Hypothetical Tetrahedrally Bonded Carbon with 4–Member Rings: A_tI8_139_h

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Prototype : C
AFLOW prototype label : A_tI8_139_h
Strukturbericht designation : None
Pearson symbol : tI8
Space group number : 139
Space group symbol : $\mbox{I4/mmm}$
AFLOW prototype command : aflow --proto=A_tI8_139_h
--params=
$a$,$c/a$,$x_{1}$


  • This structure was proposed in (Schultz, 1999) to show that it was energetically possible to form four-member rings in amorphous sp$^{3}$ carbon structures.

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =&x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ 2x_{1} \, \mathbf{a}_{3}& =&x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{C} \\ \mathbf{B}_{2} & =&- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- 2x_{1} \, \mathbf{a}_{3}& =&- x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{C} \\ \mathbf{B}_{3} & =&x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}& =&- x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{C} \\ \mathbf{B}_{4} & =&- x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}& =&x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}& \left(8h\right) & \mbox{C} \\ \end{array} \]

References

  • P. A. Schultz, K. Leung, and E. B. Stechel, Small rings and amorphous tetrahedral carbon, Phys. Rev. B 59, 733–741 (1999), doi:10.1103/PhysRevB.59.733.

Geometry files


Prototype Generator

aflow --proto=A_tI8_139_h --params=

Species:

Running:

Output: