Lattice dynamics and Raman spectra of isotopically mixed diamond

Abstract

We present coherent-potential-approximation (CPA) calculations and firstand second-order Raman spectra for diamonds with varying concentrations of ' C and ' C. The calculations are based on the valence-force model of Tubino, Piseri, and Zerbi [J. Chem. Phys. 56, 1022(1972]. Contrary to previous claims, we find that this model does not give a sharp peak in the density of states (DOS) near the Raman mode. Alternative dispersion curves that do give such a peak are discussed. Raman results are reported for high-quality, single-crystal synthetic diamonds with isotopic compositions ranging from nearly pure ' C to nearly pure ' C. A measurable deviation in the Raman frequency away from a simple M (" virtual-crystal" ) dependence and an observable broadening of the firstand second-order spectra are qualitatively consistent with CPA predictions for the effects of isotopic disorder. Quantitative agreement between theory and experiment is achieved only if the reference DOS contains the abovementioned peak. This supports the interpretation of the controversial second-order Raman peak in naturally abundant diamond (1.1 at. % "C) at 2667 cm ' as a DOS effect. At all compositions, the effects of isotopic disorder are relatively weak because of the small mass difference between ' C and ' C. For 1.1 at. % ' C, the maximum broadening predicted in the CPA is less than 1 cm ', nearly two orders of magnitude smaller than a previous estimate. For the lowest-frequency modes most relevant to the thermal conductivity, the CPA scattering rate reduces to the usual co dependence first derived by Klemens for phonon-isotope scattering. Using Callaway's theory, we show that this term can easily account for the recently observed 50% enhancement in room-temperature thermal conductivity upon elimination of ' C impurities, provided that sufficient normal scattering also occurs.

Importance of shattering fragmentation in the surface-induced dissociation of protonated octaglycine

“…The MM potential energy function for the diamond surface consists of harmonic stretches and bends, with force constants chosen to fit the diamond phonon spectrum [22]. To represent the peptide-surface intermolecular potential a MM analytic function was used, comprised of two-body potential functions of the form…”

High-Resolution Raman and Luminescence Spectroscopy of Isotope-Pure ²⁸Si¹²C, Natural and ¹³C – Enriched 4H-SiC

“…This explains the same (within the experimental accuracy) position of this mode in the Raman spectra of the Si isotope mass. In most cases VCA produces only rough estimation of the experimental phonon energies, similar to the case of diamond [5]. SiC [3].…”

“…The stiffest modes (highest Raman shifts) for all the lines are observed in the 28 Si 12 C sample, as expected in view of the "lightening" of the atomic weight of both atomic species and the intuitive anticipation that the squared vibrational frequency would scale as the inverse of the atomic mass. Useful approximation used to describe the effect of mass disorder due to presence of different isotopes in any of the C or Si sublattices is the virtual crystal approximation (VCA) [4], although much more accurate theory exists for elemental crystals, e.g., diamond [5]. Hereafter we use the notations of [3,4] for the folded modes (e.g., FLA(x) for longitudinal and FTA(x) for transversal acoustic modes, respectively, with x=0, 2/4 or 4/4 for 4H-SiC, etc.).…”

Basic Properties of Diamond: Phonon Spectra, Thermal Properties, Band Structure

“…In contrast, at small x, the 'impurity' atoms are 13 C, which lower the frequency of the active modes away from the Raman energy. The disorder shift is asymmetric, maximising near x = 0.6 in this case [57]. From the measured disorder broadening, at x = 0 the line width is expected to change at the rate d /dx = 2 meV, so that in a natural diamond the isotope disorder contributes about 0.16 cm −1 , or over 10 %, to the line width.…”