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Small-angle neutron scattering investigations on sintering behavior in the powder compacts of ceria (CeO2)
Journal of Alloys and Compounds 453 (2008) 347–351
Small-angle neutron scattering investigations on sintering behavior in the powder compacts of ceria (CeO2) Vinila Bedekar a , A.K. Patra b , D. Sen b , S. Mazumder b , A.K. Tyagi a,∗ a
b
Chemistry Division, Bhabha Atomic Research Centre, Mumbai 400085, India Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India
Received 25 July 2006; received in revised form 13 November 2006; accepted 16 November 2006 Available online 19 December 2006
Abstract Nano-crystalline ceria powders have been synthesized by gel combustion process. The effect of sintering temperature on the pore morphology of the powder compacts has been investigated by small-angle neutron scattering (SANS) in the accessible scattering wave vector ‘q’ range of 0.003–0.17 nm−1 of a double crystal based instrument. The scattering profiles do not follow normal ‘q−4 ’ power law at higher q-values. The X-ray diffraction and light scattering results indicate that the ceria nano-powders are in the form of porous agglomerates. The porosity of the sintered compacts has been attributed to inter-agglomerate, inter-aggregate and intra-aggregate pores. Scattering profiles have been modeled by using a tri-modal size distribution of pores. © 2006 Elsevier B.V. All rights reserved. Keywords: Ceramics; Nano-structured materials; Sintering; Pores; Small-angle neutron scattering
1. Introduction Ceria (CeO2 ) is a candidate material for a variety of potential applications, e.g. optical glass polishing, petroleum cracking, catalyst, gas sensor and UV-absorber [1,2]. Doped ceria is a candidate material for applications in controlling air-to-fuel ratio in the automobile exhaust [3]. Doped ceria is also used as an oxide-ion electrolyte in solid-oxide fuel cell (SOFC) [4]. All these applications demand high-purity cerium oxide in the fine particulate form. The nano-particles, in general, show higher catalytic activity, better sinterability and other unusual properties as compared to their bulk counterparts. Also, a change of valence state of cerium (Ce4+ → Ce3+ ) is associated during sintering at higher temperature (>1300 ◦ C) [5]. Hence, the synthesis of nanostructured ceria powder with controlled powder characteristics is of practical importance to get dense sintered product at a lower sintering temperature. Among the available solution chemistry routes, the combustion technique is capable of producing the pure, nano-crystalline powders of oxide ceramics at comparatively low external tem∗
Corresponding author. Tel.: +91 22 2559 5330; fax: +91 22 2550 5151/2551 9613. E-mail address: [email protected] (A.K. Tyagi). 0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.11.085
peratures in a short time [6]. The success of this process is due to an intimate blending among the constituents using suitable fuel or complexing agents (e.g. glycine, citric acid, urea, etc.) in an aqueous medium followed by an exothermic redox reaction between the fuel and an oxidizer (i.e., nitrates) [7,8]. Generally, the particles of the oxide ceramic powders synthesized through solution routes exhibit porous agglomerated structure due to the agglomeration of primary particles (fine crystallites in nano-meter range). Small angle neutron scattering is a widely used nondestructive technique to characterize structural details of pores ˚ to of all types, viz. open, blind and closed ones ranging from 10 A 1 m [9]. Neutrons have absorption cross-section many orders of magnitude less compared to other probes of radiation. Because of this fact neutrons can penetrate deeper inside the condensed matter and reveal the internal structures of the bulk material. In small-angle scattering experiments the scattered beam is superimposed on the transmitted component of the incident beam. The larger the particle, the closer the scattered beam is to the incident beam. The separation of the two components depends critically on the angular width of the incident beam. Double crystal based SANS instrument produces a beam with a very low angular divergence, which enables the examination of particles up to several micrometers in diameter [10–12].
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In this manuscript we present the SANS investigations on the sintered compacts of nano-crystalline ceria powders. The pellets were sintered in the temperature range 1100–1400 ◦ C to study the evolution of pore morphology with increase in the sintering temperature. 2. Experimental 2.1. Sample preparation and size estimation AR grade cerium nitrate [Ce(NO3 )3 ·6H2 O] and glycine [NH2 CH2 COOH] were mixed in the required molar ratios in a minimum volume of de-ionized water to obtain the transparent aqueous solutions. The solution after thermal dehydration (at ≈80 ◦ C) on a hot plate (to remove the excess solvent) resulted in the highly viscous liquids hereafter termed as precursors. As soon as the viscous liquids were formed, the temperature of the hot plate was increased to ≈200 ◦ C. At this stage the viscous liquid swelled and auto-ignited, with the rapid evolution of large volume of gases to produce voluminous powders. The duration for which the auto-ignition exists is rather small (<10 s). Hence to remove traces of un-decomposed nitrates (if any) and their decomposition products, the powders obtained after auto-ignition were calcined at 600 ◦ C, to obtain chemically pure and well crystalline ceria powders. X-ray diffraction measurements were carried on the combustion-synthesized powder for phase identification and crystallite size estimation, using monochromatized Cu K␣ radiation on a Philips X-ray diffractometer, Model PW 1927, The Netherlands. Silicon was used as an external standard for correction due to instrumental broadening. The crystallite size was measured using Scherrer’s formula as explained in the later section. The agglomeration behavior of the nano-particles was investigated by dynamic light scattering. The extent and nature of agglomeration was studied by a particle size analyzer. The equipment used was Mastersizer 2000, M/s Malvern (UK) particle size analyzer based on laser diffraction, which covers the particle size range of 0.50–100 m. The powder particles were dispersed in water. During the DLS experiments an ultrasonic treatment with a low frequency (39 Hz) has been used. The cold pressed green compacts of 10 mm diameter and ∼2 mm thickness were prepared from the calcined powder at a compaction pressure of 200 MPa by using a uni-axial hydraulic press. To find out the effect of compacting pressure on the particle size of the starting powder, one of the green compacts was thoroughly ground to powder again and its size distribution was measured. The green compacts were sintered each in the temperature range 1100–1400 ◦ C for 2 h with a heating rate of 8 ◦ C/min and a cooling rate of 6 ◦ C/min in static air. The densities of the sintered pellets were measured by liquid displacement method (Archimedes principle). The microstructure of the sintered pellet was studied by scanning electron microscopy (SEM). The sintered pellet was carbon coated before SEM studies.
2.2. SANS measurements SANS experiments were performed on the sintered pellets by using a medium resolution double crystal based diffractometer [13] at guide tube laboratory of Dhruva reactor at Trombay, India. The optical setup of the instrument consists of a non-dispersive (1, −1) setting of 1 1 1 reflections from a pair of perfect single crystals of silicon with provision to mount specimen between them. The SANS intensity I(q) was recorded at several values of scattering vector q [=4π sin(θ)/λ, where 2θ is the scattering angle and the incident neutron wavelength λ for the present experiment is 0.312 nm] by automated rotation of the analyzer crystal in fine angular steps of typical step size ∼0.0012◦ for each specimen in the accessible q range of 0.003–0.17 nm−1 of the instrument. In case of double crystal diffractometer a narrow q-resolution exists only in the horizontal direction. The analyzer collects neutrons over several degrees in the vertical direction. The de-smeared SANS intensity profile is obtained from the slit-smeared intensity using the method given in literature [14,15] after making transmission and background correction to the scattering profile of raw experimental data of each specimen.
Fig. 1. X-ray diffraction pattern of the ceria powder.
3. Results and discussion The XRD pattern of the as-prepared, calcined ceria powder is shown in Fig. 1. The crystallite size was calculated using standard Scherrer’s formula: D=
0.9λ β cos θ
(1)
where D is the crystallite size (nm), λ the radiation wavelength (0.15405 nm), θ the diffraction peak angle, and β is the corrected full width at half maxima (FWHM). In the present case, the crystallite size of the combustion-synthesized ceria powder was found out to be 17 nm. The agglomerated particle size distribution of the powder particles was measured by dynamic light scattering technique (Fig. 2). It can be seen from Fig. 2 that there is a wide distribution of the size of the particles ranging from 0.1 to 100 m. with a median size (D50 ) of 12.7 m. As the powder has been synthesized by a gel combustion route and is nano-crystalline in nature as observed from the XRD data, the agglomerates are most likely to possess complex hierarchical structures because of the Vander Wall’s attraction between the basic particles with significant surface to volume ratio. In fact because of such hierarchy, the agglomerates, in general, show three levels of structure, i.e. fine primary particles in nano-meter scale, cluster (aggregate) formation by the primary particles and finally agglomerate formation in micrometer scale by the clusters. This process gives rise to a porous structure in agglom-
Fig. 2. Particle size distribution of the initial powder obtained from combustion.
V. Bedekar et al. / Journal of Alloys and Compounds 453 (2008) 347–351
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Fig. 3. Particle size distribution of powder obtained after grinding the cold pressed green compact (compacted at 200 MPa pressure).
erates having inter-aggregate and intra-aggregate pores. As the agglomerates are relatively easier to break than the aggregates, grinding modifies the agglomerated particle size distribution. The particle size distribution after the grinding of the green pellet is plotted in the Fig. 3. It is quite interesting to see that in this case the size distribution shows a bimodal type distribution. The primary median size is shifted significantly to lower side to ∼1 m and there is a small contribution of the nongrinded agglomerated particles with a median size ∼12 m. Hence, it can be conclusively said that the powder particles are not compact solid particles, but are soft agglomerates formed by aggregate growth processes; as is evident from X-ray diffraction and light scattering measurements. The heat treatment of ceramic powder compact at high temperature causes densification due to transport of matter from region of higher concentration to that of lower concentration by various diffusion processes. The densification temperature depends considerably on the dimensions of the pore network, the connectivity of the pores and the pore surface area in the compact. With gradual increase in sintering temperature the thickness of the inter-particle necks increases and this process leads to grain growth and decrease in porosity. The pores are gradually eliminated from the matrix and the density of the compact ultimately approaches near theoretical density and strength of the material is increased. Thus, it is evident from Table 1 that the sintered densities increase systematically on increasing the sintering temperature. A typical sintered microstructure is shown in Fig. 4. It is observed that all the grains were of fairly regular shape with most of the grains being smaller than 1.0 m. The pores were found to be nearly spherical in shape. Small-angle scattering phenomenon using collimated beam of monochromatic neutrons is basically the diffraction of neutrons by regions (inhomogeneities) in the sample in which the coherent scattering length density (CSLD) (defined as the product of the mean scattering length per atom and the atomic number Table 1 Density data of the ceria pellets sintered at different temperatures Temperature (◦ C)
Density of pellet (%)
1100 1200 1300 1400
84 85 87 90
Fig. 4. SEM micrograph of sintered pellet.
density) is significantly different from that in the surrounding medium. The square of the difference in CSLD is known as scattering contrast in SANS terminology. In case of porous solids the pores can be considered as inhomogeneities having zero CSLD, dispersed in the homogeneous solid matrix of finite CSLD. Information about the size and shape of the pores present in the porous medium is obtained by analysis of the SANS profile [16,17]. The scattering profile IM (q) of the raw data obtained from a specimen is the sum of transmitted part, SANS part and background intensities. The expression for IM (q) is given by dΣ 2 2 IM (q) = T I0 (q) + C dqv Wv (qv ) +B q + qv dΩ (2) where T is the sample transmission; I0 (q) the direct beam profile; qv the component of q in the vertical direction; dΣ/dΩ the desmeared differential scattering cross-section of the specimen; Wv (q) is the normalized resolution function of the instrument along the vertical direction in q-space; C is a scale factor independent of q but depends on thickness of the sample, the solid angle subtended by the analyzer, intensity of the neutron beam incident on the sample and efficiency of the detector and B is the background. Thus the transmission and background corrected and slit smeared SANS profile Ism (q) is given by / 2 2 dqv Wv (qv )I Ism (q) = C (3) q + qv where Ism (q) is the de-smeared SANS profile of the specimen in arbitrary scale and C/ is a scale factor independent of q. In the present study, the de-smeared SANS profiles for the specimens have been obtained using the procedure mentioned in the literature [14]. As the porosity of the specimens is known and we are interested only in the size and the size distribution of the pores, it is not mandatory to go for intensity in absolute scale for data analysis in the present case.
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contribution from the inter-aggregate pores that constitute the agglomerate and the third term corresponds to scattering from intra-aggregate pores. P(q, R) is the square of the form factor of the inhomogeneity (pore in the present case). In the present case to simplify the analysis the pores are assumed to be spherical in shape. The form factor for scattering from spherical particle is given by the expression [18,19]: 3(sin(qR) − qR cos(qR)) 2 (5) P(q, R) = (qR)3 D(R) represents size distribution function, i.e., D(R) dR corresponds to the probability of finding a pore between radius R to R + dR. In the present analysis log-normal distribution [20,21] has been used and is represented by
1 [ln(R/R0 )]2 D(R) = √ (6) exp − 2σ 2 2πσ 2 R2
Fig. 5. SANS profiles of the specimens sintered at different temperatures.
In this investigation, the thickness of the green specimens used was ∼2 mm and that of all the sintered specimens was less than 2 mm. Even though slow neutrons have more penetrating power than X-rays of comparable wavelength, multiple scattering corrections are often applied to SANS data from thick samples of porous ceramic materials. As in the present case the samples are not very thick and the wavelength of probing neutrons is not too large, the SANS data is not likely to be affected significantly by multiple scattering. Hence data analysis has been carried out assuming single scattering (first order Born) approximation. SANS profiles of the sintered specimens (compacts sintered between 1100 and 1400 ◦ C each) are shown in Fig. 5 in double logarithmic scale. It is interesting to note that the profiles do not follow normal ‘q−4 ’ power law at higher q-values. Also the measurement of slope of the profile at three different regions of ‘q’ yields different values, which change with increase in the sintering temperature. Hence, the profiles with such characteristics cannot be modeled by poly-disperse spherical or ellipsoidal pores with mono-modal size distribution. As mentioned earlier the powder particles are porous bodies containing fine and ultrafine porosity. In that case it would be reasonable to assume a model pore size distribution at three different length scales for the sintered powder compacts. Hence to model scattering over whole accessible ‘q’ range of the profile a tri-modal size distribution of pores has been applied. As small-angle scattering intensity I(q) from these three levels of pore structure is cumulative, I(q) can be expressed as sum of three intensity contributions Ra max I(q) = a1 P1 (q, R)D1 (R)(V (R))2 dR Ra min Rb max
where R is the particle size (radius) and D(R) is the size distribution. R0 and σ are the two parameters of the distribution. R0 is related to the mean by = R0 exp(σ 2 /2). It is important to note that without the contributions of the second and the third terms in Eq. (4), the experimental profiles cannot be fitted in the whole experimental q range, particularly in the higher q region. This also indicates the presence of the inter-aggregate and intra-aggregate pores in the matrix. The information on various pore size distributions at different temperatures extracted from analysis of SANS data is shown in Figs. 6–8. It could be seen from Fig. 6 that in case of sintering of ceria compacts, the inter-agglomerate pore size distribution shifts towards lower side of abscissa representing pore radius, which indicates shrinkage of agglomerates with increase in sintering temperature. Another noteworthy finding is that at 1400 ◦ C the peak of the distribution is shifted to significantly lower value as compared to the same at other temperatures. As the distance, at which, mass transport through atomic diffusion takes place is less in case of finer pores, the kinetics of their elimination is relatively faster compared to the coarser ones. So sintering at higher temperature leads to the faster elimination of the small pores and significant
+a2
+a3
Rb min Rb max
Rb
P2 (q, R)D(R)(V (R))2 dR P3 (q, R)D(R)(V (R))2 dR
(4)
min
The first term of Eq. (4) represents scattering from the polydispersed inter-agglomerate pores, the second term is scattering
Fig. 6. Inter-agglomerate pore size distribution.
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pores has been applied to model the SANS profiles. It was observed from the SANS experiments that for the sintered specimens of ceria the scattering intensity is due to superposition of the scattering intensities from inter-aggregate and intra-aggregate pores on that from the inter-agglomerate pores. The size distribution of inter-agglomerate pores gradually shift towards lower radius side with the increase in the sintering temperature due to shrinkage of agglomerates. On the other hand a reverse trend has been observed for inter-aggregate and intraaggregate pores with their size distribution shifting towards higher radius side. In the future, it will be interesting to study the effect of the different dopants and the polydispersity of the basic particles on the agglomerate properties and the three levels of pore size distribution. Fig. 7. Inter-aggregate pore size distribution.
Acknowledgement The authors thank S. Ramnathan of Materials Science Division for his kind help in measurement of particle size distribution. References
Fig. 8. Intra-aggregate pore size distribution.
inter-aggregate and intra-aggregate pore coalescence. The size distributions for inter-aggregate and intra-aggregate pores is shown in Figs. 7 and 8, respectively, showing pore size distribution shifting towards higher radius direction of abscissa. It is important to note that SANS profile of the sample sintered at 1400 ◦ C has been modeled by applying a bimodal size distribution of pores. This could be due to merging of inter-aggregate pores size distribution with inter-agglomerate pores size distribution. In this case also without a scattering contribution from intra-aggregate pores the profile could not be modeled in the entire q region. 4. Conclusion With the complementary information available from laser light scattering and XRD, a tri-modal size distribution of the
[1] R.E. Kiork, D.F. Othmer, Encyclopedia of Chemical Technology, 5., 3rd ed., Wiley, New York, 1979, pp. 315–337. [2] H. Wang, J.-J. Zhu, J.-M. Zhu, X.-H. Liao, S. Xu, T. Ding, H.-Y. Chen, Phys. Chem. Chem. Phys. 4 (2002) 3794. [3] E.M. Logothetis, National Symposium on Ceramics on the Service of Men, Washington, DC, June 7, 1976. [4] G.B. Jung, T.J. Huang, C.L. Chang, J. Mater. Sci. 36 (2001) 5839. [5] Y.C. Zhou, M.N. Rahaman, Acta Mater. 45 (1997) 3635. [6] S.V. Chavan, A.K. Tyagi, J. Mater. Res. 19 (2004) 474. [7] S. Bhaduri, S.B. Bhaduri, E. Zhou, J. Mater. Res. 13 (1998) 156. [8] L.R. Pederson, L.A. Chick, G.J. Exarhos, Metal oxide ceramic powders and thin films and the manufacturer, US patent No. 5114702, May 19, 1992. [9] A.K. Patra, S. Ramanathan, D. Sen, S. Mazumder, J. Alloys Compd. 397 (2005) 300. [10] T.M. Sabine, The Physicist 36 (3) (1999) 1. [11] P. Miluka, P. Lukas, F. Eichhorn, J. Appl. Cryst. 21 (1988) 33. [12] M. Agamalian, G.D. Wignall, R. Triolo, J. Appl. Cryst. 30 (1997) 345. [13] S. Mazumder, D. Sen, T. Saravanan, P.R. Vijayaraghavan, J. Neutron Res. 9 (2001) 39. [14] J.A. Lake, Acta Cryst. 23 (1967) 191. [15] P.W. Schmidt, J. Appl. Cryst. 21 (1988) 602. [16] A.J. Allen, C.G. Windsor, V. Rainey, D. Pearson, D.D. Double, N. McN Alford, J. Phys. D: Appl. Phys. 15 (1982) 1817. [17] D. Sen, A.K. Patra, S. Mazumder, S. Ramanathan, J. Alloys Compd. 361 (2003) 270. [18] L. Rayleigh, Proc. Roy. Soc. (Lond.) A90 (1914) 219. [19] A. Guinier, G. Fournet, Small-angle Scattering of X-rays, Wiley, New York, 1955, p. 19. [20] J. Aitchison, J.A.C. Brown, The Lognormal Distribution, Cambridge University Press, Cambridge, 1957. [21] N.A. Fuchs, Mechanics of Aerosols, Pergamon Press, New York, 1964.
Small-angle neutron scattering investigations on sintering behavior in the powder compacts of ceria (CeO2) Vinila Bedekar a , A.K. Patra b , D. Sen b , S. Mazumder b , A.K. Tyagi a,∗ a
b
Chemistry Division, Bhabha Atomic Research Centre, Mumbai 400085, India Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India
Received 25 July 2006; received in revised form 13 November 2006; accepted 16 November 2006 Available online 19 December 2006
Abstract Nano-crystalline ceria powders have been synthesized by gel combustion process. The effect of sintering temperature on the pore morphology of the powder compacts has been investigated by small-angle neutron scattering (SANS) in the accessible scattering wave vector ‘q’ range of 0.003–0.17 nm−1 of a double crystal based instrument. The scattering profiles do not follow normal ‘q−4 ’ power law at higher q-values. The X-ray diffraction and light scattering results indicate that the ceria nano-powders are in the form of porous agglomerates. The porosity of the sintered compacts has been attributed to inter-agglomerate, inter-aggregate and intra-aggregate pores. Scattering profiles have been modeled by using a tri-modal size distribution of pores. © 2006 Elsevier B.V. All rights reserved. Keywords: Ceramics; Nano-structured materials; Sintering; Pores; Small-angle neutron scattering
1. Introduction Ceria (CeO2 ) is a candidate material for a variety of potential applications, e.g. optical glass polishing, petroleum cracking, catalyst, gas sensor and UV-absorber [1,2]. Doped ceria is a candidate material for applications in controlling air-to-fuel ratio in the automobile exhaust [3]. Doped ceria is also used as an oxide-ion electrolyte in solid-oxide fuel cell (SOFC) [4]. All these applications demand high-purity cerium oxide in the fine particulate form. The nano-particles, in general, show higher catalytic activity, better sinterability and other unusual properties as compared to their bulk counterparts. Also, a change of valence state of cerium (Ce4+ → Ce3+ ) is associated during sintering at higher temperature (>1300 ◦ C) [5]. Hence, the synthesis of nanostructured ceria powder with controlled powder characteristics is of practical importance to get dense sintered product at a lower sintering temperature. Among the available solution chemistry routes, the combustion technique is capable of producing the pure, nano-crystalline powders of oxide ceramics at comparatively low external tem∗
Corresponding author. Tel.: +91 22 2559 5330; fax: +91 22 2550 5151/2551 9613. E-mail address: [email protected] (A.K. Tyagi). 0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.11.085
peratures in a short time [6]. The success of this process is due to an intimate blending among the constituents using suitable fuel or complexing agents (e.g. glycine, citric acid, urea, etc.) in an aqueous medium followed by an exothermic redox reaction between the fuel and an oxidizer (i.e., nitrates) [7,8]. Generally, the particles of the oxide ceramic powders synthesized through solution routes exhibit porous agglomerated structure due to the agglomeration of primary particles (fine crystallites in nano-meter range). Small angle neutron scattering is a widely used nondestructive technique to characterize structural details of pores ˚ to of all types, viz. open, blind and closed ones ranging from 10 A 1 m [9]. Neutrons have absorption cross-section many orders of magnitude less compared to other probes of radiation. Because of this fact neutrons can penetrate deeper inside the condensed matter and reveal the internal structures of the bulk material. In small-angle scattering experiments the scattered beam is superimposed on the transmitted component of the incident beam. The larger the particle, the closer the scattered beam is to the incident beam. The separation of the two components depends critically on the angular width of the incident beam. Double crystal based SANS instrument produces a beam with a very low angular divergence, which enables the examination of particles up to several micrometers in diameter [10–12].
348
V. Bedekar et al. / Journal of Alloys and Compounds 453 (2008) 347–351
In this manuscript we present the SANS investigations on the sintered compacts of nano-crystalline ceria powders. The pellets were sintered in the temperature range 1100–1400 ◦ C to study the evolution of pore morphology with increase in the sintering temperature. 2. Experimental 2.1. Sample preparation and size estimation AR grade cerium nitrate [Ce(NO3 )3 ·6H2 O] and glycine [NH2 CH2 COOH] were mixed in the required molar ratios in a minimum volume of de-ionized water to obtain the transparent aqueous solutions. The solution after thermal dehydration (at ≈80 ◦ C) on a hot plate (to remove the excess solvent) resulted in the highly viscous liquids hereafter termed as precursors. As soon as the viscous liquids were formed, the temperature of the hot plate was increased to ≈200 ◦ C. At this stage the viscous liquid swelled and auto-ignited, with the rapid evolution of large volume of gases to produce voluminous powders. The duration for which the auto-ignition exists is rather small (<10 s). Hence to remove traces of un-decomposed nitrates (if any) and their decomposition products, the powders obtained after auto-ignition were calcined at 600 ◦ C, to obtain chemically pure and well crystalline ceria powders. X-ray diffraction measurements were carried on the combustion-synthesized powder for phase identification and crystallite size estimation, using monochromatized Cu K␣ radiation on a Philips X-ray diffractometer, Model PW 1927, The Netherlands. Silicon was used as an external standard for correction due to instrumental broadening. The crystallite size was measured using Scherrer’s formula as explained in the later section. The agglomeration behavior of the nano-particles was investigated by dynamic light scattering. The extent and nature of agglomeration was studied by a particle size analyzer. The equipment used was Mastersizer 2000, M/s Malvern (UK) particle size analyzer based on laser diffraction, which covers the particle size range of 0.50–100 m. The powder particles were dispersed in water. During the DLS experiments an ultrasonic treatment with a low frequency (39 Hz) has been used. The cold pressed green compacts of 10 mm diameter and ∼2 mm thickness were prepared from the calcined powder at a compaction pressure of 200 MPa by using a uni-axial hydraulic press. To find out the effect of compacting pressure on the particle size of the starting powder, one of the green compacts was thoroughly ground to powder again and its size distribution was measured. The green compacts were sintered each in the temperature range 1100–1400 ◦ C for 2 h with a heating rate of 8 ◦ C/min and a cooling rate of 6 ◦ C/min in static air. The densities of the sintered pellets were measured by liquid displacement method (Archimedes principle). The microstructure of the sintered pellet was studied by scanning electron microscopy (SEM). The sintered pellet was carbon coated before SEM studies.
2.2. SANS measurements SANS experiments were performed on the sintered pellets by using a medium resolution double crystal based diffractometer [13] at guide tube laboratory of Dhruva reactor at Trombay, India. The optical setup of the instrument consists of a non-dispersive (1, −1) setting of 1 1 1 reflections from a pair of perfect single crystals of silicon with provision to mount specimen between them. The SANS intensity I(q) was recorded at several values of scattering vector q [=4π sin(θ)/λ, where 2θ is the scattering angle and the incident neutron wavelength λ for the present experiment is 0.312 nm] by automated rotation of the analyzer crystal in fine angular steps of typical step size ∼0.0012◦ for each specimen in the accessible q range of 0.003–0.17 nm−1 of the instrument. In case of double crystal diffractometer a narrow q-resolution exists only in the horizontal direction. The analyzer collects neutrons over several degrees in the vertical direction. The de-smeared SANS intensity profile is obtained from the slit-smeared intensity using the method given in literature [14,15] after making transmission and background correction to the scattering profile of raw experimental data of each specimen.
Fig. 1. X-ray diffraction pattern of the ceria powder.
3. Results and discussion The XRD pattern of the as-prepared, calcined ceria powder is shown in Fig. 1. The crystallite size was calculated using standard Scherrer’s formula: D=
0.9λ β cos θ
(1)
where D is the crystallite size (nm), λ the radiation wavelength (0.15405 nm), θ the diffraction peak angle, and β is the corrected full width at half maxima (FWHM). In the present case, the crystallite size of the combustion-synthesized ceria powder was found out to be 17 nm. The agglomerated particle size distribution of the powder particles was measured by dynamic light scattering technique (Fig. 2). It can be seen from Fig. 2 that there is a wide distribution of the size of the particles ranging from 0.1 to 100 m. with a median size (D50 ) of 12.7 m. As the powder has been synthesized by a gel combustion route and is nano-crystalline in nature as observed from the XRD data, the agglomerates are most likely to possess complex hierarchical structures because of the Vander Wall’s attraction between the basic particles with significant surface to volume ratio. In fact because of such hierarchy, the agglomerates, in general, show three levels of structure, i.e. fine primary particles in nano-meter scale, cluster (aggregate) formation by the primary particles and finally agglomerate formation in micrometer scale by the clusters. This process gives rise to a porous structure in agglom-
Fig. 2. Particle size distribution of the initial powder obtained from combustion.
V. Bedekar et al. / Journal of Alloys and Compounds 453 (2008) 347–351
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Fig. 3. Particle size distribution of powder obtained after grinding the cold pressed green compact (compacted at 200 MPa pressure).
erates having inter-aggregate and intra-aggregate pores. As the agglomerates are relatively easier to break than the aggregates, grinding modifies the agglomerated particle size distribution. The particle size distribution after the grinding of the green pellet is plotted in the Fig. 3. It is quite interesting to see that in this case the size distribution shows a bimodal type distribution. The primary median size is shifted significantly to lower side to ∼1 m and there is a small contribution of the nongrinded agglomerated particles with a median size ∼12 m. Hence, it can be conclusively said that the powder particles are not compact solid particles, but are soft agglomerates formed by aggregate growth processes; as is evident from X-ray diffraction and light scattering measurements. The heat treatment of ceramic powder compact at high temperature causes densification due to transport of matter from region of higher concentration to that of lower concentration by various diffusion processes. The densification temperature depends considerably on the dimensions of the pore network, the connectivity of the pores and the pore surface area in the compact. With gradual increase in sintering temperature the thickness of the inter-particle necks increases and this process leads to grain growth and decrease in porosity. The pores are gradually eliminated from the matrix and the density of the compact ultimately approaches near theoretical density and strength of the material is increased. Thus, it is evident from Table 1 that the sintered densities increase systematically on increasing the sintering temperature. A typical sintered microstructure is shown in Fig. 4. It is observed that all the grains were of fairly regular shape with most of the grains being smaller than 1.0 m. The pores were found to be nearly spherical in shape. Small-angle scattering phenomenon using collimated beam of monochromatic neutrons is basically the diffraction of neutrons by regions (inhomogeneities) in the sample in which the coherent scattering length density (CSLD) (defined as the product of the mean scattering length per atom and the atomic number Table 1 Density data of the ceria pellets sintered at different temperatures Temperature (◦ C)
Density of pellet (%)
1100 1200 1300 1400
84 85 87 90
Fig. 4. SEM micrograph of sintered pellet.
density) is significantly different from that in the surrounding medium. The square of the difference in CSLD is known as scattering contrast in SANS terminology. In case of porous solids the pores can be considered as inhomogeneities having zero CSLD, dispersed in the homogeneous solid matrix of finite CSLD. Information about the size and shape of the pores present in the porous medium is obtained by analysis of the SANS profile [16,17]. The scattering profile IM (q) of the raw data obtained from a specimen is the sum of transmitted part, SANS part and background intensities. The expression for IM (q) is given by dΣ 2 2 IM (q) = T I0 (q) + C dqv Wv (qv ) +B q + qv dΩ (2) where T is the sample transmission; I0 (q) the direct beam profile; qv the component of q in the vertical direction; dΣ/dΩ the desmeared differential scattering cross-section of the specimen; Wv (q) is the normalized resolution function of the instrument along the vertical direction in q-space; C is a scale factor independent of q but depends on thickness of the sample, the solid angle subtended by the analyzer, intensity of the neutron beam incident on the sample and efficiency of the detector and B is the background. Thus the transmission and background corrected and slit smeared SANS profile Ism (q) is given by / 2 2 dqv Wv (qv )I Ism (q) = C (3) q + qv where Ism (q) is the de-smeared SANS profile of the specimen in arbitrary scale and C/ is a scale factor independent of q. In the present study, the de-smeared SANS profiles for the specimens have been obtained using the procedure mentioned in the literature [14]. As the porosity of the specimens is known and we are interested only in the size and the size distribution of the pores, it is not mandatory to go for intensity in absolute scale for data analysis in the present case.
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contribution from the inter-aggregate pores that constitute the agglomerate and the third term corresponds to scattering from intra-aggregate pores. P(q, R) is the square of the form factor of the inhomogeneity (pore in the present case). In the present case to simplify the analysis the pores are assumed to be spherical in shape. The form factor for scattering from spherical particle is given by the expression [18,19]: 3(sin(qR) − qR cos(qR)) 2 (5) P(q, R) = (qR)3 D(R) represents size distribution function, i.e., D(R) dR corresponds to the probability of finding a pore between radius R to R + dR. In the present analysis log-normal distribution [20,21] has been used and is represented by
1 [ln(R/R0 )]2 D(R) = √ (6) exp − 2σ 2 2πσ 2 R2
Fig. 5. SANS profiles of the specimens sintered at different temperatures.
In this investigation, the thickness of the green specimens used was ∼2 mm and that of all the sintered specimens was less than 2 mm. Even though slow neutrons have more penetrating power than X-rays of comparable wavelength, multiple scattering corrections are often applied to SANS data from thick samples of porous ceramic materials. As in the present case the samples are not very thick and the wavelength of probing neutrons is not too large, the SANS data is not likely to be affected significantly by multiple scattering. Hence data analysis has been carried out assuming single scattering (first order Born) approximation. SANS profiles of the sintered specimens (compacts sintered between 1100 and 1400 ◦ C each) are shown in Fig. 5 in double logarithmic scale. It is interesting to note that the profiles do not follow normal ‘q−4 ’ power law at higher q-values. Also the measurement of slope of the profile at three different regions of ‘q’ yields different values, which change with increase in the sintering temperature. Hence, the profiles with such characteristics cannot be modeled by poly-disperse spherical or ellipsoidal pores with mono-modal size distribution. As mentioned earlier the powder particles are porous bodies containing fine and ultrafine porosity. In that case it would be reasonable to assume a model pore size distribution at three different length scales for the sintered powder compacts. Hence to model scattering over whole accessible ‘q’ range of the profile a tri-modal size distribution of pores has been applied. As small-angle scattering intensity I(q) from these three levels of pore structure is cumulative, I(q) can be expressed as sum of three intensity contributions Ra max I(q) = a1 P1 (q, R)D1 (R)(V (R))2 dR Ra min Rb max
where R is the particle size (radius) and D(R) is the size distribution. R0 and σ are the two parameters of the distribution. R0 is related to the mean by
+a2
+a3
Rb min Rb max
Rb
P2 (q, R)D(R)(V (R))2 dR P3 (q, R)D(R)(V (R))2 dR
(4)
min
The first term of Eq. (4) represents scattering from the polydispersed inter-agglomerate pores, the second term is scattering
Fig. 6. Inter-agglomerate pore size distribution.
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pores has been applied to model the SANS profiles. It was observed from the SANS experiments that for the sintered specimens of ceria the scattering intensity is due to superposition of the scattering intensities from inter-aggregate and intra-aggregate pores on that from the inter-agglomerate pores. The size distribution of inter-agglomerate pores gradually shift towards lower radius side with the increase in the sintering temperature due to shrinkage of agglomerates. On the other hand a reverse trend has been observed for inter-aggregate and intraaggregate pores with their size distribution shifting towards higher radius side. In the future, it will be interesting to study the effect of the different dopants and the polydispersity of the basic particles on the agglomerate properties and the three levels of pore size distribution. Fig. 7. Inter-aggregate pore size distribution.
Acknowledgement The authors thank S. Ramnathan of Materials Science Division for his kind help in measurement of particle size distribution. References
Fig. 8. Intra-aggregate pore size distribution.
inter-aggregate and intra-aggregate pore coalescence. The size distributions for inter-aggregate and intra-aggregate pores is shown in Figs. 7 and 8, respectively, showing pore size distribution shifting towards higher radius direction of abscissa. It is important to note that SANS profile of the sample sintered at 1400 ◦ C has been modeled by applying a bimodal size distribution of pores. This could be due to merging of inter-aggregate pores size distribution with inter-agglomerate pores size distribution. In this case also without a scattering contribution from intra-aggregate pores the profile could not be modeled in the entire q region. 4. Conclusion With the complementary information available from laser light scattering and XRD, a tri-modal size distribution of the
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