(Phonon) Density of States - American Chemical Society

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Structural Determination of Metal Nanoparticles from their Vibrational (Phonon) Density of States Huziel Enoc Sauceda, and Ignacio L. Garzon J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp510666v • Publication Date (Web): 05 Nov 2014 Downloaded from http://pubs.acs.org on November 9, 2014

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The Journal of Physical Chemistry

Structural Determination of Metal Nanoparticles from their Vibrational (Phonon) Density of States Huziel E. Sauceda and Ignacio L. Garzón Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México, D. F., México

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* To whom correspondence should be addressed. Email: [email protected] Phone: +52-55-56225147 Fax: +52-55-56161535

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ABSTRACT. The vibrational (phonon) density of states of metal nanoparticles with size between 2-6 nm can be measured using nuclear resonant inelastic x-ray or plasmon resonance Raman scattering. In this work, we present atomistic calculations, based on a semiempirical tight-binding many-body Gupta potential, of the vibrational density of states (VDOS) for FCC, decahedral, and icosahedral (ICO) gold and silver nanoparticles with sizes ∼ 4 nm (∼ 2000 atoms). The calculated VDOS are compared with experimental data, recently published for gold and silver nanoparticles of similar size, obtained through plasmon resonance Raman scattering. The best agreement between the calculated and measured VDOS’s is obtained for the ICO morphology for both metal nanoparticles. These results indicate that most of the nanoparticles in the experimental samples should have icosahedral structures. The present study also shows that, as in the case of molecular systems and small clusters, vibrational spectroscopy of metal nanoparticles with few nanometers in size, together with theoretical calculations, are powerful tools for their structure determination.

KEYWORDS: Au nanoparticles, Ag nanoparticles, Vibrational frequencies, Raman scattering


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Introduction To determine the geometrical structure of metal clusters and nanoparticles is a fundamental issue in Nanoscience and Nanotechnology.1 Important progress had been achieved by using x-ray analysis when the metal clusters can be crystalized into a nanostructured material.2 For supported metal nanoparticles, aberration corrected transmission electron microscopy (TEM) had provided reliable structural information, although electron beam effects need to be controlled.3 The atomic structure of metal clusters in gas phase had also been widely investigated using photoelectron4,5 and optical absorption6 spectroscopies, as well as trapped ion electron diffraction.7,8 Nevertheless, the last three experimental techniques should be combined with theoretical calculations, mostly based on first-principle methods, of the most stable cluster structures.9-11 On the other hand, vibrational spectroscopy of molecular systems12 and small clusters13 together with theoretical calculations had been also used to determine their geometrical structure. One open question is if this procedure can be applied for the structural determination of larger nanostructures like metal nanoparticles in the size range 2-10 nm. In this respect, measurements and calculations of the vibrational spectrum of metal nanoparticles would be necessary. On the experimental side, there had been a report on the size-dependent behavior of the vibrational density of states (VDOS) of supported Fe nanoparticles in the size range of 2-6 nm measured by nuclear inelastic x-ray scattering.14 More recently, plasmon resonance Raman scattering had been used to extract the VDOS of supported Au and implanted Ag nanoparticles with size ∼ 5 nm.15,16 It was claimed from these experimental results that the VDOS would provide enough information on the interplay between atomic vibrations and the internal structure of the metal nanoparticles.15,16 Theoretical calculations of the VDOS for metal nanoparticles are more abundant. One of them showed that there is an enhancement in the VDOS at low frequencies and the appearance of a high frequency tail as compared with the bulk VDOS.17 Other study on silver nanograins indicated that


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indeed their morphology introduces a high degree of complexity into their phonon spectra and VDOS.18 Also, it had been reported that the VDOS of copper nanoclusters shows a shape dependence, particularly in the high frequency region, when FCC and icosahedral (ICO) structures are compared.19 Interestingly, similar differences between the VDOS of FCC and ICO morphologies had also been found for gold-silver nanoalloys.20 More recently, we have discussed the dependence of the VDOS on the material, size, and shape for Au, Pt, and Ag nanoparticles in the size range 0.5 – 4 nm with FCC, ICO and decahedral (DEC) morphologies.21 Moreover, we also have shown the usefulness of the VDOS to calculate the low-temperature behavior of the thermal energy and specific heat of sodium clusters22 and gold nanoparticles.23 In this work, we present a comparison of the calculated VDOS for FCC, ICO, and DEC Au and Ag nanoparticles with recent published experimental data obtained using plasmon resonance Raman scattering.15,16 From this analysis it is obtained that the ICO morphology produce a theoretical VDOS that gives the best agreement with the experimental one for both silver and gold nanoparticles. We also provide a discussion related with the consistency of these results with those indicating that FCC morphologies are the ones observed by transmission electron microscopy (TEM).15,16,24,25 In this way, it is shown that vibrational spectroscopy of metal nanoparticles, together with theoretical calculations are useful techniques for their structural determination.

Methodology The atomic interactions in the Au and Ag nanoparticles were modeled by a many-body Gupta potential using parameters fitted to bulk properties given by Cleri and Rosato.26 Nanoparticles with FCC, DEC, and ICO morphologies containing ∼ 2000 atoms were structurally optimized without symmetry constraints. For this purpose, it was implemented a simulated quenching technique27-29 using constant-energy molecular dynamics, before the vibrational normal modes analysis was performed. The vibrational density of states (VDOS) was constructed using a Gaussian broadening (with a width of


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0.045 and 0.060 THz for Au and Ag, respectively) of the 3N-6 eigenvalues obtained from the diagonalization of the dynamical matrix.

Results and Discussion Figure 1 shows the calculated VDOS of ~ 4 nm Au and Ag nanoparticles with ICO, FCC, and DEC morphologies. Although the VDOS corresponding to the FCC and DEC morphologies display similar lineshapes, that one corresponding to the ICO geometry shows clear differences like the decrease and broadening of the most intense peak around 4.5 THz for the Ag nanoparticles and 3.5 THz for the Au ones. The shape dependence on the VDOS has been discussed in our previous studies on the vibrational properties of metal nanoparticles.21,23 In particular, the damping of the high frequency peak in the VDOS of the ICO nanoparticles has been attributed to the larger strain and twining existing in this morphology,18 and to the smaller lattice contraction and internal pressure as compared with those present in the FCC nanoparticles.19 A similar distinct behavior had been obtained in the calculations of the VDOS for ICO and FCC nanoparticles in which the atoms interact through a pairwise LennardJones potential, indicating that this effect is not related with the type of bonding existing in the nanoparticle.30


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Figure 1. VDOS of Ag and Au nanoparticles with ICO, FCC, and DEC morphologies. It should be noticed the decrease and broadening of the most intense high frequency peak around 4.7 THz for Ag and 3.5 THz for Au nanoparticles when the structure change from FCC and DEC to ICO.

Once it has been shown the existence of an unambiguous shape dependence in the calculated VDOS of metal nanoparticles, it would be interesting to compare with recently published experimental results for the VDOS of Au and Ag nanoparticles.15,16 In one of these experiments, plasmon resonance Raman scattering has been used to extract the VDOS of functionalized Au nanoparticles deposited on a substrate consisting of a bilayer composed of a thin SiO2 layer grown on a Si wafer.15 The average diameter of the Au nanoparticles, as determined by TEM is of ~ 5 nm with a standard deviation of 15%.15 It was claimed that the presence of the ligands in the protected nanoparticles should not affect their VDOS since they vibrate at much higher frequencies than the Au atoms.15 In a second experiment,


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the VDOS of Ag nanoparticles embedded near to the free surface of a SiO2 layer grown on a Si wafer was also obtained using plasmon resonance Raman scattering.16 TEM analysis indicated that the average particle size is ~ 4.6 nm with a standard deviation of ~1.0 nm.16 As the experimental determination of the VDOS by Raman scattering is quite new, we briefly recall the experimental procedure (but the synthesis) and the main assumptions to obtain such result (full details can be found in Refs. 15 and 16). Due to the narrow cross section of the nanoparticles, the experiment required an optical amplification of the Raman signal. This was achieved by a specific surface architecture (a thin SiO2 layer over a Si substrate) and a special experimental set up. The laser wavelength was set to fit the plasmon resonance condition. Also, the thickness of the dielectric layer was chosen in such a way that the total electric field reaches its maximum amplitude at the free surface (antireflective condition), enhancing the whole Raman spectrum. In order to reduce spurious scattering, dark-field Raman spectroscopy was used, and the illumination of the charge-couple device (CCD) detector at the spectrometer was restricted to the intermediate frequency range, the “bulk” phonons (0.12 – 5 THz). Additional considerations were taken in each case (supported and embedded nanoparticles) to discriminate between Raman and photoluminescence processes. To keep just the vibrational contribution of the scattered spectrum, the recorded Raman intensity was corrected by subtracting the electronic contributions (electron-hole excitations), and dividing by the thermal (BoseEinstein) population factor. In this way, to relate the corrected Raman signal with the VDOS, a classical description is assumed, where the Raman-scattering spectral response is described as the space-time Fourier component of the autocorrelation function of the dielectric tensor fluctuations.31 By considering that the vibrational normal modes in the nanoparticles are localized, the momentum selection rules break down and causes that the whole spectrum contributes to the scattering signal, providing a direct relation between the corrected Raman signal and the VDOS.15,16,31


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Figure 2 displays the experimental VDOS (black dots) for the Au and Ag nanoparticles extracted from Raman scattering experiments.15,16 These VDOS’s show a very similar profile for the two metal nanoparticles, in which two broad bands can be distinguished. It should be noticed that the high frequency band has a smaller intensity than the one lying at low frequencies. Interestingly, a similar behavior has been found in the VDOS measured for Fe nanoparticles in the size range 2-6 nm using nuclear inelastic x-ray scattering.14 The smaller intensity of the high frequency band measured for Au, Ag, and Fe nanoparticles is in contrast with the experimental VDOS behavior of the corresponding bulk metals that show a much higher intensity in the high frequency peak.14-16 The calculated VDOS for the Au2057 and Ag2057 nanoparticles with icosahedral geometry (blue line) are also displayed in Fig. 2. The agreement with the experimental data is excellent, although a scaling by a factor of 1.2 has been applied to the frequency dependence of the calculated VDOS for the Au nanoparticle to match the maximum of the high frequency band of the experimental VDOS. While no scaling was necessary in the comparison of the Ag nanoparticles, for Au it is known that the semiempirical Gupta potential underestimates by about 20% the bulk maximum phonon frequency.15,26 This inadequacy to account for the phonon high frequencies in gold had been ascribed to strong contributions from non-central many-body forces.15,26 On the other hand, the Gupta potential has correctly predicted the magnitude of the size dependence of the period corresponding to the quasi-breathing mode (QBM) of Au nanoparticles, that was measured using pump-probe spectroscopy.21 Since the frequency of the QBM lies in the low frequency region for 4 nm Au nanoparticles,21 it is justified to apply a 1.2 scaling factor to the frequency dependence of the VDOS, instead of displacing it by using a constant blue shift. In any event, the clear differences in the VDOS lineshape of the ICO morphology with respect to the ones corresponding to the FCC and DEC structures, shown in Fig. 1, indicate that the latter geometries are not adequate to reproduce the experimental data of the VDOS for both Ag and Au nanoparticles. It should be also mentioned that although the present calculations were performed for free nanoparticles


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(with 4 nm in size), the effect of the embedding matrix15,16 or the protecting ligands32 only produce slight distortions at their surface, that do not strongly modify the differences in the VDOS lineshapes described above. Since it has been found that the ICO morphology gives the best agreement between the calculated and experimental VDOS, it can be concluded that this morphology would be the most abundant in the experimental samples. Nevertheless, this conclusion might be in contrast with the information mentioned in Refs. 15 and 16, indicating that the samples correspond to crystalline Ag and Au nanoparticles, according to TEM measurements. If this information is verified, confirming a higher abundance of nanocrystalline Ag and Au morphologies in the experimental samples, two possible explanations exist to solve this controversy. One of them is related with recent experimental results on a statistical investigation of size-selected Au nanoparticles containing 923 atoms via aberration-corrected TEM, showing that virtually all of the ICO nanoclusters undergo a structural transformation into DEC and FCC morphologies after electron irradiation.24,25 Then, it would be possible that the samples used for the Raman scattering experiments described in Refs. 15 and 16 indeed correspond to ICO nanoparticles, but the TEM images displaying crystalline patterns are the result of similar structural transformations as reported in Refs. 24 and 25. In fact, theoretical calculations of the free energy within the harmonic approximation indicated that at room temperature ICO nanoparticles are as energetically stable as the FCC and DEC ones (see, for example, Fig. S1 in Ref. 21). Other explanation is that the plasmon resonance Raman scattering measurements would not be providing the total VDOS of the Ag and Au nanoparticles, although this possibility has been ruled out, as can be noticed in the discussion of the experimental results reported in Refs. 15 and 16. In any event, the comparison of theoretical and experimental results for the VDOS of Au and Ag nanoparticles presented in this work should motivate additional experimental analysis to make consistent the above results.


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Figure 2. Calculated (blue line) and experimental (black dots) VDOS of Au and Ag nanoparticles. The calculated VDOS’s correspond to the ICO morphology with 2057 atoms. A 1.2 scaling factor was applied to the frequency dependence of the VDOS corresponding to the Au2057 nanoparticle in order to match the maximum of the experimental high frequency band. The experimental data are taken from Refs. 15 and 16.


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In order to gain additional insight into the vibrational properties of metal nanoparticles it is useful to further investigate the origin of the differences in the VDOS of ICO and FCC nanoparticles, particularly the distinct relative intensity of the high frequency peak shown in Fig. 1. Figure 3 displays the frequency spectrum and VDOS for the Au55 with ICO and FCC morphologies calculated using the many-body Gupta potential. For this cluster size, the number of vibrational modes is much smaller than for the 4 nm nanoparticles, such that the analysis and animation of the high frequency modes can be performed with higher detail. In fact, the main difference in the VDOS’s shown in Fig. 3 is at the high frequency region. The maximum cutoff frequency for the FCC Au55 cluster is 4.68 THz, whereas for the ICO morphology it is 5.31 THz. In addition, a group of 12 vibrational modes (1 five-fold-, 2 three fold-, and 1 non-degenerated) lie in the frequency range 4.89-5.31 THz, well beyond the FCC-like isomer maximum cutoff frequency. The higher values of these 12 frequencies might be related with the larger internal compression and stress (due to shorter radial distances between the central atom and the 12 atom shells) in the ICO geometry. In contrast, the radial distances in the less compact FCC isomer are larger such that their corresponding higher 12 vibrational modes lie at much lower frequencies. The shorter radial distances characterizing the ICO geometry as well as the larger ones existing in the FCC isomer can be noticed in Fig. 4(a). The animation of the 12 highest frequency modes confirms that indeed the higher compression and stress (due to shorter radial distances) in the ICO isomer are the responsible for their separation toward higher values of frequency with respect to those of the FCC isomer. In fact, these 12 high frequency modes involve radial motions of the 13-atom core and antibreathing oscillations of the first atomic shell against the second one for both isomers, as well as atomic oscillations along the 5-fold (ICO) and 3-fold (FCC) axis. Interestingly, similar trends had been also obtained after analyzing the calculated highest frequencies of Ni and Cu clusters with up to 150 atoms in size.33 The separation of a group of high frequency modes for the ICO morphology is also obtained for


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larger sizes as can be appreciated in the VDOS’s of the ICO Au2057 nanoparticle (see Fig. 1). Moreover, Fig. 4(b) shows that the radial distances of the Au13 core forming the Au2057 nanoparticle are slightly shorter than in the isolated Au55 cluster, increasing the compression and stress in the larger nanoparticle. On the other hand, when the FCC isomers grow in size, the high frequency modes accumulate at not so large frequencies increasing the intensity of the high frequency peak. As a matter of fact, the size evolution of the VDOS from 0.6 up to 4 nm of Au nanoparticles can be seen in Figs. 1 and 2 of Ref. 21, displaying the behavior commented above. In this way, by examining and counting the high frequency modes of the Au55 ICO and FCC isomers, it is possible to gain additional insight into the origin of the different features of the VDOS’s for larger nanoparticles.

Figure 3. Vibrational frequency spectra (blue bars) and VDOS (red line) of the Au55 cluster with ICO and FCC morphologies. The dashed line at 4.5 THz separates the 12 highest frequency modes.


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Figure 4. Radial distances from the central atom of (a) ICO Au55 (blue dots) and FCC Au55 (red dots). (b) ICO Au55 core within Au2057 (green dots) and isolated ICO Au55 (blue dots).

Summary A comparison of the calculated VDOS for 4 nm Ag and Au nanoparticles having ICO, FCC, and DEC morphologies with those extracted from plasmon resonance Raman scattering measurements was presented. From this comparison it is found that the best agreement is obtained for the ICO morphology, for both metal nanoparticles. This result indicates the higher abundance of ICO nanoparticles in the experimental samples. Nevertheless, TEM images show the existence of nanocrystalline shapes for both Ag and Au nanoparticles.15,16 We suggest that this discrepancy might be attributed to a structural transformation from ICO to FCC morphologies after electron irradiation during the TEM measurements, as has been reported for size-separated gold clusters with 923 atoms.24,25 A less probable explanation would be related with an incomplete extraction of the whole VDOS from the Raman scattering data


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reported in Refs. 15 and 16. In any event, the present study shows that it is possible to use the calculated and measured VDOS’s for the structural determination of metal nanoparticles in the sizes around 4-5 nm. These results should also motivate additional experimental analysis to solve the discrepancies mentioned above.

ACKNOWLEDGMENT We acknowledge support from Conacyt-México under Project 177981. Calculations were done using resources from the Supercomputing Center DGTIC-UNAM. HES acknowledges support from Programa de Doctores Jóvenes de la Universidad Autónoma de Sinaloa. We thank Israel Acuña for programing in CUDA language the molecular dynamics and vibrational analysis codes used in this work.

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SYNOPSIS TOC


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93x105mm (300 x 300 DPI)



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68x57mm (300 x 300 DPI)


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39x22mm (300 x 300 DPI)


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(Phonon) Density of States - American Chemical Society

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