Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: ABC_oP6_59_a_a_a

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

CNCl Structure: ABC_oP6_59_a_a_a

Picture of Structure; Click for Big Picture
Prototype : CNCl
AFLOW prototype label : ABC_oP6_59_a_a_a
Strukturbericht designation : None
Pearson symbol : oP6
Space group number : 59
Space group symbol : $\text{Pmmn}$
AFLOW prototype command : aflow --proto=ABC_oP6_59_a_a_a
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$


Simple Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & =&\frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{1} \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \text{C} \\ \mathbf{B}_{2} & =&\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \text{C} \\ \mathbf{B}_{3} & =&\frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \text{Cl} \\ \mathbf{B}_{4} & =&\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{2} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \text{Cl} \\ \mathbf{B}_{5} & =&\frac14 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ z_{3} \, \mathbf{a}_{3}& =&\frac14 \, a \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \text{N} \\ \mathbf{B}_{6} & =&\frac34 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}& =&\frac34 \, a \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \text{N} \\ \end{array} \]

References

Found in

  • R. W. G. Wyckoff, Crystal Structures Vol. 1 (Wiley, 1963), 2nd edn., pp. 173-174.

Geometry files


Prototype Generator

aflow --proto=ABC_oP6_59_a_a_a --params=

Species:

Running:

Output: