Isotope effects on cubic boron nitride investigated by x-ray scattering

We have investigated effects of boron isotope enrichment of cubic boron nitride (cBN). X-ray Raman scattering spectra of B-10 and B-11 enriched samples did not show any chemical shift. meV-resolved inelastic x-ray scattering was used to measure the phonon dispersion. The shift of phonon frequencies between a sample with the natural abundance of B (20% B-10) and a sample nearly 100% enriched in B-10 was reasonably explained by treating the mass difference with the same force constants--i.e., purely an isotope effect. The observed shifts were also consistent with first-order perturbation theory which gives the frequency shift, Delta(omega j), as Delta(omega j)/omega(j) = -1/2 Delta M-d/M-d e(jd)* center dot e(jd), where M-d, Delta M-d, e(jd), and omega(j) are the atomic mass, change in mass, the eigenvector, and the phonon angular frequency for atom d and phonon mode j, respectively.