Original BN ($B12$) Structure (Obsolete): AB_hP4_186_b_a-001
| Prototype | BN |
| AFLOW prototype label | AB_hP4_186_b_a-001 |
| Strukturbericht designation | $B12$ |
| ICSD | none |
| Pearson symbol | hP4 |
| Space group number | 186 |
| Space group symbol | $P6_3mc$ |
| AFLOW prototype command |
aflow --proto=AB_hP4_186_b_a-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}$ |
- This is the BN structure found in (Ewald, 1931) p. 95 and (Wilson, 1961) 125-126. (Pease, 1950) later determined that the true boron nitride structure is what is now known as the $B_{k}$ structure. We leave this structure here for historical reasons. It is crystallographically equivalent to, and hence a binary representation of, the buckled graphite structure.
- Space group $P6_{3}mc$ #186 does not specify the origin of the $z$-axis. Here we chose $z_{1} = 0$ for the boron (2a) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | N I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | N I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2b) | B I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | B I |
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, eds., Strukturbericht 1913-1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
Found in
- A. J. C. Wilson, ed., Structure Reports for 1947–1948, Structure Reports, vol. 18 (N.V.A. Oosthoek's Uitgevers, Utrecht, 1961).
Prototype Generator
aflow --proto=AB_hP4_186_b_a --params=$a,c/a,z_{1},z_{2}$