Ti3O (Room–temperature) Structure: AB3_hP24_149_acgi_3l

Picture of Structure; Click for Big Picture
Prototype : Ti3O
AFLOW prototype label : AB3_hP24_149_acgi_3l
Strukturbericht designation : None
Pearson symbol : hP24
Space group number : 149
Space group symbol : $P312$
AFLOW prototype command : aflow --proto=AB3_hP24_149_acgi_3l
--params=
$a$,$c/a$,$z_{3}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$


Trigonal 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(1a\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} & \left(1c\right) & \mbox{O II} \\ \mathbf{B}_{3} & = & z_{3} \, \mathbf{a}_{3} & = & z_{3}c \, \mathbf{\hat{z}} & \left(2g\right) & \mbox{O III} \\ \mathbf{B}_{4} & = & -z_{3} \, \mathbf{a}_{3} & = & -z_{3}c \, \mathbf{\hat{z}} & \left(2g\right) & \mbox{O III} \\ \mathbf{B}_{5} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O IV} \\ \mathbf{B}_{6} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(2i\right) & \mbox{O IV} \\ \mathbf{B}_{7} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti I} \\ \mathbf{B}_{8} & = & -y_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{5}-y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti I} \\ \mathbf{B}_{9} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(-x_{5}+\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti I} \\ \mathbf{B}_{10} & = & -y_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{5}+y_{5}\right)a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti I} \\ \mathbf{B}_{11} & = & \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{5}+y_{5}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti I} \\ \mathbf{B}_{12} & = & x_{5} \, \mathbf{a}_{1} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(x_{5}-\frac{1}{2}y_{5}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti I} \\ \mathbf{B}_{13} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{6}+y_{6}\right)a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti II} \\ \mathbf{B}_{14} & = & -y_{6} \, \mathbf{a}_{1} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{6}-y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti II} \\ \mathbf{B}_{15} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(-x_{6}+\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti II} \\ \mathbf{B}_{16} & = & -y_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{6}+y_{6}\right)a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti II} \\ \mathbf{B}_{17} & = & \left(-x_{6}+y_{6}\right) \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{6}+y_{6}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{6}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti II} \\ \mathbf{B}_{18} & = & x_{6} \, \mathbf{a}_{1} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(x_{6}-\frac{1}{2}y_{6}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{6}a \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti II} \\ \mathbf{B}_{19} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}\left(x_{7}+y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{7}+y_{7}\right)a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti III} \\ \mathbf{B}_{20} & = & -y_{7} \, \mathbf{a}_{1} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}x_{7}-y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti III} \\ \mathbf{B}_{21} & = & \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(-x_{7}+\frac{1}{2}y_{7}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{7}a \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti III} \\ \mathbf{B}_{22} & = & -y_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -\frac{1}{2}\left(x_{7}+y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}\left(-x_{7}+y_{7}\right)a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti III} \\ \mathbf{B}_{23} & = & \left(-x_{7}+y_{7}\right) \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(-\frac{1}{2}x_{7}+y_{7}\right)a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{7}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti III} \\ \mathbf{B}_{24} & = & x_{7} \, \mathbf{a}_{1} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(x_{7}-\frac{1}{2}y_{7}\right)a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}y_{7}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(6l\right) & \mbox{Ti III} \\ \end{array} \]

References

  • A. Jostsons and A. S. Malin, The ordered structure of Ti3O, Acta Crystallogr. Sect. B Struct. Sci. 24, 211–213 (1968), doi:10.1107/S0567740868001974.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


Prototype Generator

aflow --proto=AB3_hP24_149_acgi_3l --params=

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