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Acoustic Vibrations of Monoclinic Zirconia Nanocrystals Frederic Demoisson, Moustapha Ariane, and Lucien Saviot* Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 5209 CNRS-Universite de Bourgogne, 9 Av. A. Savary, BP 47 870, F-21078 Dijon Cedex, France ABSTRACT: Polarized low-frequency Raman spectra originating from confined acoustic vibrations are reported for monoclinic ZrO2 nanoparticles with a narrow size distribution synthesized from a continuous supercritical water process. The monoclinic lattice structure is taken into account for the interpretation of the spectra by comparing with isotropic and anisotropic continuum elasticity calculations for monodomain nanocrystals. The various mechanisms leading to the broadening of the Raman peaks are discussed. We demonstrate that an accurate determination of the size distribution of the nanoparticles is possible using the Raman peak due to the fundamental breathing vibration which is hardly broadened by the elastic anisotropy and the shape distribution.
’ INTRODUCTION During the past decades, a large amount of works have been devoted to the study of the Raman scattering from nanoparticles. While most of these works were focused on the usual Raman bands of the corresponding bulk solids, some others were dedicated to the low-frequency part of the Raman spectra.1 In this domain below 50 cm 1, the vibrations which can be observed are confined acoustic waves. In the continuum elasticity approximation, the frequency of these vibrations varies as the inverse of the size of the nanoparticles. This variation is larger than the one expected for the optical phonons. Low-frequency Raman scattering is therefore a clear indicator of the presence of nanoparticles, and it can be used to create maps, for example.2 Low-frequency Raman scattering has been used to determine the size of very small nanoparticles (less than ∼10 20 nm). In particular, the simple inverse size dependence of the frequency of the confined acoustic vibrations enables the determination of the size distribution of the nanoparticles using the shape of the lowfrequency Raman peaks.3 7 Recent works have revealed the richness of low-frequency Raman spectra for model materials because of the sensitivity to the size, shape, composition, and environment of the nanoparticles but also because the vibrations depend on the inner lattice structure.8 10 In the present work, we attempt to clarify whether the broadening of the peaks is mainly due to the size distribution or whether the broadening due to the elastic anisotropy resulting from the crystalline structure of the nanoparticles plays a significant role. To reach that goal, ZrO2 nanoparticles were synthesized, and their sizes and crystalline structure were determined. Their Raman spectra have been recorded, and the low-frequency part has been compared to continuum elasticity frequency calculations for monodomain monoclinic ZrO2 nanospheres. Finally, the sizes and the size distributions determined from the low-frequency Raman r 2011 American Chemical Society
peaks are compared with those obtained with other usual experimental methods.
’ EXPERIMENTAL RESULTS Sample Preparation. Zirconia nanocrystals (ZrO2) were synthesized under supercritical water conditions (T > 647 K and P > 22.1 MPa) from a homemade continuous process.11 The diagram of the continuous hydrothermal synthesis process apparatus is presented elsewhere.12 14 The patented countercurrent flow reactor was fed in zirconyl nitrate salt (ZrO(NO3)2) purchased from Sigma Aldrich (0.05 mol 3 L 1) and demineralized water using high-pressure pumps. The total flow rate was set up at 30 mL 3 min 1 (water, 10 + 10; salt, 10; residence time, 8 s) and 60 mL 3 min 1 (water, 20 + 20; salt, 20; residence time, 4 s) to synthesize samples S30 and S60, respectively. The pressure was regulated at 30 MPa thanks to a back pressure regulator and the temperature at 773 K using tubular ceramic furnaces. At the exit of the reactor, the suspension was rapidly quenched in a cold bath. Two filters made of 7 and 2 μm porous stainless steel removed agglomerated particles. Then the suspension was centrifuged and washed with demineralized water under ultrasonication. The sol formed was freeze-dried to reduce the agglomeration of the nanoparticles. Supercritical conditions led to instantaneous formation of a large number of hydroxide nuclei. Short residence times reduce the number of large nanoparticles. Sample Characterizations. X-ray diffraction (XRD) measurements were carried out using a Siemens D5000 powder Received: March 24, 2011 Revised: May 24, 2011 Published: June 27, 2011 14571
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Figure 1. TEM image of sample S30.
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the measured specific area by assuming identical nanoparticles with a spherical shape The values are also reported in Table 1. Samples S30 and S60 were investigated by Raman scattering experiments at room temperature using an Horiba T64000 setup equipped with a confocal microscope and using the 514.5 nm line of a Spectra-Physics Stabilite 2018 Ar Kr laser and a charged coupled device (CCD) cooled by liquid nitrogen as the detector. Figure 2 presents the Raman spectra obtained for both samples in the parallel configuration for which the polarizations of the incident and scattered photons are parallel. The peak positions of the most intense Raman peaks above 80 cm 1 are located at 103, 178, 189, 220, 309, 332, 345, 382, 478, 613, and 627 cm 1 and are in agreement with the monoclinic structure of ZrO2.7,15 The tetragonal crystalline phase could not be evidenced from the Raman spectra. Two lowfrequency Raman peaks can be clearly identified below 80 cm 1 in these raw spectra (no temperature correction). Both their sizedependent positions and strong intensities make them good candidates to deduce the size of the nanoparticles. Figure 3 and Figure 4 show the low-frequency range for samples S60 and S30 in the parallel and crossed configurations for which the polarizations of the incident and scattered photons are parallel and perpendicular, respectively. The comparison of the parallel and crossed spectra shows that the spectra are composed of at least two contributions, the highest-frequency one being polarized. The depolarization factor varies when focusing the laser at a different place due to multiple scattering as will be discussed later.
’ DISCUSSION
Figure 2. Raman spectra of samples S30 (bottom) and S60 (top) in the parallel configuration. The spectra are vertically shifted for clarity.
diffractometer equipped with a back diffracted beam graphite monochromator with Cu KR radiation (λ = 1.3922 10 10 m). The instrumental broadening correction was determined from a sintered SiO2 standard reference material from Bruker. The diffraction bands for sample S60 can be assigned to the monoclinic phase. For sample S30, a minor contribution from the tetragonal phase was also observed. The crystallite size was determined with the Rietveld refinement method with the TOPAS software (version 2.1). The size and shape of the nanoparticles were observed by using transmission electron microscopy (TEM). TEM experiments were conducted on a JEOL JEM-2100 LaB6 microscope operating at 200 kV equipped with a high tilt pole-piece achieving a point-to-point resolution of 0.25 nm. An example TEM image is shown in Figure 1 for sample S30 where almost spherical nanoparticles can be seen. The size distribution for both samples was determined by measuring 300 nanoparticles and is shown in Figure 5, while the average diameters are reported in Table 1. Nitrogen adsorption desorption isotherms were obtained using a BELSORP Mini apparatus from Bel Japan for surface area measurement using the Brunauer Emmett Teller (BET) method. The diameter of the nanoparticles was determined from
Depolarization Ratio. As can be seen in Figure 3 and Figure 4, the low-frequency Raman spectra for the parallel and crossed polarization configurations differ. This is in contrast with what has been reported for large nanoparticles16 but also for small SnO26 and even ZrO27 ones. From previous works,7 15 two Raman peaks are expected which were attributed to the fundamental isotropic spheroidal modes S2 and S0 with l = 2 and l = 0, respectively. Selection rules derived by Duval17 predict that these vibrations are Raman active and that the breathing modes (S0) are not observable in the crossed configuration. In the case of nanoparticles with a lower symmetry due for example to their shape or inner lattice structure, the depolarization ratio for totally symmetric and nontotally symmetric vibrations is also expected to be different. The reason why this polarization behavior was not observed in the previously mentioned works was attributed to multiple scattering. This is due to the elastic scattering of either the incident or Raman scattered photons by the nanoparticles. However, it should be noted that the intensity of the Rayleigh scattering from particles much smaller than the wavelength of light varies as d6 where d is the diameter of the nanoparticles. The probability of multiple scattering events increases also with the number of nanoparticles per unit volume. Therefore, for small enough nanoparticles and low enough concentrations of nanoparticles, it is possible to strongly diminish the probability of multiple scattering events and therefore to observe the change of the intensity of the Raman peaks due to the breathing modes. This is the reason why polarized scattering was observed before for matrix embedded nanoparticles18 where the distance between nanoparticles is most of the time much larger than in a nanopowder. Therefore, we paid attention not to compact the samples or to investigate pellets which can be obtained by applying a 14572
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Table 1. Characterizations of Samples S30 and S60 phase sample
XRD
surface (m2 3 g
1
)
average diameter (nm)
BET
BET
XRD
Raman
TEM
S30
monoclinic and tetragonal
142
7
6.3
6.9
6
S60
monoclinic
208
5
5.5
5.2
5
Figure 3. Low-frequency Raman spectra (crosses, blue) of sample S60 for the parallel (bottom) and crossed (top) configurations. The curves (continuous lines) are the decomposition into two log-normal profiles. The vertical arrows are located at the frequency of the Raman active vibrations of a monoclinic ZrO2 sphere of diameter d = 5.6 nm, and their heights are proportional to their projection onto the fundamental isotropic S2 and S0 vibrations for the arrows located below and above 30 cm 1, respectively.
moderate pressure. For our samples, the relative intensities of the two low-frequency Raman peaks vary when probing different parts of the nanopowders. We attribute this result to the varying number of nanoparticles per unit volume which is hard to control. This prevents an accurate determination of the depolarization ratio of the peaks. Nevertheless, the different depolarization ratios of the bands can be evidenced, and this helps in assigning the Raman peaks and decomposing the spectra. Eigenvibrations of ZrO2 Spheres. The vibrations are described using continuum elasticity as in previous works8 using the elastic constants for the cubic, tetragonal, and monoclinic ZrO2 lattice structures19 and the mass densities from the respective ICDD cards. Isotropic sound velocities were computed by averaging the quasi-longitudinal and quasi-transverse sound velocities over all the propagation directions for the monoclinic structure. We obtained vL = 7422 and vT = 4320 m/s. Eigenfrequencies were obtained using the model by Lamb20 for the isotropic approximation of ZrO2 and using a numerical approach in the case of elastic anisotropy.21 The symmetry of the different vibration modes was also computed. This required an extension of a previous work8 to handle the case of the monoclinic symmetry which was not considered before. The Raman active isotropic S2 vibrations (degeneracy 5) split into Eg + T2g, A1g + B1g + B2g + Eg, and 3Ag + 2Bg for the cubic, tetragonal, and monoclinic lattice structures, respectively. The Raman active isotropic S0 vibrations (degeneracy 1) are of course not split and transform into the fully symmetric representation (Ag or A1g). In addition to eventual splittings, these modes can also be mixed with other vibrations having the same irreducible representations and a close frequency.8
Figure 4. Same as Figure 3 for sample S30 and d = 7.4 nm.
Influence of the Inner Lattice Structure. Changing the lattice structure and twins of ZrO2 nanocrystals changes their eigenvibrations and therefore the low-frequency Raman spectra. However, measurements are available only for large numbers of nanocrystals. Nanocrystals can in principle differ by the number and location of internal twins. In that case, the isotropic approximation is expected to be suitable to interpret the average peak positions of an ensemble of spherical nanocrystals.9 However, the anisotropy still contributes to the broadening of the peaks. In our case, HRTEM photos of our samples revealed a large amount of nanoparticles without internal twins, so elastic anisotropy can play a significant role. The projections plotted in Figure 3 and Figure 4 demonstrate this effect. The vertical arrows correspond to the projections of all the eigenmodes of a monoclinic ZrO2 nanocrystal onto all the fundamental spheroidal l = 2 isotropic eigenmodes and the l = 0 one. The height of these arrows is proportional to the corresponding projections. The diameter of the nanoparticle was chosen so that the frequencies of the polarized Raman peak and the projections onto the l = 0 mode match. Projecting onto the Raman active modes of an isotropic sphere is a very simple way to predict how much each anisotropic mode contributes to the Raman process. Of course, it is not a rigorous method to calculate a Raman spectrum but rather a quick way to identify the main contributing modes. When comparing with experimental Raman spectra in these two figures, the projections onto l = 2 are shown to be scattered over a larger frequency range than the l = 0 ones. This is a clear demonstration that the broadening of the depolarized Raman peak depends rather strongly on the internal lattice structure of the nanoparticles. On the opposite, the polarized peaks are hardly affected. Similar results have been obtained when considering the cubic and tetragonal lattice structures of ZrO2. While the exact details of the calculations differ, the conclusions reached for the broadening due to measurements for an ensemble of nanoparticles are the same as for the monoclinic structure. This is due to the fact 14573
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Figure 5. Comparison of the normalized size distributions obtained for sample S60 (left) and S30 (right) by TEM (histogram, black) and lowfrequency Raman scattering using the polarized (line, red) and depolarized (dashed, blue) peaks.
that in these two structures the elastic anisotropy also significantly splits the spheroidal l = 2 isotropic eigenmodes but not the breathing one. However, no significant shifts are expected for the Raman peaks. Influence of the Shape of the Nanoparticles. Shape can also contribute to the broadening of the Raman peaks of an ensemble of nanoparticles. For an isotropic material, the spheroidal l = 2 eigenmodes are split due to the degeneracy. Assuming spheroidal shapes with an aspect ratio close to 1, the l = 2 modes are split into three branches.8,22,23 The variation of the frequency as a function of eccentricity is significantly different for these branches which results in an additional broadening. On the opposite, the breathing mode is almost unaffected for aspect ratio close to 1 as long as the volume of the nanoparticle is unchanged. This is due to the absence of degeneracy which prevents any splitting when lowering the symmetry. It can therefore only mix with other totally symmetric modes provided their frequency is close. As a result, the inhomogeneous broadening of the Raman peaks due to the shape distribution is also more pronounced for the spheroidal l = 2 modes than for the l = 0 one. Size Distributions. Size distributions from the TEM photos are compared for both samples in Figure 5 with the size distributions deduced from both the S0 and S2 low-frequency Raman peaks assuming a broadening due to the size distribution only and using the same method as in ref 5. For the fits which are presented in Figure 3 and Figure 4, the positions and widths of the peaks were kept identical in the parallel and crossed configurations. From the previous considerations, only the polarized Raman peak is expected to be suitable for a reliable determination of the size. Indeed, in these two figures the size distribution obtained using the depolarized peak differs significantly from the two other ones. This is due in part to the contributions of the shape distribution and of the elastic anisotropy discussed before. This is also due to the difficulty of accurately fitting the shape of this peak on the low-frequency side due to the overlapping with the quasi-elastic scattering. The size distributions obtained by TEM and using the polarized Raman peak are very similar, and their difference can be attributed to the accuracy of both techniques.
’ CONCLUSION In summary, monoclinic ZrO2 nanoparticles have been prepared in supercritical water using a continuous process. The narrow size distributions and low mass density of the powders
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enabled the observation of two well-resolved low-frequency Raman peaks having different depolarization ratios. The size and size distributions of the nanoparticles have been investigated using various common methods, and low-frequency Raman scattering was shown to be an accurate method to reliably determine the size distribution in agreement with the one obtained by TEM. This accuracy is increased when it is possible to use the polarized Raman peak corresponding to the isotropic breathing vibration. While other mechanisms may contribute to the broadening,24 we demonstrated that the elastic anisotropy associated to the lattice structure plays a significant role since it splits the spheroidal l = 2 vibrations which are often the most intense feature of such spectra.25 Because low-frequency Raman spectra can be acquired within a few minutes without sample preparation, this method is an effective alternative way to measure the size distribution.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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(23) Margueritat, J.; Gonzalo, J.; Afonso, C. N.; Mlayah, A.; Murray, D. B.; Saviot, L. Nano Lett. 2006, 6, 2037. (24) Gao, F.; Li, T. H.; Wu, X. L.; Cheng, Y. C.; Shen, J. C.; Chu, P. K. Appl. Phys. Lett. 2009, 95, 211903. (25) Mattarelli, M.; Montagna, M.; Rossi, F.; Chiasera, A.; Ferrari, M. Phys. Rev. B 2006, 74, 153412.
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