Al2Mo3C Structure : A2BC3_cP24_213_c_a_d

Picture of Structure; Click for Big Picture
Prototype : Al2CMo3
AFLOW prototype label : A2BC3_cP24_213_c_a_d
Strukturbericht designation : None
Pearson symbol : cP24
Space group number : 213
Space group symbol : $P4_{1}32$
AFLOW prototype command : aflow --proto=A2BC3_cP24_213_c_a_d
--params=
$a$,$x_{2}$,$y_{3}$


Other compounds with this structure

  • Ag2Pd3Sn, Al2Nb3C, Al2Nb3N, Al2Ta3C, Cr2Re3B, Li2Pd3B, Li2Pt3B, Mn2Rh3P, Ni2W3N, Rh2Mo3N, and (Fe2–xRhx)Mo3N

  • This is a filled $\beta$–Mn ($A13$) structure, with the aluminum and molybdenum atoms almost exactly on the sites of the manganese atoms in $A13$.

Simple Cubic primitive vectors:

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

Basis vectors:

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

References

  • W. Jeitschko, H. Nowotny, and F. Benesovsky, Ein Beitrag zum Dreistoff: Molybdän–Aluminium–Kohlenstoff, Monatsh. Chem. Verw. Teile\ Anderer\ Wiss. 94, 247–251 (1963), doi:10.1007/BF00900244.

Found in

  • A. Iyo, I. Hase, H. Fujihisa, Y. Gotoh, N. Takeshita, S. Ishida, H. Ninomiya, Y. Yoshida, H. Eisaki, and K. Kawashima, Superconductivity induced by Mg deficiency in noncentrosymmetric phosphide Mg2Rh3P, Phys. Rev. Mater. 3, 124802 (2019), doi:10.1103/PhysRevMaterials.3.124802.

Geometry files


Prototype Generator

aflow --proto=A2BC3_cP24_213_c_a_d --params=

Species:

Running:

Output: