Black Phosphorus ($A17$) Crystal Structure: A_oC8_64_f

Picture of Structure; Click for Big Picture
Prototype : P
AFLOW prototype label : A_oC8_64_f
Strukturbericht designation : $A17$
Pearson symbol : oC8
Space group number : 64
Space group symbol : $\mbox{Cmca}$
AFLOW prototype command : aflow --proto=A_oC8_64_f
--params=
$a$,$b/a$,$c/a$,$y_{1}$,$z_{1}$


  • Note that $\alpha$–Ga (A_oC8_64_f, $\alpha$–Ga), black phosphorus (A_oC8_64_f, P), and molecular iodine (A_oC8_64_f, I) have the same AFLOW prototype label. They are generated by the same symmetry operations with different sets of parameters (––params) specified in their corresponding CIF files.

Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& - y_{1} \, \mathbf{a}_{1} + y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& y_{1} \, b \, \mathbf{\hat{y}} + z_{1} \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{P} \\ \mathbf{B}_{2} & =& \left(\frac12 + y_{1}\right) \, \mathbf{a}_{1} + \left(\frac12 - y_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - y_{1} \, b \, \mathbf{\hat{y}} + \left(\frac12 + z_{1}\right) \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{P} \\ \mathbf{B}_{3} & =& \left(\frac12 - y_{1}\right) \, \mathbf{a}_{1} + \left(\frac12 + y_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 - z_{1}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + y_{1} \, b \, \mathbf{\hat{y}} + \left(\frac12 - z_{1}\right) \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{P} \\ \mathbf{B}_{4} & =& y_{1} \, \mathbf{a}_{1} - y_{1} \, \mathbf{a}_{2} - z_{1} \, \mathbf{a}_{3}& =& - y_{1} \, b \, \mathbf{\hat{y}} - z_{1} \, c \mathbf{\hat{z}}& \left(8f\right) & \mbox{P} \\ \end{array} \]

References

  • A. Brown and S. Rundqvist, Refinement of the crystal structure of black phosphorus, Acta Cryst. 19, 684–685 (1965), doi:10.1107/S0365110X65004140.

Geometry files


Prototype Generator

aflow --proto=A_oC8_64_f --params=

Species:

Running:

Output: