Monoclinic Co4Al13 Structure : A13B4_mC102_8_17a11b_8a2b

Picture of Structure; Click for Big Picture
Prototype : Al13Co4
AFLOW prototype label : A13B4_mC102_8_17a11b_8a2b
Strukturbericht designation : None
Pearson symbol : mC102
Space group number : 8
Space group symbol : $Cm$
AFLOW prototype command : aflow --proto=A13B4_mC102_8_17a11b_8a2b
--params=
$a$,$b/a$,$c/a$,$\beta$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$,$x_{12}$,$z_{12}$,$x_{13}$,$z_{13}$,$x_{14}$,$z_{14}$,$x_{15}$,$z_{15}$,$x_{16}$,$z_{16}$,$x_{17}$,$z_{17}$,$x_{18}$,$z_{18}$,$x_{19}$,$z_{19}$,$x_{20}$,$z_{20}$,$x_{21}$,$z_{21}$,$x_{22}$,$z_{22}$,$x_{23}$,$z_{23}$,$x_{24}$,$z_{24}$,$x_{25}$,$z_{25}$,$x_{26}$,$y_{26}$,$z_{26}$,$x_{27}$,$y_{27}$,$z_{27}$,$x_{28}$,$y_{28}$,$z_{28}$,$x_{29}$,$y_{29}$,$z_{29}$,$x_{30}$,$y_{30}$,$z_{30}$,$x_{31}$,$y_{31}$,$z_{31}$,$x_{32}$,$y_{32}$,$z_{32}$,$x_{33}$,$y_{33}$,$z_{33}$,$x_{34}$,$y_{34}$,$z_{34}$,$x_{35}$,$y_{35}$,$z_{35}$,$x_{36}$,$y_{36}$,$z_{36}$,$x_{37}$,$y_{37}$,$z_{37}$,$x_{38}$,$y_{38}$,$z_{38}$


  • Following (Hudd, 1962), the Al–IV and Al–XIII sites are occupied 30% of the time, while the occupation of Al–VI, Al–IX, Al–XIV, and Al–XVII is 70%. This gives a nominial occupation of Al91Co30, though the authors state the actual composition is Al68.3Co24.4.
  • Space group $Cm$ #8 allows an arbitrary choice for the origin of the $z$–axis. We follow (Hudd, 1962) and set the $z_{26} = 0$.
  • AFLOW-SYM yields space group $Cm$ #8 consistently for small and large tolerances. However, if we allow a rather large uncertainty of 0.3 Å in the atomic positions with FINDSYM, the symmetry is set as $C2/m$ #12. That crystal has the Al13Fe4 prototype.

Base-centered Monoclinic primitive vectors:

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

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} + z_{1} \, \mathbf{a}_{3} & = & \left(x_{1}a+z_{1}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{1}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al I} \\ \mathbf{B}_{2} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & \left(x_{2}a+z_{2}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{2}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al II} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & \left(x_{3}a+z_{3}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{3}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al III} \\ \mathbf{B}_{4} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \left(x_{4}a+z_{4}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{4}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al IV} \\ \mathbf{B}_{5} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}a+z_{5}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{5}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al V} \\ \mathbf{B}_{6} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}a+z_{6}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{6}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VI} \\ \mathbf{B}_{7} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}a+z_{7}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{7}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VII} \\ \mathbf{B}_{8} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(x_{8}a+z_{8}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{8}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al VIII} \\ \mathbf{B}_{9} & = & x_{9} \, \mathbf{a}_{1} + x_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(x_{9}a+z_{9}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{9}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al IX} \\ \mathbf{B}_{10} & = & x_{10} \, \mathbf{a}_{1} + x_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(x_{10}a+z_{10}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{10}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al X} \\ \mathbf{B}_{11} & = & x_{11} \, \mathbf{a}_{1} + x_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(x_{11}a+z_{11}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{11}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XI} \\ \mathbf{B}_{12} & = & x_{12} \, \mathbf{a}_{1} + x_{12} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & \left(x_{12}a+z_{12}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{12}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XII} \\ \mathbf{B}_{13} & = & x_{13} \, \mathbf{a}_{1} + x_{13} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & \left(x_{13}a+z_{13}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{13}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XIII} \\ \mathbf{B}_{14} & = & x_{14} \, \mathbf{a}_{1} + x_{14} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & \left(x_{14}a+z_{14}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{14}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XIV} \\ \mathbf{B}_{15} & = & x_{15} \, \mathbf{a}_{1} + x_{15} \, \mathbf{a}_{2} + z_{15} \, \mathbf{a}_{3} & = & \left(x_{15}a+z_{15}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{15}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XV} \\ \mathbf{B}_{16} & = & x_{16} \, \mathbf{a}_{1} + x_{16} \, \mathbf{a}_{2} + z_{16} \, \mathbf{a}_{3} & = & \left(x_{16}a+z_{16}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{16}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XVI} \\ \mathbf{B}_{17} & = & x_{17} \, \mathbf{a}_{1} + x_{17} \, \mathbf{a}_{2} + z_{17} \, \mathbf{a}_{3} & = & \left(x_{17}a+z_{17}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{17}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Al XVII} \\ \mathbf{B}_{18} & = & x_{18} \, \mathbf{a}_{1} + x_{18} \, \mathbf{a}_{2} + z_{18} \, \mathbf{a}_{3} & = & \left(x_{18}a+z_{18}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{18}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co I} \\ \mathbf{B}_{19} & = & x_{19} \, \mathbf{a}_{1} + x_{19} \, \mathbf{a}_{2} + z_{19} \, \mathbf{a}_{3} & = & \left(x_{19}a+z_{19}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{19}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co II} \\ \mathbf{B}_{20} & = & x_{20} \, \mathbf{a}_{1} + x_{20} \, \mathbf{a}_{2} + z_{20} \, \mathbf{a}_{3} & = & \left(x_{20}a+z_{20}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{20}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co III} \\ \mathbf{B}_{21} & = & x_{21} \, \mathbf{a}_{1} + x_{21} \, \mathbf{a}_{2} + z_{21} \, \mathbf{a}_{3} & = & \left(x_{21}a+z_{21}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{21}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co IV} \\ \mathbf{B}_{22} & = & x_{22} \, \mathbf{a}_{1} + x_{22} \, \mathbf{a}_{2} + z_{22} \, \mathbf{a}_{3} & = & \left(x_{22}a+z_{22}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{22}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co V} \\ \mathbf{B}_{23} & = & x_{23} \, \mathbf{a}_{1} + x_{23} \, \mathbf{a}_{2} + z_{23} \, \mathbf{a}_{3} & = & \left(x_{23}a+z_{23}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{23}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VI} \\ \mathbf{B}_{24} & = & x_{24} \, \mathbf{a}_{1} + x_{24} \, \mathbf{a}_{2} + z_{24} \, \mathbf{a}_{3} & = & \left(x_{24}a+z_{24}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{24}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VII} \\ \mathbf{B}_{25} & = & x_{25} \, \mathbf{a}_{1} + x_{25} \, \mathbf{a}_{2} + z_{25} \, \mathbf{a}_{3} & = & \left(x_{25}a+z_{25}c\cos\beta\right) \, \mathbf{\hat{x}} + z_{25}c\sin\beta \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{Co VIII} \\ \mathbf{B}_{26} & = & \left(x_{26}-y_{26}\right) \, \mathbf{a}_{1} + \left(x_{26}+y_{26}\right) \, \mathbf{a}_{2} + z_{26} \, \mathbf{a}_{3} & = & \left(x_{26}a+z_{26}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{26}b \, \mathbf{\hat{y}} + z_{26}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XVIII} \\ \mathbf{B}_{27} & = & \left(x_{26}+y_{26}\right) \, \mathbf{a}_{1} + \left(x_{26}-y_{26}\right) \, \mathbf{a}_{2} + z_{26} \, \mathbf{a}_{3} & = & \left(x_{26}a+z_{26}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{26}b \, \mathbf{\hat{y}} + z_{26}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XVIII} \\ \mathbf{B}_{28} & = & \left(x_{27}-y_{27}\right) \, \mathbf{a}_{1} + \left(x_{27}+y_{27}\right) \, \mathbf{a}_{2} + z_{27} \, \mathbf{a}_{3} & = & \left(x_{27}a+z_{27}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{27}b \, \mathbf{\hat{y}} + z_{27}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XIX} \\ \mathbf{B}_{29} & = & \left(x_{27}+y_{27}\right) \, \mathbf{a}_{1} + \left(x_{27}-y_{27}\right) \, \mathbf{a}_{2} + z_{27} \, \mathbf{a}_{3} & = & \left(x_{27}a+z_{27}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{27}b \, \mathbf{\hat{y}} + z_{27}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XIX} \\ \mathbf{B}_{30} & = & \left(x_{28}-y_{28}\right) \, \mathbf{a}_{1} + \left(x_{28}+y_{28}\right) \, \mathbf{a}_{2} + z_{28} \, \mathbf{a}_{3} & = & \left(x_{28}a+z_{28}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{28}b \, \mathbf{\hat{y}} + z_{28}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XX} \\ \mathbf{B}_{31} & = & \left(x_{28}+y_{28}\right) \, \mathbf{a}_{1} + \left(x_{28}-y_{28}\right) \, \mathbf{a}_{2} + z_{28} \, \mathbf{a}_{3} & = & \left(x_{28}a+z_{28}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{28}b \, \mathbf{\hat{y}} + z_{28}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XX} \\ \mathbf{B}_{32} & = & \left(x_{29}-y_{29}\right) \, \mathbf{a}_{1} + \left(x_{29}+y_{29}\right) \, \mathbf{a}_{2} + z_{29} \, \mathbf{a}_{3} & = & \left(x_{29}a+z_{29}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{29}b \, \mathbf{\hat{y}} + z_{29}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXI} \\ \mathbf{B}_{33} & = & \left(x_{29}+y_{29}\right) \, \mathbf{a}_{1} + \left(x_{29}-y_{29}\right) \, \mathbf{a}_{2} + z_{29} \, \mathbf{a}_{3} & = & \left(x_{29}a+z_{29}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{29}b \, \mathbf{\hat{y}} + z_{29}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXI} \\ \mathbf{B}_{34} & = & \left(x_{30}-y_{30}\right) \, \mathbf{a}_{1} + \left(x_{30}+y_{30}\right) \, \mathbf{a}_{2} + z_{30} \, \mathbf{a}_{3} & = & \left(x_{30}a+z_{30}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{30}b \, \mathbf{\hat{y}} + z_{30}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXII} \\ \mathbf{B}_{35} & = & \left(x_{30}+y_{30}\right) \, \mathbf{a}_{1} + \left(x_{30}-y_{30}\right) \, \mathbf{a}_{2} + z_{30} \, \mathbf{a}_{3} & = & \left(x_{30}a+z_{30}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{30}b \, \mathbf{\hat{y}} + z_{30}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXII} \\ \mathbf{B}_{36} & = & \left(x_{31}-y_{31}\right) \, \mathbf{a}_{1} + \left(x_{31}+y_{31}\right) \, \mathbf{a}_{2} + z_{31} \, \mathbf{a}_{3} & = & \left(x_{31}a+z_{31}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{31}b \, \mathbf{\hat{y}} + z_{31}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIII} \\ \mathbf{B}_{37} & = & \left(x_{31}+y_{31}\right) \, \mathbf{a}_{1} + \left(x_{31}-y_{31}\right) \, \mathbf{a}_{2} + z_{31} \, \mathbf{a}_{3} & = & \left(x_{31}a+z_{31}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{31}b \, \mathbf{\hat{y}} + z_{31}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIII} \\ \mathbf{B}_{38} & = & \left(x_{32}-y_{32}\right) \, \mathbf{a}_{1} + \left(x_{32}+y_{32}\right) \, \mathbf{a}_{2} + z_{32} \, \mathbf{a}_{3} & = & \left(x_{32}a+z_{32}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{32}b \, \mathbf{\hat{y}} + z_{32}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIV} \\ \mathbf{B}_{39} & = & \left(x_{32}+y_{32}\right) \, \mathbf{a}_{1} + \left(x_{32}-y_{32}\right) \, \mathbf{a}_{2} + z_{32} \, \mathbf{a}_{3} & = & \left(x_{32}a+z_{32}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{32}b \, \mathbf{\hat{y}} + z_{32}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXIV} \\ \mathbf{B}_{40} & = & \left(x_{33}-y_{33}\right) \, \mathbf{a}_{1} + \left(x_{33}+y_{33}\right) \, \mathbf{a}_{2} + z_{33} \, \mathbf{a}_{3} & = & \left(x_{33}a+z_{33}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{33}b \, \mathbf{\hat{y}} + z_{33}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXV} \\ \mathbf{B}_{41} & = & \left(x_{33}+y_{33}\right) \, \mathbf{a}_{1} + \left(x_{33}-y_{33}\right) \, \mathbf{a}_{2} + z_{33} \, \mathbf{a}_{3} & = & \left(x_{33}a+z_{33}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{33}b \, \mathbf{\hat{y}} + z_{33}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXV} \\ \mathbf{B}_{42} & = & \left(x_{34}-y_{34}\right) \, \mathbf{a}_{1} + \left(x_{34}+y_{34}\right) \, \mathbf{a}_{2} + z_{34} \, \mathbf{a}_{3} & = & \left(x_{34}a+z_{34}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{34}b \, \mathbf{\hat{y}} + z_{34}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVI} \\ \mathbf{B}_{43} & = & \left(x_{34}+y_{34}\right) \, \mathbf{a}_{1} + \left(x_{34}-y_{34}\right) \, \mathbf{a}_{2} + z_{34} \, \mathbf{a}_{3} & = & \left(x_{34}a+z_{34}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{34}b \, \mathbf{\hat{y}} + z_{34}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVI} \\ \mathbf{B}_{44} & = & \left(x_{35}-y_{35}\right) \, \mathbf{a}_{1} + \left(x_{35}+y_{35}\right) \, \mathbf{a}_{2} + z_{35} \, \mathbf{a}_{3} & = & \left(x_{35}a+z_{35}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{35}b \, \mathbf{\hat{y}} + z_{35}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVII} \\ \mathbf{B}_{45} & = & \left(x_{35}+y_{35}\right) \, \mathbf{a}_{1} + \left(x_{35}-y_{35}\right) \, \mathbf{a}_{2} + z_{35} \, \mathbf{a}_{3} & = & \left(x_{35}a+z_{35}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{35}b \, \mathbf{\hat{y}} + z_{35}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVII} \\ \mathbf{B}_{46} & = & \left(x_{36}-y_{36}\right) \, \mathbf{a}_{1} + \left(x_{36}+y_{36}\right) \, \mathbf{a}_{2} + z_{36} \, \mathbf{a}_{3} & = & \left(x_{36}a+z_{36}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{36}b \, \mathbf{\hat{y}} + z_{36}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVIII} \\ \mathbf{B}_{47} & = & \left(x_{36}+y_{36}\right) \, \mathbf{a}_{1} + \left(x_{36}-y_{36}\right) \, \mathbf{a}_{2} + z_{36} \, \mathbf{a}_{3} & = & \left(x_{36}a+z_{36}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{36}b \, \mathbf{\hat{y}} + z_{36}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Al XXVIII} \\ \mathbf{B}_{48} & = & \left(x_{37}-y_{37}\right) \, \mathbf{a}_{1} + \left(x_{37}+y_{37}\right) \, \mathbf{a}_{2} + z_{37} \, \mathbf{a}_{3} & = & \left(x_{37}a+z_{37}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{37}b \, \mathbf{\hat{y}} + z_{37}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co IX} \\ \mathbf{B}_{49} & = & \left(x_{37}+y_{37}\right) \, \mathbf{a}_{1} + \left(x_{37}-y_{37}\right) \, \mathbf{a}_{2} + z_{37} \, \mathbf{a}_{3} & = & \left(x_{37}a+z_{37}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{37}b \, \mathbf{\hat{y}} + z_{37}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co IX} \\ \mathbf{B}_{50} & = & \left(x_{38}-y_{38}\right) \, \mathbf{a}_{1} + \left(x_{38}+y_{38}\right) \, \mathbf{a}_{2} + z_{38} \, \mathbf{a}_{3} & = & \left(x_{38}a+z_{38}c\cos\beta\right) \, \mathbf{\hat{x}} + y_{38}b \, \mathbf{\hat{y}} + z_{38}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co X} \\ \mathbf{B}_{51} & = & \left(x_{38}+y_{38}\right) \, \mathbf{a}_{1} + \left(x_{38}-y_{38}\right) \, \mathbf{a}_{2} + z_{38} \, \mathbf{a}_{3} & = & \left(x_{38}a+z_{38}c\cos\beta\right) \, \mathbf{\hat{x}}-y_{38}b \, \mathbf{\hat{y}} + z_{38}c\sin\beta \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Co X} \\ \end{array} \]

References

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.
  • T. B. Massalski, H. Okamoto, P. R. Subramanian, and L. Kacprzak, eds., Binary Alloy Phase Diagrams, vol. 1 (ASM International, Materials Park, Ohio, USA, 1990), 2nd edn. Ac–Ag to Ca–Zn.

Geometry files


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aflow --proto=A13B4_mC102_8_17a11b_8a2b --params=

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