^{1,a)}, Yurii M. Solonin

^{1}, David N. Batchelder

^{2}and Rik Brydson

^{3}

### Abstract

The structural properties of both nanodiamond particles synthesized by detonation and the products of their transformation into carbon onions via vacuum annealing at 1000 and have been studied using high-resolution transmission electron microscopy(HRTEM), electron energy-loss spectroscopy, x-ray diffraction(XRD), small-angle x-ray scattering (SAXS), and Raman spectroscopy. The advantages of UV Raman spectroscopy over visible Raman spectroscopy for the analysis of these carbon nanomaterials are demonstrated. It was found that the synthesized nanodiamond particles have a composite core-shell structure comprising an ordered diamond core covered by a disordered (amorphous) outer shell formed by the mixed bonding of carbon atoms. The observed structure of the nanodiamond particles are comparable with the structure of the bucky diamond clusters comprising a diamond core and a reconstructed surface which stabilizes the cluster at the average diameter of , as predicted recently from theoretical studies. Assuming a spherical shape for the particles and employing a two-step boundary model of electron density distribution developed in this work to describe the SAXS patterns produced by the core-shell structure of the nanodiamond particles, it was evaluated that the average diameter of the core is and the average thickness of the shell is ; values which are in agreement with results obtained from HRTEM and XRD measurements. A discrepancy between these results and average diamond crystallite size obtained from Raman spectra by applying the phonon confinement model is discussed. It is hypothesized from analysis of broadening of the XRDdiamond peaks that at the nanoscale under influence of the particle shape, which is not strictly of a cubic (or spherical) symmetry, a slight hexagonal distortion of the cubic diamondstructure appears in the nanodiamond particles. The transformation of the nanodiamond into carbon onions proceeds from the amorphous outer shell of the particles inwards towards the particles’ diamond core. UV Raman spectroscopy effectively senses the initial stage of the transformation revealing a reconstruction of the mixed bonding of carbon atoms located in the outer shell, into -bonded carbon atoms similar to those in nanocrystalline graphite. It is shown that intershell distance in carbon onions formed from nanodiamonds depends on the temperature of the transformation and relates to the linear thermal expansion coefficient of the graphitestructure along the stacking direction of the graphene layers (the axis). In accordance with SAXS results, there is evidence for an increase of the average particle size of the synthesized nanodiamond after transformation into carbon onions .

O.O.M. is grateful to the University of Leeds (School of Physics and Astronomy and School of Chemistry) for a Visiting Fellowship. The authors thank Prof. Ian W. Hamley for assistance with the SAXS experiment.

I. INTRODUCTION

II. EXPERIMENT

A. Materials

B. Methods

1. High-resolution transmission electron microscopy and electron energy-loss spectroscopy

2. X-ray powder diffraction

3. Small-angle x-ray scattering

4. Raman spectroscopy

III. RESULTS AND DISCUSSION

A. High-resolution electron microscopy

B. X-ray diffraction

C. Small-angle x-ray scattering

D. Raman spectroscopy

IV. CONCLUSIONS

### Key Topics

- Carbon
- 173.0
- Nanocarbon composites
- 139.0
- Diamond
- 107.0
- X-ray diffraction
- 73.0
- Elemental semiconductors
- 61.0

## Figures

HRTEM image of the nanodiamond recorded at the Scherzer defocus. The two white parallel lines show an interplanar distance of , corresponding to {111} of the diamond crystal structure.

HRTEM image of the nanodiamond recorded at the Scherzer defocus. The two white parallel lines show an interplanar distance of , corresponding to {111} of the diamond crystal structure.

EELS spectra of a general area of the nanodiamond (a), carbon onions found in the partially transformed nanodiamond shown in Fig. 3(b) (b), and carbon onions∕polyhedrons found in the fully transformed nanodiamond (c).

EELS spectra of a general area of the nanodiamond (a), carbon onions found in the partially transformed nanodiamond shown in Fig. 3(b) (b), and carbon onions∕polyhedrons found in the fully transformed nanodiamond (c).

HRTEM images of the nanodiamond annealed in vacuum at for (a) and (b) and (c) and (d) recorded at the Scherzer defocus. Two white parallel lines in part (c) of the figure show an intershell spacing of .

HRTEM images of the nanodiamond annealed in vacuum at for (a) and (b) and (c) and (d) recorded at the Scherzer defocus. Two white parallel lines in part (c) of the figure show an intershell spacing of .

XRD patterns (Cu radiation) of a diamond powder, grain size , used for measurements of an instrumental broadening of the diffractometer (a), the nanodiamond (b), and the nanodiamond annealed in vacuum at for (c) and (d). Positions of diamond (space group , ) and graphite (space group , and ) reflections assigned by Miller indices are shown for reference at the bottom and the top of the figure respectively (wavelength of x-ray radiation has been used in the calculations).

XRD patterns (Cu radiation) of a diamond powder, grain size , used for measurements of an instrumental broadening of the diffractometer (a), the nanodiamond (b), and the nanodiamond annealed in vacuum at for (c) and (d). Positions of diamond (space group , ) and graphite (space group , and ) reflections assigned by Miller indices are shown for reference at the bottom and the top of the figure respectively (wavelength of x-ray radiation has been used in the calculations).

The physical broadening of the diamond diffraction peaks (assigned by Miller indices) in the nanodiamond plotted vs . The solid line is a linear fit to the data used in the Williamson–Hall analysis.

The physical broadening of the diamond diffraction peaks (assigned by Miller indices) in the nanodiamond plotted vs . The solid line is a linear fit to the data used in the Williamson–Hall analysis.

Calculated curves of apparent physical broadening of the diamond diffraction peaks caused by a hexagonal distortion of the diamond cubic cell ( is used as a distortion parameter). The curves are assigned by the Miller indices of the diamond diffraction peaks (Miller indices corresponding to superimposed hexagonal peaks are given in brackets). It has been accepted in the calculations that the nanodiamond crystallites are spherical (average diameter ), the shape of the diffraction peaks is Lorentzian, , where and are volumes of hexagonal unit cells corresponding to the perfect (cubic) diamond crystal structure and to a diamond structure with hexagonal distortion , respectively. The calculations have been made only within a range of values where hexagonal 110 and 104 peaks corresponding to a cubic 022 cannot be resolved experimentally (, where is a full width at half maximum of a Lorentzian).

Calculated curves of apparent physical broadening of the diamond diffraction peaks caused by a hexagonal distortion of the diamond cubic cell ( is used as a distortion parameter). The curves are assigned by the Miller indices of the diamond diffraction peaks (Miller indices corresponding to superimposed hexagonal peaks are given in brackets). It has been accepted in the calculations that the nanodiamond crystallites are spherical (average diameter ), the shape of the diffraction peaks is Lorentzian, , where and are volumes of hexagonal unit cells corresponding to the perfect (cubic) diamond crystal structure and to a diamond structure with hexagonal distortion , respectively. The calculations have been made only within a range of values where hexagonal 110 and 104 peaks corresponding to a cubic 022 cannot be resolved experimentally (, where is a full width at half maximum of a Lorentzian).

A plot of the spacing derived from the angle position of the 002 carbon onion reflection measured in this work (open circle) and another work (see Ref. 10) (closed squares) vs the annealing temperature used for a transformation of nanodiamond into carbon onions. The solid curve represents the thermal dependence of the spacing in a perfect graphite structure [the linear thermal expansion coefficient along the direction of graphene layers stacking, axis, for the calculation was taken from a Handbook (see Ref. 58).

A plot of the spacing derived from the angle position of the 002 carbon onion reflection measured in this work (open circle) and another work (see Ref. 10) (closed squares) vs the annealing temperature used for a transformation of nanodiamond into carbon onions. The solid curve represents the thermal dependence of the spacing in a perfect graphite structure [the linear thermal expansion coefficient along the direction of graphene layers stacking, axis, for the calculation was taken from a Handbook (see Ref. 58).

Porod plot of SAXS patterns for the nanodiamond (diamonds) and the nanodiamond after annealing in vacuum at for (squares) and (circles).

Porod plot of SAXS patterns for the nanodiamond (diamonds) and the nanodiamond after annealing in vacuum at for (squares) and (circles).

The Porod region of SAXS patterns plotted on a logarithmic scale (log–log plot) for the nanodiamond (a), the nanodiamond annealed in vacuum at for (b), and (c). The patterns are fitted by the classical Porod law [dashed lines in (a), (b), and (c)] and by Porod’s law corrected by the sigmoidal-gradient model [solid curves in (a) and (b)].

The Porod region of SAXS patterns plotted on a logarithmic scale (log–log plot) for the nanodiamond (a), the nanodiamond annealed in vacuum at for (b), and (c). The patterns are fitted by the classical Porod law [dashed lines in (a), (b), and (c)] and by Porod’s law corrected by the sigmoidal-gradient model [solid curves in (a) and (b)].

A schematic illustration of the relationship between core-shell structure of a nanodiamond spherical particle with a two-step boundary (a) and electron density variation in the radial direction of the sphere: the sigmoidal gradient model (see Refs. 63 and 79) (b) and a nanodianond particle with a two-step boundary (c). The following parameters , , , , , ), and have been used to plot the scheme.

A schematic illustration of the relationship between core-shell structure of a nanodiamond spherical particle with a two-step boundary (a) and electron density variation in the radial direction of the sphere: the sigmoidal gradient model (see Refs. 63 and 79) (b) and a nanodianond particle with a two-step boundary (c). The following parameters , , , , , ), and have been used to plot the scheme.

Representative multiwavelength Raman spectra of the nanodiamond. Each curve is identified by the wavelength (and photon energy) of exciting laser radiation. The sharp band at of the Raman spectrum excited by originates from vibrational states of oxygen molecules present in a surrounding air. The Raman spectrum excited by is plotted after subtraction of luminescence background approximated by a cubic polynomial.

Representative multiwavelength Raman spectra of the nanodiamond. Each curve is identified by the wavelength (and photon energy) of exciting laser radiation. The sharp band at of the Raman spectrum excited by originates from vibrational states of oxygen molecules present in a surrounding air. The Raman spectrum excited by is plotted after subtraction of luminescence background approximated by a cubic polynomial.

A comparison of experimental Raman spectrum of the nanodiamond (open circles) recorded within a region of the diamond optical modes frequency of with Raman scattering patterns (lines) simulated for nanodiamond crystallites (diameter 30, 35, 45, and ) using the phonon confinement model with Ager *et al.* parameters (see Ref. 26) for an approximation of the diamond dispersion curves. Similar patterns could be achieved with Yoshikawa *et al.* parameters (see Ref. 73) for crystallites of diameter 36, 41, 53, and , respectively. The inset compares the one-dimensional approximation of the diamond dispersion curves at vicinity of the point using both the Ager *et al.* (see Ref. 26) and Yoshikawa *et al.* (see Ref. 73) parameters.

A comparison of experimental Raman spectrum of the nanodiamond (open circles) recorded within a region of the diamond optical modes frequency of with Raman scattering patterns (lines) simulated for nanodiamond crystallites (diameter 30, 35, 45, and ) using the phonon confinement model with Ager *et al.* parameters (see Ref. 26) for an approximation of the diamond dispersion curves. Similar patterns could be achieved with Yoshikawa *et al.* parameters (see Ref. 73) for crystallites of diameter 36, 41, 53, and , respectively. The inset compares the one-dimensional approximation of the diamond dispersion curves at vicinity of the point using both the Ager *et al.* (see Ref. 26) and Yoshikawa *et al.* (see Ref. 73) parameters.

Representative UV Raman spectra (excited by laser radiation with ) of the nanodiamond (a) and the nanodiamond annealed in vacuum at for (b) and (c). Positions of diamond optical mode band at and graphite mode band at are marked, respectively, by the dashed and dotted lines crossing the figure. The inset shows the phonon density of states of diamond. (see Ref. 74). Sharp bands located at and correspond to Raman bands of oxygen and nitrogen molecules, respectively, present in the surrounding air.

Representative UV Raman spectra (excited by laser radiation with ) of the nanodiamond (a) and the nanodiamond annealed in vacuum at for (b) and (c). Positions of diamond optical mode band at and graphite mode band at are marked, respectively, by the dashed and dotted lines crossing the figure. The inset shows the phonon density of states of diamond. (see Ref. 74). Sharp bands located at and correspond to Raman bands of oxygen and nitrogen molecules, respectively, present in the surrounding air.

## Tables

Relation of the Miller indices of the diamond diffraction peaks assigned either in a cubic unit cell (, space group ) or in a hexagonal unit cell ( and , space group ).

Relation of the Miller indices of the diamond diffraction peaks assigned either in a cubic unit cell (, space group ) or in a hexagonal unit cell ( and , space group ).

Characteristics of samples used in the SAXS measurements (the density of the carbon material , the mean density of the powder sample , and the volume fraction of the carbon material in the sample ) and parameters of the samples determined from the SAXS measurements (the Porod constant , the Porod invariant determined from the curve by the numerical integration, the specific surface area , the range of “inhomogeneity” (see Ref. 59), the mean particle core radius (see Ref. 59), the transition-layer width , and the mean diameter of carbon particles ). The results of fitting by two models (the classical Porod law and the Porod law modified by the sigmoidal electron-density gradient model) are presented for the nanodiamond and for the partially transformed nanodiamond. All values have been rounded to significant figures after calculations.

Characteristics of samples used in the SAXS measurements (the density of the carbon material , the mean density of the powder sample , and the volume fraction of the carbon material in the sample ) and parameters of the samples determined from the SAXS measurements (the Porod constant , the Porod invariant determined from the curve by the numerical integration, the specific surface area , the range of “inhomogeneity” (see Ref. 59), the mean particle core radius (see Ref. 59), the transition-layer width , and the mean diameter of carbon particles ). The results of fitting by two models (the classical Porod law and the Porod law modified by the sigmoidal electron-density gradient model) are presented for the nanodiamond and for the partially transformed nanodiamond. All values have been rounded to significant figures after calculations.

Diamond crystallite size (Å) obtained by different methods.

Diamond crystallite size (Å) obtained by different methods.

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