Letter pubs.acs.org/NanoLett
Near-Surface Strain in Icosahedra of Binary Metallic Alloys: Segregational versus Intrinsic Effects Darius Pohl,*,†,‡ Ulrich Wiesenhütter,§,‡ Elias Mohn,† Ludwig Schultz,†,‡ and Bernd Rellinghaus*,† †
Institute for Metallic Materials, Leibniz Institute for Solid State and Materials Research (IFW) Dresden, P.O. Box 270116, D-01171 Dresden, Germany ‡ Institute for Solid State Physics, Technische Universität (TU) Dresden, Dresden, Germany § Institute of Ion Beam Physics and Materials Research, Helmholtz Zentrum Dresden Rossendorf (HZDR), P.O. Box 510119, D-01314 Dresden, Germany S Supporting Information *
ABSTRACT: A systematic structural analysis of FePt, CuAu, and Au icosahedral nanoparticles is presented. The uncovered particles are prepared by inert gas condensation and thermally equilibrated through in-flight optical annealing. Aberration-corrected high-resolution transmission electron microscopy reveals that the crystal lattice is significantly expanded near the particle surface. These experimental findings are corroborated by molecular statics simulations that show that this near-surface strain originates from both intrinsic strain due to the icosahedral structure and a partial segregation of the larger of the two alloy constituents to the particle surface. KEYWORDS: Nanoparticles, aberration-corrected HRTEM, FePt, segregation, icosahedra
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gained from the low-energy {111} facets that exclusively terminate these MTPs. In addition to such structural modification, another peculiarity may arise in small particles of binary (or more complex) alloys. As (i) the surface free energy is typically lower for one alloy constituent as compared to the other one(s) and (ii) because the gain in enthalpy of mixing is limited for surface atoms due to their reduced number of binding partners (i.e. their reduced coordination number), the high fraction of surfaces in nanoparticles may effectively promote segregation in these tiny alloys. Whereas the formation of MTPs is frequently observed,3,5,7−9 particle size-induced segregation phenomena are scarcely reported. This is largely owed to the general difficulty to spatially resolve variations of the chemical composition at the required (sub)nanometer length scale. In general, modern highresolution scanning transmission electron microscopy (HRSTEM) in combination with energy dispersive X-ray spectroscopy (EDXS) or electron energy loss spectroscopy (EELS) provide appropriate tools to investigate such segregation effects. However, high current densities in the imaging electron beams are required to generate spectroscopic signals with sufficiently high signal-to-noise ratios. Unfortunately, such intense electron beams usually modify the particles of interest, and protective embedment measures would immediately alter the surface properties of the particles. Aberration-corrected microscopes, however, provide the allowance for delocalization-free imaging
ithin the last decades, the research on nanoparticles has attracted steadily increasing attention due to both the desire to understand the novel and partially unique physical properties of these materials and the request to utilize their multilateral size−structure−property relationships to tailor these properties to specific needs. Today, nanoparticles are of significant importance in a variety of applications that reach from magnetic data storage and nanoelectronics over catalysis to medical diagnosis and therapy. The particles’ properties that are modified with respect to those of their macroscopic materials counterparts are primarily owed to two peculiarities. On the one hand, their nanoscopic size mainly causes an increase of the electronic level spacings and hereby largely modified electronic or optical properties specifically of semiconductors. On the other hand, what renders this material class special is the fact that a large fraction of the material is affected by its surfaces. Because of their reduced coordination, atoms residing at surface positions need to locally redistribute their electronic charges that give rise to surface states, modified physicochemical properties, and structural relaxations to name a few. Last but not least, the contribution of the surface free energy to the total energy increases with decreasing particle size and as a consequence, the thermodynamic equilibrium structure of a nanoparticle may substantially differ from its bulk structure and also vary with size. It is, for example, wellknown that metals with face-centered cubic (fcc) structures in their bulk form are frequently multiply twinned particles (MTPs) such as icosahedra or decahedra when they are sufficiently small.1−6 The expense in strain and twinning energy in these structures is compensated for by surface free energy © 2014 American Chemical Society
Received: November 18, 2013 Revised: February 10, 2014 Published: March 3, 2014 1776
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finally deposited onto commercially available 10 nm thin amorphous carbon films supported by copper grids. Unlike in preparation methods based on colloidal chemistry where the particles are to be terminated by organic molecules for steric separation, gas phase based preparation provide uncovered and clean particle surfaces that are mandatory in order to study surface-related phenomena. Atomic resolution structural characterization of the particles was conducted utilizing a FEI Titan3 80−300 transmission electron microscope equipped with a monochromator and an image CS corrector (CETCOR, CEOS GmbH, Heidelberg) at an acceleration voltage of 300 kV. The aberration corrector was used to set the coefficient of the spherical aberration to a minimum of CS < 1 μm. We have determined the uncertainty of the CS measurement from the standard deviation to be roughly 1 μm, which is in good agreement with other reports.19 As a consequence, CS = 0 was used for all later HRTEM contrast simulations. The focus was adjusted close to the optimimum focus of roughly −1 nm to push the point resolution up to the information limit. At these conditions, atomic columns appear with black contrast at minimum delocalization in the HRTEM images. Molecular statics (MS) simulations were conducted using the PARCAS code.20 The interatomic interaction in the binary Fe− Pt alloy was modeled by means of an analytic bond-order potential (ABOP) which was proven to successfully mimic the FePt phase diagram and the size dependence of the L10 ordering in FePt nanoparticles, respectively.21,22 All calculations were carried out for NVT ensembles. The time step was set to 0.01 fs, and a Berendsen thermostat (with time constant τ = 500 fs) was used to gently reduce the temperature of the system that was initially set during the initialization process. The simulations were run until a stable energy configuration was reached and changes in the energy could no longer be observed. In order to describe segregation phenomena, Monte Carlo (MC) simulations have been performed prior to the MSsimulations. Therefore a lattice MC simulation using the Metropolis algorithm with atom exchange and configurational energies, which were determined from the bulk phase diagram and surface segregation of thin films, have been applied.23 HRTEM contrast simulations were carried out using the MacTempas software package.24 For the simulations of the HRTEM contrast of the FePt nanoparticles (for a 300 keV electron beam), a spherical aberration coefficient of CS = 0, a focus spread of Δ = 2.7 nm and a convergence angle of α = 0.25 mrad were used as imaging parameters. Figure 1 demonstrates the large impact of the electron beam on the atomic configuration at the nanoparticle surface. The electron beam induces interparticle coalescence (sintering) already at an electron dose of 2 × 106 e−/nm2/s. The atomically resolved micrograph shows two adjacent FePt particles both of which are icosahedra with one of their two-fold symmetry axes suitably parallel to the incident electron beam. During the exposure to the imaging electron beam the particles are gently heated and as a consequence, interparticle coalescence is stimulated within the microscope. Starting with the image in Figure 1a, a series of HRTEM images taken at different times was acquired. Figure 1d−h shows enlarged details of a section of the right particle that is close to the interparticle connection as marked with a dashed yellow square in Figure 1a. In order to guide the eyes of the reader to the particle surface, the central part of the particle is covered with a green shade. The time elapsed since taking the first image (cf. Figure 1a) is denoted in
of surface and interfaces with unrivaled resolution and thus provide the opportunity to indirectly determine segregation phenomena in different crystallographic directions from precision measurements of the lattice distortions associated with them. Recently, a core−shell structure in Pt−Co and Pt−Ni catalyst nanoparticles could be observed by aberrationcorrected HR-STEM in combination with EELS analysis.10,11 Here, a Pt shell around a Ni/Co rich core was always found, which is in agreement with theoretical work.12,13 The provision of direct experimental evidence for a partial, more gradual segregation in nanoparticles (with atomic resolution) is, however, very challenging. It would require local STEM/ EELS measurements with a very fine probe. Under such conditions, the local beam damage is extreme, and beaminduced changes of the sample cannot be avoided. Furthermore, the accuracy of distance measurements with STEM is much smaller than in bright-field mode. A direct observation of the Pt segregation with local EELS is further impeded by the energetic position of the Pt M edges and the small excitation volume in nanoparticles. We have therefore chosen an indirect approach and measure the surface near lattice relaxation, which will be correlated with structural models. For FeNi nanoparticles (with close to cubic shapes), this approach was shown to successfully describe a segregation of Fe that was confirmed by additional local EELS measurements.14 In the binary system Fe−Pt, the segregation of Pt toward the particle surface was reported for a single crystalline dealloyed Pt−Fe catalyst nanoparticle,15 for a FePt catalyst particle within a carbon nanotube grown from it,16 and for a single icosahedral FePt nanoparticle.8 For the latter, a near-surface expansion of the lattice was determined from a focal series of (conventional) high-resolution transmission electron microscopy (HR-TEM) images. The investigation, however, has also revealed that the long time exposure of the particle to the electron beam led to a depletion of the surface layers thereby highlighting the necessity to keep the impact of the electron beam as low as possible in order to avoid beam induced artifacts. It remains furthermore unclear (i) to which extent the observed surfacenear lattice expansion is to be attributed to a Pt segregation or if it is rather due to the intrinsic strain in icosahedral particles,17 (ii) in how far the observed phenomenon is affected or even caused by the impact of the imaging electron beam, (iii) if the reported finding is representative for FePt icosahedra, and (iv) if the surface segregation is a peculiarity of FePt alloys or rather a more common phenomenon among nanoparticles of binary alloys. The present study aims at shedding light on these open issues thereby providing a more thorough understanding of both the surface relaxation and the phase stability of icosahedra of metallic alloys. Hereto, we report on a comprehensive investigation of the surface-near lattice structures in icosahedral particles of FePt, CuAu, and of elemental Au, respectively. Particular attention is being paid to minimizing the impact of the electron beam on the particle structure throughout the study and on the statistical relevance of the observations. FePt, CuAu, and Au nanoparticles were prepared by inert gas condensation through DC magnetron-assisted sputtering in Ar.9,18 After their nucleation and growth in an atmosphere of roughly 1.5 mbar of Ar the nanoparticles were ejected into a high vacuum deposition chamber (10−6 mbar ≤ p ≤ 10−3 mbar), optionally subjected to in-flight optical heating, and 1777
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determine these lattice spacings from HRTEM images, three independent methods are used: (i) acquisition of intensity (i.e., gray scale) line scans in the crystallographic direction of interest (e.g., along a ⟨111⟩ direction), (ii) a fit of parallel lines to the manually measured projected positions of atomic columns of a common lattice plane and the subsequent evaluation of the resulting plane spacings, and (iii) a fit of two-dimensional (2D) Gaussians to the intensity distribution of the atomic columns and a subsequent (subpixel precise) determination of the perpendicular to the two adjacent columns (see Figure 2b). Figure 2a shows a FePt icosahedron as seen along one of its two-fold symmetry axes with the four visible tetrahedra (labeled 1−4). The atomic columns are marked with white circles. Atomic columns which belong to a twinning plane are marked in red. In the blow-up in Figure 2b the method of fitting 2D Gaussians in order to determine local perpendicular spacings is sketched in detail. The lattice spacing is determined locally and is then averaged for each shell. The resulting d111 lattice spacing is shown in Figure 2c for all of the four tetrahedra together with the resulting mean value from the surface toward the core of the particle. Already this single particle measurement reveals an expansion of the lattice of roughly 5% from the core to the surface of the icosahedral particle (from 0.22 to 0.23 nm). Figure 3a summarizes the statistical analysis of the lattice spacings of 54 FePt-tetrahedra measured with the 2D Gaussian method using single shot HR-TEM images. The black squares represent the single particle measurements, whereas red spheres are the corresponding mean values. The error bars in the single particle measurements result from the standard deviation of the mean lattice parameters among the four tetrahedra for each given shell. Even though the single particle measurements show a relatively large scatter of the resulting lattice parameter, for the mean values a clear expansion of 9.5% from the core toward the surface of the particles is found (from (0.211 ± 0.002) nm to (0.231 ± 0.001) nm). Figure 3b compares all three measurements techniques. As can be seen, all data nicely agree and the measured surface-near lattice expansion turn out to be independent from the evaluation method. Consequently, a systematic error due to the method of measurement itself can be ruled out. Surprisingly, the results obtained from the focusseries reconstruction of conventional HRTEM images of Wang and co-workers8 are in good agreement with our results, although the authors had analyzed only one particle in detail. Apparently, the longer exposure to the electron beam during the acquisition of the focal series, and the hereby induced alternations of the surface atom configurations, effectively resulted in an intrinsic sampling that is compare in its result with our quasi-static measurement of many different particles. As the atomic volume of (fcc) Pt26 is significantly larger than that of (fcc) Fe27 the assumption lies close that the observed surface-near lattice expansion is indicative of a segregation of Pt toward the particle surface.8 Such a segregation can, however, not account for a lattice spacing that exceeds that of elemental fcc Pt. There are in fact two alternative possibilities for the origin of this experimental finding: (i) structural relaxations as a consequence of redistribution of electronic charges due to the symmetry breaking at surfaces are a common phenomenon on metal surfaces. (ii) The multiply twinned structure of icosahedral particles are inherently strained, and this strain is expected to result in lattice distortion at the surface.1,2,17,28 In the following, we will therefore address these alternative scenarios. We will show that (i) the observed lattice expansion is not inherent to the mere surface and (ii) there is a
Figure 1. Electron beam induced interparticle coalescence (sintering) at an electron dose of 2 × 106 e−/nm2/s. (a) Overview HRTEM micrograph of the initial situation of two adjacent icosahedra at t = 0. (b) Atomistic model of the icosahedra in panel a. (c) The two icosahedra after electron irradiation for t = 84 s. (d−h) Temporal sequence of magnified HRTEM image sections of the surface region of the right icosahedron as indicated by the yellow square in (a,b). Here, “TB” denotes the common twin boundary of two neighboring tetrahedral building blocks of the icosahedron. The motion of surface atoms is highlighted by yellow marks and arrows, respectively.
each individual micrograph. In the first 50 s, atoms (or atomic columns) on top of the right of the two particle facets are successively shuffled to the left facet in order to first complete the previously incomplete surface atomic layer there (i.e., on the left facet). Once being completed, all but the right corner atom or atomic column (marked with a yellow circle in the image at t = 66 s) in this layer of surface atoms have then reached the highest possible coordination and thus a lowenergy configuration. Consequently, as can be seen from a comparison of the images obtained at t = 66 s and t = 84 s, this corner atom (column) is the first to leave the layer in order to continue the sintering process. It is to be emphasized here that all material transport observed is directed toward the newly forming sintering neck between the primary particles, that is, toward the left side in the detail images. A very similar behavior was recently observed in Au nanoparticles where the electron beam induced diffusion could even be quantified by evaluating the kinetics of the surface atoms.25 Hence, in order to minimize the impact of the electron beam on the measurement of the local lattice parameter, single shot aberration-corrected HR-TEM images (rather than timeconsuming focal series of multiple exposures) were taken from several icosahedral nanoparticles oriented along one of its two-fold symmetry axes. This procedure provides the advantage that changes of the surface atom configuration due to the impact of the electron beam can be largely avoided. In addition, the investigation of many appropriately oriented particles allows for the conduction of statistically relevant analyses. When an icosahedron is oriented with one of its two-fold symmetry axes in the viewing direction, 4 of its 20 tetrahedral building blocks are visible along a [110] orientation and can be used to evaluate the radial lattice spacing. The other tetrahedra mainly contribute to a diffuse background intensity, because they do not lie in a zone axis orientation. Consequently, the atoms are not stacked within columns and electron channeling is largely reduced. The diffuse background increases with increasing thickness of the overlaying tetrahedra toward the particle core. This leads to a fading of the contrast arising from the tetrahedra of interest and to a limitation of the range of measurement to the tetrahedra’s outermost layers. In order to 1778
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Figure 3. Statistical analysis of the surface-near (111) lattice spacing, d111. (a) d111 as function of the distance from the particle surface (in units of interlayer spacings) as obtained from 2D Gaussian fits to the atomic column positions in 54 individual tetrahedral subunits (black squares) and after averaging over all tetrahedra (red spheres). (b) Comparison of the results obtained from different techniques to measure the positions of the atomic columns: 2D Gaussian (red spheres), intensity line scans (blue squares), and manual measurements (black triangles).
Figure 4a,b shows images of these particles at 0 s and after 413 s of exposure to the electron beam, respectively. The lattice spacings were analyzed again utilizing the 2D Gaussian method for both images. The resulting dependence of the spacing of {111} planes d111 on the distance from the (original) surface is shown in Figure 4d for the starting configuration (red squares) and after 413 s (blue circles). Prior to the sintering, the lattice spacing shows the same surface-near lattice expansion as found for the isolated FePt nanoparticles (see Figure 3). After Δt = 413 s, a sintering neck is formed and four additional atomic layers have “grown” onto the original surfaces. The common twinning plane of the icosahedra (yellow dashed line) serves as a line of orientation for the lattice measurement in both images. The measured d111 spacing is constant in the newly formed sintering neck and has a value of roughly d111 = 0.23 nm. Within the two tetrahedral subunits of the previous icosahedron and in due consideration of the error bars, the original trend of a lattice expansion toward the particle surface is preserved. The gray triangular area in Figure 4d illustrates the range of possible slopes at which d111 could possibly be interpreted to vary upon approaching the original particle surface. Under no circumstances can a collapse of the originally expanded lattice be deduced from the data. This finding that the surface-near lattice expansion in FePt icosahedra “survives” an overgrowths and hereby the loss of its surface properties proves that the origin for this expansion does not live in the nature of the surface itself. In how far the constant lattice spacing within the newly formed sintering neck is a consequence of Pt segregation or if it is rather due to the quasi-epitaxial growth on the preexisting {111} facets of the icosahedra remains unclear. To investigate if the observed surface-near lattice expansion is a peculiarity of FePt icosahedra or if it is rather a more common phenomenon among nanoparticles of binary alloys, CuAu
Figure 2. Local measurement of surface-near lattice spacings: (a) Determination of the position of individual atomic columns from aberration-corrected HRTEM images. The position mapping is conducted for all four visible tetrahedral subunits (labeled 1−4) of the FePt icosahedron that is seen along one of its two-fold symmetry axes. The atomistic model in the upper left corner indicates the orientation of the particle. (b) Illustration of the measurement of local interplanar (111) distances in a magnified section of the image in (a) (cf. red rectangle in (a)). See text for details. (c) Resulting variation of the (111) lattice spacings, d111, as function of the distance from the particle surface for the four individual tetrahedra (black squares) and as mean value (red spheres).
contribution to the surface-near lattice relaxation that is intrinsic to the icosahedral structure. In order to investigate if the lattice expansion is a direct consequence of the properties of a surface, we have studied the overgrowth of two {111} surfaces of an FePt icosahedron through electron beam induced interparticle coalescence. 1779
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Figure 5. {111} lattice spacings, d111, as function of the distance from the particle surface (in units of interlayer spacings) for (a) CuAu and (b) Au icosahedra. The results are obtained by 2D Gaussian fits to the atomic column positions. Data was acquired from 35 and 24 individual tetrahedral subunits (black squares) within the CuAu and Au particles, respectively. Red spheres represent the according layer averages.
a binary alloy, which is similar to FePt in many respects it may likewise suffer from a segregation of Au toward the surface. In order to assess the effect of a possible intrinsic strainrelated expansion of the lattice, elemental Au icosahedra were examined as a reference. Figure 5b shows variation of the resulting averaged {111} lattice spacing upon approaching the particle surface. Even for the elemental Au icosahedra, a lattice expansion of 5% is observed (from (0.233 ± 0.002) nm to (0.242 ± 0.002) nm). This suprisingly large “intrinsic” lattice deformation of the icosahedra is on the one hand ascribed to the strain that is inherent to the multiply twinned structure in these icosahedral particles17,28 and on the other hand to an outward directed lattice relaxation on extended (111) surfaces as reported for some metals (especially Au).29−32 MS simulations of Au icosahedra using a tight-binding potential33 confirm the strain-related intrinsic expansion of the lattice from the core toward the surface which only occurs in multiply twinned particles.34 The surface state related outward lattice relaxation, however, cannot be accounted for with these atomic potentials. Here, detailed ab initio simulations are to be performed. This comparison of the lattice relaxation in nanoparticles of binary alloys with that in elemental Au icosahedra clearly shows that the large surface-near lattice expansion found in FePt and CuAu icosahedra cannot be solely attributed to segregation but is partially due to strain inherent to the icosahedral morphology. In order to confirm that the particularly large surface-near lattice relaxations in FePt (and CuAu) icosahedra are indeed due to the segregation of Pt (Au) to the particle surface, additional model calculations are conducted. Therefore model particles with different atomic configurations and with a size comparable to the experimental ones are constructed. Three different models are computed: (i) a FePt nanoparticle with a random distribution of Fe and Pt atoms, (ii) a nanoparticle that
Figure 4. Overgrowth of two {111} facets of an FePt icosahedron (right particle) through electron beam-induced interparticle coalescence with an adjacent particle. (a) Initial state of the imaging process at time t = 0 and (b,c) after electron irradiation for t = 413 s. (d) (111) interlayer spacing, d111, as function of the distance from the original particle surface before (red squares) and after the overgrowth (blue circles), respectively. The notations of the interlayer spacings are in accordance with the labels provided in Figure (c). Here, dij denote the layers within the original particle, whereas dij* indicate the overgrown layers. The red and blue line are guides to the eye.
nanoparticles are prepared and likewise analyzed. Figure 5a shows the relaxation of the d111 lattice spacings near the surface of CuAu icosahedra. Gaussian fits were used to quantitatively analyze 35 tetrahedral subunits of CuAu icosahedra. The d111 lattice parameter increases from (0.220 ± 0.002) nm to (0.242 ± 0.001) nm (core to the surface). This 10% expansion of the lattice parameter at the particle surface is almost identical to the expansion measured in the FePt particles. In both alloy nanoparticles, the outermost layer spacing even exceeds the bulk lattice parameter of pure Pt or Au, respectively. As CuAu is 1780
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is subjected to MC simulations, and (iii) a nanoparticle with a forced radial Pt segregation. To obtain disordered (A1 phase) FePt icosahedra (Fe46Pt54) like the ones investigated in the experiment and to include diffusion driven segregation, MC simulations have been performed at 1800 K and thus above the thermodynamic ordering temperature. This results in disordered particles with a small segregation of Pt atoms toward the surface. The Pt atoms are found to mainly segregate to lowly coordinated atom position such as corners and edges. The resulting Fe and Pt distributions are provided in the Supporting Information.34 After subsequent structural relaxation by means of MS simulation, the model particles are placed on top of a 5 nm thick amorphous carbon layer, and the complete stack is then used as input data for HRTEM contrast simulations. First simulations have reduced a significant drop of the (111) layer spacing d12 for the outermost pair of layers with respect to the subsequent inner shells, which is not observed in the experiment (cf. Figure 3). A similar finding was reported by Wang et al.35 who had conducted MD simulations on the nearsurface lattice relaxation in CuPt icosahedron. The authors observed that this phenomena could be suppressed by removing all atoms from the edges formed between adjacent (111) facets. They have thus attributed this effect to a vacancy generation preferentially along those edges. As a consequence, we have also removed all edge atoms from the model particle and repeated the simulation. Surprisingly, however, the drop in d12 did still occur, although it was slightly reduced. Only upon simulating the perfect icosahedron and subsequently removing the edge atoms prior to conducting the HRTEM contrast simulation was the drop of the d12 successfully suppressed. Accordingly and unlike Wang et al., we assume that the potentials used in MD/MS simulations (which are adapted to reproduce the bulk properties of FePt) fail to describe the physics of lowly coordinated edge atoms (coordination number 8 rather than 12 in the bulk). Consequently, all simulations presented below were conducted following to the abovedescribed procedure. In the following, the various phenomena that contribute to the surface-near lattice expansion in FePt icosahedra are discussed by analyzing the simulated model particles. Figure 6a,b shows as examples the structure model used for the simulations of a FePt icosahedron and the resulting simulated HRTEM image. Figure 6c summarizes the lattice expansion as obtained for the three modeling scenarios (random element distribution, MC simulation, and forced radial Pt segregation). The purple triangles in Figure 6c show the lattice relaxation for the randomly distributed FePt icosahedron. Along the direction from the particle core toward the surface, the d111 spacing increases from (0.212 ± 0.001) nm to (0.218 ± 0.001) nm. Because the simulated structure does not contain any elemental enrichment at the particle surface, this steady 3% expansion is assumed to be intrinsic and seems to stem from the icosahedral structure itself. In order to rule out that this observation is an artifact caused by the HRTEM contrast simulation of icosahedral nanoparticles, the next-neighbor distance (NND) is also directly determined from the resulting 3D particle structure. Figure 7 shows the particle after its structural relaxation by means of MS simulation. Here, the color of the atoms represents the NND. Red (mainly present in the vicinity of the surface) corresponds to larger NND, whereas blue and green (in the core region) represent smaller values. This color representation clearly shows that the NND steadily increases from the core toward the surface. Hence, in agreement with the
Figure 6. Comparison between experiment and model calculations. (a) Atomistic model structure of a disordered FePt icosahedron of 8217 atoms (Fe = red, Pt = blue) on a 10 nm thick amorphous carbon support. (b) Calculated HR-TEM image as obtained from TEM contrast simulation of the model particle in (a) after structural relaxation through molecular static (MS) simulations. (c) {111} lattice spacings, d111, as function of the distance from the particle surface (in units of interlayer spacings). Experimental data (red spheres, cf. 3). MS simulation of a FePt icosahedron with random atom distribution (violet triangles). Monte Carlo (MC) simulation of a disordered Fe46Pt54 at T = 1800 K and subsequent MS simulation (magenta triangles). MS simulation of a FePt icosahedron with radial segregation of Pt toward the particle surface. From all model particles, the edge and corner atoms are removed after MS simulation in order to account for an erroneous compression of the surface layer due to MS simulation artifacts; see text for details.
Figure 7. Color-coded image of the variation of the next nearest neighbor distances across a disordered FePt icosahedron of 8217 atoms after structural relaxation through MS simulations. (a) Perspective image of the particle. (b) Cross section through the particle center as seen along one of its five-fold symmetry axes.
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the MS simulation of a homogeneously alloyed FePt icosahedron this contribution amounts to 3%. Within the second modeling scenario, the simulated annealing through MC simulations results in a small segregation of Pt toward the surface, leading to an average Pt concentration of 58 atom % for the last atomic shell. Here, the surface-near lattice relaxation as determined after subsequent MS simulation of the icosahedron (magenta triangles in Figure 6c) is larger than for the homogeneously alloyed particle. The lattice parameter increases from (0.212 ± 0.002) nm in the center of the particle to (0.222 ± 0.001) nm at the surface which amounts to a relative expansion of 5%. Already, this small segregation of Pt atoms leads to an additional expansion of the lattice parameter. Nevertheless, the effect is yet to small to fully account for the experimentally observed expansion. Therefore, a radial segregation of Pt toward the surface is modeled within the third scenario. Because the overall composition is fixed to Fe50Pt50, the core becomes Fe rich by the strong radial Pt segregation (average Pt concentration of 88 atom % at the surface34). In Figure 6c, the d111 spacing is shown for this case of a the forced radial Pt segregation (blue squares). The lattice parameter increases from (0.213 ± 0.003) nm in the center of the particle to (0.227 ± 0.001) nm at the surface which corresponds to a relative expansion of 7% that is now comparable to the experimental expansion in the first five layers. Although within this last scenario the experimental trend is nicely reproduced, it is at least questionable if such a strong segregation is a realistic assumption for a miscible system with such a high enthalpy of mixing (in the volume). Additionally, a likewise segregation results in a core−shell structure that should be recognizable in local element specific analyses like EDXS or EELS that, however, was not observed. Even though the results of the lattice parameter analysis from the experimental HRTEM images of FePt, CuAu, and Au icosahedra are clear and consistent, it becomes apparent that a quantitative description of the different contributions to the observed surface-near lattice expansion is difficult. From both, simulations and experiments it is obvious that the lattice expansion in icosahedra of binary metallic alloys can be ascribed to a combination of contributions from morphology related strain and a segregation of the heavier/larger elements toward the {111} facets. On the basis of the presented simulations, the intrinsic strain-related expansion amounts to roughly 3%. Thus, the main part of the observed 10% surface-near lattice expansion in the FePt icosahedra has to be contributed to a strong Pt segregation. On the basis of the differences in the surface energies of the alloy constituents, thermodynamic considerations and MC simulations37,38 support the observed segregation of Pt and Au, respectively. In both binary alloys, the larger constituent (Pt, 3 111 Au) has the smaller surface energy (γ111 Pt = 1.49 J/m , γAu = 1.61 J/m3) as compared to the smaller/lighter Fe/Cu atoms (γ111 Au = 3 13,39 = 2.203 J/m ). This surface energy 1.96 J/m3, γ111 γ−Fe difference therefore strongly supports the above made conclusion of a Pt/Au segregation toward the icosahedral {111} surfaces. A detailed description of the total energy of the nanoparticle would also need to include strain energy and surface strain.36,40 However, for the here described system, the contribution of the surface stress is small and the strain energy will be nearly the same for Pt and Fe, because their shear moduli are comparable (cγ−Fe = 77 GPa and cPt 44 44 = 77.4 41,42 Even though some segregation already occurs in the GPa) here presented MC simulations of the FePt icosahedra,23 the
experimental results obtained from Au icosahedra, also FePt icosahedra exhibit an intrinsic lattice expansion that appears to be due to the strain inherent to the icosahedral morphology. This intrinsic strain within an icosahedron is known to cause convex bending of the {111} facets.17,28,36 Figure 8 clearly
Figure 8. Illustration of the bending of near-surface atomic layers. (a) Atomistic structure of a disordered FePt icosahedron of 8217 atoms after structural relaxation through MS simulations (Fe = red, Pt = blue). For a better perspective view, the particle is slightly tilted away from one of its three-fold symmetry axis. (b) Enlarged view at a section of an atomic surface layer. (c) View at the identical section as in (b), but now for the particle in perfect 3-fold symmetry axes orientation. Note the broadening of the projection of the atomic columns due to the bending. (d) Magnified section of a calculated HRTEM image obtained from contrast simulations of the MS-relaxed model particle. The imaged section is identical to the section displayed in (c). (e) Comparable section from the {111} of tetrahedron #3 in the experimental HR-TEM image of the FePt icosahedron displayed in Figure 2. The dashed curves in panels (c−e) are identical and serve as guides to the eyes only.
reveals the convex curvature of the {111} facets both in the simulated model particle (Figure 8a−c) and in the experimental HRTEM images (Figure 8d,e). The bending of the atomic columns parallel to the beam results, if at all, only in a slight broadening of the column intensity. On the basis of this finding, it is thus to be concluded that part of the comparably large surface-near lattice expansion in icosahedral FePt nanoparticles is due to the strain inherent to icosahedra. From the result of 1782
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effect seems to be underestimated and based on the experimental data, a stronger Pt/Au segregation needs to be assumed. Aberration-corrected high-resolution transmission electron microscopy has been used in combination with molecular statics, Monte Carlo, and HRTEM contrast simulations, respectively, to systematically investigate the near-surface lattice relaxation in icosahedral nanoparticles of FePt, CuAu, and Au. In order to avoid electron beam induced modifications of the particle surfaces, single shot images of the particles were acquired to minimize their exposure to the beam. In all cases, the lattice was found to be expanded at the particle surface as compared to the particle core. Whereas in Au icosahedra, a moderate 5% expansion is observed, in FePt and CuAu icosahedra the near-surface lattice expansion is as high as roughly 10%. A comparative measurement on particles before and after their beam-induced coalescence, which shows that this lattice expansion persists, even if the original surface is subsequently buried, proves that this expansion is not a mere surface-related phenomenon but rather due to a physicochemical modification of the outermost shells of the particles. The experimental finding of a, though smaller, near-surface lattice expansion also in Au icosahedra implies that part of the comparably large effect in the FePt and CuAu icosahedra is due to strain inherent to the multiply twinned structure of these icosahedral particles. The consistent observation of clearly curved (111)-type facets in both MS simulations and experimental HRTEM images lends strong support to this assumption. Further MS simulations, which are partly complemented by additional MC simulations, show that the remaining discrepancy between a merely strain-related nearsurface lattice expansion and the experimentally observed expansion in FePt icosahedra can only be accounted for by a segregation of Pt toward the particle surface. This result is consistent with the differences in the surface energies of Fe (Cu) and Pt (Au) that provides the thermodynamic driving force for the termination of these alloy particles with their larger constituents (Pt or Au). It further highlights the limited validity of bulk phase diagrams for structures at the nanoscale, which are increasingly affected by the energetics of their surfaces.
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ASSOCIATED CONTENT
* Supporting Information S
Additional HRTEM images of icosahedral FePt nanoparticles, Au NND (MS simulation), FePt element distribution for MC, and radial segregated FePt nanoparticles. This material is available free of charge via the Internet at http://pubs.acs.org.
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Letter
AUTHOR INFORMATION
Corresponding Authors
*E-mail: (D.P.)
[email protected]. *E-mail: (B.R.)
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are indebted to Alexander Surrey for fruitful discussion and to Karsten Albe and Tommi Järvi for discussions concerning the MS simulations. 1783
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