Results and discussion
4.2 Raman Spectra of Nanodiamonds
Nanodiamond is an attractive material both for experimentalists and theoreticians.90 Its potential applications are ultrathin and ultrahard antifriction coatings, optical coatings, and insulating or semiconducting layers in electronic devices.91,92 Higher diamondoids were isolated in 200393; this stimulated the characterization of nanodiamonds. The experimental Raman spectrum of a single crystal diamond has an unique triply degenerate T2g peak appearing at 1332 cm-1. Several theoretical studies had been devoted to the Raman spectra of molecular diamond94,95. These works tried to find out the signature of the nanodiamond Raman spectra. The different goal of this work is to observe the evolution of the Raman spectra of diamond from the molecular level to the bulk scale, tracing the appearance of the unique 1332 cm-1 peak. This study can be helpful for the future experimental also theoretical investigation of the Raman sectra of nanodiamond clusters.
Figure 4.13 presents the models being considered in the present study. Note that the
original space group of single crystal diamond isFd m3 , but owing to the missing inversion symmetry operation, it reduces to the Td symmetry for molecular diamond.
There are two distinct structures belonging to the Td point group: octahedron and tetrahedron. In this study we chose both series of nanodiamonds. We saturate the surface carbon atoms with hydrogen atoms to stabilize the structure. For simplicity, new notations for these two series of diamonds have been made. Their molecular formulas and notations are listed in Figure 4.13. We call adamantane (C10H16) as A; it is the smallest molecule in both octahedral and tetrahedral diamond series. By counting how many layers of “caves” in one tetrahedron formed by sp3 carbon networks in one molecule, we use symbols O2 to O8 to present the octahedral diamonds, and T2 to T10 for the tetrahedral diamonds. The temperature is set to be 25
°C and the laser frequency is 514.5 nm, which are corresponding to experimental environment for obtaining Raman intensity.
The SCC-DFTB Raman spectra are shown in Figure 4.14; we perform the DFT vibrational spectra calculations for selected molecules, A, O1, O2, O3, T2, T3, and T4.
The BLYP density functional and 3-21G basis set are used for geometric optimizations and vibrational spectra calculation. For A and T2, we calculate the vibrational spectra using a larger 6-31+G* basis set. Here we truncate the high frequency CH stretching signal from the spectra, because this signal will not appear in real experimental Raman spectra of single crystal diamond. At first glance, one can easily observe that the spectra from the two different methods show an overall agreement. Especially for the BLYP/6-31+G* Raman spectra of A and T2, the agreement is even closer. The most significant deviation of the spectra is the peak at around 1500 cm-1. This signal corresponds to the CH scissoring mode. The deviation is probably due to that the SCC-DFTB repulsive parameters for the carbon-hydrogen pair is not accurate enough, the new optimization of these parameters is under process.
The other discrepant peak appears at around 1150 cm-1, this is a T2 CC waving mode.
The discrepancy of the frequency is around 50 cm-1, which is within a reasonable range as reported in the previous benchmark.5 These facts provide us with an evidence for the quality of the SCC-DFTB Raman spectra of larger nanodiamonds.
Further, the SCC-DFTB Raman spectra of both tetrahedral and octahedral diamonds are shown in Figure 4.15. As pointed out by Filik et al95, the peaks assemble into three groups. The lowest frequency group contains the A1 cage breathing mode. This mode is the peak that lowest in energy. As mentioned before95, this mode has been justified that it can not be a characteristic of nanodiamond Raman spectra. The second group of peaks explains that with the growing molecular size, the peaks get closer. If we go into more detail, as shown in figure 4.16, where we enlarge the spectra for the last three molecules of both series, the peaks belonging to T2 rise up at frequency around 1200 cm-1. Note that for the spectra of O6 ~ O8, there is not the misleading E symmetric band as in the spectra of tetrahedral nanodiamonds.
The strongest peak in the spectra of O6 ~ O8 is of T2 symmetry. The mode of this peak is the CC-stretching mode, which is consistent to the mode at 1332 cm-1 of the experimental Raman spectra of nanodiamonds. This mode is in fact slightly red–shifting with growing molecular size. But for the largest systems we had here, it is almost not moving.
We try to examine whether or not the present peaks on the Raman spectra are those we expect. As previously proposed by Negri96 for polycyclic aromatic hydrocarbons (PAH), and Filik95 for molecular diamonds, the mass of the terminating hydrogen atoms are artificially changed to 100 amu, which leads to a result that only the carbon atoms enclosed by the hydrogens are allowed to vibrate. This simulates the condition of the carbon atoms in a real crystal, and decouples the noisy signals caused by the CH vibrations within the same region of the CC stretching mode for real diamond crystal in the Raman spectrum. Following the same idea, we set the mass of
spectra calculations for all the diamond models, aiming to obtain the peak in the Raman spectra corresponding to the 1332 cm-1 peak in the experimental Raman spectrum of bulky diamond. We term these diamonds “infinitely heavy hydrogens”
(infH) diamonds. Only the modes related to carbon vibration are left in the infH spectra. Obviously, the peak of T2 symmetry ~1200 cm-1 shown in Figure 4.17 is the strongest signal in both series of infH diamonds.
In the end of this preliminary study, we present the infH Raman spectra that only contain T2-symmetric modes. The spectra are given in Figure 4.18 and Figure 4.19.
They give the evidence that the ~1200 peak is almost solely from the T2 mode intensities. Although the present value of the frequency is ~130 cm-1 from the real experimental result. The theoretically calculated frequency of diamond Raman spectra had been shown that depend strongly on the method used.97 At this stage, we can conclude that the 1200 cm-1 is the SCC-DFTB signal of nanodiamond Raman spectra.
Tetrahedral diamond hydrocarbons
Figure 4.13 The structures, molecular formula, and abbreviations of the tetrahedral and octahedral nanodiamonds.
Octahedral diamond hydrocarbons
Figure 4.14 Comparison of the Raman specra calculated by BLYP/3-31G, SCC-DFTB,
Figure 4.15 The Raman spectra evolution with respect to the size of the tetrahedral and octahedral nanodiamonds.
Figure 4.16 The evolution of the T peak in the Raman spectra of the three 2 largest nanodiamonds for tetrahedral and octahedral nanodiamonds.
Figure 4.17 The evolution of Raman spectra for both tetrahedral and octahedral nanodiamonds with “infH” case.
Figure 4.18 The formation of the band at around 1200 cm-1 of the “infH” tetrahedral nanodiamonds.
Figure 4.19 The formation of the band at around 1200 cm-1 of the octahedral nanodiamonds.
A1g D band E2g G band