electronic reprint Paracrystalline structure of gold ...

electronic reprint

ISSN: 1600-5767

journals.iucr.org/j

Paracrystalline structure of gold, silver, palladium and platinum nanoparticles ´ Karolina Jurkiewicz, Michał Kaminski, Wojciech Glajcar, Natalia Wo´znica, ´ ´ Maciej Fanon Julienne, Piotr Bartczak, Jarosław Polanski, Jozef Lelatko, Zubko and Andrzej Burian

J. Appl. Cryst. (2018). 51, 411–419

IUCr Journals CRYSTALLOGRAPHY JOURNALS ONLINE c International Union of Crystallography Copyright Author(s) of this paper may load this reprint on their own web site or institutional repository provided that this cover page is retained. Republication of this article or its storage in electronic databases other than as specified above is not permitted without prior permission in writing from the IUCr. For further information see http://journals.iucr.org/services/authorrights.html

J. Appl. Cryst. (2018). 51, 411–419

Karolina Jurkiewicz et al. · Paracrystalline structure of metallic nanoparticles

research papers Paracrystalline structure of gold, silver, palladium and platinum nanoparticles ISSN 1600-5767

Received 19 October 2017 Accepted 29 January 2018

Edited by Th. Proffen, Oak Ridge National Laboratory, USA Keywords: metal nanoparticles; X-ray diffraction; pair distribution function; paracrystalline structure. Supporting information: this article has supporting information at journals.iucr.org/j

Karolina Jurkiewicz,a,b* Michał Kamin´ski,a,b Wojciech Glajcar,a,b Natalia Wozńica,a,b Fanon Julienne,c Piotr Bartczak,b,d Jarosław Polan´ski,b,d Jo´zef Lela˛tko,b,e Maciej Zubkob,e and Andrzej Buriana,b a

A. Chełkowski Institute of Physics, University of Silesia, ulica Uniwersytecka 4, 40-007 Katowice, Poland, bSilesian Center for Education and Interdisciplinary Research, ulica 75 Pułku Piechoty 1A, 41-500 Chorzo´w, Poland, cUniversite´ Bretagne Loire, Universite´ du Maine, IMMM, UMR 6283 CNRS, 72000 Le Mans, Cedex 9, France, dInstitute of Chemistry, University of Silesia, ulica Szkolna 9, 40–006 Katowice, Poland, and eInstitute of Materials Science, University of Silesia, ulica 75 Pułku Piechoty 1a, 41-500 Chorzo´w, Poland. *Correspondence e-mail: [email protected]

Metallic nanoparticles are of great importance because of their unique physical, chemical, antimicrobial, diagnostic, therapeutic, biomedical, sensing, biosensing, catalytic and optical properties. Detailed knowledge of the atomic scale structure of these materials is essential for understanding their activities and for exploiting their potential. This paper reports structural studies of silicasupported silver, gold, palladium and platinum nanoparticles using X-ray diffraction and high-resolution transmission electron microscopy. Electron microscopy observation allowed the determination of nanoparticle sizes, which ˚ , and their distribution. The were estimated to be in the range of 45–470 A obtained histograms exhibit a multimodal distribution of the investigated nanoparticle sizes. The X-ray diffraction data were analyzed using the Rietveld method in the form of Williamson–Hall plots, the PDFgui fitting procedure and model-based simulation. The Williamson–Hall plots provide evidence for the presence of strain in all investigated samples. The PDFgui fitting results indicate that the investigated nanoparticles consist of atomic clusters with different sizes and degrees of disorder as well as slightly different lattice parameters. The detailed structural characterization performed via model-based simulations proves that all samples exhibit a face-centered cubic type structure with paracrystalline distortion. The degree of disorder predicted by the paracrystalline theory is correlated with the sizes of the nanoparticles. The catalytic properties of the investigated noble metals are discussed in relation to their disordered structure.

1. Introduction

# 2018 International Union of Crystallography

J. Appl. Cryst. (2018). 51, 411–419

Metallic nanoparticles represent a wide class of materials which can be regarded as a bridge between molecules and bulk materials. Their domain size does not exceed 100 nm (or ˚ ). These materials exhibit a variety of unique proper1000 A ties which make them increasingly important in areas of chemistry, physics, biology, medicine and materials science from both fundamental and application points of view. Detailed knowledge of the atomic scale structure is one of the more important factors allowing an understanding of and prediction of the properties of metal nanoparticles. Diffraction patterns of nanomaterials contain broadened peaks as well as continuous diffuse components owing to their small sizes and the possible presence of structural disorder. Such features have been recognized and reported by Egami & Billinge (2003), Billinge & Kanatzidis (2004), Balzar et al. (2004), Petkov et al. (2005, 2008) and Billinge & Levin (2007). That is why structural studies of nanomaterials are complex and https://doi.org/10.1107/S1600576718001723

electronic reprint

411

research papers difficult, making the ‘nanostructure problem’ one of the great challenges in nanotechnology (Petkov, 2008). Approaches alternative to conventional diffraction techniques based on the crystallographic formalism have been proposed for the purpose of obtaining quantitative information about the atomic scale structure, structural defects, strain and lattice distortion for noble metal nanoparticles and their alloys (Cervellino et al., 2003, 2015; Bertolotti et al., 2016; Petkov et al., 2005, 2007, 2008; Petkov & Shastri, 2010; Petkov et al., 2012, 2013; Yin et al., 2012; Sanchez et al., 2013). Interpretation of the diffraction data can be done by analysis in reciprocal space using the Debye equation (Debye, 1915; Cervellino et al., 2003, 2015; Bertolotti et al., 2016) or in real space applying the pair distribution function (PDF) formalism (Petkov et al., 2005, 2007, 2008; Petkov & Shastri, 2010; Petkov et al., 2012, 2013; Yin et al., 2012; Sanchez et al., 2013). A general conclusion resulting from diffraction studies is that the atomic structure of the noble metal nanoparticles is of the face-centered cubic (f.c.c.) type. It has been shown that these materials exhibit structural disorder leading to strain and lattice distortion, and hence to deviation from strictly periodic translation symmetry. Slight shortening of the lattice parameters with respect to the bulk forms has been noticed. Other methods, such as high-resolution transmission electron microscopy (HRTEM) (Harris, 1995; Jose´-Yacamań et al., 2001; Kim et al., 2003; Chang et al., 2010) and extended X-ray absorption fine structure (EXAFS) (Battaglin et al., 2003; Erenburg et al., 2007, 2009; Lin et al., 2007; Comaschi et al., 2008), have also been used for probing nanomaterials. Although the HRTEM method has provided valuable information about the structure of nanostructured materials including their morphology, possible twinning and disorder, this technique is sensitive to a small sample volume and is a local probe. On the other hand, the EXAFS and PDF methods yield averaged information about the atomic scale structure that is derived from a larger sample volume. Combining data obtained using the above-mentioned methods is necessary to create a self-consistent base for modeling studies whose results can then be compared with the experimental data. Therefore, these methods can be regarded as complementary. The EXAFS studies provided evidence that smaller metallic nanoparticles are more disordered and the interatomic distances are slightly shorter than those observed for the bulk counterparts. In this paper, we describe X-ray diffraction and HRTEM studies of gold, silver, palladium and platinum nanoparticles. The enhanced catalytic activity of these materials was studied and their effectiveness in chemical reactions was reported (Bujak et al., 2012; Korzec et al., 2014; Kapkowski et al., 2014, 2015; Polanski et al., 2015; Rams-Baron et al., 2015). The main aim of this work is precise and detailed characterization of the atomic structure of the investigated nanoparticles. The Rietveld (1969) and PDFgui (Farrow et al., 2007) fitting procedures were used in the first step of the structural analysis, which provided a rough estimation of the lattice parameters and the size of the nanoparticles and information about lattice deformation caused by strain. The HRTEM images allowed precise

412

Karolina Jurkiewicz et al.

Table 1 Preparation of the composition: M/SiO2. Metal (M)

Precursor

M/SiO2 metal content† (wt%)

Gold Silver Palladium Platinium

HAuCl4 Ag(CH3COO) PdCl2 H2PtCl6

0.70 0.98 0.93 1.00

† Metal content as found by the AAS method.

estimation of the nanoparticle sizes and their distribution. In the next step model-based simulations of diffraction patterns in the form of both the structure factor and the pair distribution function were carried out using the paracrystalline theory developed by Hosemann and his group (Hosemann & Bagchi, 1960; Hosemann et al., 1983; Hindeleh & Hosemann, 1988, 1991; Hosemann & Hindeleh, 1995). In this approach, the paracrystalline lattice distortion is imposed on the computer-generated models via the generalized Debye– Waller factor. Paracrystalline modeling takes into account correlations between the degree of disorder and the size of the investigated nanoparticles and therefore can be considered as an efficient tool for structural studies of such materials. It allows analysis of the diffraction data in both reciprocal and real space. The previously proposed methods cannot account for this correlation of the materials in question.

2. Experimental details 2.1. Sample preparation

Nanosized metal particles were supported on amorphous SiO2 prepared using the Sto¨ber sol–gel technique (Sto¨ber et al., 1968). In particular, in a typical procedure deionized water (100 ml) was added to the amorphous SiO2 (20 g) and the mixture was placed in an ultrasound bath and sonicated for 20 min. Then, an aqueous saturated solution containing nanometal precursor (Table 1) was added dropwise into a suspension of colloidal silica and mixed in an ultrasound bath for 20 min. The mixture was dried at 333–363 K for 12 h, ground and sieved. Finally, the reduction was conducted in an oven (FCF 7 SMW system) under hydrogen at 773 K for 1 h, affording nanosized metallic particles dispersed on the SiO2 carrier. The content of nanoparticles on silica for each type of the composite (Table 1) was determined using atomic absorption spectrophotometry (AAS, Varian model AA 1275 series atomic absorption spectrophotometer). Nanosized metal particles dispersed on the silica (20 g) were added to deionized water (100 ml), placed in an ultrasound bath and stirred for 10 min. Then, sodium hydroxide solution (50 ml, 40% w/w) was added and the suspension was stirred for 4 h at 353 K. Next, the suspension was cooled to room temperature and centrifuged. After decantation, the sediment was washed five times with deionized water. The resulting material was dried at room temperature to constant mass.

Paracrystalline structure of metallic nanoparticles

electronic reprint

J. Appl. Cryst. (2018). 51, 411–419

research papers 2.2. X-ray diffraction

Table 2

The X-ray diffraction measurements were carried out at room temperature. A Rigaku Denki D/MAX RAPID II-R diffractometer with a rotating silver anode was used. The ˚ ) using a incident beam was monochromated ( = 0.5608 A (002) graphite monochromator. An image plate in the Debye– Scherrer geometry was employed as a two-dimensional detector for the intensity measurements. This value of the ˚ 1. wavelength was low enough to extend the Q range to 20 A The size of the cylindrical image plate was 460 256 mm and the camera length was 127.4 mm. The pixel size for the detector was 100 100 mm. The beam size at the sample was 0.3 mm. The investigated sample was placed inside a glass capillary (0.3 mm in diameter and 0.01 mm wall thickness) and measurements were carried out for the sample in the capillary and for the empty capillary. The intensity for the empty capillary was then subtracted. The sample was placed precisely at the center of the image plate using a CDD camera. The data collection time was 60 min per scan. Twenty scans were carried out, and the individual data sets were then summarized to achieve good counting statistics. A semiconducting laser with an excitation light wavelength of 650 nm and a power of 30 mW was used in a reader device. Geometrical calibration of the detector was performed using the NIST Si powder standard. The recorded two-dimensional diffraction patterns were then accordingly converted to one-dimensional intensity data using the RINT RAPID control software supplied by Rigaku. The measured intensities were corrected for absorption, polarization and Compton scattering and then normalized using a procedure developed for high-energy X-rays. The structure factor S(Q) was calculated with a procedure adapted from high-energy X-ray diffraction (Poulsen et al., 1995; Schlenz et al., 2003; Hawelek et al., 2005). 2.3. Transmission electron microscopy

The lattice parameters a for Ag, Au, Pd and Pt nanoparticles obtained from the Rietveld refinement, the lattice parameters of the bulk crystals abulk (taken from http://periodictable.com/Properties/A/LatticeConstants. html), the average sizes of the coherently scattering domains D, the lattice strain coefficients " and the displacement parameters Biso.

Au Ag Pd Pt

˚) a (A

˚) abulk (A

˚) D (A

"

˚ 2) Biso (A

4.0731 4.0682 3.8660 3.8968

4.0782 4.0853 3.8907 3.9242

72.7 132.5 93.2 103.0

0.00829 0.00097 0.00543 0.00055

0.2932 0.6996 0.5275 0.1804

Hall plot (Williamson & Hall, 1953) are commonly used tools for a preliminary, mostly qualitative, assessment of the influence of coherently scattering domain size and lattice strain on diffraction line broadening (Klug & Alexander, 1974; Warren, 2014). The X-ray powder diffraction profiles of gold, silver, palladium and platinum are shown together with the fitted intensity functions in Fig. 1. The Williamson–Hall expression that correlates the full width at half-maximum (FWHM) of the intensity peak with the dimension of the coherently scattering domain size D and the lattice strain " can be written as cosðÞ ¼

K þ C" sinðÞ: D

ð1Þ

The fitting procedures were performed as described by Toby (2006) and McCusker et al. (1999). The fitting parameters are listed in Table 2. In the Rietveld fitting procedures, the scale factors, the lattice parameters, the Debye–Waller temperature factors, the polynomial background, and the microstructural size and strain effect parameters were refined. The instrumental broadening was taken into account by measurements of the Si standard that was also used for calibration of the instrument.

The TEM observations were performed using a JEOL JEM 3010 microscope. The samples were suspended in ethanol and sonicated for 15 min in an ultrasound bath, and the resulting materials were deposited on carbon films. The average sizes of the investigated nanoparticles were determined by analyzing different TEM images.

3. Results and discussion 3.1. Structural characterization by the Rietveld fitting procedure

In the first step a traditional analysis of the recorded X-ray diffraction (XRD) profiles using the Rietveld (1969) fitting method was applied. The Scherrer formula (Scherrer, 1918; Patterson, 1939) and the Williamson– J. Appl. Cryst. (2018). 51, 411–419

Figure 1 The XRD diffraction patterns of Au, Ag, Pd and Pt nanoparticles and the Rietveld fits. The lower curves show the differences between the observed and calculated intensities. The Williamson–Hall (W-H) plots are inset, together with the least-squares linear fits as a guide to the eye. Karolina Jurkiewicz et al.

electronic reprint


413

research papers The quality of the Rietveld fit is shown in Fig. 1 as the difference between the measured and calculated intensities as recommended by Toby (2006). For the constants appearing in equation (1), K ¼ 2½lnð2Þ=1=2 ffi 0:94 and C = 4 are taken for calculations according to Stokes & Wilson (1944) and Warren (2014). In equation (1), indicates the Bragg angle and is the wavelength. Note that the Williamson–Hall method allows the separation of size and strain broadening analysis because these two components have a different dependence on . However, it is based on several assumptions about the constants K and C and the isotropic nature of microstrain (Langford & Wilson, 1978; Balzar et al., 2004; Scardi et al., 2004). Therefore, the values of the parameters D and " obtained from the Williamson–Hall plots should be regarded as estimations. Moreover, the reliability of the Williamson– Hall results and their quantitative meaning are limited in the case of broad or even multimodal size distribution (Langford et al., 2000; Scardi et al., 2004). But this method can be a useful tool if used in a relative sense to follow trends in series of similarly treated samples (Langford & Wilson, 1978), here metallic nanoparticles. From the Rietveld fitting procedure, it can be concluded that all the investigated nanoparticles have the f.c.c. type structure. The obtained values of the lattice parameters for the Ag, Au, Pd and Pt nanoparticles are shorter than those of the bulk crystals. Note that reasonable agreement between the experimental and calculated intensities was achieved if distortion of the f.c.c. type structure in the form of a strained lattice was assumed. The resulting Williamson–Hall plots allowed estimation of the coherently scattering domain sizes D and the strain coefficients " ¼ d=d expressed as the relative change of the interplanar distances d. The greater discrepancies between the experimental and fitted curves are seen for the Au, Pd and Ag nanoparticles in the region of the first and second peaks. The fit for Pt is better in this range. This difference can be explained if one takes into account that the size distribution for Pt, shown in Fig. 3 below (see x3.3), is significantly narrower in comparison with Au, Pd and Ag. Therefore, the fit for Pt is better because in the fitting procedure only one size of the investigated nanoparticles was assumed. Moreover, the estimated value of the ˚, mean nanoparticle size is 103.0 A which is significantly greater than the value corresponding to the maximum shown in Fig. 3.

three-dimensional structure to the PDF data using the leastsquares method and can be regarded as the real-space analog of the Rietveld refinement. Values of crystallographic parameters including lattice parameters, atomic positions and site occupations, anisotropic displacement parameters, atomic vibrational correlations, and particle diameters can be obtained using this routine. The experimental PDF, G(r), can be determined by the Fourier transformation of the structure factor S(Q) as follows: GðrÞ ¼ ð2=Þ

QRmax

Q½SðQÞ 1 sinðQrÞ dQ;

ð2Þ

0

where the scattering vector magnitude Q ¼ 4 sin =, Qmax being the maximum value of Q available in the experiment ˚ 1), 2 is the angle between the incident and scat(here 20 A tered beam, is the wavelength of the radiation used for measurements, and r is the interatomic distance. The structure factor for materials consisting of one atomic species is given by SðQÞ ¼ IðQÞ=f 2 , where I(Q) is the intensity corrected and normalized to electron units and f indicates the atomic scattering factor (Klug & Alexander, 1974; Warren, 2014). In this approach the total intensity measured in a given experimental range of the scattering vector is taken into account. The PDF provides information about the interatomic distances in the investigated material. The first peak corresponds to the nearest-neighbor distance and the subsequent peaks are related to second-, third- and next-neighbor coordination spheres. The results of the PDFgui fitting are compared with the experimental functions in Fig. 2. The PDFs show structural features in a wide range of interatomic distances that extends ˚ . The fall-off in the PDF amplitudes seen for higher up to 80 A values of r suggests that the f.c.c. type structure is modified by the so-called size effect, which reduces the coordination

3.2. PDFgui fitting

In the next step the PDFgui fitting procedure was applied for interpretation of the diffraction data converted to a real-space representation in the form of the pair distribution function (Farrow et al., 2007). PDFgui allows fitting of the

414


Figure 2 The results of the PDFgui fitting compared with the experimental PDFs. The discrepancies between the calculated and experimental functions are displayed in the bottom part of each plot and shifted for clarity.


electronic reprint

J. Appl. Cryst. (2018). 51, 411–419

research papers Table 3 The lattice parameters a, the diameters of nanoparticles D, the anisotropic displacement parameters, the parameters taking into account correlated atomic motions 1 and weights of individual nanoparticles obtained from PDFgui fitting. The meaning of these parameters can be found at http://www.diffpy.org/doc/ pdfgui/pdfgui.html#SEC43.

Au Ag Pd Pt

˚) a (A

˚) D (A

Anisotropic displacement ˚ 2) parameter (A

˚) 1 (A

Weight

4.0394 4.0748 4.0429 4.0690 3.9073 3.8753 3.9160 4.0690

25.5705 150.0000 41.0064 149.2580 52.3787 69.9753 46.6623 96.9137

0.03262 0.01342 0.01183 0.00754 0.09969 0.00908 0.14460 0.00727

1.2986 1.8913 0.1529 0.1529 1.4465 1.3918 1.4912 1.4912

0.68 0.32 0.38 0.62 0.42 0.58 0.62 0.38

numbers of atoms with increasing r in comparison with the bulk crystals. Moreover, such a tendency can be related to intrinsic disorder of the nanoparticles. All the PDF peaks can be attributed to the f.c.c. type structure. Fitting procedures based on models consisting of spherical nanoparticles of two different sizes allowed reasonable reconstruction of the PDF peak positions and their amplitudes. If the number of model nanoparticles was greater than two, the fitting procedure did not converge and strong correlations between refined parameters occurred. The values of the best fit refined parameters are listed in Table 3. Attempts to fit the experimental data with the hexagonal close packed (h.c.p.) structure were ineffective because the fitting results are clearly inconsistent with the experimental data, as is shown in the supporting information. The Qbroad = 0.04 and Qdamp = 0.0033 parameters, which account for increased intensity noise at high Q and limited Q-space resolution, respectively, were taken for computation. In the fitting procedure, the 1 parameter was chosen because the measurements were carried out at a room temperature that is greater than the Debye temperature of Au, Ag, Pd and Pt. The displacements of atoms from their average positions due to thermal vibration are accounted for by Gaussians with the actual widths defined as 1=2 ; ij ¼ ij0 1 1 þ Q2broad r2ij rij

3.3. Transmission electron microscopy observations

In order to obtain more precise information about the distribution of nanoparticle sizes TEM observations were carried out. Examples of the TEM images together with the size distributions of the nanoparticles are shown in Fig. 3. The TEM images show that the investigated nanoparticles have approximately spherical shapes and exhibit relatively broad and multimodal size distributions. The presented histograms were obtained from a few hundred individual nanoparticle measurements. Such information about the distribution of the metallic nanoparticles prompted us to compute the theoretical

ð3Þ

where ij0 is the width related to the anisotropic displacement parameters without correlation and the next terms describe the effect of correlated atomic motion and the Q resolution of the diffractometer (Jeong et al., 1999; Proffen & Billinge, 1999). rij denotes the interatomic distance between the atoms i and j. J. Appl. Cryst. (2018). 51, 411–419

The differences between the calculated and experimental functions are plotted in the bottom parts of the plots shown in Fig. 2, allowing estimation of the goodness of fit. Several conclusions can be drawn from the PDFgui fitting results. The lattice parameters are slightly smaller for the nanoparticles with smaller sizes for Au, Ag and Pt. In the case of the Pd nanoparticles the fitting procedure showed the opposite tendency. The mean square atomic displacements u2 are greater for the nanoparticles with smaller diameters for all the investigated samples, which suggests a greater degree of disorder in the atomic arrangement for smaller nanoparticles. The discrepancies between the experimental and fitted PDFs, greatest for the Pt sample, can be related to the presence of disorder in the investigated samples that cannot be accounted for in the fitting procedure, in which the Debye–Waller factor describes only the thermal atomic oscillations. Therefore, the peak amplitudes that lead to modulations in the difference curves cannot be correctly reconstructed. Such behavior can be understood if one tries to fit the experimental structure factor and PDF assuming only thermal disorder.

Figure 3 TEM micrographs and the corresponding nanoparticle size distributions for Au, Ag, Pd and Pt. The sums of the Gaussian functions are superimposed on the histograms. Karolina Jurkiewicz et al.

electronic reprint


415

research papers structure factors for nanoparticles of spherical shape with the sizes that appeared with higher frequencies in the histograms shown in Fig. 3. The presented distributions are approximated by the sum of the Gaussian type functions which are superimposed on the histograms. 3.4. Paracrystalline modeling

The structure factor for the nanoparticle containing N atoms of the same kind can be calculated according to the Debye equation (Debye, 1915; Klug & Alexander, 1974; Warren, 2014; Scardi et al., 2016) as " # N X N sinðQrij Þ Q2 ij2 1 X exp ; ð4Þ SðQÞ ¼ 1 þ N i¼1 j¼1 ðQrij Þ 2 i6¼j

where rij indicates the interatomic distance between the atoms i and j, and ij2 is the mean square deviation of rij from its equilibrium value. Attempts made to reproduce all features of the experimental structure factors and PDFs assuming the perfect f.c.c. structure of the investigated nanoparticles with a given size and distorted only by the thermal vibration proved

to be ineffective. As an example, the experimental and calculated functions for Au are compared in Figs. 4. The peaks of the calculated structure factor and PDF are sharper and have higher amplitudes when compared with the experimental data. Such findings are in agreement with the conclusions derived from the Williamson–Hall plots, which clearly suggest the defective structure of the nanoparticles. This comparison indicates that additional disorder of the models should be imposed and it is desirable to consider the size distribution of the nanoparticles in order to obtain a reliable description of their real structure. Therefore, in order to improve the models, it was necessary to impose additional static disorder on the atomic arrangement of the nanoparticles. Good agreement with the experimental data was achieved when the paracrystalline lattice distortion was imposed on the models based on the f.c.c. type structure. The ij2 parameter appearing in the generalized Debye–Waller factor for the defective structure, describing both thermal vibrations of the atoms and paracrystalline static disorder, can be written as 1 2 2 2 þ paracrystal rij ; ð5Þ ij ¼ temp 1 rij

Figure 4 (a) The experimental and calculated structure factors for the Au nanoparticle with lattice parameter ˚ , a size of 70 A ˚ and a perfect f.c.c. structure. (b) The PDFs calculated from the structure a = 4.05 A factors. An isotropic displacement parameter accounting for the thermal vibrations equal to ˚ 2 was chosen to fit the amplitude of the first PDF peak. 0.018 A

where 1 allows for correlations in atomic motion. The concept of paracrystallinity was suggested by Max von Laue (1960) and the paracrystal theory was mathematically formulated and developed by Hosemann and his coworkers (Hosemann & Bagchi, 1960; Hosemann et al., 1983; Hindeleh & Hosemann, 1988, 1991; Hosemann & Hindeleh, 1995). The paracrystalline distortion spreads out through the lattice in a manner corresponding to the Gaussian law of error propagation. According to equation (5) the distortion propagates proportionally paracrystal r1=2 ij to the square root of the interatomic distances. Such a rule is based on the assumption that the distances from any atom to its nearest neighbors fluctuate without statistical correlations. Note that Hosemann’s approach is preferably applicable to microparacrystals, which obey the so-called relation (Hosemann & Bagchi, 1960; Hosemann et al., 1983; Hindeleh & Hosemann, 1988, 1991; Hosemann & Hindeleh, 1995): hNi1=2 g ¼ ;

Figure 5 Comparison of the calculated and experimental structure factors of Au, Ag, Pd and Pt nanoparticles. The open circles represent the experimental data, and the black lines are the model-based simulations of the f.c.c. paracrystalline structure. The residuals, shifted for clarity, are shown as blue lines in the bottom part of each plot.

416



electronic reprint

0:1 0:2;

ð6Þ

where hNi indicates the average number of net planes in the paracrystal and the distortion parameter g ¼ ½ðhd2 i hdi2 Þ=hdi2 1=2 is related to the relative statistical deviation of the J. Appl. Cryst. (2018). 51, 411–419

research papers Table 4

interplanar spacing d for the net planes with the highest density of atoms. h i indicates the statistical average value of the quantity in the brackets. This empirical relation implies 2 2 ˚ ) Weight a (A ˚ ) paracrystal ˚ 2) temp ˚ 2) 1 (A ˚ ) * D (A (A (A that there is a limit to the growth of the paracrystal or, in other words, it explains that large paracrystals cannot be heavily Au 45 0.55 4.0370 0.00423 0.0144 1.50 0.19 84 0.15 4.0700 0.00360 0.0144 1.50 0.20 disordered. 115 0.25 4.0750 0.00250 0.0144 1.80 0.20 Model-based simulations of the diffraction data both in 160 0.05 4.0750 0.00123 0.0100 1.80 0.19 reciprocal and in real space were performed for Au, Ag, Pd Ag 55 0.33 4.0475 0.00360 0.0140 1.30 0.19 115 0.65 4.0675 0.01230 0.0864 1.75 0.16 and Pt nanoparticles with sizes corresponding to the maxima 470 0.02 4.0675 0.00023 0.0049 1.75 0.14 of the Gaussian functions that approximate the distributions Pd 45 0.66 3.8700 0.00303 0.0169 1.5 0.16 shown in Fig. 3. The structure factors were computed 80 0.30 3.8700 0.00102 0.0121 1.8 0.13 180 0.04 3.8800 0.00032 0.0100 2.0 0.11 according to equation (4) with ij2 parameters defined by Pt 40 0.65 3.8700 0.00490 0.0169 1.0 0.20 equation (5). The results of the simulations are compared with 120 0.30 3.9000 0.00090 0.0081 1.0 0.15 the experimental data in Fig. 5. 210 0.05 3.9100 0.00017 0.0036 1.0 0.10 The model parameters are displayed in Table 4. The lattice 2 2 , paracrystal , 1 and the weights of the indiparameters a, temp vidual nanoparticles are the adjustable parameters of the models, which were chosen by trial and error to reconstruct all the features of both structure factors and PDFs. In paracrystalline modeling the size of the individual nanoparticle defined by N and the degree of disorder given by g are related by the relation. Therefore, this relation imposes constraints on the model parameters. The values were estimated according to Hosemann et al. (1983), taking into account the distribution of the nearestneighbor interatomic distances and the diagonal statistics. In general, the agreement between the calculated and experimental structure factors is good, especially in the Q range from 4 to ˚ 1. The greatest discrepancies are 20 A Figure 6 The PDFs calculated from the structure factors shown in Fig. 5. seen in the close vicinity of the first two peaks. The performed calculations show that the paracrystalline models reproduce correctly the experimental data and account very well for attenuation of the diffraction peaks in the higher Q range. These conclusions are reinforced by comparison of the calculated and experimental PDFs shown in Fig. 6. From the histograms shown in Fig. 3 it can be concluded that in all the investigated samples there are nanoparticles ˚ , and with smaller sizes, about 40–55 A ˚. larger sizes, in the range 80–120 A Moreover, nanoparticles with sizes ˚ are extending up to 160–470 A observed, but their statistical weights are very low. In the case of Ag, conglomerates with even larger sizes Figure 7 can be seen but their number is negliThe values of the parameters plotted as a function of the square root of the interatomic distances gible in the model-based computations. for Au, Ag, Pd and Pt nanoparticles. 2 The nanoparticle sizes D, their weights, the lattice parameters a, paracrystal , 2 temp , 1 and * for paracrystalline modeling.

J. Appl. Cryst. (2018). 51, 411–419


electronic reprint


417

research papers ˚ . In a higher r PDF oscillations are seen up to the limit of 80 A range the structural oscillations are significantly weaker, which can be related to a lower contribution of the larger nanoparticles to the total PDFs. Note also that the amplitudes of the PDF peaks at higher r values are strongly attenuated. Such behavior can be explained by the paracrystalline structure of the studied nanoparticles, for which the degree of disorder increases with the square root of the interatomic distances. This is visualized in Fig. 7, where the values of the parameters accounting for both thermal and static paracrystalline disorder are plotted as a function of r1/2. It is apparent that the structure of smaller nanoparticles is disordered to a higher degree in comparison with larger nanoparticles, and this tendency is noticeable for all the studied samples. It is predicted by the relation and is a consequence of the paracrystalline nature of the nanoparticle structures. Moreover, the atomic displacements from their average positions for larger interatomic distances are mainly due to the paracrystalline distortion of the model structures and are clearly higher than those related to the thermal atomic motion.

References

4. Conclusions In summary, we have shown that silica-supported Au, Ag, Pd and Pt nanoparticles have an f.c.c. paracrystalline structure. The approach proposed here, based on X-ray diffraction experiments, the formalism of the pair distribution function, transmission electron microscopy and modeling studies, is an efficient means for description of the nanostructures, providing detailed information about the atomic arrangement in such materials. The applied computational procedures allow reconstruction of all features of the diffraction data, both in reciprocal and in real space. They yielded three-dimensional structural models of the noble metal nanoparticles in terms of the atomic coordinates and the generalized Debye–Waller factors. This is highly important because the X-ray intensities are more sensitive to longer-range correlations and the pair distribution functions provide precise information about short-range ordering. Using this complex approach, we are able to characterize the structure of nanomaterials in these aspects. It is likely that information obtained in such a way will have profound implications for explaining the properties of nanoscale materials that are important from the application point of view. Paracrystalline modeling is a slightly more time-consuming task in comparison with the Rietveld and PDFgui methods and it requires precise information about the real distribution of the nanoparticle sizes. But in the case of the noble metal nanoparticles neither the Rietveld nor the PDFgui method can provide detailed information about the structure as they are based on assumptions which are not fully applicable to these complex structures. In the old Taylor concept of ‘active sites’, it was assumed that the catalytic activity of the surface is conditioned by the

418


nature of the arrangement and the spacing of the atoms in the surface layer (Taylor, 1925). This idea has been recently developed using HRTEM observations accompanied by density functional theory simulations (Johnson et al., 2008; Baker et al., 2010; Chang et al., 2010; Stenlid & Brinck, 2017). From this work it has been concluded that the catalytic activity of the noble metal nanoparticles can be understood by assuming the defective and strained nature of their surface structure. The defects lead to significant electronic structure changes due to the presence of low-coordinated surface atoms. It has been suggested that under-coordinated surface atoms are the key factor to noble metal catalytic activity. The proposed models predict such disordered structure. Paracrystalline modeling revealed correlations between nanoparticle size, network distortion and the atomic scale structure in the investigated nanoparticles. Moreover, taking into account that the ratio of the number of surface atoms to the number of atoms in the whole nanoparticle is higher for smaller paracrystals, the results of the present work highlight the importance of the detailed structure in real non-periodic materials composed of nanoparticles.

Baker, T. A., Kaxiras, E. & Friend, C. M. (2010). Top. Catal. 53, 365– 377. Balzar, D., Audebrand, N., Daymond, M. R., Fitch, A., Hewat, A., Langford, J. I., Le Bail, A., Loue¨r, D., Masson, O., McCowan, C. N., Popa, N. C., Stephens, P. W. & Toby, B. H. (2004). J. Appl. Cryst. 37, 911–924. Battaglin, G., Cattaruzza, E., Gonella, F., Polloni, R., D’Acapito, F., Colonna, S., Mattei, G., Maurizio, C., Mazzoldi, P., Padovani, S., Sada, C., Quaranta, A. & Longo, A. (2003). Nucl. Instrum. Methods Phys. Res. B, 200, 185–190. Bertolotti, F., Moscheni, D., Migliori, A., Zacchini, S., Cervellino, A., Guagliardi, A. & Masciocchi, N. (2016). Acta Cryst. A72, 632–644. Billinge, S. J. L. & Kanatzidis, M. G. (2004). Chem. Commun. pp. 749– 760. Billinge, S. J. L. & Levin, I. (2007). Science, 316, 561–565. Bujak, O., Bartczak, P. & Polanski, J. (2012). J. Catal. 295, 15–21. Cervellino, A., Frison, R., Bertolotti, F. & Guagliardi, A. (2015). J. Appl. Cryst. 48, 2026–2032. Cervellino, A., Giannini, C. & Guagliardi, A. (2003). J. Appl. Cryst. 36, 1148–1158. Chang, L. Y., Barnard, A. S., Gontard, L. C. & Dunin-Borkowski, R. E. (2010). Nano Lett. 10, 3073–3076. Comaschi, T., Balerna, A. & Mobilio, S. (2008). Phys. Rev. B, 77, 075432. Debye, P. J. W. (1915). Ann. Phys. 351, 809–823. Egami, T. & Billinge, S. J. L. (2003). Underneath the Bragg Peaks. Oxford: Elsevier. Erenburg, S. B., Moroz, B. L., Bausk, N. V., Bukhtiyarov, V. I. & Nikitienko, S. (2007). Nucl. Instrum. Methods Phys. Res. A, 575, 103–108. Erenburg, S., Trubina, S., Bausk, N., Moroz, B., Kalinkin, A., Bukhtiyarov, V. & Nikitenko, S. (2009). J. Phys. Conf. Ser. 190, 012121. Farrow, C. L., Juhas, P., Liu, J. W., Bryndin, D., Bozˇin, E. S., Bloch, J., Proffen, T. & Billinge, S. J. L. (2007). J. Phys. Condens. Matter, 19, 335219. Harris, P. J. F. (1995). Int. Mater. Rev. 40, 97–115. Hawelek, L., Koloczek, J., Burian, A., Dore, J. C., Honkima¨ki, V. & Kyotani, T. (2005). J. Alloys Compd. 401, 51–54.


electronic reprint

J. Appl. Cryst. (2018). 51, 411–419

research papers Hindeleh, A. M. & Hosemann, R. (1988). J. Phys. C Solid State Phys. 21, 4155–4170. Hindeleh, A. M. & Hosemann, R. (1991). J. Mater. Sci. 26, 5127–5133. Hosemann, R. & Bagchi, S. N. (1960). Direct Analysis of Diffraction by Matter. Amsterdam: North Holland. Hosemann, R., Hentschel, M. P., Balta´-Calleja, F. J. & Yeh, G. S. Y. (1983). J. Phys. C Solid State Phys. 16, 4959–4971. Hosemann, R. & Hindeleh, A. M. (1995). J. Macromol. Sc. Part B, 34, 327–356. Jeong, I.-K., Proffen, Th., Mohiuddin-Jacobs, F. & Billinge, S. J. L. (1999). J. Phys. Chem. A, 103, 921. Johnson, C. L., Snoeck, E., Ezcurdia, M., Rodrı´guez-Gonza´lez, B., Pastoriza-Santos, I., Liz-Marzań, L. M. & Hy¨tch, M. J. (2008). Nat. Mater. 7, 120–124. Jose´-Yacamań, M., Marıń-Almazo, M. & Ascencio, J. A. (2001). J. Mol. Catal. A Chem. 173, 61–74. Kapkowski, M., Bartczak, P., Korzec, M., Sitko, R., Szade, J., Balin, K., Lela˛tko, J. & Polanski, J. (2014). J. Catal. 319, 110–118. Kapkowski, M., Siudyga, T., Sitko, R., Lela˛tko, J., Szade, J., Balin, K., Klimontko, J., Bartczak, P. & Polanski, J. (2015). PLoS One, 10, e0142668. Kim, S.-W., Park, J., Jang, Y., Chung, Y., Hwang, S., Hyeon, T. & Kim, Y. W. (2003). Nano Lett. 3, 1289–1291. Klug, H. P. & Alexander, L. E. (1974). X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials. New York: Wiley. Korzec, M., Bartczak, P., Niemczyk, A., Szade, J., Kapkowski, M., Zenderowska, P., Balin, K., Lela˛tko, J. & Polanski, J. (2014). J. Catal. 313, 1–8. Langford, J. I., Loue¨r, D. & Scardi, P. (2000). J. Appl. Cryst. 33, 964– 974. Langford, J. I. & Wilson, A. J. C. (1978). J. Appl. Cryst. 11, 102–113. Laue, M. von (1960). Ro¨ntgenstrahl-Interferenzen, 3rd ed., ch. 3. Frankfurt: Akademie Verlagsges. Lin, C.-M., Hung, T.-L., Huang, Y.-H., Wu, K.-T., Tang, M.-T., Lee, C.-H., Chen, C. T. & Chen, Y. Y. (2007). Phys. Rev. B, 75, 125426. McCusker, L. B., Von Dreele, R. B., Cox, D. E., Loue¨r, D. & Scardi, P. (1999). J. Appl. Cryst. 32, 36–50. Patterson, A. L. (1939). Phys. Rev. 56, 978–982. Petkov, V. (2008). Mater. Today, 11, 28–38. Petkov, V., Bedford, N., Knecht, M. R., Weir, M. G., Crooks, R. M., Tang, W., Henkelman, G. & Frenkel, A. (2008). J. Phys. Chem. C, 112, 8907–8911.

J. Appl. Cryst. (2018). 51, 411–419

Petkov, V., Ohta, T., Hou, Y. & Ren, Y. (2007). J. Phys. Chem. C, 111, 714–720. Petkov, V., Peng, Y., Williams, G., Huang, B., Tomalia, D. & Ren, Y. (2005). Phys. Rev. B, 72, 195402. Petkov, V. & Shastri, D. (2010). Phys. Rev. B, 81, 165428. Petkov, V., Shastri, S., Shan, S., Joseph, P., Luo, J., Zhong, C. J., Nakamura, T., Herbani, Y. & Sato, S. (2013). J. Phys. Chem. C, 117, 2231–2241. Petkov, V., Wanjala, B. N., Loukrakpam, R., Luo, J., Yang, L., Zhong, C. J. & Shastri, S. (2012). Nano Lett. 12, 4289–4299. Polanski, J., Bartczak, P., Ambrozkiewicz, W., Sitko, R., Siudyga, T., Mianowski, A., Szade, J., Balin, K. & Lela˛tko, J. (2015). PLoS One, 10, e0136805. Poulsen, H. F., Neuefeind, J., Neumann, H. B., Schneider, J. R. & Zeidler, M. D. (1995). J. Non-Cryst. Solids, 188, 63–74. Proffen, T. & Billinge, S. J. L. (1999). J. Appl. Cryst. 32, 572–575. Rams-Baron, M., Dulski, M., Mrozek-Wilczkiewicz, A., Korzec, M., Cieslik, W., Spaczyn´ska, E., Bartczak, P., Ratuszna, A., Polanski, J. & Musiol, R. (2015). PLoS One, 10, e0131210. Rietveld, H. M. (1969). J. Appl. Cryst. 2, 65–71. Sanchez, S. I., Small, M. W., Bozin, E. S., Wen, J. G., Zuo, J. M. & Nuzzo, R. G. (2013). ACS Nano, 7, 1542–1557. Scardi, P., Billinge, S. J. L., Neder, R. & Cervellino, A. (2016). Acta Cryst. A72, 589–590. Scardi, P., Leoni, M. & Delhez, R. (2004). J. Appl. Cryst. 37, 381–390. Scherrer, P. (1918). Nachr. Ges. Wiss. Go¨ttingen, 26, 98–100. Schlenz, H., Neuefeind, J. & Rings, S. (2003). J. Phys. Condens. Matter, 15, 4919–4926. Stenlid, J. H. & Brinck, T. (2017). J. Am. Chem. Soc. 139, 11012– 11015. Sto¨ber, W., Fink, A. & Bohn, E. (1968). J. Colloid Interface Sci. 26, 62–69. Stokes, A. R. & Wilson, A. J. C. (1944). Proc. Phys. Soc. 56, 174– 181. Taylor, H. S. (1925). Proc. R. Soc. London Ser. A, 108, 105–111. Toby, B. H. R. (2006). Powder Diffr. 21, 67–70. Warren, B. E. (2014). X-ray Diffraction. New York: Dover Publications. Williamson, G. K. & Hall, W. H. (1953). Acta Metall. 1, 22–31. Yin, J., Shan, S., Yang, L., Mott, D., Malis, O., Petkov, V., Cai, F., Shan Ng, M., Luo, J., Chen, B. H., Engelhard, M. & Zhong, Ch. (2012). Chem. Mater. 24, 4662–4674.


electronic reprint


419