Phonons of hexagonal BN under pressure: Effects of isotopic composition

Raman scattering experiments on isotopically enriched hexagonal boron nitride have been performed under pressure up to 11 GPa at room temperature. The sublinear increase of the Raman-active $E_{2g}$ mode frequencies has been characterized. The pressure behavior has been analyzed by means of a bond-stiffness–bond-length scaling parameter $\gamma$ which takes into consideration the vast differences in $a$- and $c$-axis compressibilities. The interlayer shear mode exhibits a $\gamma$ parameter similar to that of graphite, and the mode frequency in isotopically pure samples separates faster at low pressures as a result of van der Waals interactions. Because of the extremely low $a$-axis compressibility, the intralayer mode exhibits a rather large scaling parameter. Within experimental uncertainties, no systematic departures related to isotopic mass have been observed.

Figure 1

Representative Raman spectra of the $h$-BN Raman-active modes of $E_{2g}$ symmetry at three different pressures. The spectra have been normalized to the intensity of the $E_{2g}^{\mathrm{high}}$ mode at ambient pressure to account for the slight thickness differences among the exfoliated samples.

Figure 2

Pressure dependence of the two $E_{2g}$ modes of $h$-BN up to the phase-transition pressure for different isotopic compositions. Symbols correspond to Raman scattering measurements, whereas the solid line displays the results of the ab initio calculations. The dashed lines correspond to fits of a Murnaghan-type expression to the data (see text).

Figure 3

Pressure coefficients of the two $E_{2g}$ modes of $h$-BN for different isotopic compositions compared to the ab initio calculations (dashed lines).

Figure 4

(a) Pressure dependence of the $E_{2g}^{\mathrm{low}}$ frequency after subtraction of a common linear trend for all the isotopic compositions studied. Symbols are experimental data, and solid lines are the results of ab initio calculations. (b) Frequency difference between the $E_{2g}^{\mathrm{low}}$ interlayer shear modes of ${}^{10}\mathrm{B}\mathrm{N}$ and ${}^{11}\mathrm{B}\mathrm{N}$ isotopically pure samples at different pressures. The solid line is the result of ab initio calculations including the density-functional dispersion correction DFT-D3(BJ) to account for van der Waals interactions; the dotted line is calculated without nonlocal van der Waals corrections.