A Reduction in Particle Size Generally Causes Body-Centered-Cubic

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A Reduction in Particle Size Generally Causes Body-CenteredCubic Metals to Expand but Face-Centered-Cubic Metals to Contract Dhani Nafday, Subhrangsu Sarkar, Pushan Ayyub, and Tanusri Saha-Dasgupta ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b03360 • Publication Date (Web): 06 Jun 2018 Downloaded from http://pubs.acs.org on June 7, 2018

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A Reduction in Particle Size Generally Causes Body-Centered-Cubic Metals to Expand but FaceCentered-Cubic Metals to Contract

Dhani Nafday,1‡ , Subhrangsu Sarkar,2‡§ Pushan Ayyub,2* Tanusri Saha-Dasgupta1†* 1

Department of Condensed Matter Physics and Materials Science, S. N. Bose National Centre for

Basic Sciences, Kolkata 700106, India. 2

Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental

Research, Mumbai 400005, India.

KEYWORDS: Nanoparticle, crystal structure, density functional theory, surface passivation, lattice expansion, lattice contraction.

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ABSTRACT. From a careful analysis of existing data as well as new measurements, we show that the size-dependence of the lattice parameters in metal nanoparticles with face-centered cubic (fcc) and body-centered cubic (bcc) symmetries display opposite trends: nanoparticles with fcc structure generally contract with decreasing particle size, while those with bcc structure expand. We present a microscopic explanation for this apparently puzzling behavior based on first-principles simulations. Our results, obtained from density functional theory calculations, indicate that the nanoparticles are capped by a surface monolayer of oxygen atoms, which is routinely detected by surface-sensitive techniques. The bcc- and fcc-based nanoparticles respond in contrasting fashion to the presence of the oxygen capping layer, and this dictates whether the corresponding lattice parameter would increase or decrease with size reduction. The metal-oxygen bonds at the surface, being shorter and stronger than typical metal-metal bonds, pull the surface metal atoms outward. This outward movement of surface atoms influences the core regions to a larger extent in the relatively open bcc geometry, producing a rather large overall expansion of the cluster, compared to the bulk. In case of fcc clusters, on the other hand, the outward movement of surface metal atoms does not percolate too far inside, resulting in either a smaller net expansion or contraction of the cluster depending on the extent of surface oxygen coverage. Our study therefore provides a convincing physico-chemical basis for the correlation between the underlying geometry and the nature of change of the lattice parameters under size reduction.


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A reduction in the particle size in most crystalline solids is known to cause significant changes in the electronic, optical, magnetic and several other physico-chemical properties due to quantum confinement1 as well as surface enhancement. While there exists a reasonable level of microscopic understanding of these aspects, the effect of size reduction on the local atomic structure and coordination – probably no less fundamental than the above – is understood to a much lesser extent. It has been known for some time that a decrease in the size alters the interatomic spacing (lattice parameters) and – in some cases – the local crystallographic symmetry.2 An early explanation for the size-induced lattice expansion in oxide nanoparticles was based on the dipole-dipole repulsion between the dangling bonds on the surface.3 Several observations on nanoparticles of metal oxides4,5 as well as semiconducting chalcogenides6,7,8 also indicate that size reduction tends to make the system more symmetric. This has been argued to be related to size-dependent changes in the ionic/covalent character of the local chemical bonding.9 What happens, then, in purely metallic nanoparticles in which the bonds do not usually have a marked ionic/covalent character? In the absence of strongly directional bonding, we may naively expect all metals to show an isotropic lattice contraction with decreasing particle size, assuming the nanoparticle to be represented by a liquid droplet model in which size-dependent, surfacetension-like forces are the most dominant.10 As a matter of fact, a large class of metallic nanoparticles do show a contraction in the lattice parameters as compared to the bulk value. These include Ag,11 Al,12 Au,13,14 Cu,15,16 Ni,16 Pd,17 Pt,15 Bi,18 Sn,18 and several others. In all these cases, the lattice contraction is more or less isotropic. An interesting exception is Ag, in which case a hexagonal polytypic phase is found to be kinetically stabilized at small particle sizes and under special conditions.19,20,21 We point out that among the metal nanoparticles listed above that exhibit a lattice contraction, most (Ag, Al, Au, Cu, Ni, Pd and Pt) have a face centered 3 ACS Paragon Plus Environment

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cubic (fcc) crystal structure, while Sn is tetragonal and Bi, monoclinic. The size dependence of the lattice parameter in the fcc metals can be fitted to a Laplace-Young type equation,22 thus appearing to validate the rather simplistic liquid droplet model. However, a few metals are known to exhibit a systematic lattice expansion in the nanoparticle form. These include: Cr,23 Fe,24 Nb,25 V26 and Ta,27 and – interestingly – each one happens to have a body centered cubic (bcc) structure. In order to investigate whether such a correlation is genuine or coincidental, we measured or verified the data for four of the bcc metals (Nb, Ta, V and Mo), synthesized and analysed by the same techniques. These data continue to confirm the general trend that fcc metals contract with decreasing particle size, while bcc metals expand. Up-to-date crystal structure data for the bulk metals were obtained from the online resource: ‘WebElements’.28 What is the physical basis for this striking empirical correlation? We note that even though lattice expansion has been observed earlier, this has been usually ascribed rather trivially to “negative surface stress”, though a recent review of this field29 suggests that future studies should consider the “systematic inclusion of the environment”. Clearly, a detailed microscopic study is necessary. In this paper, we discuss a microscopic model based on ab-initio density functional theory (DFT), which elucidates the importance of a capping layer on the metal nanoparticles and succeeds in leading us to a consistent understanding of this apparently puzzling observation. Finally, it is important to appreciate that size-driven changes in the lattice parameters is a non-trivial effect with significant consequences, in some cases dominating over quantum size effects and other types of surface effects. For instance, size-induced lattice expansion plays a crucial role in the: (a) persistence of superconductivity down to unexpectedly small sizes,27 (b) appearance of a magnetic moment in isolated Fe atoms embedded in a nanocrystalline metals,30 and (c) destruction of ferroelectricity in nanocrystalline oxides.4 4 ACS Paragon Plus Environment

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RESULTS AND DISCUSSION In order to compare data from samples of the same type, we prepared sputter-deposited nanocrystalline thin films (in case previous data on such samples were not available) and carried out careful measurements of the lattice parameters as a function of particle size in four of the bcc metals: Nb, Ta, V and Mo. The dc/rf magnetron sputtering technique was used to synthesize nanocrystalline, phase-pure thin films of these metals with different mean particle sizes, typically in the range of 2–50nm, with a typical spread of 15%. See the Materials and Methods section for further details. For these samples, we define the mean particle size, dXRD, as the coherently diffracting crystallographic domain size obtained from line profile analysis of the powder x-ray diffraction (XRD) scans after correcting for instrumental broadening. Figure 1 shows the size dependent changes in the lattice parameters, representing a compilation of the available experimental data on four selected fcc metals (Al, Au. Cu, Pd), as well as our results on the bcc metals (Nb, Ta, V, Mo). As mentioned earlier, several other fcc (Ag, Pt, Ni,) and bcc (Fe, Ni) metals also conform to the same trend but have not been included in the figure for the sake of clarity. We point out that the data presented or cited here refer to either free-standing nanoparticles (produced, e.g., by thermal evaporation) or loosely aggregated nanoparticles produced by soft-landing on the substrate (e.g., due to sputtering at relatively high pressure and low temperature). These systems can therefore be approximated by isolated nanoparticles rather than by a compacted “bulk microstructure” with well-defined grain boundaries. Evidently, there is a marked contrast in the size dependence of the lattice parameters in fcc and bcc metals. While the former group consistently shows a small, monotonic contraction (1–2%) in 5 ACS Paragon Plus Environment

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the lattice parameters with decreasing particle size, the latter exhibits an expansion, usually of a larger magnitude (2‒6%). Thus, our new results substantially strengthen the empirical correlation between the underlying geometry and the qualitative nature of the change (contraction or expansion) in the crystal lattice at reduced sizes. It is important to point out that our observations about the size dependence of the lattice constants (drawn from 12 cited references, in addition to our own data) involve different techniques of measuring the lattice parameters: XRD, electron diffraction and extended X-ray absorption fine structure or EXAFS. The particle size has been measured by transmission electron microscopy (TEM) imaging and XRD line shape analysis. In other words, these generalizations are robust and virtually independent of the exact methods of measurement and sample preparation. Referring to our model systems (see below), mutually consistent values of the lattice contraction in 2nm Cu nanoparticles were measured by electron diffraction15 and EXAFS.16 Similar values of lattice expansion were observed in Nb nanoparticles by electron diffraction and x-ray diffraction.25 We investigated the physical origin of this striking correlation on the basis of an ab-initio approach within the framework of DFT. We considered Cu and Nb nanoparticles as representatives of the fcc and bcc categories, respectively. The cluster diameters selected for simulation were 1.7 and 2.0 nm, which were partly dictated by the available computational resources. However, this size is quite close to the minimum, experimentally accessible size, at which the largest changes were generally observed. For example, the lattice contraction in Cu nanoparticles reduces from 2.5% at a cluster size of about 2nm down to less than 0.2% in 8nm clusters. DFT calculations were performed in the pseudo-potential plane wave basis as implemented in the VASP (Vienna Ab-initio Simulation) Package, further details of which are available in the Materials and Methods section. 6 ACS Paragon Plus Environment

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Spherical nanoclusters were cut out from a 9×9×9 supercell of the DFT-optimized bulk structure. In the case of Nb, the lattice constant and nearest neighbour Nb-Nb bond-length of the optimized bulk structure with Im-3m (bcc) symmetry were found to be 3.32Å and 2.875Å, respectively. The corresponding values for bulk Cu with Fm-3m (fcc) symmetry, were 3.64Å and 2.57Å. In both cases, the calculated lattice constants were well within 1% of their reported values.28 This construction procedure led to 321 (225) atoms in the 2.0nm (1.7 nm) Cu nanocluster and 259 (169) atoms in the 2.0nm (1.7 nm) Nb nanocluster. Note that the exposed surfaces of a small metal cluster could be quite different from the highly faceted surface of a bulk crystalline metal, which is known to influence the nature of the surface relaxation.31 There was no perceptible faceting in the spherical nanoparticles used for our simulations even after structural relaxation was allowed to occur. However, in order to investigate the possible role of the initial topology of the nanoparticles, we carried out additional simulations with the initial having cubic and icosahedral (for fcc) or dodecahedral (for bcc) shapes. These simulations reproduced the same general trends exhibited by the spherical model, though there were marginal changes in the actual values of the lattice parameters. For simplicity, we restrict further discussion to results pertaining to the spherical geometry. In addition to bare nanoclusters, we also considered those in which each metal atom in the outermost shell was connected to an oxygen atom, thereby leading to a surface-passivating oxygen monolayer. Detailed structural analyses of the DFT-optimized geometry of the nanoclusters were carried out via a shell-wise decomposition of the clusters, with each shell being defined by its fixed radial distance, d, measured from the center of mass of the cluster. Thus the outermost shell is specified by the largest value of d. Figure 2 summarizes the simulation results for the representative case of 2nm clusters, with the left and right columns referring to Cu and Nb clusters, respectively. 7 ACS Paragon Plus Environment

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Figures 2(a-d) show the variation of the average coordination number, CN (vertical bars) and metal-metal bond-length, bavg (red circles connected by line segments), averaged over the atoms belonging to a given shell, plotted as a function of the shell number, identified by d. Figures 2(ab) correspond to unpassivated, bare clusters, while Figures 2(c-d) represent surface-passivated clusters with the outermost metal atoms being bonded to an oxygen atom. We find that the coordination number of atoms in the inner core region retains the bulk value (12 for fcc and 8 for bcc), but decreases progressively on moving closer to the surface. The CN for the atoms in the outermost layer is found to be just half that of the bulk. The average metal-metal bond-length over the entire cluster, , is obtained by averaging bavg over all the shells except the last one, which has an abnormally low CN. In the bare clusters of both Cu and Nb, we find that the metal-metal bond lengths in the outer shells are progressively lower than the corresponding bulk bond length. This reflects the effect of surface tension that leads to an overall contraction in the average metal-metal bond length, . Compared to the bulk bond-lengths of 2.574Å for Cu and 2.875Å for Nb (shown as a dashed horizontal line in each figure), the simulated nanoclusters exhibit an overall contraction of 0.77% in the case of Cu and 0.56% in Nb. The insert at the top left of each figure shows the corresponding values of and (b), where (b) denotes the net change in the globally averaged bond length. The corresponding changes in the lattice parameters are −1.09% and −0.65%, for the Cu and Nb nanoclusters, respectively. Since these predictions do not explain the observed trend, even qualitatively, we may conclude that the bare cluster model does not completely capture the real situation. In practice, unless special precautions are adopted, many types of metal nanoparticles acquire an oxygen capping layer on being exposed to the atmosphere. The presence of oxygen in the inter-granular regions in nanocrystalline Nb has, in 8 ACS Paragon Plus Environment

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fact, been experimentally confirmed by electron energy loss spectroscopy.32 Similarly, small Mo clusters with less than 200 atoms were found to be highly reactive and rapidly oxidize even in high vacuum.33 Thus, a realistic microscopic model should account for the effect of surface oxidation, which is considered next. As shown in Fig. 2(c,d), capping by a monolayer of oxygen causes significant changes: the metal-metal bond lengths of atoms close to the surface increase by a large extent in the case of Nb, and by a moderate extent in Cu, as compared to the corresponding bare clusters. This is ascribed to the surface atoms getting pulled outwards due to the formation of metal-oxygen bonds, which are much shorter and stronger than the metal-metal bonds within the cluster. This model is shown schematically in Figs. 2(e,f). The Nb-O bond-lengths in the optimized structure were in the 1.73-1.83Å range, about 40% smaller than the typical Nb-Nb bond-lengths in the core. Similarly, the Cu-O bond-lengths were found to be within 1.71-1.74Å, about 30% smaller than the typical Cu-Cu bond-length. In case of the Nb cluster with the relatively open bcc structure, the inter-shell spacings are large enough for the surface effect to percolate inside the cluster (as shown in Fig. 2f). This results in a net increase in (b) (as compared to the bulk) by +2.16% in the case of Nb clusters, with the corresponding expansion in the lattice parameter being 2.49%. Note that the main difference between the fcc and bcc structures is in the degree of atomic packing: while the fcc structure (also known as cubic close packed) is close-packed with an optimal packing fraction of 0.74, the more open bcc structure has a packing fraction of 0.68. So, we may expect clusters with the fcc structure to have closely placed shells, leaving very little space for the effect of outward displacement of the surface atoms to propagate to the core. The value of (b) for the fully capped Cu cluster thus shows only a small increase of 0.15%, causing an expansion of 0.21% in the lattice parameter. 9 ACS Paragon Plus Environment

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Referring to a table34 of standard reduction potentials (E0), we find that E0(Nb3++3e→Nb) = −1.1V, and E0(Cu2++2e→Cu) = +0.34V, which implies that Nb has a substantially higher affinity towards oxygen than Cu, a fact that needs to be considered in our simulation model. A simple first approach would be to assume that the oxygen coverage in the case of a Cu cluster is only partial. We thus carried out an additional set of calculation under the assumption that only 50% of the Cu atoms on the surface of the Cu cluster are bonded to oxygen atoms. A structural analysis similar to that carried out earlier, yielded a net change of −0.62% in the Cu-Cu bondlength, which corresponds to a lattice parameter contraction of 0.88% in the partially passivated Cu cluster. This confirms the trend that the lattice contraction in Cu reduces slightly with increasing oxygen coverage. Comparing with the experimental data (Fig.1), we may conclude that the surface of the Cu nanocluster is essentially devoid of oxygen, which would lead to a calculated lattice contraction of 1.09% (Table 1). The numerical results of the computer simulations on the 1.7 nm and 2nm spherical clusters, presented in Table I, thus correctly reproduce the qualitative trend observed experimentally. Thus, a typical fcc nanocluster (Cu) shows a small lattice contraction, while a typical bcc nanocluster (Nb) shows a relatively larger lattice expansion with respect to the bulk lattice. More importantly – by underlining the influence of the oxygen capping layer – the simulation provides a clear microscopic understanding of the nature of size dependence of the lattice parameter in metal nanoparticles. As expected, the size effect on the lattice parameter is mediated by surface stress, but our non-trivial prediction is that the effect of an oxygen capping layer produces different types of stresses in bcc and fcc structures. The simulation also correctly reproduces the experimentally observed size dependence: comparing the results for 1.7 nm and 2 nm nanoclusters, it is clear that both expansion and contraction increase with decreasing size. 10 ACS Paragon Plus Environment

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However, the magnitude of contraction in fcc nanoparticles as well as expansion in bcc nanoparticles are both underestimated by our simulation, when compared to the experimental data. For example, the simulation of 2nm oxygen-passivated Nb nanocluster predicts a 2.5% expansion in the lattice parameter, while experiments report a 6% expansion in 4nm nanoparticles.

Table 1. Calculated values of the percentage change in the cubic lattice parameters of Nb and Cu for both cluster and slab geometries. The last column displays the average values of the deviation along with the standard deviation. We list the deviations for both the bare and oxygen-passivated nanoclusters with respect to their bulk values. For the slab geometry, the last column reflects the additional percentage change due to the interstitial oxygen over and above the effect of surface oxygen passivation.

Geometry

Cluster

Slab

System

Dimension

Surface state

Nb

2.0 nm dia

Nb

1.7 nm dia

Cu

2.0 nm dia

Cu

1.7 nm dia

Nb Nb Nb Cu Cu Cu

7-layer 11-layer 13-layer 9-layer 11-layer 15-layer

Bare Passivated Bare Passivated Bare Passivated Bare Passivated Passivated + Interstitial Passivated + Interstitial Passivated + Interstitial Passivated + Interstitial Passivated + Interstitial Passivated + Interstitial


Change (%) in lattice constant −0.65 ± 0.04 +2.49 ± 0.07 −1.46 ± 0.05 +2.77 ± 0.02 −1.09 ± 0.03 +0.21 ± 0.04 −2.25 ± 0.03 −0.74 ± 0.01 +2.92 ± 0.09 +1.36 ± 0.04 +1.19 ± 0.05 + 0.05 ± 0.004 + 0.06 ± 0.000 + 0.01 ± 0.005

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In an attempt to account for the larger changes in the observed lattice constants, we considered the additional effect of interstitial oxygen atoms. Given the high affinity of many metal nanoparticles for oxygen, the presence of oxygen atoms in interstitial positions near the surface is not improbable. As it is computationally challenging to explore this scenario within the cluster model, we considered the slab geometry, which makes it easier to capture the essential features. We carried out simulations with Cu and Nb slabs with three different values of layer thickness, in order to investigate the effect of size reduction in this model. As shown in Figure 3, we placed interstitial oxygen atoms just below the surface of the Cu and Nb slabs, in addition to the passivating oxygen layer at the surface. The probability of finding oxygen atoms at these interstitial sites is the largest, given the finite diffusion length of oxygen atoms in metals. Results obtained for the slab geometry are summarized in the lower half of Table 1. Note that the values listed in the last column corresponding to the slab calculations denote the additional percentage change due to the presence of interstitial oxygen (as compared to that in capped slab geometry without interstitial oxygen). The net expansion or contraction needs to take account of the contribution of the surface passivation, calculated earlier for the spherical clusters. However, the contributions due to surface oxygen capping and the presence of interstitial oxygen cannot be added in a simple-minded way, as they have been obtained from different types of models. Thus, the results of the slab-geometry calculations need to be interpreted in a qualitative sense, as shown below. Analysis of various metal-metal bond-lengths in the optimized slab geometry with surface passivation, with and without the interstitial oxygen, clearly indicates that the presence of interstitial oxygen atoms causes substantial expansion of metal-metal bond-lengths at the surface of both Nb and Cu slabs. Significantly, however, this expansion is found to propagate with ease 12 ACS Paragon Plus Environment

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to the sub-surface layers in the relatively open bcc structure of Nb, but not in the close-packed fcc structure of Cu. The effect of the surface oxygen layer on bcc and fcc structures in the passivated spherical nanoclusters was also found to be very similar. The presence of interstitial oxygen in the 11 layer geometry is found to produce a 1.18% expansion in the average Nb-Nb bond-length in addition to that produced by only the surface oxygen layers. This translates to +1.36% change in the lattice parameter. In sharp contrast, the interstitial oxygen contributes an additional expansion of only 0.06% in the lattice parameter for the 11 layer slab of Cu. On comparing the results for the 7-, 11- and 13-layer slabs of bcc Nb, we further find that the magnitude of the expansion due to interstitial oxygen shows a significant size dependence. In Cu, the change is anyway marginal and there is no clear size effect. While the above exercise successfully uncovers the microscopic origin of the observed trends in the variation of the lattice parameters in fcc and bcc nanoparticles, we should not expect complete quantitative agreement with data, owing to uncertainties at several levels. Experimental data were obtained from several sources, in which the ‘particle size’ may have been extracted from different types of measurements (and may have even been defined differently), and from various kinds of samples with varying size distributions. The theoretical model, on the other hand, considers ideal, spherical nanoparticles capped by only one species of chemisorbed atoms. Further, the geometry-optimized structures were obtained with specific choice of exchangecorrelation functional of DFT, namely GGA. Repeating the calculations with LDA led to the same general trends, but gave different values of expansion or contraction, indicating the influence of the choice of exchange-correlation functional. GGA was preferred by us as it showed better agreement with the lattice constant data for the bulk metals. We have also neglected possible contributions from correlation effects beyond GGA. 13 ACS Paragon Plus Environment

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CONCLUSIONS X-ray and electron diffraction analyses of sub-10nm metallic nanoparticles reveal a systematic trend in their lattice parameter variation: nanoparticles with fcc structure contract with decreasing size, while those with bcc structure expand. We investigate the microscopic origin of this rather striking correlation on the basis of simulations using state-of-art ab initio density functional theory. Our simulations on representative bcc (Nb) and fcc (Cu) nanoclusters indicate that the lattice parameters of bare clusters of both Nb and Cu exhibit a small contraction, as might be expected from a simple, liquid droplet model. The lattice expansion in bcc nanoclusters arises mainly from the presence of oxygen atoms as a surface capping layer and possibly also in sub-surface interstitial sites. Analyses of the simulated cluster geometries with an oxygen capping layer show that the outermost metal atoms are pulled outwards due to the formation of the relatively short bonds with the surface oxygen atoms. It is significant that the effect of the outward displacement of the surface metal atoms percolates down to the core regions in the relatively open bcc geometry, but remains confined to the sub-surface layers in the close-packed fcc geometry. As a result of this surface relaxation process, nanoparticles with the bcc structure exhibit a relatively large expansion, while fcc nanoparticles show a smaller expansion or contraction, depending on the degree of oxygen coverage. Thus, while nanoparticles of the nonreactive fcc metals (Ag, Au, Pd, Pt) always contract, there are occasional reports of lattice expansion in fcc metals that may pick up a surface layer of oxygen atoms under favourable conditions, such as Cu35 or relatively reactive ones such as Ni36, a possibility that is already envisaged by our analysis. Conversely, our explanation also implies that bcc nanoparticles grown and studied in an ultraclean environment might in fact exhibit a small contraction with respect to 14 ACS Paragon Plus Environment

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the bulk. Though avoiding even a surface monolayer of oxygen on metal surfaces is notoriously difficult, a practical route would be to cap the nanoparticles in situ with a second, relatively unreactive, metal. A recent paper37 reports data on co-sputtered Nb-Cu nanocomposites in which the Nb and Cu nanoparticles are intimately mixed during growth, such that each type of nanoparticle is essentially surrounded by the other, producing interfaces that are – at least to a large extent – oxygen-free. The authors observe a monotonic contraction in the lattice constant with decreasing size of Nb nanoparticles, to about −1% at 8nm. This work appears to directly confirm our model and clearly underlines the role of the nanoparticle interface on the lattice expansion/contraction in nanoparticles. Finally, it is important to point out that while our calculations were confined to two particular elements (bcc-Nb and fcc-Cu), none of the above conclusions are based on element-specific arguments, and refer generically to the two crystallographic sub-classes (fcc and bcc). In fact, since our arguments are based essentially on the difference in the packing fractions, it is very likely that metals belonging to the other closed-packed category (namely, hcp) also behave like fcc metals. However, not enough data is available on the size dependence in hcp nanoparticles to draw a definite conclusion.

MATERIALS AND METHODS

Sample Preparation and Characterization. Dc and rf sputtering at relatively high operating pressure and low temperature has been established as a convenient technique for the deposition of nanocrystalline thin films of a wide variety of metals, alloys and simple compounds on a range of substrates.38 High ambient pressure and low substrate temperature tend to promote ‘soft15 ACS Paragon Plus Environment

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landing’ of pre-formed nanoparticles with loosely-aggregated particles rather than a compacted microstructure. Phase-pure thin films of Ta, V and Mo nanoparticles were deposited, respectively, on SiO2/Si , R-plane sapphire, and Si substrates using dc/rf sputtering from 99.9--99.99% pure targets. The mean particle size could be varied by suitably adjusting the sputtering gas pressure and substrate temperature. Powder x-ray diffraction (XRD) data were obtained using a Philips PANalytical X'Pert Pro system. The line profile module X'Pert HighScore Plus 3.0e was employed to analyze the crystallographic phase and obtain the instrument-corrected coherently diffracting domain size (dXRD) of the as-deposited nanocrystalline thin films. The size obtained by this method matches (within experimental uncertainty) the mean size calculated from TEM image analysis of a statistically significant number of particles. This is shown, for example, in Fig. 1 of Ref. 17. The effect of lattice strain was negligible in our samples, any error due to such factors are estimated to be smaller than the size of the data points in Fig.1. The correct positioning of the sample plane was ensured by the usual techniques and confirmed by using the substrate material (Si) as an internal calibration standard. Density Functional Theory (DFT) Calculations. All the calculations were performed using the plane wave based pseudo-potential framework of DFT within the implementation of Vienna Ab initio Simulation Package (VASP).39 In particular, we used the projector augmented wave (PAW) pseudo-potentials40 and generalized gradient approximation (GGA) for exchangecorrelation functional within the formulation of Perdew-Bruke-Ernzerhof.41 The valence configurations assumed for generating the pseudopotentials were 3d104s1 (Cu), 4p65s14d4 (Nb), and 2s22p2 (O) The wave functions were expanded in the plane wave basis set with the kinetic energy cutoff of 500 eV, which was found to give sufficient convergence of total energy. The 16 ACS Paragon Plus Environment

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nanocluster was constructed by making an atom-centered, 2nm diameter spherical cut on a 999 supercell of the DFT-optimized bulk structure. The nanoparticles were then placed in a box of size 35Å35Å35Å. A vacuum of about 15Å was used to separate the nanocluster from it's periodic image. Symmetry unrestricted geometry optimization was performed for both bare and oxygen-passivated clusters using the conjugate gradient and the quasi-Newtonian methods until all the force components became less than a threshold value of 0.01 eVÅ−1. We did both spin-polarized and non-spin-polarized calculations at the  point of the Brillouin zone. For the semipassivated Cu cluster, 50% of the metal atoms in the outmost shell were connected to oxygen atoms, preference being given to surface atoms having longer bond length with the subsurface atoms.

Corresponding Authors * E-MAIL: Pushan Ayyub * E-MAIL: tanusri saha-dasgupta Present Addresses § Department of Physics, Indian Institute of Science, Bangalore 560012, India. † Center for Mathematical, Computational and Data Science, Indian Association for the Cultivation of Science, Kolkata 700032, India. Author Contributions ‡ Dhani Nafday and Subhrangsu Sarkar have contributed equally to the work.


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Acknowledgments. P.A. and S.S. acknowledge the Department of Atomic Energy (Govt. of India) for their research funding. D.N. and T.S-D would like to thank Thematic Unit of Excellence on Computational Materials Science funded by Nano-mission of Department of Science and Technology (Govt. of India) Project No. SR/NM/NS-29/2011 for the computational facility. D.N. also acknowledges a fellowship funded by Ministry of Earth Science (Govt. of India) Grant MoES/16/25/10-RDEAS.


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REFERENCES

1. Varnavski, O.; Ramakrishna, G.; Kim, J.; Lee, D.; Goodson, T. Critical Size for the Observation of Quantum Confinement in Optically Excited Gold Clusters. J. Am. Chem. Soc. 2010, 132, 16‒ 17. 2. Ayyub, P.; Palkar, V. R.; Chattopadhyay, S.; Multani, M. S. Effect of Crystal Size Reduction on Lattice Symmetry and Cooperative Properties. Phys. Rev. B 1995, 51, 6135‒6138. 3. Ayyub, P.; Multani, M. S.; Barma, M.; Palkar V. R.; Vijayaraghavan, R. Size-Induced Structural Phase Transitions and Hyperfine Properties of Microcrystalline Fe2O3. J. Phys. C: Solid State Phys. 1988, 21, 2229‒2245. 4. Chattopadhyay, S.; Ayyub, P.; Palkar V. R. Multani, M. S. Size-Induced Diffuse Phase Transition in the Nanocrystalline Ferroelectric PbTiO3. Phys. Rev. B 1995, 52, 13177‒13183. 5. Das, H.; Sangiovanni, G.; Valli, A.; Held, K.; Saha-Dasgupta, T. Size Control of Charge-Orbital Order in Half-Doped Manganite La0.5Ca0.5MnO3. Phys. Rev. Lett. 2011, 107, 197202. 6. Bandaranayake, R. J.; Wen, G. W.; Lin, J. Y.; Jiang, H. X.; Sorensen, C. M. Structural Phase Behavior in II–VI Semiconductor Nanoparticles. Appl. Phys. Lett. 1995, 67, 831‒833. 7. Banerjee, R.; Jayakrishnan R.; Ayyub, P. Effect of the Size-Induced Structural Transformation on the Band Gap in Cds Nanoparticles. J. Phys.: Condens. Matter 2000, 12, 10647‒10654. 8. Datta, S.; Kabir, M.; Saha-Dasgupta T.; Sarma, D. D. First-Principles Study of Structural Stability and Electronic Structure of CdS Nanoclusters. J. Phys. Chem. C 2008, 112, 8206‒8214.


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9. Palkar, V. R.; Ayyub, P.; Chattopadhyay S.; Multani, M. S. Size-Induced Structural Transitions in the Cu-O and Ce-O Systems. Phys. Rev. B 1996, 53, 2167‒2170. 10. Alymov, M. I.; Shorshorov, M. K. Surface Tension of Ultrafine Particles. Nanostruct. Mater. 1999, 12, 365-368 11. Wasserman, H. J.; Vermaak, J. S.; On the Determination of a Lattice Contraction in Very Small Silver Particles. Surf. Sci. 1970, 22, 164‒172. 12. Woltersdorf, J.; Nepijko, A. S.; Pippel, E. Dependence of Lattice Parameters of Small Particles on the Size of the Nuclei. Surf. Sci. 1981, 106, 64‒69. 13. Mays, C. W.; Vermaak, J. S.; Kuhlmann-Wilsdorf, D. On Surface Stress and Surface Tension: II. Determination of the Surface Stress of Gold. Surf. Sci. 1968, 12, 134‒140. 14. Müller, H.; Opitz, Ch.; Strickert, K.; Skala, L. Assessment of the Properties of Highly Dispersed Materials - Practical Use of the Analytical Cluster Model (ACM). Z. Phys. Chemie. Liepzig 1987, 268, 625‒646. 15. Wasserman, H. J.; Vermaak, J. S.; On the Determination of the Surface Stress of Copper and Platinum. Surf. Sci. 1972, 32, 168‒174. 16. Apai, G.; Hamilton, J. F.; Stohr, J.; Thompson, A. Extended X-Ray Absorption Fine Structure of Small Cu and Ni Clusters: Binding-Energy and Bond-Length Changes with Cluster Size. Phys. Rev. Lett. 1979, 43, 165‒169. 17. Lamber, R.; Wetjen, S.; Jaeger, N. Size Dependence of the Lattice Parameter of Small Palladium Particles. Phys. Rev. B 1995, 51, 10968‒10971.


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18. Yu, X. F.; Liu, X.; Zhang, K.; Hu, Z. Q. The Lattice Contraction of Nanometre-Sized Sn and Bi Particles Produced by an Electrohydrodynamic Technique. J. Phys.: Condens. Matter 1999, 11, 937‒944. 19. Chakraborty, I.; Carvalho, D.; Shirodkar, S.; Lahiri, S.; Bhattacharyya, S.; Banerjee, R.; Waghmare U.; Ayyub, P. Novel Hexagonal Polytypes of Silver: Growth, Characterization and First-Principles Calculations. J. Phys.: Condens. Matter 2011, 23, 325401. 20. Chakraborty, I.; Shirodkar, S. N.; Gohil, S.; Waghmare U. V.; Ayyub, P. A Stable, Quasi-2D Modification of Silver: Optical, Electronic, Vibrational and Mechanical Properties, and First Principles Calculations. J. Phys.: Condens. Matter 2014, 26, 025402. 21. Chakraborty, I.; Shirodkar, S. N.; Gohil, S.; Waghmare U. V.; Ayyub, P. The Nature of the Structural Phase Transition From the Hexagonal (4H) Phase to the Cubic (3C) Phase of Silver. J. Phys.: Condens. Matter 2014, 26, 115405. 22. Jiang, Q.; Liang, L. H.; Zhao, D. S. Lattice Contraction and Surface Stress of fcc Nanocrystals. J. Phys. Chem. B 2001, 105, 6275-6277. 23. Eastman, J. A.; Fitzsimmons, M. R. On the Two‐State Microstructure of Nanocrystalline Chromium. J. Appl. Phys. 1995, 77, 522. 24. Zhao, Y. H.; Sheng, H. W.; Lu, K. Microstructure Evolution and Thermal Properties in Nanocrystalline Fe During Mechanical Attrition, Acta Mater. 2001, 49, 365–375. 25. Bose, S.; Ayyub P.; Fraser, H. L. Lattice Expansion in Nanocrystalline Niobium Thin Films. Appl. Phys. Lett. 2003, 82, 4250‒4252. 26. Yang, C.C.; Huang, W.L.; Lin, Y.H.; Weng, C.Y.; Mo, Z.Y.; Chen, Y.Y. Quantum Size Effects on Vanadium Nanoparticles. IEEE Trans. Magnetics 2011. 47, 3535-3537. 21 ACS Paragon Plus Environment

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27. Sarkar, S.; Kulkarni, N.; Kulkarni, R.; Thekkepat, K.; Waghmare, U. V.; Ayyub, P. Is There a Lower Size Limit for Superconductivity? Nano Letters 2017, 17, 7027–7032. 28. https://www.webelements.com/ 29. Diehm, P.M.; Agoston, P.; Albe, K. Size-Dependent Lattice Expansion in Nanoparticles: Reality or Anomaly? ChemPhysChem 2012, 13, 2443–2454. 30. Mohanta, S. K.; Mishra, S. N.; Sarkar, S.; Ayyub, P. Size Induced Moment Formation on Isolated Fe Atoms Embedded in a Nanocrystalline Ta Matrix: Experiment and Theory. Phys. Rev. B 2014, 89, 224410. 31. Wan, J.; Fan, Y L; Gong, D. W.; Shen, S. G.; and Fan, X. Q. Surface Relaxation and Stress of fcc Metals: Cu, Ag, Au, Ni, Pd, Pt, Al and Pb. Modelling Simul. Mater. Sci. Eng. 1999, 7, 189. 32. Bose, S.; Banerjee, R.; Genc, A.; Raychaudhuri, P.; Fraser, H. L.; Ayyub, P. Size Induced Metal Insulator Transition in Nanostructured Niobium Thin Films: Intragranular and Intergranular Contributions. J. Phys.: Condensed Matter 2006, 18, 4553-4566. 33. Park, E.; Link, M.; Hierling, D.; Dollinger, A.; Gantefoer, G.; Kim. Y. D. Extreme Size Dependence of the Oxidation Behaviour of Mo Clusters. Personal communication. 34. Milazzo, G.; Caroli, S.; Sharma, V. K. Tables of Standard Electrode Potentials; Wiley; Chichester, 1978. 35. Champion, Y.; Bernard, F.; Millot, N.; Perriat, P. Surface Adsorption Effects on the Lattice Expansion of Copper Nanocrystals. Appl. Phys. Lett. 2005, 86. 231914. 36. Wei, Z.; Xia, T.; Ma, J.; Feng, W.; Dai, J.; Wang, Q.; Yan, P. Investigation of the Lattice Expansion for Ni Nanoparticles. Materials Characterization 2007, 58, 1019-1024. 22 ACS Paragon Plus Environment

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37. Parab, P.; Bagwe, V.; Chalke, B.; Muthurajan, H., Raychaudhuri, P.; Bose, S. Superconductivity in Immiscible Nb–Cu Nanocomposite Films. Supercond. Sci. Technol. 2017, 30, 055005. 38. Chandra, R.; Taneja, P.; John, J.; Ayyub, P.; Dey, G. K.; Kulshreshtha, S. K. Synthesis and TEM Study of Nanoparticles and Nanocrystalline Thin Films of Silver by High Pressure Sputtering. Nanostruct. Mater. 1999, 11, 1171. 39. Kresse G.; Furthmȕller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169‒11186. 40. Blӧchl, P. E. Projector Augmented-Wave Method, Phys. Rev. B 1994, 50, 17953‒17979. 41. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 1996, 77, 3865‒3868.


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FIGURE CAPTIONS Figure 1. Selected compilation of experimental data on fractional change in the lattice parameters of nanoparticles as a function of the mean particle size. Changes are shown as a percentage shift from the corresponding bulk values. Only face centred cubic (fcc) and bodycentred cubic metals (bcc) were considered, and the data were obtained from the following references: Al,12 Au,13,14 Cu,15,16 Pd,17 Nb,25 and Ta.27 Figure 2. Summary of the simulation results on spherical, 2-nm diameter nanoparticles of Cu (left column) and Nb (right column). The data for the bare clusters are shown in (a, b) and the data for the passivated clusters are shown in (c, d). The coordination numbers, CN (y-axis on left) are shown as vertical columns. The metal-metal bond-length, bavg (y-axis on right), averaged over all atoms belonging to a particular shell, are shown as connected data points plotted as a function of shell number (designated by the radial distance of the shell from center of mass, d). The metal-metal bond-lengths for the corresponding bulk metal are shown as dashed horizontal lines. The calculated metal-metal bond length averaged over the entire nanoparticle, , and its deviation from the bulk value, (b), are shown at the top of each figure. Finally, (e,f) are schematic depictions of the relative displacements of atoms, mainly in the outer shells of the clusters under the influence of the capping layer of oxygen atoms. Figure 3. Schematic depiction of the slab geometry considered for Cu and Nb, bounded by two surface layers on the left and right, but extended in the other direction (along the dashed lines). The metal atoms at the surface facing vacuum are passivated by oxygen atoms, with additional oxygen atom placed at interstitial sites between the outermost metal layer and the one next to it.


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The oxygen atoms at the surface, O(surf), and those at interstitial positions, O(int), are shown in different shades of green.


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FIGURES

Figure 1.


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Figure 2.


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Figure 3.


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A Reduction in Particle Size Generally Causes Body-Centered-Cubic

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