbox{B I} \\ \mathbf{B}_{9} & =& \left(\frac14 - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac14 + y_{3}\right) \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} + y_{3} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(8e\right) & \mbox{C I} \\ \mathbf{B}_{10} & =& \left(\frac14 + y_{3}\right) \, \mathbf{a}_{1} + \left(\frac14 - y_{3}\right) \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& \frac14 \, a \, \mathbf{\hat{x}} - y_{3} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(8e\right) & \mbox{C I} \\ \mathbf{B}_{11} & =& \left(\frac34 + y_{3}\right) \, \mathbf{a}_{1} + \left(\frac34 - y_{3}\right) \, \mathbf{a}_{2} + \frac34 \, \mathbf{a}_{3}& =& \frac34 \, a \, \mathbf{\hat{x}} - y_{3} \, b \, \mathbf{\hat{y}} + \frac34 \, c \mathbf{\hat{z}}& \left(8e\right) & \mbox{C I} \\ \mathbf{B}_{12} & =& \left(\frac34 - y_{3}\right) \, \mathbf{a}_{1} + \left(\frac34 + y_{3}\right) \, \mathbf{a}_{2} + \frac14 \, \mathbf{a}_{3}& =& \frac34 \, a \, \mathbf{\hat{x}} + y_{3} \, b \, \mathbf{\hat{y}} + \frac14 \, c \mathbf{\hat{z}}& \left(8e\right) & \mbox{C I} \\ \mathbf{B}_{13} & =& - y_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& y_{4} \, b \, \mathbf{\hat{y}} + z_{4} \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{B II} \\ \mathbf{B}_{14} & =& \left(\frac12 + y_{4}\right) \, \mathbf{a}_{1} + \left(\frac12 - y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - y_{4} \, b \, \mathbf{\hat{y}} + \left(\frac12 + z_{4}\right) \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{B II} \\ \mathbf{B}_{15} & =& \left(\frac12 - y_{4}\right) \, \mathbf{a}_{1} + \left(\frac12 + y_{4}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + y_{4} \, b \, \mathbf{\hat{y}} + \left(\frac12 - z_{4}\right) \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{B II} \\ \mathbf{B}_{16} & =& y_{4} \, \mathbf{a}_{1} - y_{4} \, \mathbf{a}_{2} - z_{4} \, \mathbf{a}_{3}& =& - y_{4} \, b \, \mathbf{\hat{y}} - z_{4} \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{B II} \\ \mathbf{B}_{17} & =& - y_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& y_{5} \, b \, \mathbf{\hat{y}} + z_{5} \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{C II} \\ \mathbf{B}_{18} & =& \left(\frac12 + y_{5}\right) \, \mathbf{a}_{1} + \left(\frac12 - y_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - y_{5} \, b \, \mathbf{\hat{y}} + \left(\frac12 + z_{5}\right) \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{C II} \\ \mathbf{B}_{19} & =& \left(\frac12 - y_{5}\right) \, \mathbf{a}_{1} + \left(\frac12 + y_{5}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{5}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + y_{5} \, b \, \mathbf{\hat{y}} + \left(\frac12 - z_{5}\right) \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{C II} \\ \mathbf{B}_{20} & =& y_{5} \, \mathbf{a}_{1} - y_{5} \, \mathbf{a}_{2} - z_{5} \, \mathbf{a}_{3}& =& - y_{5} \, b \, \mathbf{\hat{y}} - z_{5} \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{C II} \\ \mathbf{B}_{21} & =& - y_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& y_{6} \, b \, \mathbf{\hat{y}} + z_{6} \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{Mg II} \\ \mathbf{B}_{22} & =& \left(\frac12 + y_{6}\right) \, \mathbf{a}_{1} + \left(\frac12 - y_{6}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{6}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - y_{6} \, b \, \mathbf{\hat{y}} + \left(\frac12 + z_{6}\right) \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{Mg II} \\ \mathbf{B}_{23} & =& \left(\frac12 - y_{6}\right) \, \mathbf{a}_{1} + \left(\frac12 + y_{6}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{6}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + y_{6} \, b \, \mathbf{\hat{y}} + \left(\frac12 - z_{6}\right) \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{Mg II} \\ \mathbf{B}_{24} & =& y_{6} \, \mathbf{a}_{1} - y_{6} \, \mathbf{a}_{2} - z_{6} \, \mathbf{a}_{3}& =& - y_{6} \, b \, \mathbf{\hat{y}} - z_{6} \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{Mg II} \\ \mathbf{B}_{25} & =& \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7} + y_{7}\right) \, \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(16g\right) & \mbox{B III} \\ \mathbf{B}_{26} & =& \left(y_{7} - x_{7} + \frac12\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{7} - y_{7}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{7}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{7}\right) \, a \, \mathbf{\hat{x}}- y_{7} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{7}\right) \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{B III} \\ \mathbf{B}_{27} & =& \left(\frac12 - x_{7} - y_{7}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{7} + y_{7}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{7}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{7}\right) \, a \, \mathbf{\hat{x}}+ y_{7} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{7}\right) \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{B III} \\ \mathbf{B}_{28} & =& \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1} + \left(x_{7} - y_{7}\right) \, \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(16g\right) & \mbox{B III} \\ \mathbf{B}_{29} & =& \left(y_{7} - x_{7}\right) \, \mathbf{a}_{1} - \left(x_{7} + y_{7}\right) \, \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(16g\right) & \mbox{B III} \\ \mathbf{B}_{30} & =& \left(\frac12 + x_{7} - y_{7}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{7} + y_{7}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{7}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{7}\right) \, a \, \mathbf{\hat{x}}+ y_{7} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{7}\right) \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{B III} \\ \mathbf{B}_{31} & =& \left(\frac12 + x_{7} + y_{7} \right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{7} - y_{7}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{7}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{7}\right) \, a \, \mathbf{\hat{x}}- y_{7} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{7}\right) \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{B III} \\ \mathbf{B}_{32} & =& - \left(x_{7} + y_{7}\right) \, \mathbf{a}_{1} + \left(y_{7} - x_{7}\right) \, \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(16g\right) & \mbox{B III} \\ \mathbf{B}_{33} & =& \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8} + y_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& x_{8} \, a \, \mathbf{\hat{x}} + y_{8} \, b \, \mathbf{\hat{y}} + z_{8} \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{C III} \\ \mathbf{B}_{34} & =& \left(\frac12 + y_{8} - x_{8}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{8} - y_{8}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{8}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{8}\right) \, a \, \mathbf{\hat{x}}- y_{8} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{8}\right) \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{C III} \\ \mathbf{B}_{35} & =& \left(\frac12 - x_{8} - y_{8}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{8} + y_{8}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{8}\right) \, \mathbf{a}_{3}& =& \left(\frac12- x_{8}\right) \, a \, \mathbf{\hat{x}}+ y_{8} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{8}\right) \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{C III} \\ \mathbf{B}_{36} & =& \left(x_{8} + y_{8}\right) \, \mathbf{a}_{1} + \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2} - z_{8} \, \mathbf{a}_{3}& =& x_{8} \, a \, \mathbf{\hat{x}} - y_{8} \, b \, \mathbf{\hat{y}} - z_{8} \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{C III} \\ \mathbf{B}_{37} & =& \left(y_{8} - x_{8}\right) \, \mathbf{a}_{1} - \left(x_{8} + y_{8}\right) \, \mathbf{a}_{2} - z_{8} \, \mathbf{a}_{3}& =& - x_{8} \, a \, \mathbf{\hat{x}} - y_{8} \, b \, \mathbf{\hat{y}} - z_{8} \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{C III} \\ \mathbf{B}_{38} & =& \left(\frac12 + x_{8} - y_{8}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{8} + y_{8}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{8}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{8}\right) \, a \, \mathbf{\hat{x}}+ y_{8} \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_{8}\right) \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{C III} \\ \mathbf{B}_{39} & =& \left(\frac12 + x_{8} + y_{8}\right) \, \mathbf{a}_{1}+ \left(\frac12 + x_{8} - y_{8}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{8}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{8}\right) \, a \, \mathbf{\hat{x}}- y_{8} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{8}\right) \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{C III} \\ \mathbf{B}_{40} & =& - \left(x_{8} + y_{8}\right) \, \mathbf{a}_{1} + \left(y_{8} - x_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& - x_{8} \, a \, \mathbf{\hat{x}} + y_{8} \, b \, \mathbf{\hat{y}} + z_{8} \, c \mathbf{\hat{z}}& \left(16g\right) & \mbox{C III} \\ \end{array} \]

References

Geometry files


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