Visualizing Anisotropic Oxygen Diffusion in Ceria under Activated Conditions

Liang Zhu ,1,2 Xin Jin,1,2 Yu-Yang Zhang ,2,* Shixuan Du,1,2,5 Lei Liu ,3,† Tijana Rajh,4 Zhi Xu,1,2,5

Wenlong Wang,1,2,5 Xuedong Bai ,1,2,5,‡ Jianguo Wen,4,§ and Lifen Wang 1,4,║

1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China2School of Physical Sciences and CAS Center for Excellence in Topological Quantum Computation,

University of Chinese Academy of Sciences, Beijing 100190, China3Department of Materials Science and Engineering, College of Engineering, Peking University, Beijing 100871, China

4Center for Nanoscale Materials, Argonne National Laboratory, Lemont, Illinois 60439, USA5Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

(Received 25 October 2019; revised manuscript received 16 December 2019; accepted 8 January 2020; published 5 February 2020)

Oxygen reactivity plays a key role in the performance of ceria-based catalysts. Aberration-correctedtransmission electron microscopy and molecular dynamics simulations were used to study the oxygen atomdiffusion in ceria under activated conditions. Reactive oxygen atom and its real-time diffusion werevisualized. The interplay between cerium and oxygen atoms originating from a Coulomb interaction wasrevealed by the out-of-plane buckling of cerium atoms associated with oxygen transport. Anisotropicoxygen atom diffusion that depends on crystal orientations was discovered, demonstrating a preferential[001] crystallographic diffusion pathway. These findings reveal prospects for applications of anisotropicorientation-relevant fluorite-structured oxides.

DOI: 10.1103/PhysRevLett.124.056002

Cerium oxide (CeO2), also known as ceria, is a typicaloxide catalyst [1–3] that has been extensively investigatedin the photocatalytic water splitting for hydrogen produc-tion [4] and solid-oxide fuel cells for energy storage [5].Recyclable release and storage of oxygen atoms is the keyprocess for all of these applications [6]. The formation ofoxygen vacancies and the migration of oxygen atoms underexternal stimuli serve as the basis for functional oxidematerials and related devices [7]. Real-time visualization ofactive oxygen vacancies and the exploration of oxygendiffusion pathways on the atomic scale will give rise to thedeep understanding of the structure-property relationships,eventually facilitating the control of catalytic processes[8–10].The structural characterization using transmission elec-

tron microscopy (TEM) reveals the key phenomena forceria redox process, for example, varied surface recon-structions upon the Ce reduction from Ce4þ to Ce3þ[11,12]. However, real-time visualization of dynamic oxy-gen atoms with spatial and, in particular, elementaryresolution was a challenge due to aberration of the objectivelens. Previously reported negative spherical aberration-corrected TEM suggests that atomic resolution in oxidesis promising, as demonstrated in SrTiO3 [13]. For func-tional oxides under activated conditions, advanced methodswith the enhanced contrast of oxygen atoms are requiredfor the atom motion tracking and quantitative measure-ments. Here, taking ceria, the fluorite-structured catalyst, asa model system, we demonstrate that dynamic oxygendiffusion and its anisotropic character can be directly

visualized using the aberration-corrected TEM. The real-time interplay between the cerium cationic lattice rear-rangement and the anisotropic diffusion of oxygen atoms isunveiled at the sub-angstrom resolution. The combinedstudy by high-resolution TEM characterizations, densityfunctional theory calculations, and molecular dynamicssimulations presents a powerful tool for understandingthe reactive nature of oxygen atoms in catalysts at theatomic scale.CeO2 under the ambient condition has a fluorite struc-

ture. We apply the aberration-corrected TEM to determinethe structure of CeO2 nanoparticles in the ultrahighvacuum system. The details are provided in Fig. 1 in theSupplemental Material [14]. Under the illumination of the200 kV accelerated electron, pristine fluorite-structuredCeO2 transits to Ce2O3 with a bixbyite structure (spacegroup: Ia3) [35,36]. The atomic schematic of fluorite CeO2

and bixbyite Ce2O3 is shown in Fig. 1(a). Especially, in thebixbyite structure Ce atoms split into d-site and b-site typesaccording to the different coordination with O atoms andvacancies. All atoms slightly deviate from sites in the cubicunit of the fluorite structure. Figure 1(b) shows the over-view TEM image of a ceria nanoparticle. With a typicalimaging beam flux on the order of 104 e−=Å2 s, the 200 kVaccelerated incident electrons transfer energy up to 33 eV toO atoms in CeO2, which is beyond the previous estimate ofthe threshold displacement energy (about 27 eV) [37],enabling the observation of the fluorite-bixbyite structuretransition via the radiolysis effect. By adjusting thebeam flux, release and acquisition of oxygen atoms in

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nanoparticles can be initiated repeatedly. Figures 1(c)and 1(d) show snapshot TEM images of the near-edgearea of the nanoparticle during the radiolysis. We took theview along the h110i crystallographic direction so that Ceand O atom columns are well separated and can thus beeasily distinguished for both fluorite ceria and bixbyiteceria. Atomic models of fluorite CeO2 and bixbyite Ce2O3

are superposed on the TEM images, highlighting both Ce

and O atomic positions. Corresponding diffractograms ofthe TEM images as shown in Figs. 1(e) and 1(f) furtherverify the structures.To trace the diffusion path of O atoms in ceria, sequential

TEM images with a time interval of 0.2 s were recorded[Figs. 2(a)–2(d)] to capture intermediate states duringreduction (fluorite CeO2 to bixbyite Ce2O3). The interplaybetween cerium and oxygen atoms has been revealed.

FIG. 1. Atomic resolution TEM imaging of the structural evolution in ceria. (a) Atomic configurations of CeO2 (top half) and Ce2O3

(bottom half). (b) Low-magnification TEM image of the CeO2 nanoparticle. (c),(d) Snapshot TEM images of the near-edge area in thenanoparticle viewed along the ½11̄0� crystallographic direction superposing with relaxed atomic configurations of CeO2 and Ce2O3.Bright and gray spots in TEM images correspond to Ce and O atom columns, respectively. (e),(f) Diffractogram for (c) and (d).

FIG. 2. The interplay between Ce atom arrangement and oxygen vacancy diffusion. (a)–(d) Sequential TEM images showingrearrangement of Ce and O layers along the [001] crystallographic direction. TEM images are colored for clarity and their contrast isinverted. Blue spots with a high density represent Ce column positions. Pink spots with a low intensity show O column positions. t ¼ 0 sis the starting time for the real-time recording. (e)–(h) Snapshots of ab initio molecular dynamics simulation. Blue and red atomsrepresent Ce and O atoms, respectively. Yellow atoms are diffusing O atoms.

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When focusing on the O atom column (black arrow), theout-of-plane buckling of O atoms along the [001] directionevolves during the reduction. Displacement of the spot forthe oxygen column is up to ∼40 pm. The local intensity ofthe spot increases as shown in the sequential TEM images[Figs. 2(a)–2(d)], also see Fig. 2 in the SupplementalMaterial [14] for more details), indicating the evolutionof the O atom concentration in this column. Moreover, thenearest neighboring Ce atom columns (two blue arrows)show the simultaneous out-of-plane buckling clearly. Notethat the distance between oxygen and its nearest ceriumatom in fluorite-CeO2 is measured to be ∼2.4 Å. When adiffusing O atom travels across the Ce plane, the distancebetween Ce and O atoms decreases to ∼1.9 Å. Thus, theelectrostatic force on the Ce atoms gets enhanced dramati-cally because of the charge redistribution, causing the out-of-plane buckling of Ce atoms and the volume expansion ofthe CeO2 cell (see video and Fig. 3 in the SupplementalMaterial [14] for more details). While electron reduction isthe driving force for the O atom migration, the accom-panying lattice perturbation of surrounding Ce atomsprovides additional resistance, hindering the diffusion ofO atoms [38]. More importantly, when considering thelattice symmetry, the optimized oxygen diffusion path withthe lowest diffusion barrier may exist while the accom-panying perturbation response of the Ce sublattice wouldbe minimized, leading to an anisotropic diffusion of Oatoms in ceria.To get a better understanding of the oxygen diffusion

process in CeO2 during the reduction process, we per-formed ab initio molecular dynamics (MD) simulations. Amodel structure with half CeO2 and half Ce2O3 was firstconstructed to simulate the interface of the CeO2 reductionprocess (see Fig. 4 in the Supplemental Material [14] for

the structure employed in MD simulation). This model ismore energetically favorable than structures with a randomO vacancy distribution. An MD simulation at 2000 Kwas carried out and the resulting snapshots are shown inFigs. 2(e)–2(h). The diffusion of O atoms along the [001]direction was observed (illustrated by the motion ofthe yellow ball). During the O atom diffusion process,the related Ce plane splits in the oxygen-diffusion direc-tion [Figs. 2(f) and 2(g)] and becomes flat again at the endof the process [sparse dashed line in MD snapshots,Figs. 2(e)–2(h)]. MD calculations are in nice agreement

FIG. 3. Low-index surface dynamics in ceria under reduction. (a),(b) TEM image snapshots of the (100) surface. (c) Atomicconfiguration derived from video data. Blue and red circles represent Ce columns and O positions, respectively. (d),(e) Serial TEMimages of the (110) surface flattening under reduction. (f) Atomic configuration derived from (d)–(e). (g),(h) TEM images of the (111)surface linear defect formation. (i) Atomic configuration derived from (g)–(h). (j) Ab initio molecular dynamics simulation calculatedtrajectory of diffusing O atoms (O1–O4) with three types of diffusion processes.

FIG. 4. Intermediate chemical bonding states revealed byelectron spectroscopy. (a) Ce M-edge evolution during CeO2

reduction process. (b) O K-edge evolution during CeO2 reductionprocess. (c) Simulated EELS spectra compared with experimentaldata. Yellow and red curves are calculated O K-edge EELSspectra for CeO2 and Ce2O3, respectively.

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with the experimental findings, further revealing the inter-play between O atom diffusion and out-of-plane bucklingof Ce lattices.We then further studied the dynamic behavior of the

(001), (110), and (111) surfaces during the reduction toevaluate the diffusion path of O atoms. Figure 3 displayscomparisons of the atomic configurations of the threeexposed low-index surfaces with distinct deformationfeatures during the structural transition. For the (001)surface, frequent events of atom diffusion into the vacuum(more than 20 recorded) were recognized, demonstratingthat the (001) ceria surface has a very high activity (seevideo in the Supplemental Material [14]). Figures 3(a)and 3(b) show representative sequential images of the (001)surface during the reduction. The surface was flat and wasmostly defined by Ce atom column layers. The two yellowarrows indicate the position of two Ce spots, while theoutmost O atoms are highlighted by the green arrow. Withthe ongoing of the reduction process, the marked O atomsescaped from the crystal. Simultaneously, the distancebetween the two adjacent Ce atoms increased by ∼10%which is ascribed to the local enhanced Coulomb inter-action [8,39]. The dynamics of O atom diffusion andlocal Ce atom response is illustrated by the schematic inFig. 3(c). In addition, although the O atom diffusion path inthe bulk CeO2 is hard to be identified, the observedcontinuous O atom-releasing events along the [001] direc-tion at (001) surface not only prove the high activity of the(001) plane, but also indicate the preferential diffusion pathof O atoms. As discussed previously, such anisotropicdiffusion phenomena could be attributed to the varyinglocal lattice perturbation corresponding to the chargeredistribution. Contrary to the (001) facet, (110) surfaceshows much lower O atom diffusion activity [40]. O atomsescaping into the vacuum were barely observed, whilemigration along the [001] direction on the surface waseasily established, as shown in Figs. 3(d)–3(f). In sharpcontrast to the (001) and (110) surfaces, after the exami-nation of tens of nanoparticles no apparent atom migrationor surface reconstruction were observed on the O-termi-nated (111) surface, demonstrating the highly robust atomicconfiguration. On Ce-terminated (111) surfaces [41–43],instead of the independent diffusion of single atoms,collective behavior involving planar O atoms has beenrecorded [Figs. 3(g)–3(h)]. Figure 3(g) shows a small bumpof Ce atoms that was occasionally found on the (111)surface keeping a certain plane distance (D spacing) forstoring O atoms. During the reduction process, the Dspacing decreases with the escaping of one oxygen atomiclayer. The most probable scenario for the collective releaseof oxygen atoms on the Ce-terminated (111) surface is thesurface reconstruction induced by the polar nature andinstability [44].We further analyzed the MD results, and three types of

oxygen atom diffusion processes were identified (see Fig. 5

in the Supplemental Material [14] for details). The motiontrajectory of one O atom is highlighted in Fig. 3(j). The firsttype is denoted by Dv, in which O atoms start from theCeO2 part and diffuse along the [001] direction. In thesecond diffusion process, O atoms diffuse into the coplanarneighboring vacancy site, which is denoted by Dh. Here,O atoms will not diffuse from the CeO2 regime to theCe2O3 regime, thus contributing little to the reduction ofCeO2. The third type is the step-by-step diffusion, denotedby Dss. Dss consists of two sequential processes. First, anO atom (represented by O3) diffuses into a coplanarneighboring vacancy site, which creates a vacancy at itsoriginal location. Then, an O atom located in the next layer(represented by O4) diffuses along the [001] direction andfills the vacancy created by the O3 diffusion. Furthermore,the energy barrier for O atom diffusion was calculated (seeFig. 6 in Supplemental Material [14]). An O atom willovercome a barrier of 0.74 eV in Dv, which is comparableto previously reported experimental results [45]. O atomsdiffuse in the equivalent h001i direction in all three types ofdiffusion paths. Therefore, the three types of diffusion pathsrevealed by the simulation are consistent with our exper-imental findings that O prefers to diffuse in the h001idirection.The electron energy loss spectroscopy (EELS) measure-

ment of the Ce and O spectra, which reflects the averagevalency properties and chemical bonding, are also recordedduring the structural phase transition (Fig. 4). The Cespectra feature two sharp and strong peaks located at 883and 901 eV, corresponding to the M5 and M4 edges,respectively. The two peaks originate from the transition ofelectrons from the spin-orbit split levels 3d5=2 and 3d3=2 tothe unoccupied 4f states [46]. The M4=M5 intensity ratiodecreases from 1.12 to 0.75, with an increase in concen-tration of trivalent Ce depending on the valence state of Ce,which is in agreement with previously reported values [36].The evolution of the O K edge is shown in Fig. 4(b).

Pristine oxygen K edge for CeO2 has three main peaksmarked by I, II, and III. The spectrum for Ce2O3 showstwo of these characteristic peaks with a slight peak shift andvariation in relative intensities [15]. Peak I originates fromthe O-1s electron transition to the p-like component of thehybrid Ce 4f and O 2p states, suggesting an unoccupied 4fstate which is characteristic of tetravalent Ce. Peaks II andIII arise because of the hybridization of unoccupied O2p-like states with the crystal-field split Ce 5d-eg and Ce5d-t2g states, representing a strong local atomic arrange-ment influence of CeO8 or CeO6 [47]. After the structuretransition, all three peaks become broader, while thecontribution of peak II increases significantly with reduc-tion, leading to a different shape that is supported by thesimulations result as shown in Fig. 4(c). The highlydynamic diffusion of O atoms not only gives rise to theaccompanying local Ce lattice distortion, but also thenonsaturated chemical bonding due to transient nonstoi-chiometric configurations.

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In summary, visualization of O atoms and real-timemotion tracking by the aberration-corrected TEM demon-strated the preferred h001i diffusion path in ceria, whichwas verified by DFT calculation and MD simulations. Theattendant effects from O atom diffusion, including theneighboring Ce out-of-plane buckling and the variation ofthe chemical bonding, were demonstrated, describingbarriers for the O atom diffusion. The perturbation responseof Ce lattice has an anisotropic character, suggesting amicromechanism for the anisotropic oxygen diffusionactivities. When considering that the interaction betweencation ions and oxygen atoms is similar in fluorite-structureoxides, here the newly established mechanism for theoxygen diffusion in ceria further implies that the accom-panying response of local cation atoms may be universal,leading to the same anisotropic oxygen diffusion behaviorsin other functional fluorite-structure oxides.

This work was supported by the National NaturalScience Foundation (11974388, 11974001, 51872284,U1932153, 21872172, 21773303, and 51421002),the National Key R&D Program (2016YFA0300804,2016YFA0300903, 2018YFA0305800, 2019YFA0307801,and 2019YFA0308500), the Program from ChineseAcademy of Sciences (ZDYZ2015-1, Y8K5261B11,XDB30000000, XDB28000000, and XDB07030100), andBeijing Natural Science Foundation (2192022, Z190011).L.W. is grateful for the support from the Youth InnovationPromotion Association of CAS (2020009). This work,including Argonne Chromatic Aberration-corrected TEM,was performed at the Center for Nanoscale Materials, anOffice of Science user facility, supported by the U.S.Department of Energy, Office of Science under ContractNo. DE-AC02-06CH11357.

L. Z. and X. J. contributed equally to this work.

*zhangyuyang@ucas.ac.cn†leiliu1@pku.edu.cn‡xdbai@iphy.ac.cn§jwen@anl.gov║wanglf@iphy.ac.cn

[1] L. Nie, D. Mei, H. Xiong, B. Peng, Z. Ren, X. I. P.Hernandez, A. Delariva, M. Wang, M. H. Engelhard, L.Kovarik, A. K. Datye, and Y. Wang, Science 358, 1419(2017).

[2] Q. Fu, H. Saltsburg, and M. Flytzani-Stephanopoulos,Science 301, 935 (2003).

[3] J. A. Farmer and C. T. Campbell, Science 329, 933(2010).

[4] R. Farrauto, S. Hwang, L. Shore, W. Ruettinger, J. Lampert,T. Giroux, Y. Liu, and O. Ilinich, Annu. Rev. Mater. Res. 33,1 (2003).

[5] E. P. Murray, T. Tsai, and S. A. Barnett, Nature 400, 649(1999).

[6] C. T. Campbell and C. H. F. Peden, Science 309, 713(2005).

[7] Z.-P. Liu, S. J. Jenkins, and D. A. King, Phys. Rev. Lett. 94,196102 (2005).

[8] F. Esch, S. Fabris, L. Zhou, T. Montini, C. Africh, P.Fornasiero, G. Comelli, and R. Rosei, Science 309, 752(2005).

[9] N. V. Skorodumova, S. I. Simak, B. I. Lundqvist, I. A.Abrikosov, and B. Johansson, Phys. Rev. Lett. 89,166601 (2002).

[10] T. W. Hansen, J. B. Wagner, P. L. Hansen, S. Dahl, H.Topsøe, and C. J. H. Jacobsen, Science 294, 1508 (2001).

[11] P. A. Crozier and T.W. Hansen, MRS Bull. 40, 38 (2015).[12] H. Topsøe, J. Catal. 216, 155 (2003).[13] C. L. Jia, M. Lentzen, and K. Urban, Science 299, 870

(2003).[14] See Supplemental Material at http://link.aps.org/

supplemental/10.1103/PhysRevLett.124.056002 for a dis-cussion of the Materials and Methods, HRTEM imagecalculation to compare with experimental images, intensityprofiles of dynamic O in ceria, evaluation of the columninteractions within the atoms in ceria during oxygendiffusion, the structure employed in MD simulation, evo-lution of the fractional coordinate of four representativeO atoms in MD simulation, oxygen diffusion process inpartially reduced CeO2, combinations of O K-edge EELSspectra of the initial and final state for comparison withintermediate state, O atom diffusion in 1000 K ab initioMD simulation, and real-time TEM video of ceria nano-particle under the reduction processes, which includesRefs. [15–34].

[15] M. Nolan, S. C. Parker, and G.W. Watson, Surf. Sci. 595,223 (2005).

[16] O. Kraynis, J. Timoshenko, J. Huang, H. Singh, E. Wachtel,A. I. Frenkel, and I. Lubomirsky, Inorg. Chem. 58, 7527(2019).

[17] G. Kresse and J. Furthmuller, Comput. Mater. Sci. 6, 15(1996).

[18] G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).[19] G. Kresse and J. Hafner, Phys. Rev. B 48, 13115 (1993).[20] P. E. Blochl, Phys. Rev. B 50, 17953 (1994).[21] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett.

77, 3865 (1996).[22] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J.

Humphreys, and A. P. Sutton, Phys. Rev. B 57, 1505 (1998).[23] M. Nolan, S. Grigoleit, D. C. Sayle, S. C. Parker, and G.W.

Watson, Surf. Sci. 576, 217 (2005).[24] D. A. Andersson, S. I. Simak, B. Johansson, I. A. Abrikosov,

and N. V. Skorodumova, Phys. Rev. B 75, 035109 (2007).[25] N. Daelman, M. Capdevila-Cortada, and N. Lopez, Nat.

Mater. 18, 1215 (2019).[26] S. Nose, Mol. Phys. 52, 255 (1984).[27] S. Nose, J. Chem. Phys. 81, 511 (1984).[28] Y. S. Su and S. T. Pantelides, Phys. Rev. Lett. 88, 165503

(2002).[29] T. J. Pennycook, M. J. Beck, K. Varga, M. Varela, S. J.

Pennycook, and S. T. Pantelides, Phys. Rev. Lett. 104,115901 (2010).

[30] G. Henkelman and H. Jonsson, J. Chem. Phys. 113, 9978(2000).

[31] G. Henkelman, B. P. Uberuaga, and H. Jonsson, J. Chem.Phys. 113, 9901 (2000).

PHYSICAL REVIEW LETTERS 124, 056002 (2020)

056002-5

[32] R. Buczko, G. Duscher, S. J. Pennycook, and S. T.Pantelides, Phys. Rev. Lett. 85, 2168 (2000).

[33] W. Luo, M. Varela, J. Tao, S. J. Pennycook, and S. T.Pantelides, Phys. Rev. B 79, 052405 (2009).

[34] K. Kambe, G. Lehmpfuhl, F. Fujimoto, and Z. Naturforsch,Z. Naturforsch. 29A, 1034 (1974).

[35] I. Riess, R. Koerner, M. Ricken, and J. Noelting, Solid StateIonics 28–30, 539 (1988).

[36] M. Romeo, K. Bak, J. El Fallah, F. Le Normand, and L.Hilaire, Surf. Interface Anal. 20, 508 (1993).

[37] V. Piacente, G. Bardi, L. Malaspina, and A. Desideri, J.Chem. Phys. 59, 31 (1973).

[38] M. Nolan, J. E. Fearon, and G.W. Watson, Solid StateIonics 177, 3069 (2006).

[39] H. Y. Li, H. F. Wang, X. Q. Gong, Y. L. Guo, Y. Guo, G. Z.Lu, and P. Hu, Phys. Rev. B 79, 193401 (2009).

[40] J. Kullgren, K. Hermansson, and C. Castleton, J. Chem.Phys. 137, 044705 (2012).

[41] Y. Namai, K. Fukui, and Y. Iwasawa, J. Phys. Chem. B 107,11666 (2003).

[42] Y. Namai, K. Fukui, and Y. Iwasawa, Catal. Today 85, 79(2003).

[43] Y. Lin, Z. Wu, J. Wen, K. R. Poeppelmeier, and L. D. Marks,Nano Lett. 14, 191 (2014).

[44] C. Yang, X. Yu, S. Heißler, A. Nefedov, S. Colussi, J.Llorca, A. Trovarelli, Y. Wang, and C. Wöll, Angew. Chem.,Int. Ed. 56, 375 (2017).

[45] H. Tuller and A. Nowick, J. Phys. Chem. Solids 38, 859(1977).

[46] L. Douillard, M. Gautier, N. Thromat, M. Henriot, M. J.Guittet, J. P. Duraud, and G. Tourillon, Phys. Rev. B 49,16171 (1994).

[47] A. V. Soldatov, T. S. Ivanchenko, S. Della Longa, A. Kotani,Y. Iwamoto, and A. Bianconi, Phys. Rev. B 50, 5074(1994).

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Supplemental Material for Visualizing Anisotropic Oxygen Diffusion in Ceria under Activated Conditions

Liang Zhu,1,2,* Xin Jin,1,2,* Yu-Yang Zhang,2,† Shixuan Du,1,2,5 Lei Liu,3,‡ Tijana Rajh,4

Zhi Xu,5 Wenlong Wang,1,2,5 Xuedong Bai,1,2,5,§ Jianguo Wen,4,║ Lifen Wang1,4,¶ 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,

Chinese Academy of Sciences, Beijing 100190, China 2School of Physical Sciences and CAS Center for Excellence in Topological Quantum Computation,

University of Chinese Academy of Sciences, Beijing 100190, China 3Department of Materials Science and Engineering, College of Engineering, Peking University, Beijing 100871, China

4Center for Nanoscale Materials, Argonne National Laboratory, Lemont, IL 60439, USA 5Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

Materials and Methods

Sample preparation CeO2 nanoparticles were synthesized following the hydrothermal process [1]. 0.868 g of Ce(NO3)3·6H2O (99%

Sigma-Aldrich) were dissolved in 5 mL of deionized water. 9.6 g of NaOH (Sigma-Aldrich) were dissolved in 35 mL of deionized

water. The two solutions were then mixed with continuous stirring for 30 min in a Teflon bottle. In the next step, the Teflon bottle

with the mixture was transferred to a stainless-steel autoclave and then heated at 180 °C for 24 h. Afterwards, the fresh product was

separated by centrifugation, washed with deionized water and ethanol for several times, followed by drying at 90°C in air overnight.

The as acquired nanoparticles were dispersed in ethanol to make a suspension. Several droplets were applied to a Cu TEM grid. The

grid was put on a TEM double-tilt holder then transferred to TEM column.

Aberration-corrected TEM The TEM imaging and EELS were performed using the Argonne Chromatic Aberration-corrected

TEM (ACAT) and the JEOL JEM-ARM300F operated at an electron-accelerating voltage of 200 kV. The ACAT microscope is

equipped with image corrector with both spherical and chromatic aberration correctors. The JEOL JEM-ARM300F is equipped

with a spherical-aberration corrector. Typically, the spherical aberration was corrected to ~-5μm. The 2-fold astigmatism was

corrected to ~0 nm. The coma and 3-fold astigmatism were corrected to several nanometer. The nanoparticle on Cu grid was tilted

to <110> zone-axis for electron beam. Edge area of the nanoparticle was ~10 nm in thickness. TEM images with focus through +10

nm to -10 nm were recorded by a charge-coupled device camera with 1024 by 1024 pixels at a sampling rate of ~0.02 nm/pixel.

EELS spectra were recorded by the GIF camera with an acquire time of 0.2 s for each frame. We performed HRTEM images

calculation by wave-optical image simulation using the MacTempas software package to compared with the experimental imaging

mode. DFT calculations We performed density functional theory (DFT) calculations using the Vienna ab initio simulation package

(VASP) [2-4] with the projected augmented wave (PAW) method [5], and Perdew-Burke-Ernzerhof (PBE) exchange-correlation

function [6]. The DFT+U approach in the Dudarev form [7] was used to describe the onsite Coulomb interaction of Ce, and the

effective U is chosen as 5 eV which is widely used in CeO2 system [8-11]. The plane wave cut off energy was set at 400 eV for all

calculations, and a Γ-centered (5×5×5) k-point mesh was applied to bulk CeO2 and bulk Ce2O3. For bulk Ce2O3, a spin-polarized

calculation was performed. The cell volume and atomic position of bulk CeO2 and bulk Ce2O3 were relaxed by a conjugate gradient

method until the interaction force between atoms was less than 0.01 eV/Å.

Ab initio MD simulations and diffusion barrier The initial structure for the MD simulation was constructed by deleting 16 O

atoms from the top 4 O layers in the CeO2 2×2×4 supercell. The atomic position of the structure was fully relaxed until the

interaction force between atoms was less than 0.01 eV/Å. Then, non-spin-polarized, finite-temperature ab initio MD simulations

were performed, in which a canonical ensemble (NVT maintained) was employed. The temperature was set to 2000 K and was

controlled by using the algorithm of Nosé [12,13]. We set the temperature to 2000 K to reduce simulation time but still below the

melting point of CeO2. The O atoms diffusion rate can be estimated by ν = f0 exp(-Eb/kBT), where f0 is the vibration frequency of O

atoms, Eb is the diffusion barrier and kBT is the thermal energy. For a 2000 K simulation, kBT≈167 meV, combined with the

calculated 0.74 eV Eb, we estimated a considerable number of O diffusion events can be observed during a 10 ps simulation.

Similar approaches have been employed in previous literature [14,15]. We also performed a 1000 K MD simulation to check the

validness of the approach. We also observe diffusion of O atom along [001] direction, but in a much longer simulation time 25ps.

The bottom two atom layers (1 Ce layer and 1 O layer) were fixed to describe the interaction of the bulk, and a Γ-centered (1×1×1)

k-point mesh was applied. Diffusion barrier is calculated by climbing nudged elastic band method (CI-NEB) [16,17], based on the

relaxed structure employed in MD simulation. NEB calculation is spin-polarized to get an accurate barrier.

EELS simulations The CeO2 and Ce2O3 O K-edge EELS simulations were performed using the Z+1 approximation [18,19]. An O

atom in a 2×2×2 CeO2 bulk structure and Ce2O3 bulk structure was replaced by an F atom, and the projected density of states

(PDOS) on the p-orbital of the F atom was calculated. For the calculation of the PDOS, a Γ-centered (5×5×5) k-point mesh was

applied, and Gaussian smearing with a width of 0.5 eV was applied to the partial occupancy. Then, the unoccupied states (states

above the Fermi level) were employed to simulate the EELS spectra, which matched the experimental results well.

Fluorite-structured CeO2 has a lattice constant of 5.4 Å. The shortest O-O column spacing is 1.9 Å for the <110> zone-axis. So

the cerium and oxygen atom columns are well enough spatially separated to be resolved by spherical-aberration corrected TEM

with subangstrom resolution. But, the atomic resolution of TEM imaging for a specific specimen is complicated. For a very thin

specimen, under the weak phase object approximation, the locally variable phase shift of the electron waves is small. The

structure information is included in the transmitted beam and low-amplitude diffracted beams with phases shifted by π/2. The

amplitude information is subtracted and transformed to the HRTEM image with atomic resolution when additional phase shift is

introduced by the appropriate spherical aberration and by the favorable defocus amount of the objective lens. For a specific

experimental sample, the thickness is not very thin (~ 10 nm), the electron channeling contrast can be used to interpret the atomic

resolution HRTEM [20]. According to the theory of dynamical electron diffraction, each atom column with strong electrostatic

potential relating to atomic charge Z act as a periodically interference channel, the amplitude of exit waves varies with specimen

thickness, direct imaging of all atomic columns by the channeling contrast is thus possible. In our experiment, the thickness of

the imaging areas of CeO2 nanoparticles is about 10 nm. The atomic HRTEM image is in nice agreement with the image

simulations. Figs. 1 (a) - (j) show the calculated TEM images in conjunction with the experimental TEM images of the thin area

of CeO2 nanoparticle. Figs. 1 (k)-(m) show the experimental TEM images of the different areas of a CeO2 nanoparticle with

different thicknesses for incident electron beam. Fig. 1(m) suggests the favorable thickness area for atomic TEM imaging.

FIG. 1. HRTEM image calculation to compare with experimental images. HRTEM image calculation with the same imaging condition

except the defocus. (a) Atomic structure of fluorite CeO2 projected to the [110] zone-axis. (b-d) HRTEM images calculated with the

imaging mode from the experiment. Contrast varies with defocus. (e) Experiment obtained image is competitive with the calculated image.

(f) Atomic structure of bixbyite Ce2O3 projected to the [110] zone-axis. (g-i) HRTEM images calculated with the imaging mode from the

experiment. Contrast varies with defocus. (j) Experiment obtained image is competitive with the calculated image. (k-m) TEM images of

the different areas of a CeO2 nanoparticle with different thicknesses for incident electron beam. (m) The favorable thickness area for

atomic TEM imaging. Scale bars in TEM images are 1nm.

FIG. 2. Intensity profiles of dynamic O in ceria. (a) Atomic HRTEM image of ceria. blue spots show the Ce atom positions, pink spots

show the O atom positions. (b) Intensity profiles of O and Ce of the red rectangle marked area in (a) under reduction. (b) Intensity profiles

of O and Ce of the blue rectangle marked area in (a) under reduction. The stable intensity of Ce as a reference, intensity, and spot size of

O varies with reaction time.

The Coulomb interaction between Ce atoms due to oxygen diffusion was evaluated as shown in the following figures. Panel (a)

is the schematic of O atom diffusion in CeO2 reduction. Panels (b) and (c) are zoomed in configurations of initial and transition state

in O atom diffusion. Only the diffusing O atom and its nearest Ce atoms are shown. In the transition state, O atom locates at the

center of the “Ce cage”, as shown in panel (c), and the nearest distance between Ce and O atoms decreased to ~1.94 Å, which

significantly increased the Coulomb interaction. The forces projected into [001] direction are 1.62 eV/Å and 0.75 eV/Å for the two

neighboring Ce atoms, which results the out of plane splitting of Ce atoms in [001] direction. The calculations also indicate that the

two neighboring Ce atoms are apart from each other, resulting in the volume expansion observed in our experiment.

FIG. 3. Evaluation of the Column interactions within the atoms in ceria during oxygen diffusion. (a) Schematic of the diffusion of O atom

in CeO2 reduction. Blue and red balls represent Ce and O atoms. The trajectory of diffusing O atom is shown in orange balls, and green

balls are the nearest Ce atoms to the diffusing O atom. (b) and (c) Configurations composed by diffusing O atom and its nearest Ce atoms.

The distances between Ce and O atoms are calculated based on optimized bulk CeO2 structure.

FIG. 4. The structure employed in MD simulation. (a) Initial structure for MD simulation. The structure consists of 50% CeO2 and 50%

Ce2O3. (b) Energy difference between partially reduced CeO2 with different O vacancy distribution. The left and right configuration

possess Ce2O3-like and random O vacancy distribution respectively. Formulas of them are both CeO1.75.

FIG. 5. Evolution of the fractional coordinate of four representative O atoms in the ab initio MD simulation. (a)-(d) Evolution of the

fractional coordinate of O1 to O4 during ab initio MD simulation. The step function like the shape of the curve indicates the diffusion of O

atom. (e) Zoom in of panel c and d. The time range in which Dstep-step happened is marked by the dashed line. The end of horizontal diffusion

and the start of vertical diffusion, marked by arrows, are located at nearly the same time point, which shows the sequence of Dh and Dv

contained in Dss.

FIG. 6. Oxygen diffusion process in partially reduced CeO2. (a) Energy profile of O1’s diffusion, corresponding to the process marked by

red rectangle in the inset. The inset shows the evolution of O1’s fractional coordinate in ab initio MD simulation. (b)-(h) Zoomed in

configurations of the states shown in (a). All the configurations are viewed along direction.

FIG. 7. Combinations of O K-edge EELS spectra of initial and final state for comparison with intermediate state. For comparison, the third

peak position is alighned up for all the overlay spectrum and the intermediate spectra.

FIG. 8. O atom diffusion in 1000 K ab initio MD simulation. (a) Trajectory of a diffusing O atom in 1000 K ab initio MD simulation. (b) Coordinate evolution of corresponding O atom during ab initio MD simulation.

[1] O. Kraynis, J. Timoshenko, J. Huang, H. Singh, E. Wachtel, A. I. Frenkel, and I. Lubomirsky, Inorg. Chem. 58, 7527 (2019).

[2] G. Kresse and J. Furthmuller, Comp. Mater. Sci. 6, 15 (1996).

[3] G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).

[4] G. Kresse and J. Hafner, Phys. Rev. B 48, 13115 (1993).

[5] P. E. Blochl, Phys. Rev. B 50, 17953 (1994).

[6] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

[7] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Phys. Rev. B 57, 1505 (1998).

[8] M. Nolan, S. Grigoleit, D. C. Sayle, S. C. Parker, and G. W. Watson, Surf. Sci. 576, 217 (2005).

[9] D. A. Andersson, S. I. Simak, B. Johansson, I. A. Abrikosov, and N. V. Skorodumova, Phys. Rev. B 75, 035109 (2007).

[10] N. Daelman, M. Capdevila-Cortada, and N. Lopez, Nat. Mater. 18, 1215 (2019).

[11] M. Nolan, S. C. Parker, and G. W. Watson, Surf. Sci. 595, 223 (2005).

[12] S. Nose, Mol. Phys. 52, 255 (1984).

[13] S. Nose, J. Chem. Phys. 81, 511 (1984).

[14] Y. S. Su and S. T. Pantelides, Phys. Rev. Lett. 88, 165503 (2002).

[15] T. J. Pennycook, M. J. Beck, K. Varga, M. Varela, S. J. Pennycook, and S. T. Pantelides, Phys. Rev. Lett. 104, 115901 (2010).

[16] G. Henkelman and H. Jonsson, J. Chem. Phys. 113, 9978 (2000).

[17] G. Henkelman, B. P. Uberuaga, and H. Jónsson, J. Chem. Phys. 113, 9901 (2000).

[18] R. Buczko, G. Duscher, S. J. Pennycook, and S. T. Pantelides, Phys. Rev. Lett. 85, 2168 (2000).

[19] W. Luo, M. Varela, J. Tao, S. J. Pennycook, and S. T. Pantelides, Phys. Rev. B 79, 052405 (2009).

[20] K. Kambe, G. Lehmpfuhl, F. Fujimoto, and Z. Naturforsch, 29a, 1034 (1974).