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Fourier transform infrared spectroscopy study of nanostructured nickel oxide
Spectrochimica Acta Part A 59 (2003) 121 /134 www.elsevier.com/locate/saa
Fourier transform infrared spectroscopy study of nanostructured nickel oxide V. Biju, M. Abdul Khadar * Department of Physics, University of Kerala, Thiruvananthapuram, 695 581 Kerala, India Received 5 February 2002; accepted 2 April 2002
Abstract Nanostructured nickel oxide having different average particle sizes ranging from 3 to 16 nm were synthesized and Fourier transform infrared (FTIR) spectra of the samples were recorded in the far infrared (IR) region. The spectra were found to be dominated by surface mode absorptions with no distinct absorption corresponding to the bulk transverse optical mode. IR absorption coefficient, a , for the nanostructured NiO samples were calculated as a function of frequency using a macroscopic approach devised by Fuchs. The effects of crystalline geometry, numerical values of optical constants, filling factor and increased damping on the spectral features of the samples were analyzed. Though the simulations approximately reproduced the occurrence of a shoulder in the experimental spectra, the most intense peak in the simulated spectra was found to be about 50 cm 1 above the corresponding experimentally observed peak. It was shown that the experimentally observed absorption maximum of all the samples were in close agreement with that determined using a microscopic theory based on the rigid ion model. The weak absorption peaks in the frequency region 60 /100 cm 1 appearing in the spectra of all the samples were identified as surface induced transverse acoustical modes, vTA, which became IR active due to the breakdown of translational symmetry in the nanocrystallites. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Nanostructured materials; Nickel oxide; FTIR spectroscopy; Surface modes
1. Introduction Infrared (IR) and Raman spectra of nanostructured materials are bound to be markedly different from those of their single crystalline and coarsegrained polycrystalline counterparts due to the increasingly sharper spectral characteristics of the surface atoms [1 /5]. When crystallite sizes are
* Corresponding author E-mail address: [email protected] (M. Abdul Khadar).
comparable to or less than the wavelength of the interacting electromagnetic radiation, theories with appropriate boundary conditions predict the existence of surface polaritons (surface modes), for which the associated electromagnetic oscillations are localized near the surface [6 /12]. Several reports highlight the prominence of surface modes in the experimentally observed IR spectra of nanostructured materials. Also, in nanostructured materials, due the breakdown of translational symmetry the low frequency acoustical modes may acquire a dipole moment resulting in a weak
1386-1425/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 1 4 2 5 ( 0 2 ) 0 0 1 2 0 - 8
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surface-induced acoustical mode absorption in the far IR region. In general, vibrational spectra of nanomaterials are greatly influenced by the geometrical shape and size of the crystallites, surface to volume ratio, surface amorphousness, dielectric constant of the surrounding medium, depolarization fields due to surface charge distribution, dipolar interaction between individual particles, agglomeration etc [1 /12]. For diatomic ionic materials, surface modes exist in the frequency region between the transverse optical (vT) and the longitudinal optical (vL) phonon frequencies, in which the real part of the complex dielectric constant o (v )B/0, (i.e. wave vector k imaginary) and can be investigated conveniently using IR spectroscopy in the far IR region [1 /5]. Though numerous reports on the IR spectroscopic investigations of surface modes in a wide range of materials such as alkali halides, metal oxides etc, have appeared in literature, most of them deal either with microcrystals or at the most with relatively large nanocrystals with average particle sizes ranging from 30 to 100 nm, and there are only a few reports on the IR studies of surface modes in nanomaterials with average particle sizes of the order of 10 nm or less [12 / 25]. It is well known that when the average particle sizes are of the order of 10 nm or less, the surface to volume ratio is greatly increased (/50%) in comparison with that for relatively large nanostructures, i.e. those with average particle sizes of the order of 50 nm or more [26 /30]. Also, at very small sizes, almost all the physical properties of materials are found to be more conspicuously size dependent. Furthermore, even in the case of microcrytals, the experimental spectra dominated by surface modes and simulations based on theoretical models seldom match satisfactorily without the introduction of adjusting parameters such as an empirically determined shape factor or a suitable multiplication factor for the damping function, g [1,16,17,22]. In this context, the experimental observation of surface modes in nanostructures with average particle sizes of the order of 10 nm or less and the comparison of the experimental spectra with simulations based on theoretical models such as the effective medium approach should be of great interest. The present
paper reports the Fourier transform infrared (FTIR) spectroscopic study of surface modes in nanostructured nickel oxide, having different average particle sizes ranging from 3 to 16 nm in the far IR region.
2. Experimental NiO nanoparticles were prepared through a two-step process. In the first step, nanoparticles of nickel carbonate were prepared through arrested chemical precipitation route. Nickel nitrate and ammonium carbonate were the stating materials and ethylenedinitrilotetraacetic acid disodium salt (dihydrate), EDTA was used as the stabilizer. All the chemicals used were of analytical grade. NiO nanoparticles having different average particle sizes were obtained by the thermal decomposition of the carbonate precursor followed by air annealing. Details of sample preparation are reported elsewhere [28 /30]. The average particle size of the samples were calculated using Scherrer’s equation from the line broadening of the X-ray diffraction peaks corrected for instrumental broadening and are listed in Table 1 together with the sample codes assigned for convenience [31]. Small quantities of nanostructured samples were thoroughly mixed with polyethylene (o / 2.25) in an agate mortar and were made into thin pellets. The volume fractions of the samples were kept low so as to ensure that the nanocrystals were thoroughly dispersed in the host material. IR transmission spectra of the nanostructured samples in the far IR region were recorded using a Bruker IFS66V FTIR spectrometer for the frequency range 50 /600 cm1 at room temperature. Table 1 Details of nanostructured NiO samples Sample code
Average particle size (nm)
N1 N2 N3 N4
2 /3 4 /5 5 /7 16 /17
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3. Results Fig. 1 shows the IR transmission spectra of nanostructured NiO samples having different average particle sizes. The spectra of all the four samples exhibit a broad absorption maxima with the peak positions located in the range 420/440 cm 1. Further, this main peak becomes broader as the average particle size of the samples increases from 3 nm for sample N1 to 16 nm for sample N4. A shoulder around 530 /550 cm1 is clearly visible in the spectra of samples N1 and N2, while in the spectra of samples N3 and N4 having larger average particle sizes, this shoulder becomes less pronounced.
Fig. 1. FTIR spectra of nanostructured NiO samples in the far IR (50 /600 cm 1).
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Another interesting feature in the spectra of nanostructured NiO samples occurs in the low frequency region of 50 /100 cm 1. A magnified view of the spectra in this region shown in Fig. 2 clearly reveals the occurrence of a weak shoulder. In the spectra of sample N1, the shoulder is centered at about 85 cm 1, while the peak positions in the spectra of samples N2 and N3 are shifted towards lower frequencies and are at about 62 and 63 cm 1, respectively. For N4, the sample with largest average particle size, the shoulder at around 63 cm 1 is very weak and the spectrum shows a broad and weak transmission minimum around 73 cm 1.
Fig. 2. Magnified view of the FTIR spectra of nanostructured NiO samples in the frequency range 50 /100 cm 1.
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4. Discussion At room temperature, NiO is antiferromagnetic and has distorted NaCl structure. On heating it transforms to the paramagnetic phase (ideal NaCl structure) at 523 K (Neel temperature) [32]. Since the distortion corresponding to this magnetic transition (antiferromagnetic to paramagnetic) is quite small, for theoretical calculations and interpretation of spectral features, it is frequently assumed that the phonon spectrum does not depend on magnetic ordering [37]. IR spectroscopic studies of NiO, even in the bulk form, are fewer in number in comparison with the large number of reports on the investigation of its electronic structure, and electrical, optical and magnetic properties. Also, there exist some notable difference in the values of the optical constants (o 0, o 8, vT, vL and g) reported by different investigators either through lattice dynamical calculations or by analysis of IR reflection spectra [33 /37]. For NiO, in the bulk form, the main IR absorption maximum correspond to the long wavelength transverse optical mode, vT, in which the sublattice of Ni2 ions moves 1808 opposite to the sublattice of O2 ions [32 /36]. The transverse optical phonon frequency, vT, for bulk NiO has been reported to lie between 390 and 405 cm 1 [33 /37]. Hunt et al. had studied the IR transmission spectra in the far IR region of two small particle specimens of NiO, (i) powder with an average particle size of /35 nm; and (ii) arc produced NiO smoke with an average particle size /30 nm [18]. The spectra of both these samples were found to be much varied from those of bulk NiO due to the dominance of surface modes. The spectra of NiO small particles (average particle size 35 nm) exhibited a wide absorption band with a peak at about 485 cm 1. Though the peak position was approximately in agreement with that of a surface mode, obtained from computer simulations assuming a spherical geometry for the particles and using the bulk optical constants, the simulated spectrum was notably narrower than the observed one. This experimentally observed broadening was qualitatively explained as most likely due to the presence of additional surface modes produced by
irregular shaped particles. The spectra of arc produced NiO smoke (average particle size 30 nm) showed presence of two broad, yet well resolved, absorption maxima */one at /405 cm 1, the bulk transverse optical phonon frequency, vT, and the other at about 525 cm 1, which was identified as a surface mode. The peak positions were found to be approximately in agreement with those calculated assuming the smoke particles to be a mixture of spherical particles and randomly oriented infinite cylinders. However, for smoke particles also, the experimentally observed broadening was quantitatively unaccountable. Hunt et al. had concluded that the difference in the IR spectra of their NiO samples cannot wholly be attributed to the difference in their particle sizes alone, and suggested that the actual geometrical shape of the particles and the possible shape distribution should be considered as significant factors in the interpretation of the IR spectra of small particles [18]. 4.1. Surface modes in the IR spectra of nanostructured NiO In the present study, IR transmission spectra of nanostructured NiO having different average particle sizes ranging from 3 to 16 nm were analyzed in the frequency range 50 /600 cm 1. As has already been stated, the transmission spectrum of bulk NiO in the far IR region consists of a single absorption maximum centered at the transverse optical phonon frequency, vT, which has been reported to lie in the 390 /405 cm 1 range [33 /37]. A detailed analysis of the far IR spectra of the nanostructured samples in the present study (Fig. 1) reveals that for the samples N1, N2, N3 and N4, the frequencies of the main absorption maxima are 431.97, 431.98, 437.76 and 424.26 cm 1, respectively. The occurrence of the absorption maxima in the frequency region lying between vT and vL (/560 cm 1 for NiO) together with the absence of any well defined absorption maxima corresponding to vT clearly indicates the dominance of surface modes in the far IR spectra of nanostructured NiO samples [1 /6,18,33/37]. Further, it may also be noted from Fig. 1 that the position of the absorption maxima is not appreciably altered
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with change in particle size, though the width of the absorption maxima increases markedly with increase in the average particle size. In the following analysis, we make use of Fuchs’ theory of optical properties of small ionic crystals for simulating the IR absorption spectra of nanostructured NiO for different geometrical shapes of the crystallites and compare the results of the simulations with the experimental ones [38]. Simulations based on Fuchs’ theory had successfully explained the spectra of small particles of a number of metal oxides and alkali halides, where the particle sizes were of the order of a few micrometers or of the order of 50 /100 nm, with the proper choice of a multiplication factor (either a whole number or a fraction) for the damping function, g [22,38]. The applicability of this macroscopic theory for explaining the IR spectral features of nanostructured samples with average particle size of the order of 10 nm or less, such as in the present study, has not been experimentally verified [1,22,38].
Pav
125
(o av 1) Eav 4p
(1)
where Eav and Pav are assumed to be merely volume averages of the nearly constant fields inside the crystallites, Ei and Pi and those out side the crystallites (i.e. in the host material), Em and Pm. In this definition of the average dielectric function (o av) any interaction between the crystallites embedded in the host material, such as the possible dipole interaction, is not taken into consideration, which is rather a simplification of the actual situation. However, in the limit of small densities of crystallites such an approximation is valid [38]. According to Fuchs, if the particle density is not too high, the average dielectric function is given by: o av (v)
f4pf o(v)xR (v) [o(v) o m ][1 f ]g f4pf o m (v)xR (v) [o(v) o m ][1 f ]g
om (2)
4.2. Theoretical background for the simulation of IR spectra of nanostructured samples Fuchs, through macroscopic approach had devised a method for simulating the frequency dispersion of the absorption coefficient, a , of small ionic crystals with symmetric geometrical shapes embedded in a host dielectric medium [38]. The theory is applicable only when the crystallite sizes are much smaller than the wavelength of the interacting electromagnetic radiation so that the retardation effects (i.e. effects due to the finite velocity of electromagnetic radiation) are negligible. When the crystallites are much smaller than the wavelength of the interacting electromagnetic radiation, the scattering cross-section is negligibly small in comparison with the absorption crosssection and a system of small crystallites embedded in a host material can be characterized by an average dielectric function, o av(v ). In the macroscopic approach, the average dielectric constant, o av(v ), is defined in terms of the average electric field Eav and average polarization field Pav as:
where f is the fraction of the total volume occupied by the particles (filling factor), o m the dielectric constant of the surrounding medium, o (v ) the frequency dependent complex dielectric function of the material and xR(v) the particle susceptibility [38]. According to single oscillator model, o (v) of a diatomic ionic material is given as: o(v)o 8
(o 0 o 8 )v2T v2 igv)
(v2T
(3)
where o 0 and o 8 are the low frequency and high frequency dielectric constants, vT the bulk transverse optical phonon frequency and g the damping function [1,38]. Also, the particle susceptibility, xR(v ) of a symmetric particle is given as: xR (v)
1 X C(i) 4p i (o=o m 1)1 ni
(4)
where C (i ) and ni are, respectively, the oscillator strength and depolarization factor of the ith normal mode [38].
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Now, the absorption coefficient, a of a thin slab of host material containing the small particles can be calculated as a function of frequency as: a
v Im(o av ) pffiffiffiffiffiffi c Re( o av )
(5)
where c is the velocity of light [1,38]. Eq. (5) can be applied to particles of any arbitrary shape, if the values of the depolarization factors, ni , and the oscillator strengths, C (i ), of the corresponding normal modes of vibration are known. For small spherical particles, the main IR absorption is caused by the uniformly polarized Fro¨hlich mode, for which n /1/3 and C /1 (1, 38). Also, Fuchs had shown that the IR absorption of small cubic particles, correspond to six polariton normal modes associated with the surface polarization charge. The calculated values of the oscillator strengths of the six normal modes for a cubic particle are C (1) /0.44, C (2) /0.24, C (3) / 0.04, C (4) /0.05, C (5) /0.10, and C (6) /0.09 and the corresponding depolarization factors are, n1 /0.214; n2 /0.297; n3 /0.345; n4 /0.440; n5 / 0.563; and n6 /0.706 [38]. According to Eq. (5), the surface mode absorption peaks may be identified as the frequencies, which correspond to poles of equation for o av, i.e. Eq. (2). Neglecting the damping factor, g in the equation for o (v ) and substituting n /1/3 and C /1, the Fro¨hlich mode frequency, vF of spherical particles is given as: vF
[o 0 (1 f ) o m (2 f )]1=2 vT [o 8 (1 f ) o m (2 f )]1=2
(6)
Similarly, the frequency of the strongest absorbing surface mode for cubic particles, i.e. the mode i/1with an oscillator strength C (1) /0.44 and depolarization factor n1 /0.214 is given as: vc
[o 0 (1 f ) o m (3:67 1:62f )]1=2 [o 8 (1 f ) o m (3:67 1:62f )]1=2
vT
(7)
From Eqs. (6) and (7), the frequency of the strongest absorbing surface mode for cubic particles, vc is lower than the Fro¨hlich mode, vF for spherical particles and it appears closer to the bulk mode, vT, for the same values of f and o m. Physically, this is a consequence of the lower
depolarization factor, n1 /0.214, for vc in comparison with the depolarization factor, n /1/3, for vF. Also Eqs. (6) and (7) clearly shows that both vF and vc are shifted towards lower frequencies with increase in the filling factor, f or with an increase in the dielectric constant of the surrounding medium, o m.
4.3. Simulation of IR spectra of nanostructured NiO As may be noted from the foregoing discussion, choice of an appropriate geometrical shape for the nanocrystallites is a crucial step in the simulation procedure. However, the choice of geometrical shapes for the purpose of simulation is limited rather to a few simple ones such as spherical, cubic and cylindrical, due to the nonavailability of the values of depolarization factors and oscillation strengths for the normal modes of more complex shapes [38]. In our earlier studies, it was observed that the size dependent variation of both dc and ac electrical conductivities of nanostructured NiO (average particle sizes ranging from 3 to 16 nm), which was not a linear one, could be semiquantitatively explained on the basis of calculations assuming a 14 sided tetrakaidecahedron geometry for the nanocrystallites [28,30]. This assumption was based on the reported crystallographic studies, which had concluded that growth of the NiO crystallites occur in the tetrakaidecahedron shape [39]. However, this complex, yet symmetric geometry for the NiO nanocrystallites was not used for the IR spectral simulations since the depolarization factors and oscillator strengths of corresponding normal modes of vibration were not available. Hence, in the present analysis, we have done the simulation of IR spectra of NiO nanocrystallite for two simple geometries, viz. spherical and cubic, with polyethylene as the host material (o m /2.25). For the IR spectral simulations using macroscopic approach, the bulk optical constants of the material */vT, o 0, o 8 and g */are to be known. Since there exist notable differences between the values of optical constants of bulk NiO reported by different investigators, we have used three
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different sets of optical constants taken from literature to investigate the effect of numerical values of the bulk optical constants on the results of the spectral simulations. The values of the optical constants used and their sources are given in Table 2. An important parameter which according to Eq. (2), determines the value of the average dielectric function, o av(v ), and hence the frequencies of the surface modes is the filling factor, f [16,17,22,38]. With regard to the numerical value of f used for the simulation of IR spectra, two common practices exist, (i) use the value of f estimated from the weight ratios of the sample and host material using their bulk densities (22); or (ii) use f as an adjusting parameter so as to minimize the differences between the simulated spectra and the experimental results while ensuring that the value of f used is within the limit of applicability the macroscopic theory, ((d/l)3 /f B/0.5, where d is the average particle size and l is the wavelength of interacting electromagnetic radiation) [16,38]. In an actual experimental situation, the value of f as encountered by the IR radiation cannot be estimated accurately. This is because, even if the weight ratios of the nanoparticles to host material is accurately determined, it is impossible in practice to make pellets in which the nanocrystallites are hundred percent uniformly dispersed in the host material so that the volume fraction of nanocrystallites as encountered by the IR radiation is same as the one estimated from weight ratios irrespective of the actual location of irradiation on the pellet. Besides, the density of nanostructured materials is known to be much varied from those of the corresponding bulk phase and hence estimation of f from the weight ratios using bulk density values may introduce serious errors
127
[26,27]. In the present analysis, in order to study the effect of f on the surface mode frequencies of nanostructured NiO and hence to check whether a poor choice of f is the cause of any possible mismatch between the simulations and the experimental results, simulations were done for three different values of f, viz. 0.01, 0.1 and 0.3. It may be noted that the chosen values of f are well with in the limits of applicability of the macroscopic approach while covering a fairly good range of reasonable values of f. Another important factor that determines the features of the simulated spectra is the damping function, g . An increase in the value of g will shift the surface mode peak to slightly higher frequencies but more importantly will broaden the absorption peaks. It has been a usual practice to introduce a suitable multiplication factor (either a whole number or a fraction) for g , for explaining the experimentally observed broadening of the IR absorption peaks in the spectra of nanostructured samples [1,16,17,22,38]. The physical basis for the introduction of a multiplication factor lies with the knowledge that in nanostructured materials the damping is increased many folds in comparison with the corresponding bulk, primarily due to the large unharmonicity in small crystallites related to the relaxation of the lattice [1,22]. Also, relatively large amplitudes of vibration near the surface and extrinsic factors such as the interaction between crystallites contribute to the enhanced damping in nanostructures [1,22]. In the present study, spectral simulations were done for a wide range of values of multiplication factor for g, in order to have a detailed understanding of the effect of the multiplication factor on the width of the surface mode absorption peaks.
Table 2 Optical constants of bulk NiO used for calculation of absorption coefficient, a Set
vT (cm1)
vL (cm1)
Damping function, g
o0
oa
Reference
I II III
405 401 400
560 / 595
0.0451vT 0.06vT 0.0276vT
11.75 12.0 11.75
5.4 5.4 5.7
[34] [18] [37]
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Fig. 3. Variation of absorption coefficient, a , of nanostructured NiO simulated for spherical geometry of the crystallites for different sets of bulk optical constants.
Fig. 4. Variation of absorption coefficient, a , of nanostructured NiO simulated for cubic geometry of the crystallites for different sets of bulk optical constants.
In the present study, spectral simulations for nanostructured NiO samples dispersed in polyethylene were done assuming both spherical and cubic geometry for the nanoparticles. The effect of the numerical values of the bulk optical constants*/vT, o 0, o 8, g, the filling factor, f and the enhanced damping in nanostructures on the spectral features for both spherical and cubic geometries were analyzed in detail. The results of the spectral simulations and comparison with the experimental results are discussed in the following section.
4.4. Analysis of IR spectral simulations The results of simulations of the absorption coefficient, a , as a function of frequency for nanostructured NiO for spherical and cubic geometries are shown in Figs. 3 and 4, respectively. Figures show simulations done using three different sets of optical constants (Table 2) with the filling factor set to 0.1 and using the value of damping function, g for bulk NiO (i.e. multiplication factor /1). Also, a is plotted in an inverted scale so as to make the comparison with
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the experimental results more convenient. It is clear from Figs. 3 and 4 that the spectral features for spherical and cubic geometries differ much. For spherical geometry, the spectra consist of a single narrow absorption peak, the peak position of which shows marked dependence on the value of optical constants used for simulation. From Fig. 3, the peak positions are noted to be 517.5, 507.95 and 500.25 cm 1, respectively, for simulations using optical constants given in set I, II and III of Table 2. For cubic particles, the spectra show a number of well-defined absorption peaks (Fig. 4). The most intense peak corresponding to i/1 (C (1) /0.44 and n1 /0.241) is located at lower frequencies with respect to the absorption peak for spherical geometry using the same set of optical constants. For cubic geometry also, the peak positions of the absorption maxima show marked dependence on the value of the optical constants used for simulation. Figs. 5 and 6, respectively, show the simulated spectra for spherical and cubic geometries for different values of f. The values of optical constants given in set III of Table 2 were used for these simulations. As the value of f is increased, the absorption peaks shift more towards lower frequencies for both geometries while the width of the peaks are not markedly changed. The same is true for simulations using the other two sets of optical constants as well. For spherical geometry, with f/0.3 an additional peak appears around 540 cm 1. This is most probably an indication of the stronger interaction between the crystallites as the value of f approaches the upper limit of applicability of the macroscopic approach. The effects of enhanced damping on the spectral features for spherical and cubic particles are shown, respectively, in Figs. 7 and 8 by simulating the spectra for different multiplication factors for the damping function, g. Optical constants given in set III of Table 2 were used for these simulations. As may clearly be noted from Figs. 7 and 8, the absorption peaks are shifted slightly towards higher frequencies for larger values of g , but more importantly, the width of the absorption peaks increase markedly with increased damping. Also, it is clear that for the same value of multiplication factor the spectral broadening is much smaller for
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Fig. 5. Variation of absorption coefficient, a , of nanostructured NiO with filling factor, f simulated for spherical geometry of the crystallites.
spherical geometry than for cubic particles. Hence, multiplication factors as large as 15 were used for analyzing the spectral broadening for spherical geometry, while for cubic particles the spectral simulations were done only for multiplication factors up to 4. However, for the analysis of the spectral broadening of cubic geometry, simulations were done with the multiplication factor increased in steps of 0.5. Obviously, the larger effect of increased damping on the spectral features for the cubic particles is due to the presence of more number of absorption peaks, each of
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Fig. 7. Variation of absorption coefficient, a , of nanostructured NiO with increase in the damping function, g , simulated for spherical geometry of the crystallites. Fig. 6. Variation of absorption coefficient, a , of nanostructured NiO with filling factor, f simulated for cubic geometry of the crystallites.
which becomes wider with increased damping. Also, from Fig. 8, it may be noted that with increased damping, the higher frequency absorption peaks merge together and resembles a shoulder or a hump in the region 520/540 cm1. It may be noted that in the above analysis, the results of the simulation procedure are presented in terms of the absorption coefficient, a , (Figs. 3/ 8) while in the experimentally measured IR spectra of nanostructured NiO (Fig. 1), transmittance, T /eax , where x is the thickness of the pellet, is plotted as a function of frequency. The character-
istic features of the spectra, such as the peak frequencies, width of the peaks and appearance of shoulders are not affected by the mode of presentation of the spectra and one can have a comparison between the simulations and the experimental results without much difficulty. Analysis of Figs. 3/6 clearly show that neither the position of the experimentally observed absorption maxima nor its width is correctly reproduced by simulations for either spherical or cubic geometries using any of the three sets of optical constants (Table 2) for values of filling factor, f, ranging from 0.01 to 0.3. Also, it may be inferred from Figs. 5/8 that spectral simulations with a filling factor, f /0.1 and cubical geometry for the nanocryastallites approximately reproduce some of the experimentally observed spectral features of
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Fig. 8. Variation of absorption coefficient a , of nanostructured NiO with increase in the damping function, g simulated for cubic geometry of the crystallites.
nanostructured NiO samples, such as the occurrence of a shoulder in the frequency region /530/ 550 cm1, though the position of the most intense absorption peak for these simulations lie at least 50 cm 1 above the experimentally observed absorption maxima. Moreover, the evolution of the shape of the high frequency shoulder and the broadening of the main absorption peak with increase in average particle size as observed in the experimental spectra (Fig. 1) are at least approximately reproduced in Fig. 8, respectively, by the merging together of the high frequency absorption peaks for cubical particles and the general broadening of all the absorption peaks with increased damping. Thus it seems possible to
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picturise the experimentally obtained IR spectra of nanostructured NiO as composed of the surface modes associated with cubic geometry of the crystallites with an increased damping and some other modes of vibration lying closer to the bulk transverse optic phonon frequency, vT in the frequency region /420/440 cm 1 which correspond to more intense absorption peaks than the surface modes for the cubic particles. One simple explanation for the occurrence of the main absorption maxima at lower frequencies than those calculated from macroscopic approach, is the possibility of presence of irregularly shaped particles in the nanostructured samples analyzed [18]. However, this explanation is rather arbitrary and cannot be quantitatively established. Also, from the analysis of the simulated spectra, it may be noted that with the same numerical values of simulation parameters, the maximum intense peak for cubic and spherical geometries differ by /25 cm 1 at the most. Certainly a mismatch of /50 cm 1 between the experimental spectra and simulations cannot wholly be attributed to shape effects alone. Another factor that may contribute to the experimentally observed shifting of the main absorption maxima to lower frequencies than those simulated is the possible interactions between the nanocrystallites dispersed in the host material, which was not taken into account while defining the average dielectric function, o av(v ), used for the simulations. However, it may be noted that the position of the maximum intensity absorption peaks obtained in the simulation analysis (Figs. 3/8) are approximately in agreement with that for NiO powder with an average particle size of /35 nm reported by Hund et al. [18]. It may be reasoned that if such a strong interparticle interaction, which shifts the surface mode absorption by /50 cm 1 towards the lower frequency side exist in the case present samples with average particle sizes ranging from 3 to 16 nm, it should also be present at least in a lesser extent in NiO powder with average particle size of /35 nm, unless the interaction corresponds to an aggregation of nanocrystallites, which somehow is present in our samples but was completely absent in the samples of Hund et al. However, Clippe et al. had shown that for small spherical particles of
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NiO, the surface mode absorption peaks are shifted to higher frequencies due to aggregation of crystallites and the same is true for other geometries as well [40]. These lead to the conclusion that the occurrence of the main absorption maxima at frequencies /50 cm 1 lower than those calculated using the macroscopic approach in the experimental spectra of nanostructured NiO samples in the present study originate from the very small average particle size of the samples (3 / 16 nm). For nanostructured materials with average particle sizes of the order of 10 nm or even less, the optical properties are expected to depend strongly on the perturbed nature of the atomic layers at the surface due to the very large volume fraction of the surface atoms. Martin had pointed out that the macroscopic approach cannot be expected to describe effects which are dependent on the structure of phonon density of states and cannot be used for analyzing the vibrational modes so highly localized that the atomicity of the crystallite is important [41]. Further, he had devised an alternate method for analyzing the surface modes in very small crystallites of diatomic ionic materials, which is a lattice dynamical calculation using rigid ion model parameters in which the finite crystallite is considered as a large molecule. This approach has the advantage that it includes a microscopic description of the surface, but has the disadvantage that one must ultimately diagonalise very large matrices, the order of which depends on the number of ions constituting the finite crystallite [38,41]. These calculations had shown that, for very small diatomic ionic crystallites with average particle size /10 nm or less, the principal effect of the high volume fraction of the surface atoms is to shift the entire density of states curves to lower frequency which in turn corresponds to the shifting of the main absorption peak to lower frequencies than those estimated using the macroscopic approach. Further, these calculations highlight the importance of vibrational modes corresponding to edge and corner atoms, which lie closer to the bulk mode, vT, in determining the spectral features of nanostructures with average particle size /10 nm or less for non-spherical (cube /like) geometries of the crystallites [41].
Martin had concluded that the results of this microscopic theory are not inconsistent with those of the macroscopic approach and the fundamental absorption frequency for very small crystallites, may be calculated from the equations for the most intense absorption maxima for spherical and cubic geometries based on the macroscopic approach Eqs. (6) and (7) with the following two modifications [41]. Since, in the rigid ion model, it is assumed that the crystal has no electronic polarizability, for consistency o 8 should be set to 1. Also, since the macroscopic parameter o 0 does not enter into the determination of the rigid ion model parameters used for the macroscopic calculation, it is more appropriate to calculate o 0 from the value of vL resulting from the model calculation and Lyddane /Sachs/Teller relation, o 0 /v2L/v2T [41]. With these modifications, Eq. (6) gives the position of the most intense peak in the IR absorption of nanostructured NiO, for spherical geometry as 437.28, 434.26 and 441.90 cm 1, respectively, for calculations using the sets of optical constants I, II and III of Table 2. For these calculations, the filling factor, f, was set to 0 since the microscopic approach takes into account only a single crystallite for the density of states calculation. Also, since the value of vL for the set II was not available the corresponding peak position was estimated by using the value of vL of set I since this does not seriously alter our conclusions. Similarly, with the modifications, the position of the most intense absorption peak for cubic geometry for nanostructured NiO are estimated to be 424.48, 421.08 and 425.39 cm 1, respectively, for calculations using the sets of optical constants I, II and III of Table 2. It may be noted that these calculations are very much in agreement with the experimentally observed positions of the most intense absorption maxima for the nanostructured samples in the present study. Hence, the appearance of the most intense absorption at frequencies much lower than those estimated using the macroscopic approach in the experimental spectra of nanostructured NiO samples with average particle sizes ranging from 3 to 16 nm should be a consequence of the large surface to volume ratio of the particles owing to their very small average particle sizes which in turn makes
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the atomicity of the surface layers very important in determining the spectral features. The above discussion suggests that for explaining the spectral features of the nanostructured NiO samples with very small average particle sizes /10 nm or less, the macroscopic approach alone is not suffice and one has to include microscopic approach also, which takes into account the contributions due to large surface to volume ratio of the particles which becomes very important at these size scales. 4.5. Analysis of IR spectra of nanostructured NiO samples in the frequency region 50 /100 cm 1 From Fig. 2, it is clear that the spectra of all the four nanostructured NiO samples show presence of a weak, yet distinct absorption peak in the frequency region /60 /100 cm1, with the exact peak frequencies as already stated. This low frequency absorption peak has not been reported in the IR spectral studies of bulk NiO. Also, the peak positions and the shape of this low frequency absorption peak exhibit marked variation with change in average particle size. These lead to the conclusion that the weak absorption peak appearing in the frequency region /60/100 cm 1 is a consequence of the small average particle size of the samples and may be considered as a characteristic feature of the IR spectra of nanostructured NiO. It may be noted that, the dominance of surface modes is not the only distinct feature of the spectra of nanostructured samples in comparison with that of the corresponding bulk [1 /6,41]. There are other distinct spectral features as well, which may characterize the spectra of nanostructured samples, such as the occurrence of a very weak absorption peak corresponding to surface induced acoustical modes appearing at frequencies much lower than the bulk transverse optical mode, vT, [1 /6,41]. The acoustical mode vibrations of a diatomic single crystal with translational symmetry are not IR active [1,41]. However, in the corresponding nanostructured samples, due to the breakdown of translational symmetry the low frequency acoustical modes may acquire a dipole moment resulting in a weak absorption at fre-
133
quencies much lower than vT [41]. The exact frequencies of these surface-induced acoustical modes in nanostructures can be estimated only through microscopic approaches, such as the one devised by Martin, which takes into account the atomicity of the surface layers [41]. However, the frequencies of these surface induced acoustical modes in nanostructures will not be much varied from the acoustical mode vibration frequencies of the corresponding bulk material [41]. Studies on bulk NiO had located the longitudinal acoustical mode, vLA and transverse acoustical mode, vTA to lie in the frequency ranges /111/331 and 57/180 cm 1, respectively [42]. From the foregoing discussion, it is clear that the weak absorption peaks in the frequency range / 60/100 cm 1 appearing in the spectra of all the four nanostructured NiO samples can be identified with the surface induced transverse acoustic modes, vTA which become IR active due to the breakdown of translational symmetry in the nanostructured NiO samples [1 /6,41,42]. Also, it may be inferred that the observed variation of the position, intensity and shape of the surface induced acoustical mode absorption with average particle size is a direct consequence of the difference in the actual atomic structure of the surface layers of the nanostructured samples studied.
5. Conclusion Nanostructured NiO having different average particle sizes were synthesized and the FTIR spectra of the samples were recorded in the far IR region. The spectra were found to be dominated by the surface mode absorptions with no distinct absorption corresponding to the bulk transverse optic mode. IR absorption coefficient, a , for nanostructured NiO samples were calculated as a function of frequency using a macroscopic approach. The effects of optical constants, crystallite geometry, filling factor and increased damping on the spectral features of the samples were analyzed. An analysis of simulated spectra revealed that spectral simulations with a filling factor f/0.1 and cubical geometry for the nanocryastallites approximately reproduce the occur-
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rence of a shoulder in the frequency region /530/ 550 cm1, though the position of the most intense absorption peak for these simulations lie almost 50 cm 1 above the experimentally observed absorption maxima. It was shown that the experimentally observed absorption maxima of the samples were in close agreement with those estimated according to a microscopic theory due to Martin based on the rigid ion model. It was inferred that for explaining the spectral features of the nanostructured NiO samples with very small average particle sizes /10 nm or less, the macroscopic approach alone is not sufficient and one has to include microscopic approach, which takes into account the contributions due to large surface to volume ratio of the crystallites at these size scales. The weak absorption peaks in the frequency range 60/ 100 cm 1 appearing in the spectra of all the four samples were identified as the surface induced transverse acoustic modes, vTA, which become IR active due to the breakdown of translational symmetry in the nanocrystallites.
[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
Acknowledgements One of the authors V. Biju acknowledges Council of Scientific and Industrial Research (CSIR), Government of India for the financial support in the form of Senior Research Fellowship.
[30] [31] [32] [33] [34]
References [1] S. Hayashi, Jpn. J. Appl. Phys. 23 (1984) 665. [2] D.J. Evans, S. Ushioda, M.D. McMalen, Phys. Rev. Lett. 31 (1973) 369. [3] S. Ushioda, A. Aziza, J.B. Valdez, G. Matter, Phys. Rev. B. 19 (1979) 4012. [4] M. Abdul Khadar, K.C. George, Solid State Commun. 84 (1992) 603. [5] M. Abdul Khadar, B. Thomas, Mater. Res. Bull. 30 (1995) 1301. [6] K. Huang, Proc. Roy. Soc. (London) A. 208 (1951) 352.
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R. Fuchs, K.L. Kliewer, Phys. Rev. 140 (1965) 2076. R. Englman, R. Ruppin, Phys. Rev. Lett. 16 (1966) 898. R. Fuchs, K.L. Kliewer, J. Optic. Soc. Am. 58 (1968) 319. R. Ruppin, R. Englman, J. Phys. C. (Proc. Phys. Soc.) 1 (1968) 630. R. Ruppin, R. Englman, Rep. Prog. Phys. 33 (1970) 149. U. Kreibig, L. Genzel, Surf. Sci. 156 (1985) 678. E. Loh, Phys. Rev. 166 (1968) 673. V.V. Bryksin, Y.M. Gerbstein, D.N. Mirlin, Solid State Commun. 9 (1971) 669. T.P. Martin, Solid State Comun. 9 (1971) 623. L. Genzel, T.P. Martin, Phys. Stat. Sol. (B) 51 (1972) 91. L. Genzel, T.P. Martin, Phys. Stat. Sol. (B) 51 (1972) 101. A.J. Hunt, T.R. Steyer, D.R. Huffman, Surf. Sci. 36 (1973) 454. R. Ruppin, J. Nahum, J. Phys. Chem. Solids 35 (1974) 1311. D.B. Tanner, A.J. Sievers, Phys. Rev. B. 11 (1975) 1330. T.P. Martin, Phys. Rev. B. 15 (1977) 4071. S. Hayashi, N. Nakamori, J. Hirono, H. Kanamori, J. Phys. Soc. Jpn. 43 (1977) 2006. S. Hayashi, M. Ito, H. Kanamori, Solid State Commun. 44 (1982) 75. Y.H. Kim, D.B. Tanner, Physica. A. 157 (1989) 388. R.E. Sherrif, R.P. Devaty, Physica. A. 157 (1989) 395. C. Suryanarayana, Bull. Mater. Sci. 17 (4) (1994) 307. H. Gleiter, Acta Mater. 48 (2000) 1. V. Biju, M. Abdul Khadar, Mater. Res. Bull. 36 (2001) 21. V. Biju, M. Abdul Khadar, Mater. Sci. Eng. A. 304 /306 (2001) 814. V. Biju, M. Abdul Khadar, J. Mater. Sci. 36 (2001) 5779. H.P. Klug, L.E. Alexander, X-ray Diffraction Procedure, Wiley INC, 1970, p. 491. W.J. Moore, Seven Solid States, Benjamin, INC, New York, 1967, p. 133. N.T. McDevitt, W.L. Baun, Spectrocihmica. Acta 20 (1964) 799. P.J. Gielisse, J.N. Plendl, L.C. Mansur, R. Marshall, S.S. Mitra, R. Mykolajewycz, A. Smakula, J. Appl. Phys. 36 (1965) 2446. I.G. Austin, B.D. Clay, C.E. Turner, J. Phys. C. Proc. Phys. Soc. 1 (1968) 1418. I. Nakagawa, Bull. Chem. Soc. Jpn. 44 (1971) 3014. S. Mochizuki, M. Satoh, Phys. Stat. Sol. (B) 106 (1981) 667. R. Fuchs, Phys. Rev. B. 11 (1975) 1732. A.M. Stoneham, J. Phys. C. Solid State Phys. 10 (1977) 1175. P. Clippe, R. Evarad, Phys. Rev. B. 14 (1976) 1715. T.P. Martin, Phys. Rev. B. 7 (1973) 3906. W. Reichardt, V. Wagner, W. Kress, J. Phys. C. Solid State Phys. 8 (1975) 3955.
Fourier transform infrared spectroscopy study of nanostructured nickel oxide V. Biju, M. Abdul Khadar * Department of Physics, University of Kerala, Thiruvananthapuram, 695 581 Kerala, India Received 5 February 2002; accepted 2 April 2002
Abstract Nanostructured nickel oxide having different average particle sizes ranging from 3 to 16 nm were synthesized and Fourier transform infrared (FTIR) spectra of the samples were recorded in the far infrared (IR) region. The spectra were found to be dominated by surface mode absorptions with no distinct absorption corresponding to the bulk transverse optical mode. IR absorption coefficient, a , for the nanostructured NiO samples were calculated as a function of frequency using a macroscopic approach devised by Fuchs. The effects of crystalline geometry, numerical values of optical constants, filling factor and increased damping on the spectral features of the samples were analyzed. Though the simulations approximately reproduced the occurrence of a shoulder in the experimental spectra, the most intense peak in the simulated spectra was found to be about 50 cm 1 above the corresponding experimentally observed peak. It was shown that the experimentally observed absorption maximum of all the samples were in close agreement with that determined using a microscopic theory based on the rigid ion model. The weak absorption peaks in the frequency region 60 /100 cm 1 appearing in the spectra of all the samples were identified as surface induced transverse acoustical modes, vTA, which became IR active due to the breakdown of translational symmetry in the nanocrystallites. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Nanostructured materials; Nickel oxide; FTIR spectroscopy; Surface modes
1. Introduction Infrared (IR) and Raman spectra of nanostructured materials are bound to be markedly different from those of their single crystalline and coarsegrained polycrystalline counterparts due to the increasingly sharper spectral characteristics of the surface atoms [1 /5]. When crystallite sizes are
* Corresponding author E-mail address: [email protected] (M. Abdul Khadar).
comparable to or less than the wavelength of the interacting electromagnetic radiation, theories with appropriate boundary conditions predict the existence of surface polaritons (surface modes), for which the associated electromagnetic oscillations are localized near the surface [6 /12]. Several reports highlight the prominence of surface modes in the experimentally observed IR spectra of nanostructured materials. Also, in nanostructured materials, due the breakdown of translational symmetry the low frequency acoustical modes may acquire a dipole moment resulting in a weak
1386-1425/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 1 4 2 5 ( 0 2 ) 0 0 1 2 0 - 8
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surface-induced acoustical mode absorption in the far IR region. In general, vibrational spectra of nanomaterials are greatly influenced by the geometrical shape and size of the crystallites, surface to volume ratio, surface amorphousness, dielectric constant of the surrounding medium, depolarization fields due to surface charge distribution, dipolar interaction between individual particles, agglomeration etc [1 /12]. For diatomic ionic materials, surface modes exist in the frequency region between the transverse optical (vT) and the longitudinal optical (vL) phonon frequencies, in which the real part of the complex dielectric constant o (v )B/0, (i.e. wave vector k imaginary) and can be investigated conveniently using IR spectroscopy in the far IR region [1 /5]. Though numerous reports on the IR spectroscopic investigations of surface modes in a wide range of materials such as alkali halides, metal oxides etc, have appeared in literature, most of them deal either with microcrystals or at the most with relatively large nanocrystals with average particle sizes ranging from 30 to 100 nm, and there are only a few reports on the IR studies of surface modes in nanomaterials with average particle sizes of the order of 10 nm or less [12 / 25]. It is well known that when the average particle sizes are of the order of 10 nm or less, the surface to volume ratio is greatly increased (/50%) in comparison with that for relatively large nanostructures, i.e. those with average particle sizes of the order of 50 nm or more [26 /30]. Also, at very small sizes, almost all the physical properties of materials are found to be more conspicuously size dependent. Furthermore, even in the case of microcrytals, the experimental spectra dominated by surface modes and simulations based on theoretical models seldom match satisfactorily without the introduction of adjusting parameters such as an empirically determined shape factor or a suitable multiplication factor for the damping function, g [1,16,17,22]. In this context, the experimental observation of surface modes in nanostructures with average particle sizes of the order of 10 nm or less and the comparison of the experimental spectra with simulations based on theoretical models such as the effective medium approach should be of great interest. The present
paper reports the Fourier transform infrared (FTIR) spectroscopic study of surface modes in nanostructured nickel oxide, having different average particle sizes ranging from 3 to 16 nm in the far IR region.
2. Experimental NiO nanoparticles were prepared through a two-step process. In the first step, nanoparticles of nickel carbonate were prepared through arrested chemical precipitation route. Nickel nitrate and ammonium carbonate were the stating materials and ethylenedinitrilotetraacetic acid disodium salt (dihydrate), EDTA was used as the stabilizer. All the chemicals used were of analytical grade. NiO nanoparticles having different average particle sizes were obtained by the thermal decomposition of the carbonate precursor followed by air annealing. Details of sample preparation are reported elsewhere [28 /30]. The average particle size of the samples were calculated using Scherrer’s equation from the line broadening of the X-ray diffraction peaks corrected for instrumental broadening and are listed in Table 1 together with the sample codes assigned for convenience [31]. Small quantities of nanostructured samples were thoroughly mixed with polyethylene (o / 2.25) in an agate mortar and were made into thin pellets. The volume fractions of the samples were kept low so as to ensure that the nanocrystals were thoroughly dispersed in the host material. IR transmission spectra of the nanostructured samples in the far IR region were recorded using a Bruker IFS66V FTIR spectrometer for the frequency range 50 /600 cm1 at room temperature. Table 1 Details of nanostructured NiO samples Sample code
Average particle size (nm)
N1 N2 N3 N4
2 /3 4 /5 5 /7 16 /17
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3. Results Fig. 1 shows the IR transmission spectra of nanostructured NiO samples having different average particle sizes. The spectra of all the four samples exhibit a broad absorption maxima with the peak positions located in the range 420/440 cm 1. Further, this main peak becomes broader as the average particle size of the samples increases from 3 nm for sample N1 to 16 nm for sample N4. A shoulder around 530 /550 cm1 is clearly visible in the spectra of samples N1 and N2, while in the spectra of samples N3 and N4 having larger average particle sizes, this shoulder becomes less pronounced.
Fig. 1. FTIR spectra of nanostructured NiO samples in the far IR (50 /600 cm 1).
123
Another interesting feature in the spectra of nanostructured NiO samples occurs in the low frequency region of 50 /100 cm 1. A magnified view of the spectra in this region shown in Fig. 2 clearly reveals the occurrence of a weak shoulder. In the spectra of sample N1, the shoulder is centered at about 85 cm 1, while the peak positions in the spectra of samples N2 and N3 are shifted towards lower frequencies and are at about 62 and 63 cm 1, respectively. For N4, the sample with largest average particle size, the shoulder at around 63 cm 1 is very weak and the spectrum shows a broad and weak transmission minimum around 73 cm 1.
Fig. 2. Magnified view of the FTIR spectra of nanostructured NiO samples in the frequency range 50 /100 cm 1.
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4. Discussion At room temperature, NiO is antiferromagnetic and has distorted NaCl structure. On heating it transforms to the paramagnetic phase (ideal NaCl structure) at 523 K (Neel temperature) [32]. Since the distortion corresponding to this magnetic transition (antiferromagnetic to paramagnetic) is quite small, for theoretical calculations and interpretation of spectral features, it is frequently assumed that the phonon spectrum does not depend on magnetic ordering [37]. IR spectroscopic studies of NiO, even in the bulk form, are fewer in number in comparison with the large number of reports on the investigation of its electronic structure, and electrical, optical and magnetic properties. Also, there exist some notable difference in the values of the optical constants (o 0, o 8, vT, vL and g) reported by different investigators either through lattice dynamical calculations or by analysis of IR reflection spectra [33 /37]. For NiO, in the bulk form, the main IR absorption maximum correspond to the long wavelength transverse optical mode, vT, in which the sublattice of Ni2 ions moves 1808 opposite to the sublattice of O2 ions [32 /36]. The transverse optical phonon frequency, vT, for bulk NiO has been reported to lie between 390 and 405 cm 1 [33 /37]. Hunt et al. had studied the IR transmission spectra in the far IR region of two small particle specimens of NiO, (i) powder with an average particle size of /35 nm; and (ii) arc produced NiO smoke with an average particle size /30 nm [18]. The spectra of both these samples were found to be much varied from those of bulk NiO due to the dominance of surface modes. The spectra of NiO small particles (average particle size 35 nm) exhibited a wide absorption band with a peak at about 485 cm 1. Though the peak position was approximately in agreement with that of a surface mode, obtained from computer simulations assuming a spherical geometry for the particles and using the bulk optical constants, the simulated spectrum was notably narrower than the observed one. This experimentally observed broadening was qualitatively explained as most likely due to the presence of additional surface modes produced by
irregular shaped particles. The spectra of arc produced NiO smoke (average particle size 30 nm) showed presence of two broad, yet well resolved, absorption maxima */one at /405 cm 1, the bulk transverse optical phonon frequency, vT, and the other at about 525 cm 1, which was identified as a surface mode. The peak positions were found to be approximately in agreement with those calculated assuming the smoke particles to be a mixture of spherical particles and randomly oriented infinite cylinders. However, for smoke particles also, the experimentally observed broadening was quantitatively unaccountable. Hunt et al. had concluded that the difference in the IR spectra of their NiO samples cannot wholly be attributed to the difference in their particle sizes alone, and suggested that the actual geometrical shape of the particles and the possible shape distribution should be considered as significant factors in the interpretation of the IR spectra of small particles [18]. 4.1. Surface modes in the IR spectra of nanostructured NiO In the present study, IR transmission spectra of nanostructured NiO having different average particle sizes ranging from 3 to 16 nm were analyzed in the frequency range 50 /600 cm 1. As has already been stated, the transmission spectrum of bulk NiO in the far IR region consists of a single absorption maximum centered at the transverse optical phonon frequency, vT, which has been reported to lie in the 390 /405 cm 1 range [33 /37]. A detailed analysis of the far IR spectra of the nanostructured samples in the present study (Fig. 1) reveals that for the samples N1, N2, N3 and N4, the frequencies of the main absorption maxima are 431.97, 431.98, 437.76 and 424.26 cm 1, respectively. The occurrence of the absorption maxima in the frequency region lying between vT and vL (/560 cm 1 for NiO) together with the absence of any well defined absorption maxima corresponding to vT clearly indicates the dominance of surface modes in the far IR spectra of nanostructured NiO samples [1 /6,18,33/37]. Further, it may also be noted from Fig. 1 that the position of the absorption maxima is not appreciably altered
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with change in particle size, though the width of the absorption maxima increases markedly with increase in the average particle size. In the following analysis, we make use of Fuchs’ theory of optical properties of small ionic crystals for simulating the IR absorption spectra of nanostructured NiO for different geometrical shapes of the crystallites and compare the results of the simulations with the experimental ones [38]. Simulations based on Fuchs’ theory had successfully explained the spectra of small particles of a number of metal oxides and alkali halides, where the particle sizes were of the order of a few micrometers or of the order of 50 /100 nm, with the proper choice of a multiplication factor (either a whole number or a fraction) for the damping function, g [22,38]. The applicability of this macroscopic theory for explaining the IR spectral features of nanostructured samples with average particle size of the order of 10 nm or less, such as in the present study, has not been experimentally verified [1,22,38].
Pav
125
(o av 1) Eav 4p
(1)
where Eav and Pav are assumed to be merely volume averages of the nearly constant fields inside the crystallites, Ei and Pi and those out side the crystallites (i.e. in the host material), Em and Pm. In this definition of the average dielectric function (o av) any interaction between the crystallites embedded in the host material, such as the possible dipole interaction, is not taken into consideration, which is rather a simplification of the actual situation. However, in the limit of small densities of crystallites such an approximation is valid [38]. According to Fuchs, if the particle density is not too high, the average dielectric function is given by: o av (v)
f4pf o(v)xR (v) [o(v) o m ][1 f ]g f4pf o m (v)xR (v) [o(v) o m ][1 f ]g
om (2)
4.2. Theoretical background for the simulation of IR spectra of nanostructured samples Fuchs, through macroscopic approach had devised a method for simulating the frequency dispersion of the absorption coefficient, a , of small ionic crystals with symmetric geometrical shapes embedded in a host dielectric medium [38]. The theory is applicable only when the crystallite sizes are much smaller than the wavelength of the interacting electromagnetic radiation so that the retardation effects (i.e. effects due to the finite velocity of electromagnetic radiation) are negligible. When the crystallites are much smaller than the wavelength of the interacting electromagnetic radiation, the scattering cross-section is negligibly small in comparison with the absorption crosssection and a system of small crystallites embedded in a host material can be characterized by an average dielectric function, o av(v ). In the macroscopic approach, the average dielectric constant, o av(v ), is defined in terms of the average electric field Eav and average polarization field Pav as:
where f is the fraction of the total volume occupied by the particles (filling factor), o m the dielectric constant of the surrounding medium, o (v ) the frequency dependent complex dielectric function of the material and xR(v) the particle susceptibility [38]. According to single oscillator model, o (v) of a diatomic ionic material is given as: o(v)o 8
(o 0 o 8 )v2T v2 igv)
(v2T
(3)
where o 0 and o 8 are the low frequency and high frequency dielectric constants, vT the bulk transverse optical phonon frequency and g the damping function [1,38]. Also, the particle susceptibility, xR(v ) of a symmetric particle is given as: xR (v)
1 X C(i) 4p i (o=o m 1)1 ni
(4)
where C (i ) and ni are, respectively, the oscillator strength and depolarization factor of the ith normal mode [38].
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Now, the absorption coefficient, a of a thin slab of host material containing the small particles can be calculated as a function of frequency as: a
v Im(o av ) pffiffiffiffiffiffi c Re( o av )
(5)
where c is the velocity of light [1,38]. Eq. (5) can be applied to particles of any arbitrary shape, if the values of the depolarization factors, ni , and the oscillator strengths, C (i ), of the corresponding normal modes of vibration are known. For small spherical particles, the main IR absorption is caused by the uniformly polarized Fro¨hlich mode, for which n /1/3 and C /1 (1, 38). Also, Fuchs had shown that the IR absorption of small cubic particles, correspond to six polariton normal modes associated with the surface polarization charge. The calculated values of the oscillator strengths of the six normal modes for a cubic particle are C (1) /0.44, C (2) /0.24, C (3) / 0.04, C (4) /0.05, C (5) /0.10, and C (6) /0.09 and the corresponding depolarization factors are, n1 /0.214; n2 /0.297; n3 /0.345; n4 /0.440; n5 / 0.563; and n6 /0.706 [38]. According to Eq. (5), the surface mode absorption peaks may be identified as the frequencies, which correspond to poles of equation for o av, i.e. Eq. (2). Neglecting the damping factor, g in the equation for o (v ) and substituting n /1/3 and C /1, the Fro¨hlich mode frequency, vF of spherical particles is given as: vF
[o 0 (1 f ) o m (2 f )]1=2 vT [o 8 (1 f ) o m (2 f )]1=2
(6)
Similarly, the frequency of the strongest absorbing surface mode for cubic particles, i.e. the mode i/1with an oscillator strength C (1) /0.44 and depolarization factor n1 /0.214 is given as: vc
[o 0 (1 f ) o m (3:67 1:62f )]1=2 [o 8 (1 f ) o m (3:67 1:62f )]1=2
vT
(7)
From Eqs. (6) and (7), the frequency of the strongest absorbing surface mode for cubic particles, vc is lower than the Fro¨hlich mode, vF for spherical particles and it appears closer to the bulk mode, vT, for the same values of f and o m. Physically, this is a consequence of the lower
depolarization factor, n1 /0.214, for vc in comparison with the depolarization factor, n /1/3, for vF. Also Eqs. (6) and (7) clearly shows that both vF and vc are shifted towards lower frequencies with increase in the filling factor, f or with an increase in the dielectric constant of the surrounding medium, o m.
4.3. Simulation of IR spectra of nanostructured NiO As may be noted from the foregoing discussion, choice of an appropriate geometrical shape for the nanocrystallites is a crucial step in the simulation procedure. However, the choice of geometrical shapes for the purpose of simulation is limited rather to a few simple ones such as spherical, cubic and cylindrical, due to the nonavailability of the values of depolarization factors and oscillation strengths for the normal modes of more complex shapes [38]. In our earlier studies, it was observed that the size dependent variation of both dc and ac electrical conductivities of nanostructured NiO (average particle sizes ranging from 3 to 16 nm), which was not a linear one, could be semiquantitatively explained on the basis of calculations assuming a 14 sided tetrakaidecahedron geometry for the nanocrystallites [28,30]. This assumption was based on the reported crystallographic studies, which had concluded that growth of the NiO crystallites occur in the tetrakaidecahedron shape [39]. However, this complex, yet symmetric geometry for the NiO nanocrystallites was not used for the IR spectral simulations since the depolarization factors and oscillator strengths of corresponding normal modes of vibration were not available. Hence, in the present analysis, we have done the simulation of IR spectra of NiO nanocrystallite for two simple geometries, viz. spherical and cubic, with polyethylene as the host material (o m /2.25). For the IR spectral simulations using macroscopic approach, the bulk optical constants of the material */vT, o 0, o 8 and g */are to be known. Since there exist notable differences between the values of optical constants of bulk NiO reported by different investigators, we have used three
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different sets of optical constants taken from literature to investigate the effect of numerical values of the bulk optical constants on the results of the spectral simulations. The values of the optical constants used and their sources are given in Table 2. An important parameter which according to Eq. (2), determines the value of the average dielectric function, o av(v ), and hence the frequencies of the surface modes is the filling factor, f [16,17,22,38]. With regard to the numerical value of f used for the simulation of IR spectra, two common practices exist, (i) use the value of f estimated from the weight ratios of the sample and host material using their bulk densities (22); or (ii) use f as an adjusting parameter so as to minimize the differences between the simulated spectra and the experimental results while ensuring that the value of f used is within the limit of applicability the macroscopic theory, ((d/l)3 /f B/0.5, where d is the average particle size and l is the wavelength of interacting electromagnetic radiation) [16,38]. In an actual experimental situation, the value of f as encountered by the IR radiation cannot be estimated accurately. This is because, even if the weight ratios of the nanoparticles to host material is accurately determined, it is impossible in practice to make pellets in which the nanocrystallites are hundred percent uniformly dispersed in the host material so that the volume fraction of nanocrystallites as encountered by the IR radiation is same as the one estimated from weight ratios irrespective of the actual location of irradiation on the pellet. Besides, the density of nanostructured materials is known to be much varied from those of the corresponding bulk phase and hence estimation of f from the weight ratios using bulk density values may introduce serious errors
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[26,27]. In the present analysis, in order to study the effect of f on the surface mode frequencies of nanostructured NiO and hence to check whether a poor choice of f is the cause of any possible mismatch between the simulations and the experimental results, simulations were done for three different values of f, viz. 0.01, 0.1 and 0.3. It may be noted that the chosen values of f are well with in the limits of applicability of the macroscopic approach while covering a fairly good range of reasonable values of f. Another important factor that determines the features of the simulated spectra is the damping function, g . An increase in the value of g will shift the surface mode peak to slightly higher frequencies but more importantly will broaden the absorption peaks. It has been a usual practice to introduce a suitable multiplication factor (either a whole number or a fraction) for g , for explaining the experimentally observed broadening of the IR absorption peaks in the spectra of nanostructured samples [1,16,17,22,38]. The physical basis for the introduction of a multiplication factor lies with the knowledge that in nanostructured materials the damping is increased many folds in comparison with the corresponding bulk, primarily due to the large unharmonicity in small crystallites related to the relaxation of the lattice [1,22]. Also, relatively large amplitudes of vibration near the surface and extrinsic factors such as the interaction between crystallites contribute to the enhanced damping in nanostructures [1,22]. In the present study, spectral simulations were done for a wide range of values of multiplication factor for g, in order to have a detailed understanding of the effect of the multiplication factor on the width of the surface mode absorption peaks.
Table 2 Optical constants of bulk NiO used for calculation of absorption coefficient, a Set
vT (cm1)
vL (cm1)
Damping function, g
o0
oa
Reference
I II III
405 401 400
560 / 595
0.0451vT 0.06vT 0.0276vT
11.75 12.0 11.75
5.4 5.4 5.7
[34] [18] [37]
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Fig. 3. Variation of absorption coefficient, a , of nanostructured NiO simulated for spherical geometry of the crystallites for different sets of bulk optical constants.
Fig. 4. Variation of absorption coefficient, a , of nanostructured NiO simulated for cubic geometry of the crystallites for different sets of bulk optical constants.
In the present study, spectral simulations for nanostructured NiO samples dispersed in polyethylene were done assuming both spherical and cubic geometry for the nanoparticles. The effect of the numerical values of the bulk optical constants*/vT, o 0, o 8, g, the filling factor, f and the enhanced damping in nanostructures on the spectral features for both spherical and cubic geometries were analyzed in detail. The results of the spectral simulations and comparison with the experimental results are discussed in the following section.
4.4. Analysis of IR spectral simulations The results of simulations of the absorption coefficient, a , as a function of frequency for nanostructured NiO for spherical and cubic geometries are shown in Figs. 3 and 4, respectively. Figures show simulations done using three different sets of optical constants (Table 2) with the filling factor set to 0.1 and using the value of damping function, g for bulk NiO (i.e. multiplication factor /1). Also, a is plotted in an inverted scale so as to make the comparison with
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the experimental results more convenient. It is clear from Figs. 3 and 4 that the spectral features for spherical and cubic geometries differ much. For spherical geometry, the spectra consist of a single narrow absorption peak, the peak position of which shows marked dependence on the value of optical constants used for simulation. From Fig. 3, the peak positions are noted to be 517.5, 507.95 and 500.25 cm 1, respectively, for simulations using optical constants given in set I, II and III of Table 2. For cubic particles, the spectra show a number of well-defined absorption peaks (Fig. 4). The most intense peak corresponding to i/1 (C (1) /0.44 and n1 /0.241) is located at lower frequencies with respect to the absorption peak for spherical geometry using the same set of optical constants. For cubic geometry also, the peak positions of the absorption maxima show marked dependence on the value of the optical constants used for simulation. Figs. 5 and 6, respectively, show the simulated spectra for spherical and cubic geometries for different values of f. The values of optical constants given in set III of Table 2 were used for these simulations. As the value of f is increased, the absorption peaks shift more towards lower frequencies for both geometries while the width of the peaks are not markedly changed. The same is true for simulations using the other two sets of optical constants as well. For spherical geometry, with f/0.3 an additional peak appears around 540 cm 1. This is most probably an indication of the stronger interaction between the crystallites as the value of f approaches the upper limit of applicability of the macroscopic approach. The effects of enhanced damping on the spectral features for spherical and cubic particles are shown, respectively, in Figs. 7 and 8 by simulating the spectra for different multiplication factors for the damping function, g. Optical constants given in set III of Table 2 were used for these simulations. As may clearly be noted from Figs. 7 and 8, the absorption peaks are shifted slightly towards higher frequencies for larger values of g , but more importantly, the width of the absorption peaks increase markedly with increased damping. Also, it is clear that for the same value of multiplication factor the spectral broadening is much smaller for
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Fig. 5. Variation of absorption coefficient, a , of nanostructured NiO with filling factor, f simulated for spherical geometry of the crystallites.
spherical geometry than for cubic particles. Hence, multiplication factors as large as 15 were used for analyzing the spectral broadening for spherical geometry, while for cubic particles the spectral simulations were done only for multiplication factors up to 4. However, for the analysis of the spectral broadening of cubic geometry, simulations were done with the multiplication factor increased in steps of 0.5. Obviously, the larger effect of increased damping on the spectral features for the cubic particles is due to the presence of more number of absorption peaks, each of
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Fig. 7. Variation of absorption coefficient, a , of nanostructured NiO with increase in the damping function, g , simulated for spherical geometry of the crystallites. Fig. 6. Variation of absorption coefficient, a , of nanostructured NiO with filling factor, f simulated for cubic geometry of the crystallites.
which becomes wider with increased damping. Also, from Fig. 8, it may be noted that with increased damping, the higher frequency absorption peaks merge together and resembles a shoulder or a hump in the region 520/540 cm1. It may be noted that in the above analysis, the results of the simulation procedure are presented in terms of the absorption coefficient, a , (Figs. 3/ 8) while in the experimentally measured IR spectra of nanostructured NiO (Fig. 1), transmittance, T /eax , where x is the thickness of the pellet, is plotted as a function of frequency. The character-
istic features of the spectra, such as the peak frequencies, width of the peaks and appearance of shoulders are not affected by the mode of presentation of the spectra and one can have a comparison between the simulations and the experimental results without much difficulty. Analysis of Figs. 3/6 clearly show that neither the position of the experimentally observed absorption maxima nor its width is correctly reproduced by simulations for either spherical or cubic geometries using any of the three sets of optical constants (Table 2) for values of filling factor, f, ranging from 0.01 to 0.3. Also, it may be inferred from Figs. 5/8 that spectral simulations with a filling factor, f /0.1 and cubical geometry for the nanocryastallites approximately reproduce some of the experimentally observed spectral features of
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Fig. 8. Variation of absorption coefficient a , of nanostructured NiO with increase in the damping function, g simulated for cubic geometry of the crystallites.
nanostructured NiO samples, such as the occurrence of a shoulder in the frequency region /530/ 550 cm1, though the position of the most intense absorption peak for these simulations lie at least 50 cm 1 above the experimentally observed absorption maxima. Moreover, the evolution of the shape of the high frequency shoulder and the broadening of the main absorption peak with increase in average particle size as observed in the experimental spectra (Fig. 1) are at least approximately reproduced in Fig. 8, respectively, by the merging together of the high frequency absorption peaks for cubical particles and the general broadening of all the absorption peaks with increased damping. Thus it seems possible to
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picturise the experimentally obtained IR spectra of nanostructured NiO as composed of the surface modes associated with cubic geometry of the crystallites with an increased damping and some other modes of vibration lying closer to the bulk transverse optic phonon frequency, vT in the frequency region /420/440 cm 1 which correspond to more intense absorption peaks than the surface modes for the cubic particles. One simple explanation for the occurrence of the main absorption maxima at lower frequencies than those calculated from macroscopic approach, is the possibility of presence of irregularly shaped particles in the nanostructured samples analyzed [18]. However, this explanation is rather arbitrary and cannot be quantitatively established. Also, from the analysis of the simulated spectra, it may be noted that with the same numerical values of simulation parameters, the maximum intense peak for cubic and spherical geometries differ by /25 cm 1 at the most. Certainly a mismatch of /50 cm 1 between the experimental spectra and simulations cannot wholly be attributed to shape effects alone. Another factor that may contribute to the experimentally observed shifting of the main absorption maxima to lower frequencies than those simulated is the possible interactions between the nanocrystallites dispersed in the host material, which was not taken into account while defining the average dielectric function, o av(v ), used for the simulations. However, it may be noted that the position of the maximum intensity absorption peaks obtained in the simulation analysis (Figs. 3/8) are approximately in agreement with that for NiO powder with an average particle size of /35 nm reported by Hund et al. [18]. It may be reasoned that if such a strong interparticle interaction, which shifts the surface mode absorption by /50 cm 1 towards the lower frequency side exist in the case present samples with average particle sizes ranging from 3 to 16 nm, it should also be present at least in a lesser extent in NiO powder with average particle size of /35 nm, unless the interaction corresponds to an aggregation of nanocrystallites, which somehow is present in our samples but was completely absent in the samples of Hund et al. However, Clippe et al. had shown that for small spherical particles of
132
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NiO, the surface mode absorption peaks are shifted to higher frequencies due to aggregation of crystallites and the same is true for other geometries as well [40]. These lead to the conclusion that the occurrence of the main absorption maxima at frequencies /50 cm 1 lower than those calculated using the macroscopic approach in the experimental spectra of nanostructured NiO samples in the present study originate from the very small average particle size of the samples (3 / 16 nm). For nanostructured materials with average particle sizes of the order of 10 nm or even less, the optical properties are expected to depend strongly on the perturbed nature of the atomic layers at the surface due to the very large volume fraction of the surface atoms. Martin had pointed out that the macroscopic approach cannot be expected to describe effects which are dependent on the structure of phonon density of states and cannot be used for analyzing the vibrational modes so highly localized that the atomicity of the crystallite is important [41]. Further, he had devised an alternate method for analyzing the surface modes in very small crystallites of diatomic ionic materials, which is a lattice dynamical calculation using rigid ion model parameters in which the finite crystallite is considered as a large molecule. This approach has the advantage that it includes a microscopic description of the surface, but has the disadvantage that one must ultimately diagonalise very large matrices, the order of which depends on the number of ions constituting the finite crystallite [38,41]. These calculations had shown that, for very small diatomic ionic crystallites with average particle size /10 nm or less, the principal effect of the high volume fraction of the surface atoms is to shift the entire density of states curves to lower frequency which in turn corresponds to the shifting of the main absorption peak to lower frequencies than those estimated using the macroscopic approach. Further, these calculations highlight the importance of vibrational modes corresponding to edge and corner atoms, which lie closer to the bulk mode, vT, in determining the spectral features of nanostructures with average particle size /10 nm or less for non-spherical (cube /like) geometries of the crystallites [41].
Martin had concluded that the results of this microscopic theory are not inconsistent with those of the macroscopic approach and the fundamental absorption frequency for very small crystallites, may be calculated from the equations for the most intense absorption maxima for spherical and cubic geometries based on the macroscopic approach Eqs. (6) and (7) with the following two modifications [41]. Since, in the rigid ion model, it is assumed that the crystal has no electronic polarizability, for consistency o 8 should be set to 1. Also, since the macroscopic parameter o 0 does not enter into the determination of the rigid ion model parameters used for the macroscopic calculation, it is more appropriate to calculate o 0 from the value of vL resulting from the model calculation and Lyddane /Sachs/Teller relation, o 0 /v2L/v2T [41]. With these modifications, Eq. (6) gives the position of the most intense peak in the IR absorption of nanostructured NiO, for spherical geometry as 437.28, 434.26 and 441.90 cm 1, respectively, for calculations using the sets of optical constants I, II and III of Table 2. For these calculations, the filling factor, f, was set to 0 since the microscopic approach takes into account only a single crystallite for the density of states calculation. Also, since the value of vL for the set II was not available the corresponding peak position was estimated by using the value of vL of set I since this does not seriously alter our conclusions. Similarly, with the modifications, the position of the most intense absorption peak for cubic geometry for nanostructured NiO are estimated to be 424.48, 421.08 and 425.39 cm 1, respectively, for calculations using the sets of optical constants I, II and III of Table 2. It may be noted that these calculations are very much in agreement with the experimentally observed positions of the most intense absorption maxima for the nanostructured samples in the present study. Hence, the appearance of the most intense absorption at frequencies much lower than those estimated using the macroscopic approach in the experimental spectra of nanostructured NiO samples with average particle sizes ranging from 3 to 16 nm should be a consequence of the large surface to volume ratio of the particles owing to their very small average particle sizes which in turn makes
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the atomicity of the surface layers very important in determining the spectral features. The above discussion suggests that for explaining the spectral features of the nanostructured NiO samples with very small average particle sizes /10 nm or less, the macroscopic approach alone is not suffice and one has to include microscopic approach also, which takes into account the contributions due to large surface to volume ratio of the particles which becomes very important at these size scales. 4.5. Analysis of IR spectra of nanostructured NiO samples in the frequency region 50 /100 cm 1 From Fig. 2, it is clear that the spectra of all the four nanostructured NiO samples show presence of a weak, yet distinct absorption peak in the frequency region /60 /100 cm1, with the exact peak frequencies as already stated. This low frequency absorption peak has not been reported in the IR spectral studies of bulk NiO. Also, the peak positions and the shape of this low frequency absorption peak exhibit marked variation with change in average particle size. These lead to the conclusion that the weak absorption peak appearing in the frequency region /60/100 cm 1 is a consequence of the small average particle size of the samples and may be considered as a characteristic feature of the IR spectra of nanostructured NiO. It may be noted that, the dominance of surface modes is not the only distinct feature of the spectra of nanostructured samples in comparison with that of the corresponding bulk [1 /6,41]. There are other distinct spectral features as well, which may characterize the spectra of nanostructured samples, such as the occurrence of a very weak absorption peak corresponding to surface induced acoustical modes appearing at frequencies much lower than the bulk transverse optical mode, vT, [1 /6,41]. The acoustical mode vibrations of a diatomic single crystal with translational symmetry are not IR active [1,41]. However, in the corresponding nanostructured samples, due to the breakdown of translational symmetry the low frequency acoustical modes may acquire a dipole moment resulting in a weak absorption at fre-
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quencies much lower than vT [41]. The exact frequencies of these surface-induced acoustical modes in nanostructures can be estimated only through microscopic approaches, such as the one devised by Martin, which takes into account the atomicity of the surface layers [41]. However, the frequencies of these surface induced acoustical modes in nanostructures will not be much varied from the acoustical mode vibration frequencies of the corresponding bulk material [41]. Studies on bulk NiO had located the longitudinal acoustical mode, vLA and transverse acoustical mode, vTA to lie in the frequency ranges /111/331 and 57/180 cm 1, respectively [42]. From the foregoing discussion, it is clear that the weak absorption peaks in the frequency range / 60/100 cm 1 appearing in the spectra of all the four nanostructured NiO samples can be identified with the surface induced transverse acoustic modes, vTA which become IR active due to the breakdown of translational symmetry in the nanostructured NiO samples [1 /6,41,42]. Also, it may be inferred that the observed variation of the position, intensity and shape of the surface induced acoustical mode absorption with average particle size is a direct consequence of the difference in the actual atomic structure of the surface layers of the nanostructured samples studied.
5. Conclusion Nanostructured NiO having different average particle sizes were synthesized and the FTIR spectra of the samples were recorded in the far IR region. The spectra were found to be dominated by the surface mode absorptions with no distinct absorption corresponding to the bulk transverse optic mode. IR absorption coefficient, a , for nanostructured NiO samples were calculated as a function of frequency using a macroscopic approach. The effects of optical constants, crystallite geometry, filling factor and increased damping on the spectral features of the samples were analyzed. An analysis of simulated spectra revealed that spectral simulations with a filling factor f/0.1 and cubical geometry for the nanocryastallites approximately reproduce the occur-
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rence of a shoulder in the frequency region /530/ 550 cm1, though the position of the most intense absorption peak for these simulations lie almost 50 cm 1 above the experimentally observed absorption maxima. It was shown that the experimentally observed absorption maxima of the samples were in close agreement with those estimated according to a microscopic theory due to Martin based on the rigid ion model. It was inferred that for explaining the spectral features of the nanostructured NiO samples with very small average particle sizes /10 nm or less, the macroscopic approach alone is not sufficient and one has to include microscopic approach, which takes into account the contributions due to large surface to volume ratio of the crystallites at these size scales. The weak absorption peaks in the frequency range 60/ 100 cm 1 appearing in the spectra of all the four samples were identified as the surface induced transverse acoustic modes, vTA, which become IR active due to the breakdown of translational symmetry in the nanocrystallites.
[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
Acknowledgements One of the authors V. Biju acknowledges Council of Scientific and Industrial Research (CSIR), Government of India for the financial support in the form of Senior Research Fellowship.
[30] [31] [32] [33] [34]
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