CMo Structure: AB_hP12_194_af_bf

Picture of Structure; Click for Big Picture
Prototype : CMo
AFLOW prototype label : AB_hP12_194_af_bf
Strukturbericht designation : None
Pearson symbol : hP12
Space group number : 194
Space group symbol : $\mbox{P6}_{3}\mbox{/mmc}$
AFLOW prototype command : aflow --proto=AB_hP12_194_af_bf
--params=
$a$,$c/a$,$z_{3}$,$z_{4}$


Other compounds with this structure

  • CRe, C2GeTi3, C2SiTi3, AlC2Ti3, others.

  • Note that all of the atoms sit on close packed <0001> planes. The stacking sequence may be written: \\ \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Atom & Mo-II & C-II & C-I & C-II & Mo-II & Mo-I & Mo-II & C-II & C-I & C-II & Mo-II & Mo-I \\ \hline Position & B & C & A & B & C & A & C & B & A & C & B & A \\ \hline \end{array} \]\\ Thus the Mo–II atoms and all of the C atoms are always in an fcc-like local environment, while the Mo–I atoms are in an hcp-like local environment. Like AlN3Ti4, this is a MAX phase. For more information, see (Radovic, 2013).

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{C I} \\ \mathbf{B}_{2}& = &\frac12 \, \mathbf{a}_{3}& = &\frac12 \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{C I} \\ \mathbf{B}_{3}& = &\frac14 \, \mathbf{a}_{3}& = &\frac14 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Mo I} \\ \mathbf{B}_{4}& = &\frac34 \, \mathbf{a}_{3}& = &\frac34 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{Mo I} \\ \mathbf{B}_{5}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+\frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{C II} \\ \mathbf{B}_{6}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{C II} \\ \mathbf{B}_{7}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{C II} \\ \mathbf{B}_{8}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \left(\frac12 - z_{3}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{C II} \\ \mathbf{B}_{9}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{4} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+\frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_{4} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Mo II} \\ \mathbf{B}_{10}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Mo II} \\ \mathbf{B}_{11}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}- z_{4} \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Mo II} \\ \mathbf{B}_{12}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \left(\frac12 - z_{4}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Mo II} \\ \end{array} \]

References

  • H. Nowotny, R. Parthé, R. Kieffer, and F. Benesovsky, Das Dreistoffsystem: Molybdän–Silizium–Kohlenstoff, Monatsh. Chem. Verw. Tl. 85, 255–272 (1954).
  • M. Radovic and M. W. Barsoum, MAX phases: Bridging the gap between metals and ceramics, American Ceramic Society Bulletin 92, 20–27 (2013).

Geometry files


Prototype Generator

aflow --proto=AB_hP12_194_af_bf --params=

Species:

Running:

Output: