Original BN ($B12$) Structure: AB_hP4_186_b_a

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Prototype : BN
AFLOW prototype label : AB_hP4_186_b_a
Strukturbericht designation : $B12$
Pearson symbol : hP4
Space group number : 186
Space group symbol : $\mbox{P6}_{3}\mbox{mc}$
AFLOW prototype command : aflow --proto=AB_hP4_186_b_a
--params=
$a$,$c/a$,$z_{1}$,$z_{2}$


  • This is the BN structure found in (Ewald, 1931) 95 and (Wilson, 1961) 125-126. (Pease, 1950) later determined that the true boron nitride structure is what is now known as the Bk structure. We leave this structure here for historical reasons. Note that it is crystallographically equivalent to the buckled graphite structure.

Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2} \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}}\\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1}& = &z_{1} \, \mathbf{a}_{3}& = &z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{N} \\ \mathbf{B}_{2}& = &\left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{N} \\ \mathbf{B}_{3}& = &\frac13 \, \mathbf{a}_{1}+ \frac23 \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ z_{2} \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{B} \\ \mathbf{B}_{4}& = &\frac23 \, \mathbf{a}_{1}+ \frac13 \, \mathbf{a}_{2}+ \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}- \frac1{2\sqrt3} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \mbox{B} \\ \end{array} \]

References

  • A. Brager, X–ray examination of the structure of boron nitride, Acta Physicochimica URSS 7, 699–706 (1937).
  • R. S. Pease, Crystal Structure of Boron Nitride, Nature 165, 722–723 (1950), doi:10.1038/165722b0.
  • P. P. Ewald and C. Hermann, Strukturbericht Band I, 1913–1928 (Akademsiche Verlagsgesellschaft M. B. H., Leipzig, 1931).
  • A. J. C. Wilson, Structure Reports Vol. 18: Structure Reports for 1947–1948 (N.V.A. Oosthoek's Uitgevers, Utrecht, 1961).

Geometry files


Prototype Generator

aflow --proto=AB_hP4_186_b_a --params=

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