Growth Kinetics of ZnO Nanocrystals in the Presence of a Base: Effect

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J. Phys. Chem. C 2010, 114, 22113–22118

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Growth Kinetics of ZnO Nanocrystals in the Presence of a Base: Effect of the Size of the Alkali Cation Pralay K. Santra, Sumanta Mukherjee, and D. D. Sarma*,† Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India ReceiVed: September 9, 2010; ReVised Manuscript ReceiVed: NoVember 14, 2010

Following an earlier study (J. Am. Chem. Soc. 2007, 129, 4470) describing a very unusual growth kinetics of ZnO nanoparticles, we critically evaluate here the proposed mechanism involving a crucial role of the alkali base ion in controlling the growth of ZnO nanoparticles using other alkali bases, namely, LiOH and KOH. While confirming the earlier conclusion of the growth of ZnO nanoparticles being hindered by an effective passivating layer of cations present in the reaction mixture and thereby generalizing this phenomenon, present experimental data reveal an intriguing nonmonotonic dependence of the passivation efficacy on the ionic size of the alkali base ion. This unexpected behavior is rationalized on the basis of two opposing factors: (a) solvated cationic radii and (b) dissociation constant of the base. Introduction Synthesis of nanoparticles in the quantum confinement regime in solutions, popularly known as the bottom-up approach, has been the preferred route owing to its versatility and flexibility, leading to the synthesis of a diverse range of nanoparticles with a wide range of functionalities. Several investigations1-13 have been carried out to understand the growth of semiconductor nanoparticles within this bottom-up approach, in view of its ability to control the size of these nanoparticles, providing a powerful handle to tune electronic and optical properties of these materials. The growth process has often been discussed in terms of the Ostwald ripening process, based on the common belief that the growth of semiconductor nanoparticles in the nanometric regime proceeds via a diffusion-controlled ripening process. In this process, the average diameter of the nanoparticles, d, depends4,5 on time, t, as d3 ∝ t. There have been several reports suggesting that the growth of nanoparticles follow Ostwald ripening, for example, for TiO2,6 InAs, CdSe,7 ZnO,8 and CdS.9 However, recent theoretical10,11 as well as experimental studies12 suggest that the growth of nanoparticles can be significantly influenced by the rate of surface reactions, thereby showing departures from the diffusion-limited growth behavior. Recently, Viswanatha et al.13 have shown that the growth of ZnO nanoparticles in the presence of NaOH as a base deviates drastically from the Ostwald ripening process. This study suggests that the growth of ZnO nanoparticles in the presence of a base, such as NaOH, is hindered by the cations of the base, namely, Na+ ions, via the formation of an effective passivating layer around the negatively charged growing ZnO nanoparticles beyond a certain critical concentration of the base. This unusual phenomenon, if indeed true, should be observable in other cases as well; therefore, it is worthwhile to investigate the growth behavior of ZnO nanoparticles with other bases in order to probe the possibility of generalizing the phenomenon. In view of this, we have investigated in detail the growth of ZnO nanoparticles using LiOH and KOH as bases. This comparative study, while establishing the generality of the phenomenon of the passivation by the reactant in such cases, reveals some intriguing nonmono* To whom correspondence should be addressed. E-mail: sarma@ sscu.iisc.ernet.in. † Also at Jawarharlal Neheru Centre for Advanced Scientific Research.

tonic behavior across the series (LiOH, NaOH, and KOH), providing further insight into this phenomenon. Experimental Section Synthesis. ZnO nanocrystals were synthesized using a method similar to that reported earlier.13-15 In a typical synthesis, the required amount of zinc acetate was dissolved in 42 mL of isopropanol (i-PrOH). Separately, LiOH or KOH was prepared by dissolving these in 8 mL of i-PrOH. As LiOH is not completely soluble in i-PrOH, a very small amount (∼1 mL) of ethanol was used to dissolve LiOH first and then mixed with i-PrOH. Both the solutions were prepared at room temperature (RT). To start any reaction at RT, these two solutions were mixed at once and the reaction mixture was stirred continuously throughout the reaction. In case of any higher-temperature reaction, solutions were separately kept in an already preheated water bath at the required temperature for sufficient time to attain the reaction temperature. ZnO nanoparticles were separated out from the reaction mixture by evaporating the solvent using a rotavapor. The dry white solid powder of ZnO was washed several times using distilled water and dried overnight under vacuum for further characterization. Characterization. X-ray diffraction (XRD) studies were carried out on the properly washed dry white solid powder of ZnO nanoparticles. The XRD experiments were carried out using a Siemens D50005 diffractometer with a slow scan speed of 0.25°/min. Nanoparticles synthesized in this technique using both LiOH and KOH are formed in the wurtzite phase. We show a representative XRD plot of ZnO nanoparticles in Figure SI01 (Supporting Information); XRD of all other ZnO nanoparticles are very similar, independent of the reactants (LiOH or KOH) used or the reaction time. On comparison of the XRD pattern of the bulk ZnO presented in the same figure by the solid black line, it is evident that nanoparticles of ZnO formed using this method form in the wurtzite phase only. Carrying out an investigation of the growth process of nanoparticles using the XRD technique is severely limited by the ex situ nature of the measurements as well as by the inability of probing very fine time slices in such an approach, limiting the time resolution of the probe. Moreover, the relationship between the size and the width of a diffraction pattern from nanoparticles is dependent

10.1021/jp108613f  2010 American Chemical Society Published on Web 12/02/2010

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Figure 1. (a) UV-visible absorbance spectra collected at different times from a reaction using 0.25 mmol of Zn acetate and 0.4 mmol of LiOH at 308 K. The vertical dotted line at 3.34 eV represents the band gap of bulk ZnO. (b) Average size (black dots) of ZnO nanoparticles calculated from the UV-visible absorbance spectra shown in (a). Red dots represent the average sizes measured from TEM images at different times. Vertical bars are the error bars in the average diameter estimated from several reactions. Inset: plot of d3av vs time for the same reaction.

on the assumption of an absence of any other contributing factor, such as strain and various imperfections in nanocrystals, namely, twinning, staking faults, etc. We have taken advantage of the sensitive dependence of UV-visible absorption spectroscopy on the size of nanoparticles in the size regime of interest, to study the in situ growth kinetics of ZnO nanoparticles. UV-visible absorption spectroscopy was carried out using a PerkinElmer double-beam LM-35 spectrometer. In all the cases, pure i-PrOH was used as the blank reference solution. A very small amount (∼100 µL) of the reaction mixture was taken out from the reaction mixture and mixed with pure i-PrOH (∼3 mL) at room temperature. This solution was used immediately to measure the UV-visible absorption for the ZnO nanoparticles. The usefulness of such time-resolved absorption spectra in probing the growth kinetics of nanoparticles in solutions was earlier established13 in the context of an investigation of the growth of ZnO nanoparticles where NaOH was used as the base instead of LiOH and KOH in the present study; in this earlier report, it was shown that the growth data obtained from such absorption spectra were in very good agreement with those obtained from in situ time-resolved small-angle X-ray scattering (SAXS) experiments. Transmission electron microscopy (TEM) studies were carried out in a Tecnai T20 instrument, operating at an accelerating voltage of 200 kV. Results and Discussions A typical set of time-resolved in situ UV-visible absorption spectra, obtained at a given concentration of 0.25 mmol of zinc acetate and 0.40 mmol of LiOH, at 308 K, is shown in Figure 1a. Intensities of these absorption spectra are normalized at the peak. The band gap of the bulk ZnO is shown by the vertical dotted line in the same figure. Absorption edges of samples grown here are found at energies higher than that of the bulk band gap in every case, confirming the presence of nanoparticles in the quantum confinement regime. With increasing time, the absorption spectra systematically shift to lower energies, establishing a systematic decrease in the band gap and consequently an increase in the particle size with time. The average diameter (d) at a given time, t, of ZnO nanoparticles was calculated from the UV-visible absorption spectra using the well-established, realistic tight-binding calculations available from the literature.16-19 Average diameters calculated from UV-visible spectra presented in Figure 1a are shown by the solid black circles in Figure 1b; this plot suggests a systematic growth in the particle size with time. We have estimated error bars for the average diameter for any given reaction by carrying out and analyzing independent experiments with the given set

of reaction parameters. We found that the estimated error scales monotonically with the average diameter. Therefore, we have shown only typical error bars in Figure 1b for different size regimes for the sake of clarity. Keeping in mind the indirect nature of the probe used and, therefore, exercising caution, we have cross-checked the average diameter calculated from UV-visible spectra, by measuring the average diameter of ZnO nanoparticles from TEM at a few times during the growth of these nanoparticles. One of the TEM images is shown in Figure SI-02 in the Supporting Information. The average diameters obtained from TEM data at two different time points from the same reaction are shown by the solid red squares in the same figure (Figure 1b). The excellent agreement between the diameters obtained from the UV-visible absorption spectroscopy and TEM validates the accuracy of the size calculated from the UV-visible absorption spectroscopy. To test whether the growth of ZnO nanoparticles can be described within the well-known Ostwald ripening process, as has been established for the growth of CdS nanoparticles,9 we have plotted the cube of the average diameter (d3) as a function of the time (t), in the inset of Figure 1b corresponding to d shown in the main panel of the figure. Clearly, d3 does not follow a linear behavior with t, showing systematic deviations, more prominently at the lower t regime. This nonlinear behavior of d3 with time clearly indicates that the growth of ZnO nanoparticles synthesized in this method with LiOH and KOH does not follow the Ostwald ripening process for its growth, consistent with earlier reported observations for NaOH. Our systematic investigation by varying reactant concentrations as well as the temperature shows similar deviations over all reaction conditions. This is illustrated in Figure 2a where we plot d3 as a function of the time with 0.25 mmol of zinc acetate and different concentrations of LiOH at 308 K. Besides the deviation from the linear behavior, this figure also shows that the growth rate of the ZnO nanoparticles depends strongly on the concentration of the reactants, which is not expected in the dilute limit of the reaction condition, if the growth rate is to be controlled only by the diffusion process. We have also shown the d3 as a function of time with 0.25 mmol of zinc acetate and 0.4 mmol of LiOH at four different temperatures in Figure 2b. Although in this case also, the growth of ZnO nanoparticles deviates from the Ostwald ripening behavior, these results also show that the growth rate of ZnO nanoparticles is higher at higher temperatures. To quantify the deviation of the growth mechanism from the diffusion-limited Ostwald ripening process, we have explored whether the observed dependence of the average diameter, d, on the time (t) can be expressed in terms of an empirical

Growth Kinetics of ZnO NCs in the Presence of a Base

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Figure 2. (a) Variation of the average size of the ZnO nanoparticles with time synthesized with 0.25 mmol of zinc acetate and different concentrations of LiOH (shown by different symbols) at 308 K. (b) Variation of the average size of ZnO nanoparticles synthesized with 0.25 mmol of zinc acetate and 0.4 mmol of LiOH at different temperatures (shown by different symbols). The solid line represents the fit with the equation dtx - dx0 ) Kt in both the cases. The best fitted value of x is mentioned in each case.

Figure 3. Variation in the diameter of ZnO nanoparticles synthesized at different concentrations of LiOH at different temperatures. The reaction temperature, concentration of the base, and the exponent value x are mentioned in the legend of each figure. Typical error bars of average diameters are presented for some reactions at different size regimes.

equation: dxt - d0x ) Kt, where the dt is the average diameter and the subscript denotes the time, t. In a diffusion-controlled growth mechanism, the value of the exponent, x, is expected to be equal to 3. Exponent values, however, obtained by fitting present experimental data range between approximately 4 and 20, depending on the reaction conditions, with the corresponding fits shown by the solid lines through the data points in Figure 2a,b. Although this empirical equation has no theoretical basis, it serves to show that reaction forming ZnO under the present conditions is much slower than that expected on the basis of the cubic law of the Ostwald ripening process, with a larger value of the exponent indicating a slower reaction rate. This

drastic slowing down of the growth rate clearly suggests that the growth of ZnO nanoparticles is strongly hindered and slowed down far beyond the diffusion-controlled reaction rate in this synthetic route. To explore the specific role of the base in hindering the reaction, we have carried out the synthesis of ZnO nanoparticles using a fixed concentration of zinc acetate (0.25 mmol) at several temperatures with different concentrations of LiOH, as shown in Figure 3. This figure clearly shows that the reaction rate also depends strongly on the concentration of the base, as can be easily seen by the variation of the growth rate, given by the value of x, at a given temperature, but different concentrations of LiOH shown in different panels. We note from

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Figure 4. Three-dimensional plot showing the variation of ln(x) with different concentrations of base at different temperatures. The Z axis is plotted in natural log scale for better representation. The blue plane at ln(x) ) 1.099 indicates the ideal value of x ) 3 as expected from Ostwald ripening.

this figure as well as from Figure 2a that x systematically increases with decreasing temperature. The dependencies of x on the temperature and the base concentration are shown in Figure 4 as a three-dimensional plot, with the value of x plotted in the natural log scale for clarity over the entire range of x values. The blue plane in the same figure indicates the value of x ) 3, which is the expected value for the Ostwald ripening process. This plot shows that, irrespective of the concentration of the base and temperature, the value of x is higher than the ideal value, indicating a remarkable deviation from the Ostwald ripening for all ranges of synthetic conditions explored in the present study. It is interesting to note that x systematically approaches the expected value of 3 for higher temperatures and lower base concentrations, suggesting that these reaction conditions favor a growth rate more akin to the Ostwald ripening process, being dominantly controlled by diffusion processes. We have carried out a large number of reactions with 0.25 mmol of zinc acetate with various concentrations of the base, LiOH and KOH, at different temperatures to understand the exact role of the base in governing the growth rate of ZnO nanoparticles. The growth rate can be conveniently characterized by one of two alternative ways. We can take the difference in the average diameter at the times t ) 50 min and t ) 0 min to represent the growth rate of ZnO nanoparticles synthesized with different concentrations of the base and the temperature, as was done in ref 13. Alternately, we note that the value of x is inversely related to the growth rate (higher the x, slower is the growth); we may also use 1/x for each reaction condition, that is, fixed concentration of all reactants and a given temperature,

Santra et al. to represent the growth rate. We have shown the difference in the average diameter (d50 - d0) and the value of 1/x, as functions of LiOH concentrations at four different temperatures in Figure 5a,b, respectively, for LiOH; corresponding data for KOH are shown in Figure SI-03a,b (Supporting Information). It is clear from these results that the growth rate of ZnO nanoparticles at any given temperature rapidly decreases with an increase in the base concentration beyond a critical concentration value, which, interestingly, appears independent of the temperature. There is hardly any growth of ZnO nanoparticles beyond this critical concentration of the base (0.6 mmol for LiOH and 0.7 mmol for KOH). A similar extreme slowing down of the growth of ZnO nanoparticles has been reported earlier13 with NaOH as a base, with the temperature-independent critical concentration, independent of the temperature being 0.5 mmol for NaOH for the same concentration (0.25 mmol) of zinc acetate. Thus, it becomes evident that the critical concentration for this drastic slowing down of the growth of ZnO nanoparticles has a significant dependence on the nature of the base, while being essentially temperature-independent for any given base. In this context, we note that it was earlier eatablished13 that water from crystallization of zinc-acetate or due to the hygroscopic nature of the base does not affect any qualitative features of these experiments. To determine the effect of zinc acetate concentration on the critical concentration, we have carried out systematic studies at different concentrations of zinc acetate. We have shown the difference in average diameters (d50 - d0) with different concentrations of the base at different zinc acetate concentrations at a given temperature of 318 K in Figure 6 for LiOH and in Figure SI-04 (Supporting Information) for KOH. We observe that, with an increase in zinc acetate, there is a systematic increase in the critical concentration of the bases for which the growth of nanoparticles is almost completely stopped. These results obtained with LiOH and KOH as bases in the reaction to grow ZnO nanoparticles are qualitatively similar to results earlier reported for the growth of ZnO nanoparticles with NaOH as the base, establishing this as a general phenomenon. In analogy to the earlier case of NaOH,13 the sharp decrease in the growth rate at a certain critical base concentration can be explained with the help of the schematic diagrams shown in Figure 7. As the reaction medium is basic, the surface of the ZnO nanoparticle will be negatively charged. Because of the protic nature of the solvent, the bases (MOH, where M ) Li, Na, K) will be dissociated into its ionic form (M+ and OH-). Cations present in the reaction mixture will be present in solvated form, and these solvated cations will be attracted toward the negatively charged ZnO nanoparticle surface, forming a positively charged cloud around each nanoparticle. In the presence of an excess concentration of the base, these cations

Figure 5. (a) Variation in the difference in diameter (d50 - d0) of ZnO nanoparticles as a function of the concentration of LiOH at different temperatures. (b) Variation of 1/x with the LiOH concentration. The vertical dotted line indicates the critical concentration.

Growth Kinetics of ZnO NCs in the Presence of a Base

Figure 6. Variation of the difference of diameter (d50 - d0) of ZnO nanoparticles as a function of the concentration of LiOH for different zinc acetate concentrations.

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Figure 8. Variation of the product of critical concentration of the base and the diameter of the nanoparticles as a function of zinc acetate concentration. The data of NaOH is taken from ref 13.

Figure 7. Schematic diagram showing the passivation of ZnO nanoparticles by cations.

will provide an effective passivating sphere around the nanoparticles, as shown in Figure 7, inhibiting any further growth. Let us consider the radius of the ZnO nanoparticle and the solvated cation to be RNC and RM+, respectively. The critical concentration of the cation, CCritical M+ , required to form a complete shell around the ZnO nanoparticle is proportional to the ratio of the surface area of the nanoparticle and the cross-sectional 2 2 Critical 2+ ∝ (4πRNC )/(πRM ) ) (4RNC )/ area of the cation, that is, CM + 2+ (RM ). It is clear from this expression that, for a given size of the nanoparticle, different concentrations of three bases will be required to stop the growth due to the different sizes of the solvated cations, (Li+, Na+, K+). This is clearly reflected in the fact that the critical concentrations for LiOH, NaOH, and KOH for a fixed Zn concentration of 0.25 mmol are 0.6, 0.5 and 0.7, respectively. The schematic presented in Figure 7 to explain the effective passivation of ZnO nanoparticles in the presence of an excess base suggests a specific dependence of the critical concentration with zinc acetate concentration. It was mentioned earlier that Critical required to provide the near-complete passivation is CM + proportional to the total surface of the nanoparticles, which can be easily shown13 to be proportional to CZn/RNC, where CZn is should the concentration of zinc acetate. This means that CCritical M+ Critical / RNC ∝ be proportional to CZn/RNC or, in other words, CM + Critical CZn. We have shown CM / RNC versus CZn for all three + different bases in Figure 8. The dominantly linear behaviors of these plots for all the bases are evident in the figure, establishing the aforementioned proportionality and thereby providing credence to the mechanism proposed in ref 13 and here to explain the observed phenomenon of a critical slowing down of the growth rate beyond a certain concentration of the base. Figure 8, however, presents us with a puzzling nonmonotonic behavior with respect to the periodic table, showing the lowest slope of the straight line behavior for NaOH. This is also reflected in the critical concentration being the lowest for the case of NaOH for a given Zn2+ concentration, as already mentioned. This is in contrast to the usual expectation of the critical concentration varying inversely with the solvated cationic (Li+, Na+, K+) size, as expressed earlier in the text by the Critical 2 + + + equation, CM ∝ (1)/(RM + +). We know that RLi 〉 RNa 〉 RK , and this demands the critical concentration to vary as CLi+

Figure 9. Passivation of ZnO nanoparticles by the cations and dissociation of the base in the reaction medium.

〈 CNa+ 〈 CK+. The contrasting variation observed here for the critical concentrations of the bases, namely, CNa+ 〈 CLi+ 〈 CK+ can be rationalized in the following way using the schematic diagram, as shown in Figure 9, that partially modifies the earlier interpretation (Figure 7). In Figure 7, we have considered only the solvated ionic radius of the cation, implicitly assuming a complete dissociation of the base in the solvent. The concentration of the cation in the reaction mixture is, in reality, given by the dissociation constant of the base (KDMOH). The dissociation 〈 KNaOH 〈 KKOH constants of these bases follow20 the trend, KLiOH D D D , which means a lesser amount of KOH will give rise to more numbers of cations compared with NaOH and LiOH. Thus, there are two independent factors, namely, the size of the basic cation and the dissociation constant of the base, that influence the critical concentration at which the growth is effectively stopped via the formation of a passivating layer of cations around the negatively charged, growing nanocrystals. Interestingly, both these factors vary in a monotonic manner across the series, Li, Na, and K, but in the opposing sense. For example, the solvated ionic radii decreases in the sequence of Li, Na, and K, whereas the dissociation constant increases. Thus, these two opposing trends give rise to the nonmonotonic dependence observed here with NaOH exhibiting the lowest value of the critical concentration. Conclusion We have extended the earlier work on growth kinetics of ZnO nanoparticles synthesized using a strong base, NaOH. Our work using LiOH and KOH as bases supports the earlier observation that the growth rate of ZnO nanoparticles in the presence of such strong bases is very slow compared with the well-known diffusion-controlled Ostwald ripening process. In both cases of LiOH and KOH, we find that the growth rate of ZnO nanoparticles depends on the base concentration in a nontrivial way, exhibiting a critical concentration beyond which the growth of ZnO nanoparticles is almost completely inhibited. This comparative study using different bases establishes an intriguing

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nonmonotonic behavior for the critical concentration of the base required to stop the growth, with NaOH exhibiting the lowest value of the critical concentration in comparison with LiOH and KOH. Extending earlier interpretations, we show that this unexpected behavior arises from two opposing factors, namely, solvated cationic radii and the dissociation constant across the series, LiOH, NaOH, and KOH. Acknowledgment. The authors thank Michael D. Clark and Sanat K. Kumar for useful discussions. Department of Science and Technology, Government of India, is gratefully acknowledged for funding. D.D.S. acknowledges the J. C. Bose Fellowship. Supporting Information Available: XRD and TEM images of ZnO nanoparticles and growth kinetic results of ZnO nanoparticles using KOH as a base. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Steigerwald, M. L.; Brus, L. E. Acc. Chem. Res. 1990, 23, 183. (2) Murray, C. B.; Kangan, C. R.; Bawendi, M. G. Annu. ReV. Mater. Sci. 2000, 30, 545. (3) Qu, L.; Yu, W.; Peng, X. Angew. Chem., Int. Ed. 2004, 4, 465. (4) Lifshitz, I. M.; Slyozov, V. V. J. Phys. Chem. Solids 1961, 19, 35.

Santra et al. (5) Wagner, C. Z. Elektrochem. 1961, 65, 581. (6) Oskam, G.; Nellore, A.; Penn, R. L.; Searson, P. C. J. Phys. Chem. B 2003, 107, 1734. (7) Peng, X.; Wickham, J.; Alivisatos, A. P. J. Am. Chem. Soc. 1998, 120, 5343. (8) Bartels, J.; Lembke, U.; Pascova, R.; Schmelzer, J.; Gutzow, I. J. Non-Cryst. Solids 1991, 136, 181. (9) Viswanatha, R.; Amenitsch, H.; Santra, S.; Sapra, S.; Datar, S. S.; Zhou, Y.; Nayak, S.; Kumar, S. K.; Sarma, D. D. J. Phys. Chem. Lett. 2010, 1, 304. (10) Embden, J. V.; Sader, J. E.; Dadivson, M.; Mulvaney, P. J. Phys. Chem. C 2009, 113, 16342. (11) Talapin, D. V.; Rogach, A. L.; Hasse, M.; Weller, H. J. Phys. Chem. B 2001, 105, 12278. (12) Viswanatha, R.; Santra, P. K.; Dasgupta, C.; Sarma, D. D. Phys. ReV. Lett. 2007, 98, 255501. (13) Viswanatha, R.; Amenitsch, H.; Sarma, D. D. J. Am. Chem. Soc. 2007, 129, 4470. (14) Viswanatha, R.; Sapra, S.; Satpati, B.; Satyam, P. V.; Dev, B. N.; Sarma, D. D. J. Mater. Chem. 2004, 14, 661. (15) Viswanatha, R.; Santra, P. K.; Sarma, D. D. J. Cluster Sci. 2009, 20, 389. (16) Viswanatha, R.; Sarma, D. D. Chem.sEur. J. 2006, 12, 180. (17) Sapra, S.; Shanthi, N.; Sarma, D. D. Phys. ReV. B 2002, 66, 205202. (18) Sapra, S.; Sarma, D. D. Phys. ReV. B 2004, 69, 125304. (19) Viswanatha, R.; Sapra, S.; Saha-Dasgupta, T.; Sarma, D. D. Phys. ReV. B 2005, 72, 045333. (20) Das, A. K. Fundamental Concepts in Inorganic Chemistry (Part I and II); CBS Publishers and Distributors: New Delhi, 2000.

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