AlN3Ti4 Structure: AB3C4_hP16_194_c_af_ef

Picture of Structure; Click for Big Picture
Prototype : AlN3Ti4
AFLOW prototype label : AB3C4_hP16_194_c_af_ef
Strukturbericht designation : None
Pearson symbol : hP16
Space group number : 194
Space group symbol : $\mbox{P6}_{3}\mbox{/mmc}$
AFLOW prototype command : aflow --proto=AB3C4_hP16_194_c_af_ef
--params=
$a$,$c/a$,$z_3$,$z_4$,$z_5$


  • This is a so-called 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{N I} \\ \mathbf{B_2} & = & \frac12 \mathbf{a}_{3} & = & \frac12 \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{N I} \\ \mathbf{B_3} & =& \frac13 \mathbf{a}_{1} + \frac23 \mathbf{a}_{2} + \frac14 \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Al} \\ \mathbf{B_4} & =& \frac23 \mathbf{a}_{1} + \frac13 \mathbf{a}_{2} + \frac34 \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Al} \\ \mathbf{B_5} & =& z_3 \, \mathbf{a}_{3}& =& z_3 \, c \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Ti I} \\ \mathbf{B_6} & =& \left(\frac12 + z_3\right) \, \mathbf{a}_{3}& =& \left(\frac12 + z_3\right) \, c \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Ti I} \\ \mathbf{B_7} & =& - z_3 \, \mathbf{a}_{3}& =& - z_3 \, c \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Ti I} \\ \mathbf{B_8} & =& \left(\frac12 - z_3\right) \, \mathbf{a}_{3}& =& \left(\frac12 - z_3\right) \, c \, \mathbf{\hat{z}}& \left(4e\right) & \mbox{Ti I} \\ \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{N 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{N 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{N 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{N II} \\ \mathbf{B_13} & =& \frac13 \mathbf{a}_{1} + \frac23 \mathbf{a}_{2} + z_5 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + z_5 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Ti II} \\ \mathbf{B}_{14} & =& \frac23 \mathbf{a}_{1} + \frac13 \mathbf{a}_{2} + \left(\frac12 + z_5\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_5\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Ti II} \\ \mathbf{B}_{15} & =& \frac23 \mathbf{a}_{1} + \frac13 \mathbf{a}_{2} - z_5 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} - z_5 \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Ti II} \\ \mathbf{B}_{16} & =& \frac13 \mathbf{a}_{1} + \frac23 \mathbf{a}_{2} + \left(\frac12 - z_5\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 - z_5\right) \, c \, \mathbf{\hat{z}}& \left(4f\right) & \mbox{Ti II} \\ \end{array} \]

References

  • M. W. Barsoum, C. J. Rawn, T. El–Raghy, A. T. Procopio, W. D. Porter, H. Wang, and C. R. Hubbard, Thermal Properties of Ti4AlN3, J. Appl. Phys. 87, 8407–8414 (2000), doi:10.1063/1.373555.
  • 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=AB3C4_hP16_194_c_af_ef --params=

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