BN ($B_{k}$) Structure: AB_hP4_194_c_d

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Prototype : BN
AFLOW prototype label : AB_hP4_194_c_d
Strukturbericht designation : $B_{k}$
Pearson symbol : hP4
Space group number : 194
Space group symbol : $\mbox{P6}_{3}\mbox{/mmc}$
AFLOW prototype command : aflow --proto=AB_hP4_194_c_d
--params=
$a$,$c/a$


Other compounds with this structure

  • ZnO nanowires

  • This is the corrected boron nitride structure found by (Pease, 1950) and (Pease, 1952). See further discussion on the B12 page.

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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{B} \\ \mathbf{B}_{2}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{B} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac34 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \mbox{N} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(2d\right) & \mbox{N} \\ \end{array} \]

References

  • R. S. Pease, Crystal Structure of Boron Nitride, Nature 165, 722–723 (1950), doi:10.1038/165722b0.

Found in

  • R. W. G. Wyckoff, Crystal Structures Vol. 1 (Wiley, 1963), 2nd edn., pp. 184-5.

Geometry files


Prototype Generator

aflow --proto=AB_hP4_194_c_d --params=

Species:

Running:

Output: