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  • Ceria nanoparticles: Size, size distribution, and shapeFeng Zhang, Qiang Jin, and Siu-Wai Chan

    Citation: Journal of Applied Physics 95, 4319 (2004); doi: 10.1063/1.1667251 View online: http://dx.doi.org/10.1063/1.1667251 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/95/8?ver=pdfcov Published by the AIP Publishing

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  • Ceria nanoparticles: Size, size distribution, and shapeFeng Zhang, Qiang Jin,a) and Siu-Wai Chanb)Department of Applied Physics and Applied Mathematics, Materials Research Science and EngineeringCenter, Columbia University, New York 10027

    ~Received 8 September 2003; accepted 19 January 2004!

    Nanocrystalline ceria particles have been prepared by mixing aqueous solutions of cerium nitrateand hexamethylenetetramine at room temperature. The smallest size of nanoparticles synthesized is2 nm. For each batch prepared, a narrow size distribution is found with a standard deviation lessthan 615%. A transmission electron microscopy ~TEM! investigation shows that these particles aresingle crystals having either an octahedral shape with eight $111% surfaces, or with an additional$200% surface-truncated octahedral shape. In-situ ultraviolet-visible light absorption has beenperformed to measure the absorption edge and to monitor the growth of nanoparticles. The resultsfrom light absorption correlate well with those of the TEM images, providing an in-situ method tomeasure the particle size during synthesis. 2004 American Institute of [email protected]: 10.1063/1.1667251#


    Cerium oxide has been widely investigated as an elec-trolyte for solid oxygen fuel cells,1 a buffer material betweensuperconducting materials and silicon substrates,2 and as apotential candidate for gate oxides in metal oxide semicon-ductor devices.3 Because of its high oxygen storage capacity~OSC!, another important application for cerium-based ox-ides is as a support material in three-way catalysts ~TWCs!.4Recently nanocrystalline CeO2 has drawn great attention inmany applications. As a catalyst, it is found that nanosizecerium dioxide has a better performance than micron-sizepowder, due to the larger surface to volume ratio.5

    Previous computer simulations68 predicted the relativestability of different surfaces of CeO2 single crystals. Thesesimulations and defect modeling provide some bases for un-derstanding the catalytic reactions of ceria. Sayle et al. pre-dicted that $111%, $220% and $422% were the three most stableplanes on the surface of CeO2 .6 Few experimental research-ers have been working on the surface structure of CeO2 .Herman9 investigated the CeO2 (001) surface using angle-resolved mass spectroscopy of recoiled ions, and found areconstruction involving oxygen ions at the surface. Only50% of oxygen sites are occupied at the outer layer to main-tain an electrically neutral surface. Norengerg and Harding10studied the ~001! surface of the CeO2 single crystal with ascanning tunneling microscope. Their results agree with Her-mans results. Lee and Shen11 investigated with transmissionelectron microscopy ~TEM! the coalescence and the twin-ning of submicron CeO2 particles which were prepared bylaser ablation. In their study, they found that CeO2 particleswere stable with $111% surfaces and appeared as octahedronsor $200%-truncated octahedrons. These particles, formed by ahighly nonequilibrium method, were twinned over $111%planes. Some particles were observed to coalesce with each

    other by connecting their $111% surfaces or $200% surfaceswith adjacent particles.

    In-situ light absorption spectroscopy with a wavelengthfrom ultraviolet ~UV! to visible is performed to monitor thegrowth of semiconductor nanoparticles.12,13 This technique isa direct measure of the widening of the bandgap due to quan-tum confinement.14 The bandgap-energy difference betweenCeO2 nanoparticles and micron-size particles was observedpreviously with few experimental details anddiscussions.15,16

    Here we study the growth of cerium oxide nanoparticleswith TEM and UV-visible light absorption. By analyzing the2-dimentional ~2-D! projection and the fast Fourier transform~FFT! of the lattice images from TEM, we determine theparticle shapes and the preferred surface planes of synthe-sized nanoparticles.


    The synthesis method uses cerium nitrate Ce~NO3)36H2O and hexamethylenetetramine (CH2)6N4 ,HMTwithout further purification.17 Both chemicals are dissolvedinto the desired concentrations ~0.0050.5 M for nitrate, and0.11.5 M for HMT! for 30 min before being mixed togetherat room temperature. The mixture is stirred continuously un-til the desired harvest time. The nanoparticles are separatedby centrifuging at a rate of 900014000 rpm for 30 min. Toestimate the time needed for separation, we use the followingcentrifuge equations:18

    v t5v2r~rp2r l!dp


    18h , ~1!

    v t5drdt , ~2!


    a!Currently at Micron Technology Inc.b!Author to whom all correspondence should be addressed; electronic mail:

    [email protected]


    43190021-8979/2004/95(8)/4319/8/$22.00 2004 American Institute of Physics [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: On: Tue, 02 Jun 2015 21:25:17

  • t t5

    lnS rmaxrmin

    Dv t

    , ~3!

    where v t is the terminal velocity, v is the angular velocity ofthe rotor, rp and r l are the density of the particles ~7.2 g/cm3for ceria! and solvent, respectively ~1.0 g/cm3 for water!, dpis the diameter of the particles, h is the viscosity of thesolution ~1 mPas!, rmax and rmin are the maximum and mini-mum rotor radii, respectively, and t t is the total time requiredfor complete separation. The calculation gives a time intervalof 0.5 h as sufficient to separate CeO2 particles of size 5 nmfrom the solution at 12000 rpm for a Sorvall SLA-1500rotor.19 After being washed with deionized water, the finepowders are dried at room temperature. Two samples with amixing time of 12 hrs are sintered at 600 and 850 C for 0.5hour to obtain larger nanoparticles for x-ray diffraction~XRD! studies.

    Transmission electron microscopic samples are preparedby taking small amounts of the mixture at 12, 24, 36, 65, 84and 240 min intervals during mixing and putting onto thecarbon thin-films supported on copper grids ~Ted Pella car-bon type-A!. The ultraviolet-visible ~UV-visible! light ab-sorption spectroscopy is used to monitor the particle growthwith a HP 8453 UV-visible system, with wavelength scannedfrom 200 to 1100 nm. Light absorption spectroscopy is si-multaneously performed at 3, 8, 25, 47, 70 and 154 minintervals to monitor the particle size.

    Shape, size and size-distribution of nanoparticles arestudied with TEMs ~Philips CM30ST and EM430!. The par-ticle size and size-distribution are determined by measuringthe diameters of more than 50 particles for each sample fromthe high-resolution lattice images. The TEM magnification iscalibrated with the atomic spacing of CeO2 (111) planes. Animage fast Fourier transform is performed on lattice imagesby using Scion Image softwear.20

    X-ray powder diffraction measurements are performedusing a Scintag X2 diffractometer with Cu Ka irradiation at ascan rate of 0.025 degree/step at 5 s/step.

    III. RESULTS AND DISCUSSIONA. X-ray diffraction

    XRD spectra of the CeO2 nanoparticles obtained in thisstudy exhibit the cubic fluorite structure, which is consistentwith the bulk CeO2 . A comparison of the two x-ray spectrafrom nanosized ceria and standard powder diffraction [email protected], by the National Bureau Standard ~U.S.!#21 of CeO2shows that all the peaks shift towards a lower angle ~see Fig.1!.

    By plotting the lattice parameter calculated from each(hkl) reflection against cos2 u, we obtain the lattice param-eter with an accuracy of four and a half significant figures,i.e., to within 0.005% accuracy.22 Five peaks are selectedwith 2u ranging from 80 to 140 for lattice parameter mea-surements. Particle sizes ~d! are also determined from x-rayresults using the Scherrer equation,


    B cos uB, ~4!

    Accordingly, d is the particle size, l is the wavelength ofCu Ka radiation, B is the full-width at half maximum~FWHM! of the Bragg peak corrected using the correspond-ing peak in micron-sized powder, and uB is the Bragg angle.The peak profiles are fitted with the PseudoVoigtfunction.23 The results, which are checked with Celrefsoftware,24 are shown in Fig. 2. Compared with micron-sizeCeO2 particles ~Alfa, ;5 micron!, the lattice parameter of6.1 nm particles increases from 5.4087 ~bulk! to 5.4330 ,i.e., by 0.45%. The lattice expansion observed with XRDagrees with Raman scattering results of the samenanoparticles17,25 where both a lattice expansion and nano-size induced lattice softening were needed to fully interpre-tate the results.

    The WilliamsonHall equation, Eq. ~5!, was used toseparate the lattice expansion effect from the heterogeneousstrain26 effect on peak broadening,

    Ddd 5

    B cos uB4 sin uB

    . ~5!

    FIG. 1. Compared with standard powder diffraction pattern, the x-ray dif-fraction spectrum of the 8 nm CeO2 particle showing a cubic fluorite struc-ture and a peak shift.

    FIG. 2. The lattice parameter increases with decreasing particle size, moreevident as the particle size becomes smaller than 20 nm.

    4320 J. Appl. Phys., Vol. 95, No. 8, 15 April 2004 Zhang, Jin, and Chan

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  • Here Dd is the difference of the interplanar spacing causedfrom the heterogeneous strain. The WilliamsonHall plots~see Fig. 3! suggest no heterogeneous strain in the nanopar-ticles of 15 nm smaller, which is sintered at 600 C. The 25nm particle, which is sintered at 850 C, shows a slight strainby a slight positive slope in the corresponding WilliamsonHall plot. This heterogeneous strain does not affect the ex-isting results of lattice expansion of ceria nanoparticleswhich only becomes observable with a particle size below 20nm.

    B. Particle morphologyFigure 4 shows a typical high resolution TEM micro-

    graph of ceria nanoparticles prepared by the nitrate-HMTmethod. Particles shown in the figure have a uniform size of5 nm, and show little aggregation. More than 400 lattice-images of the synthesized ceria nanoparticles have been ob-served. All particles are single crystals with few particles~,1%! having line dislocations and twin boundaries. Thisobservation suggests that the ceria particles synthesized arenearly perfect single crystals with few extended defects,which is different from the highly defected particles ob-served by Lee and Shen in Ref. 11.

    A lattice image of a particle along its @011# direction isshown in Fig. 5~a! with a hexagonal shape in this

    2-dimensional ~2-D! projection. A schematic representationof the particle in Fig. 5~a! and a fast Fourier transform ~FFT!of its lattice image are shown in Figs. 5~b! and 5~c!, respec-tively. For this particular particle, four $111% and two $002%surfaces as well as two sets of $111% planes and one set of$002% planes are identified based on the interplanar spacingsand plane-intersecting angles as well as the observed @011#

    FIG. 3. A WilliamsonHall plot of nanoparticles studied. Except for the 25nm particles, no heterogeneous strain exists.

    FIG. 4. A high resolution transmission electron micrograph of CeO2 nano-particles, showing a uniform particle size of 5 nm, with little aggregationsand few defects.

    FIG. 5. ~a! A high resolution transmission electron micrograph showing aCeO2 nanoparticle with a hexagonal shape projected along the ^011& direc-tion, showing four $111% and two $002% surfaces as well as two sets of $111%planes and one set of ~002! planes. ~b! A schematic representation of theparticle in ~a!. ~c! The fast Fourier transform ~FFT! image of ~a!.

    4321J. Appl. Phys., Vol. 95, No. 8, 15 April 2004 Zhang, Jin, and Chan

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  • diffraction pattern from fast Fourier transform ~FFT!. The3-dimensional ~3-D! shape of the particle is likely a ~200!surface truncated octahedron as shown later in Fig. 8~b!.

    A lattice-image of another particle in a 2-D projection isshown in Fig. 6~a! with a rhomboid shape. Here, one set of$002% planes and two sets of $111% planes are observed. Aschematic figure of the particle in Fig. 6~a! is drawn in Fig.6~b!. Only four $111% surfaces occur and no $002% surface isobserved. The 3-D shape of this particle is likely an octahe-dron, as shown later in Fig. 8~a!.

    Another particle with a rhomboid shape is shown in Fig.7~a!. From the lattice-image, four $111% surfaces and one setof $111% planes are observed and identified @Fig. 7~b!#. Toavoid the information from other particles in the image, onlythe upper corner of this middle particle is selected to obtainthe FFT image @Fig. 7~c!#. From the FFT image, instead of 2spots for $111% planes, there are four $111%, two $200% andtwo $220%, diffraction spots. Here, the FFT images which arethe diffraction equivalents of the particles often reveal moredetails than simple inspection from the original lattice imagemicrographs.

    For the particles that have only four $111% surfaces intheir @011# 2-D projections, their 3-D shape is consistent withan octahedron as shown in Fig. 8~a!, with all the line edgesbeing ^110& directions and the surfaces being parallel to $111%planes. For the particles with two more $002%-surfaces, theshape is consistent with that of a $002% truncated octahedron,as shown in Fig. 8~b!. The @011# 2-D projections of Figs. 8~a!and 8~b! are shown in Fig. 8~c! as a rhomboid and Fig. 8~d!as a hexagon, respectively. These rhombic and hexagonalshapes agree with the TEM observation in Figs. 57.

    Approximately 85% of particles are either octahedronsor $002%-truncated octahedrons based on the observation of250 particles. There are, however, some TEM images of par-ticles other than rhombic or hexagonal. For an example, as inFig. 9~a!, the lattice image of a particle shows two sets of the$002% and one set of the $220% planes. The correspondingschematic is shown in Fig. 9~b! and the FFT image in Fig.9~c!. It is difficult to definitely determine the 3-D shape ofthis particle just by analyzing this 2-D lattice image which iscomplicated by its concaved part. A possible 3-D shape and acorresponding 2-D projection of the shape along @001# direc-tion is given in Figs. 9~d! and 9~e!, respectively. This inter-pretation is consistent with the original truncated octahedronwith some $200% surfaces being rectangles instead of squares.

    FIG. 6. ~a! A high-resolution transmission electron micrograph showing aCeO2 nanoparticle with a rhombus shape, showing four $111% surfaces andtwo sets of $111% planes. ~b! A schematic representation of the particle in ~a!.~c! The FFT image of ~a!.

    FIG. 7. ~a! A high-resolution transmission electron micrograph showing aCeO2 nanoparticle with a rhombus shape, showing four $111% surfaces andtwo sets of $111% planes. ~b! A schematic representation of the particle in ~a!.~c! The FFT image of ~a!.

    4322 J. Appl. Phys., Vol. 95, No. 8, 15 April 2004 Zhang, Jin, and Chan

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  • Sayle et al.6,7 and Conesa8 calculated the surface ener-gies of some low (hkl) surfaces of CeO2 . They consideredthe electrostatic ~Coulombic! interaction energy, the effectsof short-range interactions and the polarization energies.From their results, the ~111! surface is the most stable sur-face of CeO2 . The ~220! and the ~422! surfaces possess thenext lowest surface energy. Because of the instability causedby polarization, in Sayles work, the ~200! surfaces are con-sidered impossible in CeO2 . If, however, 50% of the surfaceO22 ions are eliminated from the lattice-sites, then the zerodipole energetic requirements are met. Although the surfaceenergy of ~200! surface is still higher than that of the $220%,the energy of the ~200! surfaces is then in a reasonable en-ergy level that renders the ~200! surface appearance in CeO2nanoparticles. Alternatively, additional mechanisms for low-ering the ~200! surface energy further are hinted at by theirpredominating appearance in the present particles. The ~310!surfaces, which have not appeared in our particles, possessthe highest surface energy among all the (hkl) surfaces dis-cussed here, which is consistent with the fact that these ~310!surfaces are expected not to appear based on these energeticconsiderations.6,7

    In this work, as observed, most particles show the $111%surfaces in lattice images, which agrees well withcalculations.68 Furthermore, the next frequent surface, $200%surfaces, have been observed more frequently than the $220%surfaces, suggesting that the energy of the $200% surfaces issmaller than that of $220%, which is different from Conesaspredictions. There are possible other energy lowering defectsand surface relaxation may further lower the ~200! surfaceenergy than that of ~220! surface. More calculations need tobe performed to confirm this.

    As discussed by Sayle et al.,6,7 surfaces with a highersurface energy have a tendency to relax more, resulting in ahigher density of cations. If these surfaces are stable, they

    could provide active sites for catalytic reactions. Thus, a~200! surface would be more active than a ~111! surface cata-lytically. Surely quantitative measurements of catalytic effi-ciency on the nanoparticles with different surfaces will bevery helpful to substantiate this prediction.

    C. Mean particle size and size distributionThe size of the monodispersed nanoparticles is con-

    trolled with mixing time. Figure 10 shows that particle sizeincreases rapidly during the first 30 minutes of the reaction.Afterwards, the particle size increases linearly with time. At12 min, the mean particle size is 2.6460.30 nm; at 240 min,it is an 8.360.80 nm average around 3 minutes per 0.1 nm.

    A narrower size-distribution of CeO2 nanoparticles isachieved after mixing 0.005 M nitrate and a 1.5 M HMTsolution for 84 minutes ~see Fig. 11!. For all the samples

    FIG. 8. ~a! A schematic octahedron CeO2 nanoparticle with 12 edges par-allel to ^110& directions and 8 $111% surfaces; ~b! schematic octahedral CeO2nanoparticles with the $002%-surface truncated. All edges parallel to the^110& directions. All surfaces, except for two labeled $002% planes are par-allel to the $111% planes; ~c! the @011# projection of ~a!. The same shape andorientation can be seen in Fig. 6 and Fig. 7. ~d! The @011# projection of ~b!;the same shape and orientation can be seen in Fig. 5.

    FIG. 9. ~a! High-resolution TEM micrographs of a CeO2 particle with azone axis of @001#, showing four $200% and two $220% surfaces/edges alongwith two sets of $200% planes and one set of ~220! planes. ~b! Schematicdrawing of the particle. ~c! The FFT image of ~a!.

    4323J. Appl. Phys., Vol. 95, No. 8, 15 April 2004 Zhang, Jin, and Chan

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  • measured, the standard deviation of the size distribution isless than 615%. We list all the mean particle sizes and stan-dard deviation results in Table I.

    D. UV-visible light absorptionSince CeO2 is a direct bandgap semiconductor, a de-

    crease in particle size is expected to be manifested by a blue-shift of the absorption edge.27 For a direct-bandgap semicon-ductor, the absorption coefficient a which is wavelengthdependent is defined as

    I5I0e2a, ~6!

    I~l!5I0e2a~l!, ~7!

    a~l!52lnS I~l!I0 D , ~8!and

    a~\v!5A~\v2E*!1/2. ~9!

    Here, I is the intensity of the light after absorption, I0 is theinitial light intensity, \v is the energy of the photons, and E*is the new bandgap from the quantum confinement. Fornanoparticles, this energy E* can be expressed as


    2R2F 1me


    mhG2 1.8e2eR , ~10!

    where Eg is the bandgap ~for CeO2 , Eg53.15 eV), R is theradius of the nanoparticles, me and mh are the effectivemasses of the electron and hole, respectively, and e is therelative dielectric constant of CeO2 which is 24.5. Since littlereliable information of me and mh are found in the presentliterature, we use me5mh50.4 m where m is the mass of afree electron.

    The light absorption results of particles are shown in Fig.12. The square of the relative absorbance is plotted as afunction of light energy for a different time interval duringsynthesis. The absorption edge shifts to a lower energy withincreasing mixing time and particle size. The bandgap energyE* of nanoparticles can be obtained from Fig. 12 by extrapo-lating the linear portions of the absorption edge, and notingthe intercepts with the energy axis. The particle sizes canthen be calculated using Eq. ~10! and plotted against themixing time ~see Fig. 13!. The decrease in confinement en-ergy with increasing particle size is shown in Fig. 14.

    The results of particle size from TEM and UV-visiblelight absorption agree with each other, except for the firsttwo data points from light absorption. ~see Fig. 15! This is

    FIG. 10. An increase in particle size with the reaction time from high-resolution TEM micrographs.

    FIG. 11. Particle size histogram of CeO2 nanoparticles after 84 min mixing,showing a narrow size distribution.

    FIG. 12. Square of the relative absorbance as a function of light energy fordifferent stages of the reaction time of the synthesis.

    TABLE I. Particle size of CeO2 particles prepared with different mixingtimes.

    Mixing time~min!

    Mean particle size~nm!

    Standard deviation~nm!

    Standard deviation~%!

    12 2.64 0.30 1124 3.72 0.57 1536 3.94 0.50 1365 4.71 0.39 884 5.31 0.70 13

    240 8.36 0.80 9.5

    4324 J. Appl. Phys., Vol. 95, No. 8, 15 April 2004 Zhang, Jin, and Chan

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  • probably related to the extremely small volume fraction ofparticles in the solution when the synthesis time is short.This induces a large error when extrapolating the linear partof the absorption edge. Nonetheless, using UV-visible lightabsorption to monitor the growth of ceria nanoparticles pro-vides a useful in-situ method to monitor the particle size.


    Most ceria nanoparticles synthesized in this work pos-sess an octahedral shape with $111% surfaces or a $200%-truncated octahedral shape. Based on the TEM study, the$111% surfaces are the dominant surfaces and in all probabil-ity have the lowest surface energy. The $200% surfaces are thesecond dominant surfaces, suggesting a lower surface energythan that of $220% surfaces, which appear least. This obser-vation compares well with the previous theoretical calcula-tion, with the exception of the ~200! being more dominantthan ~220! surfaces. By comparing the particle sizes obtainedfrom TEM and UV-visible light absorption, we have a cali-brated way to use UV-visible light absorption to measure theparticle size and monitor the growth of cerium oxide nano-particles in-situ.


    The authors thank Dr. M. R. Libera for the use of mi-croscopy facilities at the Stevens Institute of Technology.This work was supported primarily by the MRSEC programof the National Science Foundation under Award No. DMR-0213574.

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    FIG. 13. An increase in particle size with mixing intervals, based on UV-visible light absorption.

    FIG. 14. A decrease in confinement energy with increasing particle size.

    FIG. 15. A comparison of the particle size determined from optical absorp-tion measurements and TEM observations with an increasing reaction time.

    4325J. Appl. Phys., Vol. 95, No. 8, 15 April 2004 Zhang, Jin, and Chan

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    4326 J. Appl. Phys., Vol. 95, No. 8, 15 April 2004 Zhang, Jin, and Chan

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