Orthorhombic Co4Al13 Structure : A13B4_oP102_31_17a11b_8a2b

Picture of Structure; Click for Big Picture
Prototype : Al13Co4
AFLOW prototype label : A13B4_oP102_31_17a11b_8a2b
Strukturbericht designation : None
Pearson symbol : oP102
Space group number : 31
Space group symbol : $Pmn2_{1}$
AFLOW prototype command : aflow --proto=A13B4_oP102_31_17a11b_8a2b
--params=
$a$,$b/a$,$c/a$,$y_{1}$,$z_{1}$,$y_{2}$,$z_{2}$,$y_{3}$,$z_{3}$,$y_{4}$,$z_{4}$,$y_{5}$,$z_{5}$,$y_{6}$,$z_{6}$,$y_{7}$,$z_{7}$,$y_{8}$,$z_{8}$,$y_{9}$,$z_{9}$,$y_{10}$,$z_{10}$,$y_{11}$,$z_{11}$,$y_{12}$,$z_{12}$,$y_{13}$,$z_{13}$,$y_{14}$,$z_{14}$,$y_{15}$,$z_{15}$,$y_{16}$,$z_{16}$,$y_{17}$,$z_{17}$,$y_{18}$,$z_{18}$,$y_{19}$,$z_{19}$,$y_{20}$,$z_{20}$,$y_{21}$,$z_{21}$,$y_{22}$,$z_{22}$,$y_{23}$,$z_{23}$,$y_{24}$,$z_{24}$,$y_{25}$,$z_{25}$,$x_{26}$,$y_{26}$,$z_{26}$,$x_{27}$,$y_{27}$,$z_{27}$,$x_{28}$,$y_{28}$,$z_{28}$,$x_{29}$,$y_{29}$,$z_{29}$,$x_{30}$,$y_{30}$,$z_{30}$,$x_{31}$,$y_{31}$,$z_{31}$,$x_{32}$,$y_{32}$,$z_{32}$,$x_{33}$,$y_{33}$,$z_{33}$,$x_{34}$,$y_{34}$,$z_{34}$,$x_{35}$,$y_{35}$,$z_{35}$,$x_{36}$,$y_{36}$,$z_{36}$,$x_{37}$,$y_{37}$,$z_{37}$,$x_{38}$,$y_{38}$,$z_{38}$


  • Space group $Pmn2_{1}$ #31 allows an arbitrary choice for the origin of the $z$–axis. We follow (Grin, 1994) and set the $z_{25} = 0$.
  • If we allow a tolerance of 0.25 Å for AFLOW-SYM and 0.6 Å in the atomic positions for FINDSYM, the symmetry is classified as $Pnnm$ #58.

Simple Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & y_{1}b \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{1}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al I} \\ \mathbf{B}_{3} & = & y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al II} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{2}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al II} \\ \mathbf{B}_{5} & = & y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al III} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al III} \\ \mathbf{B}_{7} & = & y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al IV} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al IV} \\ \mathbf{B}_{9} & = & y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al V} \\ \mathbf{B}_{10} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al V} \\ \mathbf{B}_{11} & = & y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VI} \\ \mathbf{B}_{12} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VI} \\ \mathbf{B}_{13} & = & y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VII} \\ \mathbf{B}_{14} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VII} \\ \mathbf{B}_{15} & = & y_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VIII} \\ \mathbf{B}_{16} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VIII} \\ \mathbf{B}_{17} & = & y_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al IX} \\ \mathbf{B}_{18} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al IX} \\ \mathbf{B}_{19} & = & y_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al X} \\ \mathbf{B}_{20} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al X} \\ \mathbf{B}_{21} & = & y_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XI} \\ \mathbf{B}_{22} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XI} \\ \mathbf{B}_{23} & = & y_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XII} \\ \mathbf{B}_{24} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{12} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{12}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{12}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XII} \\ \mathbf{B}_{25} & = & y_{13} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XIII} \\ \mathbf{B}_{26} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{13} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{13}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{13}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XIII} \\ \mathbf{B}_{27} & = & y_{14} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XIV} \\ \mathbf{B}_{28} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{14} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{14}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{14}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XIV} \\ \mathbf{B}_{29} & = & y_{15} \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XV} \\ \mathbf{B}_{30} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{15} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{15}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{15}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XV} \\ \mathbf{B}_{31} & = & y_{16} \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3} & = & y_{16}b \, \mathbf{\hat{y}} + z_{16}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XVI} \\ \mathbf{B}_{32} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{16} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{16}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{16}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{16}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XVI} \\ \mathbf{B}_{33} & = & y_{17} \, \mathbf{a}_{2} + z_{17} \, \mathbf{a}_{3} & = & y_{17}b \, \mathbf{\hat{y}} + z_{17}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XVII} \\ \mathbf{B}_{34} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{17} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{17}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{17}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{17}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XVII} \\ \mathbf{B}_{35} & = & y_{18} \, \mathbf{a}_{2} + z_{18} \, \mathbf{a}_{3} & = & y_{18}b \, \mathbf{\hat{y}} + z_{18}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co I} \\ \mathbf{B}_{36} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{18} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{18}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{18}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{18}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co I} \\ \mathbf{B}_{37} & = & y_{19} \, \mathbf{a}_{2} + z_{19} \, \mathbf{a}_{3} & = & y_{19}b \, \mathbf{\hat{y}} + z_{19}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co II} \\ \mathbf{B}_{38} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{19} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{19}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{19}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{19}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co II} \\ \mathbf{B}_{39} & = & y_{20} \, \mathbf{a}_{2} + z_{20} \, \mathbf{a}_{3} & = & y_{20}b \, \mathbf{\hat{y}} + z_{20}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co III} \\ \mathbf{B}_{40} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{20} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{20}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{20}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{20}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co III} \\ \mathbf{B}_{41} & = & y_{21} \, \mathbf{a}_{2} + z_{21} \, \mathbf{a}_{3} & = & y_{21}b \, \mathbf{\hat{y}} + z_{21}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co IV} \\ \mathbf{B}_{42} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{21} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{21}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{21}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{21}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co IV} \\ \mathbf{B}_{43} & = & y_{22} \, \mathbf{a}_{2} + z_{22} \, \mathbf{a}_{3} & = & y_{22}b \, \mathbf{\hat{y}} + z_{22}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co V} \\ \mathbf{B}_{44} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{22} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{22}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{22}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{22}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co V} \\ \mathbf{B}_{45} & = & y_{23} \, \mathbf{a}_{2} + z_{23} \, \mathbf{a}_{3} & = & y_{23}b \, \mathbf{\hat{y}} + z_{23}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VI} \\ \mathbf{B}_{46} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{23} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{23}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{23}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{23}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VI} \\ \mathbf{B}_{47} & = & y_{24} \, \mathbf{a}_{2} + z_{24} \, \mathbf{a}_{3} & = & y_{24}b \, \mathbf{\hat{y}} + z_{24}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VII} \\ \mathbf{B}_{48} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{24} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{24}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{24}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{24}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VII} \\ \mathbf{B}_{49} & = & y_{25} \, \mathbf{a}_{2} + z_{25} \, \mathbf{a}_{3} & = & y_{25}b \, \mathbf{\hat{y}} + z_{25}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VIII} \\ \mathbf{B}_{50} & = & \frac{1}{2} \, \mathbf{a}_{1}-y_{25} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{25}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{25}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{25}\right)c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VIII} \\ \mathbf{B}_{51} & = & x_{26} \, \mathbf{a}_{1} + y_{26} \, \mathbf{a}_{2} + z_{26} \, \mathbf{a}_{3} & = & x_{26}a \, \mathbf{\hat{x}} + y_{26}b \, \mathbf{\hat{y}} + z_{26}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XVIII} \\ \mathbf{B}_{52} & = & \left(\frac{1}{2} - x_{26}\right) \, \mathbf{a}_{1}-y_{26} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{26}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{26}\right)a \, \mathbf{\hat{x}}-y_{26}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{26}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XVIII} \\ \mathbf{B}_{53} & = & \left(\frac{1}{2} +x_{26}\right) \, \mathbf{a}_{1}-y_{26} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{26}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{26}\right)a \, \mathbf{\hat{x}}-y_{26}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{26}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XVIII} \\ \mathbf{B}_{54} & = & -x_{26} \, \mathbf{a}_{1} + y_{26} \, \mathbf{a}_{2} + z_{26} \, \mathbf{a}_{3} & = & -x_{26}a \, \mathbf{\hat{x}} + y_{26}b \, \mathbf{\hat{y}} + z_{26}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XVIII} \\ \mathbf{B}_{55} & = & x_{27} \, \mathbf{a}_{1} + y_{27} \, \mathbf{a}_{2} + z_{27} \, \mathbf{a}_{3} & = & x_{27}a \, \mathbf{\hat{x}} + y_{27}b \, \mathbf{\hat{y}} + z_{27}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XIX} \\ \mathbf{B}_{56} & = & \left(\frac{1}{2} - x_{27}\right) \, \mathbf{a}_{1}-y_{27} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{27}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{27}\right)a \, \mathbf{\hat{x}}-y_{27}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{27}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XIX} \\ \mathbf{B}_{57} & = & \left(\frac{1}{2} +x_{27}\right) \, \mathbf{a}_{1}-y_{27} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{27}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{27}\right)a \, \mathbf{\hat{x}}-y_{27}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{27}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XIX} \\ \mathbf{B}_{58} & = & -x_{27} \, \mathbf{a}_{1} + y_{27} \, \mathbf{a}_{2} + z_{27} \, \mathbf{a}_{3} & = & -x_{27}a \, \mathbf{\hat{x}} + y_{27}b \, \mathbf{\hat{y}} + z_{27}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XIX} \\ \mathbf{B}_{59} & = & x_{28} \, \mathbf{a}_{1} + y_{28} \, \mathbf{a}_{2} + z_{28} \, \mathbf{a}_{3} & = & x_{28}a \, \mathbf{\hat{x}} + y_{28}b \, \mathbf{\hat{y}} + z_{28}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XX} \\ \mathbf{B}_{60} & = & \left(\frac{1}{2} - x_{28}\right) \, \mathbf{a}_{1}-y_{28} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{28}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{28}\right)a \, \mathbf{\hat{x}}-y_{28}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{28}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XX} \\ \mathbf{B}_{61} & = & \left(\frac{1}{2} +x_{28}\right) \, \mathbf{a}_{1}-y_{28} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{28}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{28}\right)a \, \mathbf{\hat{x}}-y_{28}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{28}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XX} \\ \mathbf{B}_{62} & = & -x_{28} \, \mathbf{a}_{1} + y_{28} \, \mathbf{a}_{2} + z_{28} \, \mathbf{a}_{3} & = & -x_{28}a \, \mathbf{\hat{x}} + y_{28}b \, \mathbf{\hat{y}} + z_{28}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XX} \\ \mathbf{B}_{63} & = & x_{29} \, \mathbf{a}_{1} + y_{29} \, \mathbf{a}_{2} + z_{29} \, \mathbf{a}_{3} & = & x_{29}a \, \mathbf{\hat{x}} + y_{29}b \, \mathbf{\hat{y}} + z_{29}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXI} \\ \mathbf{B}_{64} & = & \left(\frac{1}{2} - x_{29}\right) \, \mathbf{a}_{1}-y_{29} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{29}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{29}\right)a \, \mathbf{\hat{x}}-y_{29}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{29}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXI} \\ \mathbf{B}_{65} & = & \left(\frac{1}{2} +x_{29}\right) \, \mathbf{a}_{1}-y_{29} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{29}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{29}\right)a \, \mathbf{\hat{x}}-y_{29}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{29}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXI} \\ \mathbf{B}_{66} & = & -x_{29} \, \mathbf{a}_{1} + y_{29} \, \mathbf{a}_{2} + z_{29} \, \mathbf{a}_{3} & = & -x_{29}a \, \mathbf{\hat{x}} + y_{29}b \, \mathbf{\hat{y}} + z_{29}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXI} \\ \mathbf{B}_{67} & = & x_{30} \, \mathbf{a}_{1} + y_{30} \, \mathbf{a}_{2} + z_{30} \, \mathbf{a}_{3} & = & x_{30}a \, \mathbf{\hat{x}} + y_{30}b \, \mathbf{\hat{y}} + z_{30}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXII} \\ \mathbf{B}_{68} & = & \left(\frac{1}{2} - x_{30}\right) \, \mathbf{a}_{1}-y_{30} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{30}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{30}\right)a \, \mathbf{\hat{x}}-y_{30}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{30}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXII} \\ \mathbf{B}_{69} & = & \left(\frac{1}{2} +x_{30}\right) \, \mathbf{a}_{1}-y_{30} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{30}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{30}\right)a \, \mathbf{\hat{x}}-y_{30}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{30}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXII} \\ \mathbf{B}_{70} & = & -x_{30} \, \mathbf{a}_{1} + y_{30} \, \mathbf{a}_{2} + z_{30} \, \mathbf{a}_{3} & = & -x_{30}a \, \mathbf{\hat{x}} + y_{30}b \, \mathbf{\hat{y}} + z_{30}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXII} \\ \mathbf{B}_{71} & = & x_{31} \, \mathbf{a}_{1} + y_{31} \, \mathbf{a}_{2} + z_{31} \, \mathbf{a}_{3} & = & x_{31}a \, \mathbf{\hat{x}} + y_{31}b \, \mathbf{\hat{y}} + z_{31}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIII} \\ \mathbf{B}_{72} & = & \left(\frac{1}{2} - x_{31}\right) \, \mathbf{a}_{1}-y_{31} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{31}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{31}\right)a \, \mathbf{\hat{x}}-y_{31}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{31}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIII} \\ \mathbf{B}_{73} & = & \left(\frac{1}{2} +x_{31}\right) \, \mathbf{a}_{1}-y_{31} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{31}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{31}\right)a \, \mathbf{\hat{x}}-y_{31}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{31}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIII} \\ \mathbf{B}_{74} & = & -x_{31} \, \mathbf{a}_{1} + y_{31} \, \mathbf{a}_{2} + z_{31} \, \mathbf{a}_{3} & = & -x_{31}a \, \mathbf{\hat{x}} + y_{31}b \, \mathbf{\hat{y}} + z_{31}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIII} \\ \mathbf{B}_{75} & = & x_{32} \, \mathbf{a}_{1} + y_{32} \, \mathbf{a}_{2} + z_{32} \, \mathbf{a}_{3} & = & x_{32}a \, \mathbf{\hat{x}} + y_{32}b \, \mathbf{\hat{y}} + z_{32}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIV} \\ \mathbf{B}_{76} & = & \left(\frac{1}{2} - x_{32}\right) \, \mathbf{a}_{1}-y_{32} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{32}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{32}\right)a \, \mathbf{\hat{x}}-y_{32}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{32}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIV} \\ \mathbf{B}_{77} & = & \left(\frac{1}{2} +x_{32}\right) \, \mathbf{a}_{1}-y_{32} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{32}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{32}\right)a \, \mathbf{\hat{x}}-y_{32}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{32}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIV} \\ \mathbf{B}_{78} & = & -x_{32} \, \mathbf{a}_{1} + y_{32} \, \mathbf{a}_{2} + z_{32} \, \mathbf{a}_{3} & = & -x_{32}a \, \mathbf{\hat{x}} + y_{32}b \, \mathbf{\hat{y}} + z_{32}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIV} \\ \mathbf{B}_{79} & = & x_{33} \, \mathbf{a}_{1} + y_{33} \, \mathbf{a}_{2} + z_{33} \, \mathbf{a}_{3} & = & x_{33}a \, \mathbf{\hat{x}} + y_{33}b \, \mathbf{\hat{y}} + z_{33}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXV} \\ \mathbf{B}_{80} & = & \left(\frac{1}{2} - x_{33}\right) \, \mathbf{a}_{1}-y_{33} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{33}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{33}\right)a \, \mathbf{\hat{x}}-y_{33}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{33}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXV} \\ \mathbf{B}_{81} & = & \left(\frac{1}{2} +x_{33}\right) \, \mathbf{a}_{1}-y_{33} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{33}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{33}\right)a \, \mathbf{\hat{x}}-y_{33}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{33}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXV} \\ \mathbf{B}_{82} & = & -x_{33} \, \mathbf{a}_{1} + y_{33} \, \mathbf{a}_{2} + z_{33} \, \mathbf{a}_{3} & = & -x_{33}a \, \mathbf{\hat{x}} + y_{33}b \, \mathbf{\hat{y}} + z_{33}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXV} \\ \mathbf{B}_{83} & = & x_{34} \, \mathbf{a}_{1} + y_{34} \, \mathbf{a}_{2} + z_{34} \, \mathbf{a}_{3} & = & x_{34}a \, \mathbf{\hat{x}} + y_{34}b \, \mathbf{\hat{y}} + z_{34}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVI} \\ \mathbf{B}_{84} & = & \left(\frac{1}{2} - x_{34}\right) \, \mathbf{a}_{1}-y_{34} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{34}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{34}\right)a \, \mathbf{\hat{x}}-y_{34}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{34}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVI} \\ \mathbf{B}_{85} & = & \left(\frac{1}{2} +x_{34}\right) \, \mathbf{a}_{1}-y_{34} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{34}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{34}\right)a \, \mathbf{\hat{x}}-y_{34}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{34}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVI} \\ \mathbf{B}_{86} & = & -x_{34} \, \mathbf{a}_{1} + y_{34} \, \mathbf{a}_{2} + z_{34} \, \mathbf{a}_{3} & = & -x_{34}a \, \mathbf{\hat{x}} + y_{34}b \, \mathbf{\hat{y}} + z_{34}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVI} \\ \mathbf{B}_{87} & = & x_{35} \, \mathbf{a}_{1} + y_{35} \, \mathbf{a}_{2} + z_{35} \, \mathbf{a}_{3} & = & x_{35}a \, \mathbf{\hat{x}} + y_{35}b \, \mathbf{\hat{y}} + z_{35}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVII} \\ \mathbf{B}_{88} & = & \left(\frac{1}{2} - x_{35}\right) \, \mathbf{a}_{1}-y_{35} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{35}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{35}\right)a \, \mathbf{\hat{x}}-y_{35}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{35}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVII} \\ \mathbf{B}_{89} & = & \left(\frac{1}{2} +x_{35}\right) \, \mathbf{a}_{1}-y_{35} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{35}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{35}\right)a \, \mathbf{\hat{x}}-y_{35}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{35}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVII} \\ \mathbf{B}_{90} & = & -x_{35} \, \mathbf{a}_{1} + y_{35} \, \mathbf{a}_{2} + z_{35} \, \mathbf{a}_{3} & = & -x_{35}a \, \mathbf{\hat{x}} + y_{35}b \, \mathbf{\hat{y}} + z_{35}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVII} \\ \mathbf{B}_{91} & = & x_{36} \, \mathbf{a}_{1} + y_{36} \, \mathbf{a}_{2} + z_{36} \, \mathbf{a}_{3} & = & x_{36}a \, \mathbf{\hat{x}} + y_{36}b \, \mathbf{\hat{y}} + z_{36}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVIII} \\ \mathbf{B}_{92} & = & \left(\frac{1}{2} - x_{36}\right) \, \mathbf{a}_{1}-y_{36} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{36}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{36}\right)a \, \mathbf{\hat{x}}-y_{36}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{36}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVIII} \\ \mathbf{B}_{93} & = & \left(\frac{1}{2} +x_{36}\right) \, \mathbf{a}_{1}-y_{36} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{36}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{36}\right)a \, \mathbf{\hat{x}}-y_{36}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{36}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVIII} \\ \mathbf{B}_{94} & = & -x_{36} \, \mathbf{a}_{1} + y_{36} \, \mathbf{a}_{2} + z_{36} \, \mathbf{a}_{3} & = & -x_{36}a \, \mathbf{\hat{x}} + y_{36}b \, \mathbf{\hat{y}} + z_{36}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVIII} \\ \mathbf{B}_{95} & = & x_{37} \, \mathbf{a}_{1} + y_{37} \, \mathbf{a}_{2} + z_{37} \, \mathbf{a}_{3} & = & x_{37}a \, \mathbf{\hat{x}} + y_{37}b \, \mathbf{\hat{y}} + z_{37}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co IX} \\ \mathbf{B}_{96} & = & \left(\frac{1}{2} - x_{37}\right) \, \mathbf{a}_{1}-y_{37} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{37}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{37}\right)a \, \mathbf{\hat{x}}-y_{37}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{37}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co IX} \\ \mathbf{B}_{97} & = & \left(\frac{1}{2} +x_{37}\right) \, \mathbf{a}_{1}-y_{37} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{37}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{37}\right)a \, \mathbf{\hat{x}}-y_{37}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{37}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co IX} \\ \mathbf{B}_{98} & = & -x_{37} \, \mathbf{a}_{1} + y_{37} \, \mathbf{a}_{2} + z_{37} \, \mathbf{a}_{3} & = & -x_{37}a \, \mathbf{\hat{x}} + y_{37}b \, \mathbf{\hat{y}} + z_{37}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co IX} \\ \mathbf{B}_{99} & = & x_{38} \, \mathbf{a}_{1} + y_{38} \, \mathbf{a}_{2} + z_{38} \, \mathbf{a}_{3} & = & x_{38}a \, \mathbf{\hat{x}} + y_{38}b \, \mathbf{\hat{y}} + z_{38}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co X} \\ \mathbf{B}_{100} & = & \left(\frac{1}{2} - x_{38}\right) \, \mathbf{a}_{1}-y_{38} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{38}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{38}\right)a \, \mathbf{\hat{x}}-y_{38}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{38}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co X} \\ \mathbf{B}_{101} & = & \left(\frac{1}{2} +x_{38}\right) \, \mathbf{a}_{1}-y_{38} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{38}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{38}\right)a \, \mathbf{\hat{x}}-y_{38}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{38}\right)c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co X} \\ \mathbf{B}_{102} & = & -x_{38} \, \mathbf{a}_{1} + y_{38} \, \mathbf{a}_{2} + z_{38} \, \mathbf{a}_{3} & = & -x_{38}a \, \mathbf{\hat{x}} + y_{38}b \, \mathbf{\hat{y}} + z_{38}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co X} \\ \end{array} \]

References

  • J. Grin, U. Burkhard, M. Ellner, and K. Peters, Crystal structure of orthorhombic Co4Al13, J. Alloys\ Compd. 206, 243–247 (1994), doi:10.1016/0925-8388(94)90043-4.

Found in

  • R. Addou, E. Gaudry, T. Deniozou, M. Heggen, M. Feuerbacher, P. Gille, Y. Grin, R. Widmer, O. Gröning, V. Fournée, J.–M. Dubois, and J. Ledieu, Structure investigation of the (100) surface of the orthorhombic Al13Co4 crystal, Phys. Rev. B 80, 014203 (2009), doi:10.1103/PhysRevB.80.014203.

Geometry files


Prototype Generator

aflow --proto=A13B4_oP102_31_17a11b_8a2b --params=

Species:

Running:

Output: