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Stabilization Effect of Surface Impurities on the Structure of Ultrasmall ZrO2 Nanoparticles: An Ab-Initio Study Roberto Grena,† Olivier Masson,*,‡ Laura Portal,‡ Fabien Rémondière,‡ Abid Berghout,‡ Jenny Jouin,‡ and Philippe Thomas‡ †

C. R. ENEA Casaccia, Via Anguillarese 301, 00123 Roma, Italy Laboratoire de Science des Procédés Céramiques et de Traitements de Surface (SPCTS), Université de Limoges−CNRS UMR 7315, Centre Européen de la Céramique, 12 Rue Atlantis, 87068 Limoges, France

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ABSTRACT: Real nanoparticles can hardly be considered as isolated objects in vacuum with pure stoichiometric chemical composition. It can be expected that some surface stabilizing mechanisms may occur in real systems, and they could induce more or less pronounced effects on the structure of nanoparticles. In this work, we analyzed the stabilizing effect of surface impurities on the structure of ultrasmall ZrO2 nanoparticles using ab initio simulation methods. The study was performed on ZrO2 cluster models, with a diameter around 1.25 nm, using the Car−Parrinello molecular dynamics method combined with standard structural optimization methods. After the study of the naked cluster, the stabilizing effect was investigated by adding chemisorbed water molecules at the particle surface, with a covering degree ranging from 15% to 100%. The results clearly indicated that energy minimizations leaded invariably to highly disordered structures in the case of naked nanoparticles. The structure of the models got more ordered only with increasing water coverage. The comparison, via the pair distribution functions (PDF), to the experimental data obtained from a sample of nanoparticles of comparable size showed a good agreement for a high (but not total) water coverage, indicating that a surface stabilizing effect is a sound hypothesis to explain the experimental results. Surface stabilizing effects play a crucial role in the case of ZrO2, in contrast with recent calculations performed on other chemical systems (CeO2 or TiO2, for example); thus, for ZrO2 a stabilizing mechanism, such as the one proposed in this paper, must be inevitably included in the model, and this fact markedly complicates the problem of solving the ZrO2 nanocrystal structure.

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INTRODUCTION Nanoparticles of very small size (a few nanometers in diameter) have attracted much scientific and technological interest these last decades. They generally exhibit unique and size tunable physical properties, characteristic of neither the atomic nor the bulk (solid state) limits.1 It is well-established that this behavior is mainly due to quantum confinement effects, caused by the finite size of particles.2 However, recent results suggest that nanoparticles also contain an unusual form of structural disorder that can substantially modify their properties, so that they cannot simply be considered as small pieces of bulk material.3 The present paper deals with zirconium dioxide nanoparticles. Zirconia belongs to a class of MO2 metal oxide ceramics with very important technological applications,4 such as promising applications in the field of nanoelectronics.5 In addition, it possesses a complex polymorphism, with most of the polymorphs deriving from the fluorite-type structure6−9 and well-known structural stabilization effects at the nanoscale.10,11 The problem of determining the structure of nanoparticles is far from being solved to date.12−14 In particular, the structural deviations relative to the ideal structure are not well characterized because no experimental techniques, X-ray and neutron diffraction for instance, can give univocal information for such small objects.13 Consequently, this problem cannot be tackled with experimental methods only but needs extra© XXXX American Chemical Society

information coming from theoretical modeling methods. For instance, one can generate cluster models using some energy minimization scheme and check their quality against experimental data. Such a powerful approach is routinely followed for the analysis of disordered systems (mostly glasses), by coupling, for example, molecular dynamics simulations and diffraction experiments.15 Unfortunately, when modeling the structure of nanoparticles, things become much more complicated because of the following three reasons. First, real nanoparticles can hardly be considered as isolated objects in vacuum with pure stoichiometric chemical composition. This is inherent to the chemical (possibly physical) synthesis route used. Real nanoparticles may, for instance, be aggregated with an appreciable number of surface contacts between each other, or they may be almost isolated with grafted surfactant molecules at their surface, or they may be polluted by impurities mostly located at the surface too. Second, as the structure of nanoparticles largely depends on their surface relaxation/reconstruction, any perturbations (as those stated above) of the surface environment may affect the nanoparticle structure. A good illustration has been recently given for the case of chalcogenide compounds, for which it has been shown Received: January 22, 2015 Revised: June 2, 2015

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DOI: 10.1021/acs.jpcc.5b00684 J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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that nanoparticles can undergo structural transformations, even reversible, in response to changes in the surface environment, rather than particle size.16 Lastly, it is expected that these kind of surface stabilizing effects may be more or less pronounced depending on the nanoparticles chemical system and may be induced by even very small amount of impurities, not easy to characterize experimentally. Consequently, the way the real nanoparticles system differs from the “pure stoichiometric isolated” case and affects the structure is not trivial and not easy to anticipate, and this makes the establishment of nanoparticle models more complex. The problem of surface stabilization has been addressed in the case of “large” ZrO2 faceted nanoparticles (∼10 nm in diameter) with a well-defined bulk structure, starting from the study of 2D-periodic surfaces and using the results to describe the hydration effects on the energetics and surface relaxation for different facet indices.17,18 The main aim of the present work is to address the stabilization effect in the case of ultrasmall ZrO2 nanoparticles, where no clear distinction between bulk, surface, edges, and corners can be applied and where the overall structure deviates strongly from any known crystal polymorph. The work is addressed by means of fully ab initio simulation methods, which to the authors’ knowledge, has not been done to date. Ab-initio methods have the advantage, with respect to classical methods, to avoid hypothesis on the form of the interatomic potentials, which are often (when available) environment-specific. This is especially true for ZrO2, for which no (simple) interatomic potentials are able to reproduce the energetics and relative stability of all polymorphs. In addition, computational power currently available makes such methods suited to clusters of more than 1 nm in diameter, with hundreds of valence electrons involved in the computation. The simulated systems in this work are based on a stoichiometric 129 atoms cluster (Zr43O86), with a diameter around 1.25 nm. This size is a compromise between the computational feasibility and the requirement to have large enough models to be representative of the smallest nanoparticles experimentally obtainable. The surface stabilizing effect on the particle structure was investigated by adding chemisorbed (i.e., dissociated) water molecules at the particle surface, with a covering degree ranging from 15% to 100%. Using water molecule is a simple way to saturate dangling bonds or to mimic more complex mechanisms, involving notably larger molecules or even surface contacts in aggregated systems. In addition, water molecules are realistic impurities that can be found with numerous chemical synthesis methods, even nonhydrolytic ones. For both pure and water-covered clusters, computations using Car−Parrinello molecular dynamics and structure optimization were performed in order to bring the structure near to an energy minimum. The as-obtained models were also compared to experimental data via the X-ray total scattering Pair Distribution Function (PDF) obtained from a sample of ZrO2 nanoparticles of similar size and synthesized by the sol−gel route. The PDF method19 is particularly well-suited in this context as it is sensitive to local structural disorder. In the following, we first describe the computational techniques and procedures used to generate the nanocluster models. We then give a short description of the experimental sample used for comparison and finally present results for both naked and water-covered clusters.

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COMPUTATIONAL DETAILS

Ab-Initio Computations. Computations were performed using the software CPMD (Car−Parrinello Molecular Dynamics),20 in a plane wave−pseudopotential approach. The software performs density functional (DFT) computations (ground-state computation, structure optimization) in the Kohn−Sham scheme21,22 as well as Car−Parrinello molecular dynamics.23 In order to choose the functional, the pseudopotentials, and the parameters of the simulation, test computations were made on the three structures of crystalline ZrO2 that are stable at atmospheric pressure: the monoclinic, tetragonal, and cubic phases. The energy vs volume graph was obtained for the three phases, using different functionals and pseudopotentials, and the equilibrium volumes were compared with experimental values. Simple local density (LDA) and generalized gradient (GGA) functionals were considered, since strong correlation effects, which can heavily affect computations for transition metals, do not play a significant role in the case of ZrO2 (the Zr d orbital has occupation 0 in the nominal oxidation state of Zr). After the tests, the PBE functional24 with Martins-Troullier pseudopotentials25 was chosen; after a check on convergence, an energy cutoff of 80 Ry was used. (In the tests made, using LDA functional a volume some % smaller than the experimental volume was obtained, but the energy differences among the phases were not well reproduced. Using BLYP functional, a far too large volume was obtained. No significant differences were found among different types of tested pseudopotentials, all norm-conserving.) With these parameters, the relative stability of the three zirconia phases is correctly reproduced, with the monoclinic phase being the most stable at low pressures, followed by the tetragonal and the cubic phases. The computed equilibrium volumes are larger than the experimental volumes of a few %, a typical result for PBE functional. Experimental volumes of comparison are taken from refs 6−8. Differences in energy among the various phases are compatible with previous ab initio GGA-based analyses,26−28 which show fluctuations of the order of 0.05 eV for ZrO2 units; this error unfortunately can lead to high relative errors in the energy difference, but it is unavoidable at this level of approximation. Figure 1 shows the energy vs volume curves obtained for the three structures; Table 1 shows the comparison of equilibrium volumes with the experimental values for the structures and the computed relative energies.

Figure 1. Computed energy vs volume graph of three polymorphs of ZrO2 (monoclinic, tetragonal, cubic). The energy is for a ZrO2 unit, with respect to the most stable configuration. B


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thermal agitation or static disorder from one cluster to another. Second, the partial PDF were combined in order to get the total PDF. Contrarily to the case of neutron scattering, the Xray PDF is not a simple weighted linear combination of partial PDFs. This comes from the fact that the dependence of the atomic scattering factors with the scattering vector length differs from one kind of atom to another. This shortcoming has been noticed for a long time and was first partly overcome in 1936 by Warren, Krutter, and Morningstar31 by using a mean form factor with effective number of electrons per atom. This approximation is often used nowadays but can introduce significant errors for materials combining both heavy and light elements, as for ZrO2. Two of the authors of the present work have recently derived an efficient way to exactly calculate the Xray total PDF from any structure models.32 We used this expression for calculating the nanoparticle total PDF from the partial PDF.

Table 1. Computed Equilibrium Volumes of Three Crystal Phases of Zirconia (Monoclinic, Tetragonal, Cubic), Compared to Experimental Values, and Computed Energy Differences with Respect to the Most Stable Phase (the Monoclinic Structure)a monoclinic tetragonal cubic a

V computed

V experimental

E − Emonoc (comp.)

0.03620 nm3 0.03510 nm3 0.03376 nm3

0.03522 nm3 (ref 6) 0.03491 nm3 (ref 7) 0.03316 nm3 (ref 8)

0 eV 0.12 eV 0.22 eV

All the values are given for ZrO2 unit.

This computational setup was used to investigate the properties of ZrO2 clusters. In the computation, the cluster was placed at the center of a cubic supercell of 2.646 nm (50 au), adopting the Martyna−Tuckerman (MT) correction29 to reproduce an isolated cluster. Since the diameter of all the considered clusters (including surface water) is less than 1.5 nm, any two adjacent periodic images were more than 1 nm apart; such distance, combined with the MT correction, should guarantee reliable results for an isolated system. A check on the convergence was made by varying the cell size and showing that with a supercell larger than 40 au there were no systematic effects on the energy associated with the cell size variation. The size of the cell can be reduced if the cluster has no surface impurities (in that case, a cell of 40 au was employed). The aim of the computations was to find equilibrium structures of the nanoclusters. Standard structural optimization techniques implemented in CPMD proved to be problematic to use with the analyzed clusters (with a number of atoms between 129 and 201), due to instabilities arising when the system is far from the minimum, and a Car−Parrinello (CP) based approach was chosen instead. In this approach, after finding the ground state wave function of the initial configuration, a CP simulation is started in which the system is cooled down to very low temperatures, in order to bring the structure near to an energy minimum. After the CP run, the obtained structure is refined with a standard geometrical optimization technique of CPMD (BFGS/GDIIS),30 which should work smoothly if the CP run is carefully implemented. This procedure is often employed to deal with systems for which direct optimization leads to instabilities. If desired, the CP simulation can then be continued, reheating the structure and cooling it again, to obtain a second local minimum, presumably farther from the initial structure than the minimum obtained from the first cooling. This is a standard method to explore different configurations when there are reasons to believe that the system energy landscape has a complex structure of local minima (as in the case of the naked ZrO2 cluster). The method can then be used to find a collection of reasonable structures corresponding to local minima near in energy. Such a method has been applied in the case of the naked cluster (Sec. 4.2), finding 4 local minima with very different structures. For the CP simulation, a fictitious electron mass μ of 100 au was used, with an integration time step of 0.048 fs (2 au). Computation of PDF from Ab Initio Models. Once the equilibrium configurations of the cluster were obtained, the corresponding PDF were computed in the following way. First, the partial pair correlation functions were calculated from the structure model. Each partial peak was slightly broadened by convoluting with a Gaussian function of standard deviation of 0.005 nm. This mimics atomic random displacements due to

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DESCRIPTION OF THE REAL NANOPARTICLES SYSTEM Nanoparticles Synthesis. The synthesis of very small metal oxide particle is a very challenging task. To our knowledge, no ZrO2 nanoparticles with size lower than 2 nm can be found in the literature to date. Soft-chemistry is certainly one of the best routes for producing such particles. In particular, the nonhydrolytic sol−gel methods are very powerful in obtaining small, spherical, monodisperse, and nonaggregated particles. The nanoparticles presented herein were synthesized from the hydrolytic sol−gel route within the zirconium npropoxide, n-propanol, water, and acetylacetone (chelating agent) chemical system. This route allowed obtaining, among the various synthesis methods we tested, the smallest zirconia nanoparticles (∼1.5 nm). The sols were prepared in a dry glovebox by mixing under magnetic stirring. Tetra-hydrated yttrium nitrate was also added such that the final particles contained 3 mol % of Y2O3. Although not mandatory for getting single phase nanoparticles, doping with yttria made it possible to obtain, by heat treatment, samples with larger particle sizes (up to micrometric) and with stabilized tetragonal structure, without transforming into the monoclinic polymorph (the stable phase of micrometric zirconia). It is expected that this small amount of dopant has very little influence on the structure of the nanoparticles. Indeed, larger nanoparticles (∼2.5 nm) obtained with a nonhydrolytic sol−gel route without yttrium exhibit a PDF very similar to that of the present sample heated at 350 °C (i.e., of ∼2.5 nm in size too). In particular, the same structural distortions are observed (data can be provided on request). Another confirmation of this little influence of yttrium has been obtained computationally and will be described in the Results and Discussion section. The concentration of zirconium n-propoxide was fixed to 0.25 mol L−1 and the complexing ratio (chelating agent over precursors) was fixed to 0.7. The as-obtained sols were then dried in supercritical condition (for the solvent) using an autoclave (T = 270 °C and P = 5.52 GPa) in order to obtain an aerogel powder. More details can be found in ref 33. Nanoparticles Average Structure and PDF. The average structure and PDF descriptions are based on X-ray total scattering data obtained with a homemade two-axis diffractometer of Debye−Scherrer geometry. This setup uses a molybdenum sealed tube, a graphite monochromator and rectangular collimating slits arranged in a way that the capillary sample is completely bathed in a pseudoparallel incident beam C


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nm corresponds to Zr−O bond lengths. The peak corresponding to the shortest O−O distances at 0.27 nm is hardly noticeable. The intense peak at about 0.35 nm corresponds to the shortest Zr−Zr distances. The next peaks from about 0.40 to 0.47 nm correspond mostly to Zr−O distances. However, it is worth noting that the PDF cannot accurately be reproduced by any of the ZrO2 polymorphs and exhibits structural disorder and distortion with respect to the known polymorphs.33 The structural analysis of these nanocrystals is still in progress and the detailed description of the PDF is beyond the scope of this paper.

with MoKα (0.071069 nm) radiation. Scattered signals are measured thanks to a scintillation point detector. For the experiment, a small amount of powder is placed in a thin-walled (0.01 mm) borosilicate glass capillary of 0.7 mm in diameter. Once sealed, the capillary is mounted on a goniometric head and adjusted such that its axis coincides with the goniometer axis. Experiment was performed at room temperature from Q = 0 to Q = 170 nm−1 (Q = 4π sin θ/λ) with a constant step of 0.2 nm−1 and acquisition time of 480 s per point. The sample was rotated about its axis during the experiment. Additional measurements of the scattering from the empty capillary, from an empty environment, and from the sample with an aluminum filter were performed in the same conditions for subsequent data corrections. Raw data corrections and reduction were performed using a homemade program written in Python language. Data were corrected for capillary and air scattering, absorption effects, polarization, Compton and multiple scattering, and fluorescence. Fluorescence from the sample was corrected thanks to the two measurements made with and without aluminum filter.34 Data were finally normalized and reduced into the structure function. The latter was then Fourier-transformed in order to get the total PDF. The XRD pattern of the sample (not shown in the present paper) is typical of the tetragonal polymorph with nearly cubic metrics. The nanoparticle average size and lattice microstrains were estimated by XRD line broadening analysis using the Rietveld method35 and the program FULLPROF.36 We obtained an average apparent size of 1.49 nm with a high amount of apparent microstrains. This size is slightly larger than that of the calculated clusters but is reasonably near. The size distribution could not be estimated because of a too high line broadening. The experimental PDF is shown in Figure 2. The

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RESULTS AND DISCUSSION Cluster with No Surface Impurities. The first computations were made on the naked (i.e., without water impurities) Zr43O86 cluster, starting from an initial configuration “cut” from the cubic zirconia polymorph, with a roughly spherical shape. The choice of starting from the simplest cubic structure was made because the other polymorphs simply derive from the cubic structure with atomic displacements and metric distortions easily accessible by energy minimization. In addition, the experimental PDF shows properties of the tetragonal/cubic structures. Such a cluster, with a diameter around 1.25 nm, is slightly smaller than the experimental nanoparticles but, as shown below, it already provides interesting features of the cluster behavior. Figure 3 shows the initial configuration and the four energy minimum configurations that were found with CP heating/ cooling cycles followed by BFGS optimizations. The first minimum is obtained from a direct cooling of the regular initial structure, with the introduction of a small initial random atom displacement to break the symmetry; the minima from 2 to 4 are obtained after a heating to 500, 1000, and 1500 K, respectively. Heating−cooling cycles lasted around 1 ps, with an initial steep increase of the temperature (0.2 ps) followed by relaxation. Even if the cycles are very short (for computational reasons), they proved to be sufficient to obtain good (and very different) starting points for the final BFGS optimization. The corresponding calculated PDF are compared to the experimental one in Figure 4a−d. It can be seen that the computed PDFs are significantly different from the experimental one. In particular, the two highest peaks of all the computed PDFs, at about 0.21 and 0.33 nm, are clearly shifted toward shorter r-values with respect to the experimental PDF, which suggests too short Zr−O and Zr−Zr distances in the models. More importantly, while the experimental PDF shows the presence of a partially ordered structure, the theoretical optimizations lead invariably to a highly disordered structure, with a structural disorder increasing from configuration 1 to 4. In many cases the cluster resembles an amorphous material, and the sphericity is lost for the last configuration, maybe due to a heating at too high temperatures. The surface rearrange-

Figure 2. Experimental pair distribution function.

overall envelope resembles that of the cubic or tetragonal with nearly cubic metric polymorphs. The first peak at about 0.215

Figure 3. Initial cubic configuration and four configurations that are local minima of energy, for the Zr43O86 cluster without surface impurities, found with CP heating/cooling cycles. Below each cluster, the energy loss with respect to the initial configuration is shown. D


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Figure 4. PDFs computed from the four local energy minima found for the unpassivated cluster, compared with the experimental result: direct minimization from the starting perfect cubic crystal structure (a), and heating−cooling cycles up to 500 K (b), 1000 K (c), and 1500 K (d).

9.3%, i.e., one value close to the experimental percentage (6%) and one distinctly higher. The structure of these minima exhibit similar characteristics to that of minimum 1 of the pure ZrO2 cluster (small crystal-like core with a heavily rearranged surface and a PDF far from the experimental one), showing that the small amount of yttrium in the cluster does not alter significantly the structural properties of the minimum energy clusters and cannot be responsible for the ordering found in the experimental sample. One could also argue that a similar stabilizing effect could be achieved simply by increasing the size of the cluster, thus protecting the inner part from rearrangement (as already mentioned, the synthesized particles are larger than the computed clusters). However, preliminary results we have obtained on larger clusters disprove this hypothesis as strong rearrangements leading to disordered equilibrium configurations are also observed. Finally, it is interesting to add that recent calculations we have made on CeO2 clusters (CeO2 has a fluorite-type structure as zirconia) using the same approach show a completely different behavior. Indeed, the structure of these clusters becomes just slightly disordered after energy minimization. Similarly, calculations made by other authors on TiO2 (ref 37) show that Ti29O58 clusters, despite their extreme smallness, retain a clearly recognizable crystalline anatase structure. All these remarks suggest that the large structural rearrangement obtained in this study is inherent to the ZrO2 chemical system. Clusters with Surface Impurities. From the results and discussion above, it is arguable that some stabilizing mechanisms occur in real systems to prevent excessive rearrangements of the structure of nanoparticles. One of the most straightforward hypotheses is a possible perturbation of

ment seems to be highly irregular, with no recognizable patterns, and the presence of a crystalline core is not guaranteed. Even for the first minimum (Figure 4a), which seems to preserve some memory of the starting crystalline configuration (in the PDF, this fact can be seen from the height and sharpness of the first peaks, for r < 0.5 nm), the behavior of the PDF in the region 0.5 nm < r < 1.2 nm shows that the degree of disorder is already too high, probably because of the strong surface rearrangement. It is also worth noting that not only the four found minima present an excessive disorder with respect to the experimental results, but also that the most ordered structure corresponds to a higher energy (the first minimum energy is 5.35 eV larger than the lowest minimum among the four). Consequently, the four minima presented herein are certainly sufficient to draw conclusions about the cluster behavior and a systematic search of energy minima and global minimum is not especially needed. The main conclusion is that a hypothetical sample made of isolated ZrO2 nanoparticles in vacuum with pure stoichiometric chemical composition would likely be a mix of clusters with various structures (probably depending on the particles formation process), relatively short Zr−O and Zr−Zr distances, and high positional disorder, much higher than in real synthesis conditions. As already suggested in the previous section, the small amount of yttrium added for practical reasons should not change this conclusion. In order to reinforce this idea, energy minimizations were performed on two clusters containing yttrium atoms. In the first cluster, two zirconium atoms located at the surface were substituted by two yttrium atoms, and one oxygen was eliminated for satisfying stoichiometry. In the second cluster, four yttrium atoms were substituted in the same way. The corresponding percentage of yttrium are 4.6% and E


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The Journal of Physical Chemistry C the surface environment, for example, by the presence of surface impurities on the cluster, which could saturate chemical (dangling) bonds and stabilize the cluster structure in a more crystal-like form. The stabilizing effect of impurities on nanoclusters has already been studied with ab initio methods in ref 37 in the case of a small TiO2 cluster (29 TiO2 units). The authors show that water or hydrogen impurities prevent the reorganization of the surface, thus stabilizing a crystal-like (anatase) structure. In the case of ZrO2, however, the disorder does not involve only the surface but also the particle core and shape. Moreover, impurities can cover the cluster only partially, and the structure will depend on the amount of covering. For this reason, a systematic study of the Zr43O86 cluster partially covered with chemisorbed (i.e., dissociated) water impurities was undertaken: different numbers of water molecules (from 4 to 24, at step of 4) were placed on the surface, bonding OH groups with surface Zr atoms and H atoms with surface O atoms. The impurities were placed on the surface trying to separate them as much as possible, in order to obtain a symmetric and roughly “uniform” distribution. The geometry optimization was conducted with an initial CP cooling followed by a refinement with standard geometrical optimization, as described in the Computational Details section. The results of the optimization are shown in Figure 5. One can see even from a simple visual inspection that the presence of water has a strong stabilizing effect; this is evident for the cluster covered with 24 H2O molecules, which remains almost unchanged (the only evident rearrangement being the configuration of the H2O surface molecules). The presence of a crystal-like core is clear for all the clusters with more than 12 H2O molecules on the surface. The computation of the PDFs for the optimized configurations (including of course the effect of the O atoms on the surface) allows one to better appreciate the effect of the water. Results are shown in Figure 6a−f. One can see that even only 4 H2O molecules (Figure 6a) change the PDF significantly with respect to the cases shown in Figure 4 (naked clusters), and some characteristics found in the experimental PDF emerge at least qualitatively (in particular in the region 0.5−1.2 nm, where peaks present in the experimental PDF are clearly identifiable). When adding H2O molecules, the PDF maintains the same characteristics, which become more and more defined if the covering increases, up to a covering of 20 H2O (Figure 6b−e). The highest peak of the PDFs (Zr−O and Zr−Zr distances) clearly drifts toward larger r-values as the covering increase to finally be close to the experimental positions. The overall contraction observed for the naked clusters thus disappears with a sufficient degree of coverage. Even if the effect is not large, the regularity of the trend is noteworthy. The PDF that seems to better reproduce the experimental results is the PDF relative to 20 H2O (Figure 6e), indicating the presence of a quite strong stabilizing mechanism (the cluster is almost completely covered by H2O impurities). This PDF presents some discrepancies with respect to the experimental one, but it reproduces all the main peaks and features of the experimental PDF (except of course in the region r > 1.2 nm), with an acceptable accuracy also from a quantitative point of view. When considering the totally covered cluster (24 H2O molecules), one can see that the PDF (Figure 6f) changes quite abruptly becoming the PDF of a crystal-like structure, with higher and sharper peaks; this means that the stabilization obtained with a full covering of impurities is too strong with

Figure 5. Initial and optimized configurations for clusters with dissociated H2O impurities on the surface.

respect to the experimental PDF. A certain amount of rearrangement appears in real systems. It is noteworthy that the PDF seems to maintain similar qualitative properties (number and position of peaks) for all the partial coverings, in particular from 12 to 20 H2O molecules. This seems to indicate that the exact amount of impurities is not fundamental. However, the PDF changes abruptly when the covering becomes total, passing to an almost perfect crystallike structure; on the other side, when the covering is absent, the structure undergoes high atomic displacements leading to a very disordered state. This indicates that even if the exact amount of impurities is not fundamental, a covering must be present and it should not be complete, in order to obtain a suitable stabilization mechanism. A final consideration should be made on the energy of the clusters. The energy of the clusters at different covering range was computed using the energy of the initial cubic cluster plus the energy of undissociated water molecules as a reference. Results are shown in Figure 7 (for the naked cluster, Min. 3 was considered). The observed energy decrease can be attributed to the rearrangement of the cluster and to the formation of Zr−O bonds. The second effect seems to prevail, since the decrease of energy is almost linear with the water amount, indicating that the formation of bonds with chemisorbed water is energetically F


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Figure 6. PDFs obtained from the optimized configurations with H2O surface impurities: coverage with 4 (a), 8 (b), 12 (c), 16 (d), 20 (e), and 24 (f) water molecules.

advantageous even if it prevents the cluster rearrangement. This fact confirms the tendency of the cluster to bound impurities at the surface, but it does not explain why the covering is not complete. Possible explanations can be the scarcity of impurities in the formation process or more complex mechanisms involving steric effects, which would prevent a complete passivation. The dashed line in Figure 7 illustrates the variation of the energy of the stabilized clusters with the water molecules removed. We can see that the energy increases with the covering degree, as expected because of the hindering of structure relaxation. From the viewpoint of modeling zirconia nanoparticles, this emphasizes that the best cluster model, i.e., the one that describes best the experimental PDF, cannot be generated from approaches based on energy minimization of pure ZrO2 systems. A stabilizing mechanism, as the one proposed in this paper, must be inevitably included in the particle model, which markedly complicates the problem of solving the ZrO2 nanocrystal structure. From the viewpoint of the real nanoparticle system, this emphasizes that if such a stabilizing mechanism occurs then it has to occur during the nanoparticle formation process. Indeed, if the particle is not stabilized during its growth, then the particle structure

Figure 7. Computed energy of hydrated clusters (solid line) with respect to the initial condition for the optimization (perfectly cubic cluster + undissociated water molecules). The dashed line is the energy that the final cluster configuration would have without surface water (it shows the effect of the prevented rearrangement). The difference between the two lines shows the effect of the formation of Zr−O bonds.

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mechanism must be inevitably included in the model; this markedly complicates the problem of solving ZrO2 nanocrystal structure. Even if the presence of chemisorbed water molecules, as proposed in this paper, is only one of the possible stabilizing mechanisms, it is an efficient and simple way to implement structural stabilization.

(according to the present calculations) will be amorphous-like, so that a subsequent stabilization could be hindered by a too high energy barrier for structural rearrangement. To conclude the discussion, we recall that the model presents some weak points. In particular, (i) only a size of cluster is considered, with a fixed number of atoms, while in the experimental sample a finite distribution of size is expected, (ii) only a covering configuration is considered to compute the PDF for each covering degree, while in a real sample one would expect to find different degrees of covering and different geometries, and (iii) only a stoichiometric cluster is considered, while in a real sample nonstoichiometry could be present. Regarding this last point, a stoichiometric model is reasonable as nonstoichiometry in pure zirconia is known to be small (in contrast to metal oxides with metal atoms that exhibit multiple oxidation states). However, as it is known that the thermodynamics of zirconia phase transitions is influenced by oxygen vacancies, nonstoichiometry could also participate to the structural stabilization of real nanoparticles. As stated above, the comparison with the experimental PDF gives (somewhat surprisingly) a good agreement for a water covering of 20 molecules. This fact strongly suggests that the model correctly reproduces general properties of the clusters, and these general properties determine in large measure the PDF. The results are therefore a nontrivial confirmation of the presence of a stabilization mechanism in the studied (real) sample.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +33 0587502376. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The ab initio computations were made using CRESCO HPC infrastructure of ENEA. Thanks to M. Celino, S. Giusepponi, and T. Crescenzi (ENEA) for support and advice. Thanks to University of Limoges and its international office for providing an invited position for one of the authors, with financial support.

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CONCLUSIONS The ab initio study of a ZrO2 nanocluster of a diameter around 1.25 nm was performed, focusing on the effects of surface impurities. Car−Parrinello dynamics was used as a relaxation tool, combined with standard DFT-based structural optimization methods. The effect of impurities was modeled by placing chemisorbed (i.e., dissociated) water molecules on the nanocluster surface. Results clearly show the stabilizing effect of the impurities on the cluster structure: while the naked cluster has local energy minima with a high degree of structural disorder, the clusters with surface impurities show a more ordered, crystal-like structures. The ordering increase with the amount of surface water, and the crystal structure is almost perfectly preserved for a total covering. The analysis of the energy of the clusters show that the formation of Zr−O bonds on the surface is energetically advantageous, and this effect prevails on the hindering of structure relaxation; this fact shows that clusters will tend to bind impurities, when possible. The comparison of the PDFs computed from the clusters with the experimental PDF obtained on a sample of nanoparticles of comparable size shows a good agreement (for both peaks heights and peaks positions) only when impurities are present, with the best results for a covering around 80%. These results indicate that a structural stabilization effect due to perturbations of the nanoparticles surface, as those induced by water molecules impurities, is likely to occur in real ZrO2 systems, otherwise nanoparticles would exhibit highly disordered, amorphous-like structures. Such a situation seems typical of ZrO2 as preliminary calculations made on other metal oxides systems, such as TiO2 and CeO2, show that pure clusters keep a crystal-like structure. From the viewpoint of modeling zirconia nanoparticles, this emphasizes the fact that cluster models consistent with experiment cannot be generated from approaches based on energy minimization of pure ZrO2 systems. A stabilizing H


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