Raman spectroscopy of nanocrystalline diamond: An ab initio approach

The use of Raman spectroscopy to detect nano-sized diamond crystals is controversial; the origins of peaks at $\sim 1150{\mathrm{cm}}^{-1}$ in chemical vapor deposition nanodiamond films and $\sim 500{\mathrm{cm}}^{-1}$ in nanodiamond particles, which have both been suggested as evidence for nanophase material, remain uncertain. Many studies have produced evidence showing that the $\sim 1150{\mathrm{cm}}^{-1}$ peak is in fact due to polyacetylenelike structures at grain boundaries and interfaces, but little work has been done to confirm the assignment of the $\sim 500{\mathrm{cm}}^{-1}$ peak. In this paper we approach the problem from the molecular level, using Hartree-Fock theory to calculate the Raman spectra of diamond hydrocarbons, and observe the variation of the spectra with molecular size. Molecules with $T_{\mathrm{d}}$ symmetry are studied, varying in size from adamantane to ${\mathrm{C}}_{84}{\mathrm{H}}_{64}$, an octahedral $1\mathrm{nm}$-sized diamond crystallite. For comparison with nanodiamond thin films, the mass of the terminal hydrogen atoms were artificially increased to $100\mathrm{amu}$, approximating the effects of matrix isolation. The calculated spectra are discussed in terms of the signals commonly observed in the Raman spectra of nanocrystalline diamond samples. This study finds no evidence for Raman active vibrations of diamond nanocrystals at either $\sim 1150{\mathrm{cm}}^{-1}$ or $\sim 500{\mathrm{cm}}^{-1}$, whether hydrogen terminated or confined in a matrix. Further, it appears that the only signals produced by a nanodiamond crystal are the broadened zone-center $\left(1332{\mathrm{cm}}^{-1}\right)$ mode and low frequency $(<100{\mathrm{cm}}^{-1})$ deformations/Lamb-type vibrations. This suggests any other peaks observed in the Raman spectra of nanocrystalline diamond are due to defects, surface structures, amorphous material, or any other nondiamond material in the sample, and should not be taken as definitive evidence of nanocrystalline diamond.

Figure 1

Raman spectra of adamantane, experimental (Ref. 24) and calculated (with scale factors), (a) experimental, (b) $\mathrm{B}3\mathrm{LYP}∕\mathrm{Sadlej}$ (0.9726), (c) B3LYP/6-31${\mathrm{G}}^{*}$ (0.9603), (d) HF/6-31${\mathrm{G}}^{*}$(0.8985), (e) $\mathrm{HF}∕3\text{−}21\mathrm{G}$ (0.9056), and (f) $\mathrm{HF}∕\mathrm{STO}\text{−}3\mathrm{G}$ (0.8165).

Figure 2

Octahedral diamond hydrocarbons, (a) ${\mathrm{C}}_{10}{\mathrm{H}}_{16}$, (b) ${\mathrm{C}}_{35}{\mathrm{H}}_{36}$, (c) ${\mathrm{C}}_{84}{\mathrm{H}}_{64}$; (001) reconstructed octahedral diamond hydrocarbons (d) ${\mathrm{C}}_{78}{\mathrm{H}}_{52}$, (e) ${\mathrm{C}}_{78}{\mathrm{H}}_{40}$; tetrahedral diamond hydrocarbons (f) ${\mathrm{C}}_{26}{\mathrm{H}}_{32}$, (g) ${\mathrm{C}}_{51}{\mathrm{H}}_{52}$, (h) ${\mathrm{C}}_{87}{\mathrm{H}}_{76}$, and (i) the $C_1$ symmetry diamond hydrocarbon ${\mathrm{C}}_{43}{\mathrm{H}}_{44}$.

Figure 3

Calculated Raman spectra for (a) ${\mathrm{C}}_{10}{\mathrm{H}}_{16}$, (b) ${\mathrm{C}}_{35}{\mathrm{H}}_{36}$, (c) ${\mathrm{C}}_{84}{\mathrm{H}}_{64}$, (d) ${\mathrm{C}}_{26}{\mathrm{H}}_{32}$, (e) ${\mathrm{C}}_{51}{\mathrm{H}}_{52}$, (f) ${\mathrm{C}}_{87}{\mathrm{H}}_{76}$, (g) ${\mathrm{C}}_{78}{\mathrm{H}}_{52}$, (h) ${\mathrm{C}}_{78}{\mathrm{H}}_{40}$, and (i) ${\mathrm{C}}_{43}{\mathrm{H}}_{44}$.

Figure 4

Raman spectra of diamond hydrocarbons (a) experimental Raman spectrum of ${\mathrm{C}}_{26}{\mathrm{H}}_{32}$ (peak at $518{\mathrm{cm}}^{-1}$ cropped for clarity), (Ref. 24) (b), (c), and (d) spectra of ${\mathrm{C}}_{26}{\mathrm{H}}_{32}$, calculated using HF theory and increasingly large basis sets, (e) and (f) spectra of ${\mathrm{C}}_{26}{\mathrm{H}}_{32}$, calculated using HF theory and the 3-21G and 6-31+${\mathrm{G}}^{*}$ basis set, respectively.

Figure 5

Variation in the calculated (AMBER) Raman shift of the breathing mode with molecule size. The length plotted was determined from the distance between opposite points of the octahedral structure (see inset).

Figure 6

Calculated Raman spectra for (a) ${\mathrm{C}}_{84}{\mathrm{H}}_{64}$, (b) ${\mathrm{C}}_{78}{\mathrm{H}}_{52}$, (c) ${\mathrm{C}}_{78}{\mathrm{H}}_{40}$, with H $\mathrm{mass}=100\mathrm{amu}$.