Effects of isotopic disorder on the phonon spectrum of diamond

Abstract

We examine the phonon spectrum of isotopically disordered diamond using the coherent-potential approximation (CPA). Predictions for the zone-center optic mode are compared to measurements of the first-order Raman spectrum of high-quality, single-crystal, synthetic diamonds with isotopic compositions ranging from nearly pure ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ to nearly pure ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$. The CPA accounts very well for the observed nonlinear composition dependence (‘‘bowing’’) of the Raman mode and for its asymmetric variation in width. The maximum disorder-induced broadening predicted by the CPA for naturally abundant diamond (1.1% ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$) is less than 1 ${\mathrm{cm}}^{\mathrm{-}1}$, nearly 2 orders of magnitude smaller than that assumed in a previous study of the possible effects of isotopic disorder on the thermal conductivity of diamond.