Evidence for Anomalous Bond Softening and Disorder Below 2 nm

Mar 19, 2013 - Figure 2. (a) ADPs as a function of temperature (symbols) (80–400 K) and their fits with the Debye model (solid lines). (b) MSRDs as a ...
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Evidence for Anomalous Bond Softening and Disorder Below 2 nm Diameter in Carbon-Supported Platinum Nanoparticles from the Temperature-Dependent Peak Width of the Atomic Pair Distribution Function Chenyang Shi,† Erin L. Redmond,‡ Amir Mazaheripour,† Pavol Juhas,†,∥ Thomas F. Fuller,‡ and Simon J. L. Billinge*,†,∥ †

Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, United States School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ∥ Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States ‡

S Supporting Information *

ABSTRACT: X-ray pair distribution function (PDF) analysis has been applied to five carbon-supported platinum nanoparticles with sizes ranging from 1.78(2) to 11.2(2) nm. Debye (θD) and Einstein (θE) temperatures were extracted from temperature-dependent PDF peak widths. A monotonic decrease in (θD) with nanoparticle diameter was found and could be well explained by the effect of increased surface area except in the case of the 1.78(2) nm diameter nanoparticle where the measured Debye temperature is significantly depressed from that predicted. This suggests an anomalous bond softening in the smallest sample.

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INTRODUCTION Metallic nanoparticles are of interest scientifically and in novel technological applications.1−6 They can be used as catalysts in refining petroleum, hydrogenation of carbon monoxide/fats, and so on.1,4−6 However, some of these catalysts are not stable, for example, platinum nanparticles that serve as catalysts in solid oxide full cell sometimes do not function optimally.6 A difficulty for understanding the performance arises from both the structural complexity of heterogeneous catalyst and the sensitivity of kinetic response to the surrounding environment.1,4−6 Therefore an inversitgation of the structure and bond stiffness of small catalyst nanoparticles is needed to further the understanding of this important class of materials. It is a challenge to measure the bond stiffness as a function of nanoparticle size for small nanoparticles. A common way to determine bond stiffness in bulk materials is to consider the temperature dependence of the atomic displacement parameter (ADP) measured from diffraction and fit it with a Debye7 or Einstein model.8 The stiffness is directly related to the resulting Debye (θD) or Einstein (θE) temperature. Small nanoparticles are not well studied by conventional diffraction methods, complicating this issue.9 However, the peak width in an atomic pair distribution function (PDF)10,11 or extended X-ray absorption fine-structure spectroscopy (EXAFS) measurement12−20 yields the amplitude of atomic motion even for small particles allowing θD or θE to be determined from its temperature dependence. An additional complication is that, for small nanoparticles, there is not a direct relationship between Debye temperature and bond stiffness due to the increased © 2013 American Chemical Society

fraction of undercoordinated surface atoms. These underconstrained atoms execute larger-amplitude thermal motions, and have a lower Debye temperature, even when the bond stiffness of each bond has not changed, resulting in a size dependence to θD that does not originate from bond softening. A number of EXAFS studies have been carried out to study the Debye (θD) or Einstein (θE) temperature of nanoparticles.12−20 Few studies consider the effects of the surface,14,17−20 but to treat the effect properly requires detailed knowledge of the size and shape of the nanoparticles, which is not easy to determine from EXAFS. Additionally, only the width of the nearest neighbor peak is measured in EXAFS requiring use of a correlated Debye model to account for the correlated motion of near neighbors.21 In these respects the use of the PDF to measure θD derives some advantages since it contains structural information from all neighbors. Here we report the first PDF study of Debye temperature vs nanoparticle size on five samples of Pt nanoparticles supported on carbon. Our nanoparticle samples, with sizes from 1.78(2) to 11.2(2) nm, were studied with more than 200 temperature points between 80 and 400 K. We report a protocol for extracting Debye/Einstein temperatures from experimental PDFs using the PDFgui program.22 We see a monotonic decrease in θD with diameter, D. This trend is well explained by the effect of increased surface area except in the case of the 1.78(2) nm diameter nanoparticle where the measured Debye Received: March 14, 2013 Published: March 19, 2013 7226

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becomes more prominent in samples at small sizes and the residual signal of the scattering from the carbon support. The average nanoparticle sizes were estimated by refining a PDF intensity falloff appropriate for spherical nanoparticles (SI2),26 where it should be noted that the PDF yields the average size of the coherent structural core which may be less than the physical size.27 As expected, the refined values of the nanoparticle sizes did not change significantly with temperature even though this parameter was free to refine, giving confidence that the refinement protocol is yielding physical results. The values at 295 K for Pt 100−Pt 30 were 11.2(2), 3.72(2), 3.06(2), 2.47(2), and 1.78(2) nm, respectively, and were consistent with the mean particle size seen in TEM (Figure S1), suggesting that the nanoparticles are structurally ordered up to the surface. The numbers in parentheses are the estimated uncertainties on the average nanoparticle sizes determined from the PDF. This is much smaller than the width of the particle size distribution seen in TEM. However, the PDF measures the sample-average properties and so ADPs, Debye temperatures, and so on also reflect the average behavior of the sample. In SI-4 our protocol to extract physical ADPs (Uiso) and mean square relative displacement (Debye−Waller factors, MSRDs) using PDFgui is presented. The protocol removed parameter correlations with the ADP and spdiameter (nanoparticle size) parameters at high temperature and thus ensured stable refinements yielding physical parameters over the whole temperature range. The ADP determined from a fit over wide rrange, and the MSRD of the nearest neighbor peak, were further fit with a Debye (Figure 2a) and Einstein model (Figure 2b) (SI-5), respectively. The fit results are summarized in Table 1. Panels a and b of Figure 2 show the temperature dependence of the ADPs and MSRDs, respectively, measured from the PDFgui fits for the different sized nanoparticles. As the nanoparticles get smaller the curves in both figures shift to higher values indicating more disorder. They also systematically steepen as is confirmed by the Debye/Einstein model fits that show a monotonic decrease in θD and θE with decreasing size. The Debye curves and Einstein curves fit well suggesting that these two parameter models are sufficient for fitting the data. The quantitative fitting results are presented in Table 1 where we see a monotonic decrease of θD and θE and an increase in the static offset, with decreasing nanoparticle size. In bulk materials a decrease in Debye temperature directly implies a softening of the atomic bonding. However, to deduce this in nanoparticles we first have to account for the effects of the surface. The surface atoms have larger thermal motions because they are bonded to fewer neighbors and their motion is less constrained. For example, a Pt atom in the bulk has 12 neighbors and therefore 12 bonds provide a restoring force when the atom displaces. The surface Pt atoms have fewer neighbors and even in the case where the bond strength of each bond does not change from bulk to surface, they will exhibit a lower θD. The ADP we measure from the PDF contains contributions from both the surface and bulk atoms. As a rough first approximation we may consider our measured θ̅D(D) to be the properly weighted average of the surface θSD and bulk (θBD) Debye temperatures,

temperature is significantly depressed from that predicted. This is evidence for a softening in the bonding strength of the nanoparticles below a diameter of ∼2 nm though other origins cannot be ruled out.

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EXPERIMENTAL SECTION Four carbon-supported platinum samples were obtained from Tanaka Kikinzoku Group, Japan and platinum black was purchased from Sigma Aldrich. They were denoted as Pt 100 (Pt black), Pt 70, Pt 60, Pt 50, and Pt 30, respectively, based on the Pt weight percentages (wt %). Synchrotron X-ray total scattering experiments were conducted at beamline 11-ID-B at the Advanced Photon Source at Argonne National Laboratory. The powder samples were packed in Kapton capillaries with an inner diameter of 1 mm. The samples were measured in a flowing nitrogen cryocooler at temperatures between 80 and 400 K (step = 1.4 K), using the rapid acquisition pair distribution function (RAPDF) technique23 with an X-ray energy of 58.26 keV (λ = 0.2128 Å). The raw 2D data were azimuthally integrated and converted to 1D intensity versus 2θ, using FIT2D.24 PDFgetX325 was used to correct and normalize the diffraction data and then Fourier transform them to obtain the PDF, G(r). For more information about the experiment and the PDF method see SI-1.

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RESULTS AND DISCUSSION Representative PDFs for different Pt/C samples measured at 80 K are shown in Figure 1. The PDF peaks diminish in amplitude

Figure 1. Experimental (blue) and corresponding simulated PDFs (red) with difference curve (green) offset below, for all Pt samples measured at 80 K. From top to bottom: Pt 100, Pt 70, Pt 60, Pt 50, and Pt 30, respectively.

with increasing r due to the finite size effects. For the lower Pt loadings this decrease happens more rapidly indicating their reduced sizes. We adopt the structural model of FCC bulk platinum during PDF fitting using PDFgui, and as suggested by the difference plots, the standard FCC model (space group Fm3̅m) fits well to the nanoparticle samples. Overall the fits are of high quality suggesting that the structure of these nanoparticles is well explained by the bulk FCC model, although there are larger residuals for the smallest nanoparticles. This difference may be due to an additional structural component in small nanoparticles such as contamination that

θD̅ (D) = θDB − R S(θDB − θDS)

(1)

where the surface-to-volume ratio, RS, is (see SI-6) 7227

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Figure 2. (a) ADPs as a function of temperature (symbols) (80−400 K) and their fits with the Debye model (solid lines). (b) MSRDs as a function of temperature (symbols) and their fits with the Einstein model (solid lines). From top to bottom: Pt 30, Pt 50, Pt 60, Pt 70, and Pt 100 respectively. (c) Red solid curve is the fit to the Debye temperatures (■) of Pt 50-Pt 100, using eq 1 with fixed θDB = 263.5 K. The horizontal dotted line corresponds to reported bulk θD (253 K).17 The vertical dashed line is a guide to the eye. Inset: The static offset from Debye fit (■) as a function of nanoparticle size. (d) Solid red line is the fit to Einstein temperatures (●) of Pt 50-Pt 70 with fixed dr = 0.521 rnn, using eq 3. Blue dashed line is a power law fit to all Einstein temperatures (●) using θE(D) = θE(∞)−c·Dx, where θE(∞) = 175.5(11) K, c = 383(200), x = −4.7(9), and R2 = 0.9839. The gray shaded area suggests the range of θE values of bulk Pt from the literature.15−18 Open circles (○) are reported values of Pt/C from ref 17. The vertical dashed line is a guide to the eye. Inset: The static offset from the Einstein fit (●) as a function of nanoparticle size.

We also tried fitting the measured θD(D) with θBD and θSD as variables in eq 1 (see SI-6 for derivation). Since dr is not known accurately we tried this for various dr values from 0.25rnn to rnn with an interval of 0.25rnn (if we let dr also vary, the refinements are unstable). The curve could fit the measured θD(D) of the largest four nanoparticles for all dr values, but would not fit the θD value of the smallest nanoparticle for any dr: the Pt 30 point is always offset significantly below the fit curves. Since eq 1 is derived for the case of fixed bond stiffness, the suppression of θD for Pt 30 is consistent with the bonding being softer in this smallest nanoparticle. For all dr we obtained a stable θBD around 263.5 K giving us confidence that in the current measurements θBD is 263.5 K. Fixing this parameter and using eq 1 we obtained a good fit (Figure 2c) to the four larger nanoparticles yielding physically reasonable values of θSD = 124.1(4) K and an average dr = 0.521rnn. However, if the fit includes the smallest Pt 30, the results do not yield physical values. The D-dependence of θD(D) for the larger nanoparticles can be well explained due to surface effects and not a change in bond stiffness. However, the large suppression (∼25 K) of Pt 30 from the fit curve indicates an anomalous bond softening for the 1.78(2) nm nanoparticle. Exactly at which diameter the softening sets in could be tested more accurately if we had more size-controlled samples with different diameters in this region. The effect is even more apparent in the measurements of the MSRD of the nearest-neighbor bond. The width of this PDF peak gives the relative amplitude of motion of directly bonded pairs of atoms and should be a rather direct measure of the bonding stiffness and less sensitive to static disorder. Similar to the Debye model case, we can define a size-dependent θ̅E(D) using

Table 1. Values of Average Nanoparticle Diameter D Debye, θD, and Einstein, θE, Temperatures Refined from the Fits, and Their Corresponding Static Disorder Parameters, A and σstatic2, respectivelya samples

D (nm)

θD (K)

A (Å2)

θE (K)

σstatic2 (Å2)

Pt Pt Pt Pt Pt

11.2(2) 3.72(2) 3.06(2) 2.47(2) 1.78(2)

252.4(2) 234.8(4) 226.5(3) 220.5(2) 181.1(7)

0.0024(2) 0.0030(03) 0.0032(3) 0.0041(3) 0.0051(2)

174.8(3) 176.2(2) 172.5(4) 170.2(3) 150.2(8)

0.0018(3) 0.0025(2) 0.0032(2) 0.0037(2) 0.0052(3)

100 70 60 50 30

a

The numbers in parentheses are the standard deviation on the last digit estimated from the counting statistics but not including other sources of error. 3 ⎛ 2 dr ⎞⎟ R S = 1 − ⎜1 − ⎝ D ⎠

(2)

The quantity dr is the thickness of the surface annulus (SI-6) and will have a value comparable to the nearest neighbor bond length, rnn. If we set dr = rnn, we get RS values for Pt 100 to Pt 30 to be 0.141, 0.382, 0.449, 0.532, and 0.672, respectively. For the smallest nanoparticles, up to 67% of the atoms sit at a surface. However, in reality dr is less than rnn and is not known precisely, depending, for example, on the crystallographic facet at the surface. Nonetheless, we can plot θ̅D(D) using literature values of θBD = 253 K17 and θSD = 111 K28 for bulk and surface Debye temperatures, respectively, for different values of dr = 0.5rnn, 0.75rnn, and rnn, and the results are shown with the measured θD(D) in Figure S3. Although the calculated θ̅D(D) show a similar decreasing trend as the experimental Debye temperatures do, none of them match the data, suggesting the reported θBD and θSD need to be adjusted for our case. 7228

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(3)

CONCLUSION

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ASSOCIATED CONTENT

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REFERENCES

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In this work a reasonable protocol based on the PDFgui program was presented to extract size-dependent Debye/ Einstein temperatures of carbon-supported platinum nanoparticles. The surface effect of the nanoparticles was corrected, as a first approximation, by considering surface-to-volume ratio weighted Debye temperatures. We find evidence for a significant bond softening, and an increase in nonthermal disorder, only for the smallest nanoparticle below 2 nm in diameter. More work is needed to confirm definitely that this effect comes from a bond softening and not some other overlooked effect such as a decrease in surface−atom coordination or an effect related to sample composition or chemistry. Thermodynamic properties of nanoparticles are difficult to measure directly and theoretical works based on either molecular dynamics or first principle calculations are needed for a better understanding. However, as shown in this paper, the PDF technique contains a wealth of information about very small nanoparticles that opens the door to the validation of such studies.

S Supporting Information *

Description of the experimental PDF procedure; the average particle sizes from TEM; the extractions of ADP and MSRD using PDFgui and then Debye or Einstein temperatures; and a “core-shell” structure/illustration of nanoparticles, adopted to correct the surface effect. This material is available free of charge via the Internet at http://pubs.acs.org.

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ACKNOWLEDGMENTS

Work in the Billinge-group was supported as part of the Center for ReDefining Photovoltaic Efficiency Through Molecule Scale Control, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0001085. Toyota Motor Engineering & Manufacturing North America Inc. supported the sample preparation. The Advanced Photon Source is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Services, under contract No. DE-AC02-06CH11357.

This relationship is shown, with a fixed dr = 0.521rnn and values of θBD and θSE obtained by fitting to the measured θE(D) of the Pt 50, 60, and 70 nanoparticles, as the red solid curve in Figure 2d. It was not possible to get a good fit that included either of the end-members. The curve extends to the shaded area in the figure, which indicates the range of θBE in the literature,15−18 although it is signficantly higher than the θE measured from our data. As with the Debye temperature fits, there is a dramatic drop in θE(D) for the smallest nanoparticle. To fit the measured θE for both the smallest and largest nanoparticles in our sample we carried out an empirical power law fit, shown as the blue dashed line in Figure 2d, resulting in a a power of ca. −4.7(9). This suggests there is a large deviation of θE from eq 3 for Pt 30 again consistent with a bond softening in the smallest nanoparticle. As shown in the insets of panels c and d of Figure 2, the static offsets from both the Debye and Einstein fits increase strongly with reduced nanoparticle sizes indicating significantly larger bond-length distributions in smaller nanoparticles. In particular, for the smallest nanoparticle below 2-nm diameter, there is considerable nonthermal contributions to the bondlength distribution.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 1-212-854-2918. Notes

The authors declare no competing financial interest. 7229

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