Colloid and Polymer Science

, Volume 291, Issue 9, pp 2163–2171 | Cite as

Anomalous small-angle x-ray scattering from mesoporous noble metal catalysts

Original Contribution


We present the analysis of a catalyst containing platinum nanoparticles supported on mesoporous MCM-41 silica by anomalous small-angle x-ray scattering (ASAXS). The analysis of this composite system by ASAXS is first studied by use of model calculation. Here, it is shown that the full analysis must proceed by decomposing the scattering data measured at different energies of the incident beam into three partial intensities. This evaluation is compared to a simplified method in which scattering curves measured at two different energies are subtracted from each other. The different methods are applied to experimental data obtained from platinum nanoparticles on an MCM-41 support material. The model calculations show that the simplified method leads to large deviations especially at low q in ordered systems. In the semi-ordered material MCM-41, these deviations are less pronounced, and the method of simple subtraction proves to be a good approximation for q values higher than 0.1 nm−1.


Small-angle x-ray scattering Catalyst Noble metal MCM-41 


Matrix-supported metal systems represent an important class of catalysts. They are usually obtained by impregnation of a porous support material like SiO2 or γ-Al2O3 to yield a high dispersion of the active metal [1]. In particular, ordered mesoporous silica such as MCM-41 and MCM-48 has been intensely studied as support for catalytically active noble metals [2, 3, 4]. These materials provide a high specific surface area and an ordered system of mesopores with a narrow size distribution typically in the range of 2 to 15 nm. Besides being suitable model supports, these materials can thus stabilize nanosized particles within their pore system. This is an advantage particularly for supported metals which often undergo sintering during catalytic applications, e.g. at elevated temperatures [5, 6, 7].

Small-angle x-ray scattering (SAXS) has been used for long time for the structural characterization of supported metal catalysts [8, 9]. More recently, anomalous small-angle x-ray scattering (ASAXS) has been used for structural characterization of matrix-supported metal catalysts. This method uses the anomalous dispersion of the metals and thus facilitates the separation of scattering contributions stemming from the metal and the matrix [10]. Anomalous scattering is due to the dependence of the scattering factor f of a given element on the energy E or wavelength λ of the incident radiation [11]. In general, f is a complex function of E which can be described by an energy-independent term f0 and two resonant terms f′ and f″:
$$ f={f_0}+f\prime (E)+i\,f\prime {\prime} (E) $$

f0 is the non-resonant term given by the number of electrons of the respective element and therefore constant. f′ and f″ are the so-called anomalous dispersion corrections which depend on the energy of the incident radiation and can be calculated or taken from literature [12, 13, 14]. In the vicinity of absorption edges, f′ and f″ change markedly. In this manner, the contribution of elements exhibiting strong anomalous scattering can be dissected by determining the scattered intensity at two different energies E far and near to an absorption edge. The scattered intensity of anomalous scatterers will change under these conditions, while the one of non-anomalous scatterers will remain unchanged in good approximation.

In recent years, ASAXS has been used frequently to characterize the volume as well as spatial distribution of metal catalyst particles supported by matrix materials. Usually, the matrix is made of “light” elements with low electron density while the metals are rich in electrons and exhibit absorption edges in energy ranges available at synchrotron sources. Thus, investigations have been carried out to characterize such catalyst materials containing platinum [15, 16, 17, 18, 19, 20, 21, 22], nickel [23, 24, 25], ruthenium [26, 27, 28], palladium [29, 30], germanium [31], gold [32, 33] or copper [34]. In most cases ASAXS was utilized to obtain the volume or size distribution of the structure elements formed by the metal nanoparticles.

Two methods were used for the evaluation of the ASAXS data. In many investigations, I(q) is determined at two energies, one close to the absorption edge and one far from it, and the scattering contribution of the metal is obtained by simple subtraction of two scattered intensities I(q) [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30]. In the second approach, the anomalous scattering intensity is split up into three partial intensities as shown many years ago by Stuhrmann [11]. This decomposition proceeds without additional assumptions [35, 36, 37, 38] and has been employed in numerous studies in the last decade due to the improved accuracy of ASAXS experiments [27, 28, 38]. The third partial intensity describes the scattering intensity which is solely due to the anomalous scattering units, that is, the metal particles in case of heterogeneous catalyst. Here, the question arises under which condition the simplified method may lead to meaningful results.

In an important paper, Brumberger et al. [39] showed that for metal spheres embedded in a non-ordered, randomly oriented support phase, the simple difference I(q, E) − I(q, E′) will yield an expression with a q dependence solely depending on the shape and spatial distribution of the metal particles. In this case, the supporting material and the void space which surround the metal clusters effectively can be treated like a quasi-homogenous medium. It must be noted, however, that the approach of Brumberger et al. is based on stringent assumptions that may or may not be met by the catalyst under consideration.

Here, we present the analysis of a catalyst in which platinum nanoparticles are incorporated into a mesoporous MCM-41 silica support. We combine this analysis with a general discussion of the evaluation of ASAXS data obtained from solid catalysts consisting of a matrix of light elements (SiO2 or polystyrene (PS)) and metal (Pt) nanoparticles. The general goal of this study is the assessment of partial order of the matrix on the resulting anomalous scattering intensity.

Theory and model calculations

The scattered intensity I(q) for a particle system can be expressed as
$$ I(q)=\frac{N}{V}{I_0}(q)S(q) $$
where N/V is the particle number density, I0(q) is the scattered intensity of a single particle and S(q) is the structure factor taking interparticle correlations into account. I0(q) is given by the multiplication of the scattering amplitude F(q) with its complex conjugate F*(q). In case of ASAXS, one obtains for I0(q):
$$ {I_0}(q)=F_0^2(q)+2f_{\mathrm{Pt}}^{\prime }{F_0}(q)\nu (q)+\left( {f_{\mathrm{Pt}}^{{\prime 2}}+f_{\mathrm{Pt}}^{{\prime {\prime} 2}}} \right){\nu^2}(q) $$

The term \( {F_0}^2(q) \) depicts the non-resonant contribution to the overall scattering measured far away from the adsorption edge. The second term is the cross term of the non-resonant and resonant scattering amplitudes F0(q) and ν(q), respectively. The third term v2(q) represents the resonant scattering contribution solely of the Pt particles.

Brumberger et al. [39] derived a relation for anomalous scattering from a typical catalyst which was considered to be a three-phase system (support material, void and metal). The treatment rests on the assumption that an ASAXS experiment done at two different energies can be viewed upon as an experiment where one component, namely the metal particles, has a slightly different electron density. Hence, the effect of anomalous dispersion is treated in terms of an effective electron density n. The system consists of three phases where the support is phase 1, the voids constitute phase 2 and the metal phase denoted as phase 3. The scattering intensity is calculated using the stick end distribution functions [40] Pij(r) as function of distance r. Here, Pij(r) is the probability of a stick of length r located in the system at random has one end in phase i and the other one in phase j. The resulting expression for the difference of I(q, E) at two different irradiation energies is
$$ \begin{array}{*{20}c} {I\left( {q,E} \right)-I\left( {q,E\prime } \right)=8\pi V\,{r_0}(q)\left( {{n_3}-n_3^{\prime }} \right)\times } \\ {\int\limits_0^{\infty } {\left( {{P_{13 }}{n_1}+{P_{23 }}{n_2}+{P_{33 }}{{\overline{n}}_3}-{\varphi_3}\left( {{\varphi_1}{n_1}+{\varphi_2}{n_2}+{\varphi_3}{{\overline{n}}_3}} \right)} \right){r^2}\frac{{\sin \left( {q\,r} \right)}}{{q\,r}}} \mathrm{d}\,r} \\ \end{array} $$
where ni and \( n_i^{\prime } \) denote the effective electron density of phase i at irradiation energy E and E′, respectively. V stands for the sample volume and r0 expresses the scattering length of a single electron, φi denotes the volume fraction of phase i and \( {{\overline{n}}_3} \) the average effective electron density of the metal between E and E′.
In the next step, the void and support phase are assumed to form a single-phase A with a concomitant average electron density nA, that is, both phases are randomly mixed into each other. The metal particles (phase B) are thus dispersed in a single phase, and all stick end probability functions are expressed through the respective volume fractions only and do not depend anymore on r. Evidently, this is a stringent assumption of which the validity must be proven for each system. With the spatial autocorrelation function A(r, R) of the spherical metal particles of radius R and a size distribution N(R), the difference of the scattered intensities at E and E′ is then given by
$$ \frac{{I\left( {q,E} \right)-I\left( {q,E\prime } \right)}}{{8\pi V\,{r_0}(q)\left( {{n_3}-n_3^{\prime }} \right)}}=\left( {{{\overline{n}}_3}-{n_A}} \right){\varphi_3}\left( {1-{\varphi_3}} \right)\int\limits_0^{\infty } {N(R)\int\limits_0^{\infty } {A\left( {r,R} \right){r^2}\frac{{\sin \left( {q\,r} \right)}}{{q\,r}}} \mathrm{d}r\,\mathrm{d}R\ } $$

i.e., the q-dependent part of I(q, E) − I(q, E′) depends only on size and distribution of the metal particles. In this case, the information about the metal nanoparticles in the system can be obtained by analysing the difference curves according to Eq. (5). A similar method of evaluation has been used by Yu et al. [22]. Here too it is assumed that the total ASAXS signal from platinum embedded in porous material consists of two parts IPt(q, E) and Ipores(q) which add up linearly. Thus, the scattering function is separated via subtraction of two curves I(q, E) determined at two different energies [22]. However, the discussion of Eq. (5) demonstrates that this above approach is only valid under the assumption that the combined void and support phase forms a non-ordered system throughout all relevant length scales. In order to elucidate this problem further, model calculations will be presented in the following.

Figure 1 shows the system used for the model calculations. One sphere is large and composed of typical support material for catalysts (here: PS or silica (SiO2)). Attached to this “matrix” is a small sphere made of platinum (Pt). We start by constructing a randomly packed system of large spheres that models the carrier material to which small spheres of the anomalously scattering material are attached at random (see Fig. 1).
Fig. 1

Scheme of the composite particle used for model calculations. It consists of a large sphere (RPS = 500 nm, grey circle) made of PS or SiO2 onto which a small platinum sphere (RPt = 5 nm, black circle) was attached. Calculations were performed for a single particle and an ensemble with a volume fraction ϕ = 0.6 in vacuo. RPS = RSiO2 = 500 nm or RPS = RSiO2 = 250 nm

For the system of two attached spheres shown in Fig. 1, the three partial intensities depicted in Eq. (3) can be calculated analytically. I0(q) is given by:
$$ {I_0}(q)=F(q)F\ast(q) $$
F(q) contains the contribution of both the PS and Pt sphere:
$$ F(q)={F_{\mathrm{PS}}}(q)+{F_{\mathrm{Pt}}}(q) $$
Each partial amplitude Fi(q) is given by
$$ {F_i}(q)={f_i}{V_i}a\left( {q\,{R_i}} \right) $$
where fi is the scattering length as defined in Eq. (1), Vi is the volume of the particle and a(q Ri) is the q-dependent wave function which corresponds to the Fourier transform of the density distribution function, i.e. a2(q Ri) is proportional to the Fourier integral in Eq. (5) for a given system. Only fPt contains complex parts that are due to the anomalous scattering of platinum. Figure 2 depicts f′(E) and f″(E) for Pt in the range from 7 to 14 keV.
Fig. 2

Anomalous dispersion corrections f′ and f″ as function of E around the Pt-L3 absorption edge. The data were taken from Chantler [14]

In case of spherical particles, a(q Ri) follows as
$$ a\left( {q\,{R_i}} \right)=\frac{{3\left( {\sin \left( {q\,{R_i}} \right)-q\,{R_i}\,\cos \left( {q\,{R_i}} \right)} \right)}}{{{{{\left( {q\,{R_i}} \right)}}^3}}} $$

The PS and Pt spheres are located at a distance of \( L={R_{\mathrm{PS}}}+{R_{\mathrm{Pt}}} \) from each other. Cross terms FPS(q)FPt(q) therefore have to be multiplied by the factor sin(q L)/(q L) in order to take into account the interference between the small and the large sphere [41].

Relations (6)–(9) now may serve for the calculation of the overall scattered intensity I0(q) for a single composite particle. Defining the non-resonant in Eq. (10), one obtains three terms for the scattered intensity as defined in Eq. (3):
$$ {F_0}(q)={F_{\mathrm{PS}}}(q)+{f_{{0,\mathrm{Pt}}}}\,{V_{\mathrm{Pt}}}\,a\left( {q\,{R_{\mathrm{Pt}}}} \right)={f_{{0,\mathrm{PS}}}}{V_{\mathrm{PS}}}a\left( {q\,{R_{\mathrm{PS}}}} \right)+{f_{{0,\mathrm{Pt}}}}\,\nu (q) $$
$$ F_0^2(q)={f_{{0,\mathrm{Pt}}}}^2\,{V_{\mathrm{PS}}}^2\,{a^2}\left( {q\,{R_{\mathrm{PS}}}} \right)+2\,{f_{{0,\mathrm{Pt}}}}\,{V_{\mathrm{PS}}}\,a\left( {q\,{R_{\mathrm{PS}}}} \right){f_{{0,\mathrm{Pt}}}}\,\nu (q)\frac{{\sin \left( {q\,L} \right)}}{{q\,L}}+{{\left( {{f_{{0,\mathrm{Pt}}}}\,\nu (q)} \right)}^2} $$
$$ \left( {f_{\mathrm{Pt}}^{{\prime 2}}+f_{\mathrm{Pt}}^{{\prime \prime 2}}} \right){\nu^2}(q)=\left( {f_{\mathrm{Pt}}^{{\prime 2}}+f_{\mathrm{Pt}}^{{\prime \prime 2}}} \right)V_{\mathrm{Pt}}^2{a^2}\left( {q\,{R_{\mathrm{Pt}}}} \right) $$
$$ 2\,f_{Pt}^{\prime }{F_0}(q)\nu (q)=2\left( {{f_{0,PS }}{V_{PS }}\,a\left( {q\,{R_{PS }}} \right)\,f_{Pt}^{\prime}\nu (q)\frac{{\sin \left( {q\,L} \right)}}{{q\,L}}+{f_{0,Pt }}\,f_{Pt}^{\prime }{\nu^2}(q)} \right) $$
In order to obtain I0(q) in units of per centimetre, instead of scattering length fi, the scattering length density ρi has to be employed:
$$ {\rho_i}={f_i}\frac{{{r_0}}}{{{V_i}}} $$
Here Vi is the volume corresponding to the scattering factor fi. Table 1 and 2 gather the parameters for present computations. The PS and Pt spheres were modelled as polydisperse ensembles, and thus, formula 2 was convoluted with a normal distribution with average values μ = 500 and 250 nm, respectively. The standard deviations were σ = 50 and 25 nm.
Table 1

Simulation parameters for the two attached PS/SiO2 and Pt spheres




ρ0,i/(1010 cm−2)













Table 2

Coefficients f′ and f″ for the calculation of the scattering length of Pt as function of energy of the incident radiation [14]













In order to model a system of platinum spheres dispersed in a disordered carrier system, additional calculation was done with a particle number density N/V corresponding to a volume fraction ϕ = 0.6:
$$ \frac{N}{V}=\frac{{\varphi V}}{{\left( {{V_{\mathrm{PS}}}+{V_{\mathrm{Pt}}}} \right)V}}\approx \frac{\varphi }{{{V_{\mathrm{PS}}}}} $$

Here, the small-volume fraction of the Pt spheres can be safely neglected, i.e. ϕ is considered to be solely occupied by support particles. Moreover, we disregard any mutual interference of the Pt spheres in the course of the model calculations. The effect of interparticle correlations between the large spheres was model by using the structure factor S(q) for a system of hard spheres given by the Percus–Yevick approximation [42]. This approximation was shown to give an excellent description of the scattering intensity of a system of randomly packed spheres [43, 44]. An algorithm as implemented in the software SASfit was used for the computation [45]. The computation of I(Q) according to the formulas outlined above was performed with the software Mathematica [46]. Polydispersity of the PS/SiO2 particles was introduced by the convolution of the respective radii with a normal distribution. The hard sphere repulsion radius of the structure factor S(q) was set equal to the radii of the large support particles. This procedure is of course an approximation for a polydisperse system. It will turn out, however, that this approximation is inconsequential.

Figure 3 depicts the three scattering contributions Ii(q) according to formula (2) decomposed into Eqs. (11), (12) and (13) at an irradiation energy E = 11.55 keV for a Pt sphere (RPt = 5 nm) attached to a SiO2 sphere with a radius of 500 nm. The overall I(q) is dominated by the scattering from the embedding matrix silicate. At low q, the influence of the structure factor S(q) can be seen which leads to a decrease of the scattered intensity at low q. However, the influence of S(q) vanishes beyond a given q value. For the present system, its influence may be safely dismissed for q > 0.03 nm−1 which is the typical range of many ASAXS experiments. The difference I(q, E = 9 keV) − I(q, E = 11.55 keV) in Fig. 3c differs from the pure resonant contribution at low q values. Only at higher momentum transfer q the characteristics of the differences and ν(q) agree. Note that the larger scattering length contrast between Pt and PS as compared to Pt and SiO2 leads to a broader q regime in which I(q, 9 keV) − I(q, 11.55 keV) and ν(q) exhibit the same slope. Thus, the simple subtraction of scattered intensities at different irradiation energies represents an approximation for the extraction of the resonant scattering only. A large difference in scattering length density between metal and matrix contributes to the validity of this approximation. Even within the ASAXS window the deviations may become noticeable. At smaller q values, they may become very large and even negative (not shown in Fig. 3).
Fig. 3

Shown are a the non-resonant scattering contribution \( F_0^2(q) \), b the mixed scattering term 2 \( f_{\mathrm{Pt}}^{\prime } \)F0ν0 at E = 11.55 keV as well as c the pure resonant scattering \( \nu (q)\left( {f_{\mathrm{Pt}}^{{\prime 2}}+f_{\mathrm{Pt}}^{{\prime \prime 2}}} \right) \) into N/V and S(q), respectively, for platinum particles adsorbed to a large SiO2 sphere (R = 500 nm, 10 % polydispersity, see Eqs. (2), (3) and (11)–(13)). Moreover the result for the simple subtraction of the overall scattered intensities at 9.03 and 11.55 keV is depicted for the support material SiO2 and PS in c

Experimental section

The MCM-41-type silica was prepared according to a procedure reported earlier [47]. For incorporation of Pt, the MCM-41 powder (2 g) was loaded with [Pt(NH3)4]Cl2 (Chempur, 99.5 wt%) from an aqueous solution (deionized water) by incipient wetness impregnation. The target loading was 4 wt% Pt. Subsequently, the sample was pressed (20 MPa), crushed and sieved to obtain the particle fraction of 1.1–1.6 mm. Batches of 0.5 g of the pelletized material were treated in a flow of air (150 cm3 min−1) at 250 °C for 3 h and then, in flowing hydrogen (150 cm3 min−1) at 280 °C for 2 h to obtain Pt nanoparticles supported on MCM-41 (Pt/MCM-41).

The platinum content of the resulting Pt/MCM-41 materials was determined by optical emission spectrometry with inductively coupled plasma (ICP-OES instrument: PerkinElmer, Plasma 400) after dissolution in 50 vol% hydrofluoric acid (Fluka, 40 wt% in water) and 50 vol% hydrochloric acid (Fluka, 37 wt% in water). Thus, a Pt loading of 3.4 wt% was obtained.

The textural properties of the Pt/MCM-41 material were characterized by nitrogen physisorption at −196 °C on a micromeritics, ASAP2010C equipment. Prior to analysis, the samples were activated at 350 °C for 12 h at a pressure <1 Pa. The same instrument was used for determination of the Pt dispersion via hydrogen chemisorption at 30 °C. In this case, the samples were activated at 350 °C for 2 h at a pressure <1 Pa.

X-ray diffractograms were recorded on a Siemens D5000 instrument using CuKα radiation (30 mA, 40 kV). For characterizing the structure of the MCM-41 material, the 2θ range of 1.5° to 7° (step size, 0.2°; 5 s/step) was scanned. The Pt particle size was estimated using the Scherrer equation using the full width at half maximum from a Gaussian fit of scanning time of 20 s/step. TEM micrographs were obtained from the Pt(111) − reflection at 2θ = 39.7°. For this, a field emission electron microscope (type Jeol, JSM-2100F) at the Institute for Physical Chemistry and Electrochemistry at the Leibniz Universität Hannover was employed.

ASAXS measurements were performed at the JUSIFA beamline [48] at HASYLAB, DESY Hamburg at three different energies in the energy range of the LIII absorption edge of platinum at 11.564 keV with a precision in the resolution regime 10−3 < ΔI/I < 10−2 (separated pure resonant scattering with respect to the overall scattering). Precise corrections (background, sensitivity, transmission, normalization, dead-time correction, dark current) and the calibration of the scattering curves into absolute units are mandatory and have to meet these accuracy requirements (i.e., should be better by one order in magnitude). Transmission measurements were performed with a precision of 10−4 using a special (windowless) photodiode (Hamamatsu S2387-1010N). The dead-time correction of the MWPC detector was measured for each exposure and corrected for in the data reduction. The normalization of the scattering pattern was performed by measurements of the primary photon flux with a sodium-iodine scintillation counter with an accuracy of better than 10−4.

The scattering curves of all sample measurements have been calibrated into macroscopic scattering cross section in units of cross section per unit volume [cm2/cm3] = [cm−1] by using the JUSIFA glassy carbon standards. The errors have been calculated via error propagation law from the statistical errors of the photon counts of all contributing measurements (i.e. measurements of sample, sensitivity, background, dark current).

Results and discussion

The 3.4 Pt/MCM-41 material (Pt loading of 3.4 wt%) shows an x-ray diffractogram typical of the ordered mesoporous MCM-41-type silica support (see Online resource, Fig. S1) [49]. Also, as expected, the nitrogen sorption isotherms are of type IV according to the IUPAC classification corresponding to a specific surface area of 1,018 m2 g−1 and a pore diameter of 2.3 nm (BJH model) (see Online resource, Fig. S2).

Assuming a spherical geometry and an fcc structure of the Pt particles, an average diameter of 16.6 nm (Pt dispersion of 7 %) was determined by XRD applying the Scherrer equation to the Pt(111) reflection at 2θ = 39.7°. From hydrogen chemisorption, a clearly lower average particle diameter of 3.3 nm (Pt dispersion, 33 %) was obtained. It should be noted, however, that Pt particles with diameters lower than 1 nm cannot be detected by XRD and that particles of low crystallinity and deviations of the fcc structure do not substantially contribute to the Pt(111) reflection [50]. XRD, therefore, may overestimate the actual average Pt particle size, especially when smaller particles are present. On the other hand, hydrogen chemisorption often underestimates the noble metal particle size as deviations of the assumed stoichiometry of H/Pt of 1 to higher values, corresponding to higher Pt dispersions than 100 %, may result [49].

These considerations are supported by the TEM micrographs. Figure 4 shows a broad distribution of Pt particle sizes and shapes. Especially, rather large and unevenly shaped particles with sizes up to 30 nm are clearly visible. These are undoubtedly located outside the MCM-41 mesopores. However, an even distribution of the smaller Pt particles, particularly with diameters <5 nm, is observed as well. Moreover, a large fraction of these particles is located within the mesopores of the MCM-41 support.
Fig. 4

TEM micrographs of 3.4 Pt/MCM-41

Non-resonant, mixed and resonant terms extracted from experimental data on the 3.4 Pt/MCM-41 material are shown in Fig. 5. Moreover, the result of a simple subtraction of scattered intensities determined at different energies is shown for comparison. The pure resonant term can be well fitted with a model describing the Pt particles as an ensemble of two populations, each consisting of polydisperse spheres modelled as log-normal distributions with different characteristic radii. The first population exhibits a characteristic radius of 27 nm with a respective width parameter σ of 0.2 and a particle density of 1.4 × 1013 ml−1. For the second population, values of 1.8 nm, 0.2 and 6 × 1015 ml−1 were found. The pure resonant scattering lacks the correlation peak, which is visible at q ≈ 0.2 nm−1. This finding indicates that the Pt particles are spread evenly on the support material and are evenly distributed over the material. They are also consistent with the characterization of the Pt particle size distribution by the TEM results. Most importantly, however, the ASAXS technique provides a quantitative determination of the particle sizes at two different length scales. No correlation of the location of the Pt particles with the MCM-41 mesopores (diameter of 2.3 nm) can be seen. This can be argued directly from the absence of a peak in the third scattering function resulting solely from the Pt particles (triangles in Fig. 5). If the nanoparticles would be strongly correlated to the mesopores, the peak resulting from the pores filled by Pt particles should be seen in this scattering function, too. Clearly, this is not seen, and there is no correlation of the Pt particles to the pore as visible from the absence of the pronounced correlation peak in ν2(q) which is present in \( F_0^2(q) \). This is in full agreement with the results obtained earlier from TEM. The fluctuation of I(q) around 2 nm−1 visible for the extracted intensities of the resonant scattering as well as in the mixed term might be due to the influence of a structure factor indicative for the distribution of the smaller Pt particles. However, present data basing on data from a single concentration of Pt do not allow to draw unambiguous conclusions on the origin of the fluctuations around 2 nm−1.
Fig. 5

Non-resonant (black squares), mixed (red circles) and pure resonant (green triangles) terms as obtained by decomposition of scattered intensities I(q) at irradiation energies of 10.620, 11.433 and 11.551 keV. The blue diamonds depict the difference of the scattered intensities determined at 10.620 and 11.551 keV; the according fit is given by a blue line. The green line denotes a fit to the pure resonant contribution assuming the Pt particles to consist of two polydisperse populations described via log-normal distributions. The lower inset depicts the ratio of I(q, 10620 eV) − I(q, 11551 eV) over ν2(q) N/V divided by a divisor of 1,000 in order to scale the y-axis to unity for the visible plateau region between 0.2 and 1 nm−1

From Eqs. (5) and (12), it is evident that the resonantly scattered intensity extracted by simple subtraction and the one extracted by decomposition are just separated by a constant factor and thus should exhibit the same q dependency. The difference I(q, 10.620 keV) − I(q, 11.551 keV) indeed exhibits over a broad range a similar q dependency as compared to the resonant term ν2(q) obtained by decomposition of the data. However, at lowest and highest q, the latter data set follows a different pattern as compared to ν2(q) (see Fig. 5, inset). The differences at low q are much more pronounced and have a considerable impact on the fitting results. The characteristic radius of 1.8 nm determined for the population of the small Pt spheres agrees well with the one obtained from fitting ν2(q). Here, just the characteristic width parameter σ increases to 0.25. The characteristic radius of the population of large Pt spheres, however, changes due to the deviation of the subtracted curve from ν2(q). A characteristic radius of 20 nm (σ = 0.25) instead of 27 nm is obtained which means that this value differs by more than 25 %. The tendency of the curve calculated by simple subtraction to differ especially at low q from the decomposed one has already been seen at the example of the theoretical curves (see Fig. 3). Thus, the experimental data support qualitatively the finding already obtained from the model calculations. But the simple subtraction method represents a good approximation to obtain the pure resonant scattering for high q values. It yields reliable fitting values for the small Pt particles, i.e. in the high q region. These findings are fully supported by the model calculations showing that the main problem of this method resides at low scattering angles.


We considered the anomalous small-angle x-ray scattering of a heterogeneous system consisting of large polydisperse spheres (PS and SiO2), containing small platinum spheres. We showed that the complete extraction of the pure resonant scattering contribution requires the determination of I(q, E) at three different energies at least and the subsequent decomposition into the three partial scattered intensities. The result obtained by the simple subtraction of I(q, E) at two different energies as suggested by Brumberger et al. [39] was found to give the purely resonant contribution in good approximation for high q values but may lead to erroneous results at smaller scattering angles. This finding is supported by comparison with experimental results obtained from platinum supported on the ordered mesoporous silica MCM-41. The full decomposition into three partial intensities is the superior way inasmuch as it gives the scattering function of the metal particles without any prior assumption or condition.



The authors would like to thank Prof. Dr. Armin Feldhoff of the Leibniz Universität Hannover, Germany, for taking the TEM micrographs. Part of this work was funded by the Ministry of Science, Research and the Arts as well as the Landesstiftung foundation of Baden Wuerttemberg (Az: 23-720.431-1.8/1)

Supplementary material

396_2013_2951_MOESM1_ESM.doc (1 mb)
ESM 1(DOC 1050 kb)


  1. 1.
    Gates BC (1995) Supported metal clusters: synthesis, structure, and catalysis. Chem Rev 95:511–522CrossRefGoogle Scholar
  2. 2.
    Taguchi A, Schüth F (2005) Ordered mesoporous materials in catalysis. Microporous Mesoporous Mater 77:1–45CrossRefGoogle Scholar
  3. 3.
    Yao N, Pickney C, Lim S, Pak C, Haller GL (2001) Synthesis and characterization of Pt/MCM-41 catalysts. Microporous Mesoporous Mater 44–45:377–384CrossRefGoogle Scholar
  4. 4.
    Junges U, Jacobs W, Voigt-Martin I, Krutzsch B, Schüth F (1995) MCM-41 as a support for small platinum particles: a catalyst for low-temperature carbon monoxide oxidation. J Chem Soc Chem Commun 2283–2284Google Scholar
  5. 5.
    Lembacher C, Schubert U (1998) Nanosized platinum particles by sol–gel processing of tethered metal complexes: influence of the precursors and the organic group removal method on the particle size. New J Chem 22:721–724CrossRefGoogle Scholar
  6. 6.
    Eswaramoorthy M, Niwa S, Toba M, Shimada H, Raj A, Mizukami F (2001) The conversion of methane with silica-supported platinum catalysts: the effect of catalyst preparation method and platinum particle size. Catal Lett 71:55–61CrossRefGoogle Scholar
  7. 7.
    Ryoo R, Ko CH, Kim JM, Howe R (1996) Preparation of nanosize Pt clusters using ion exchange of Pt(NH3) 4 2+ inside mesoporous channel of MCM-41. Catal Lett 37:29–33CrossRefGoogle Scholar
  8. 8.
    Goodisman J, Brumberger H, Cupelo R (1981) Determination of surface areas for supported-metal catalysts from small-angle scattering. J Appl Cryst 14:305–308CrossRefGoogle Scholar
  9. 9.
    Matyi RJ, Schwartz LH, Butt JP (1987) Particle size, particle size distribution, and related measurements of supported metal catalysts. Catal-Rev-Sci Eng 29:41–87CrossRefGoogle Scholar
  10. 10.
    Goerigk G, Haubold HG, Lyon O, Simon JP (2003) Anomalous small-angle X-ray scattering in materials science. J Appl Cryst 36:425–429CrossRefGoogle Scholar
  11. 11.
    Stuhrmann HB (1985) Resonance scattering in macromolecular structure research. Adv Polym Sci 67:123–163CrossRefGoogle Scholar
  12. 12.
    Cromer DT, Libermann DA (1970) Relativistic calculation of anomalous scattering factors for x rays. J Chem Phys 53:1891–1898CrossRefGoogle Scholar
  13. 13.
    Cromer DT, Libermann DA (1981) Anomalous dispersion calculations near to and on the long-wavelength side of an absorption edge. Acta Cryst A37:267–268Google Scholar
  14. 14.
    Chantler CT (1995) Theoretical form factor, attenuation and scattering tabulation for Z = 1–92 from E = 1–10 eV to E = 0.4–1.0 MeV. J Phys Chem Ref Data 24:71–643CrossRefGoogle Scholar
  15. 15.
    Haubold HG, Wang XH (1995) ASAXS studies of carbon supported electrocatalysts. Nucl Instrum Methods Phys Res, Sect B 97:50–54CrossRefGoogle Scholar
  16. 16.
    Haubold HG, Wang XH, Jungbluth H, Goerigk G, Schilling H (1996) In situ anomalous small-angle X-ray scattering and X-ray absorption near-edge structure investigation of catalyst structures and reactions. J Mol Struct 383:283–289CrossRefGoogle Scholar
  17. 17.
    Haubold HG, Wang XH, Goerigk G, Schilling H (1997) In situ anomalous small-angle x-ray scattering investigation of carbon-supported electrocatalysts. J Appl Cryst 30:653–658CrossRefGoogle Scholar
  18. 18.
    Bönnemann H, Waldöfner, Haubold HG, Vad T (2002) Preparation and characterization of three-dimensional Pt nanoparticle networks. Chem Mater 14:1115–1120Google Scholar
  19. 19.
    Haubold HG, Vad T, Waldöfner N, Bönnemann H (2003) From Pt molecules to nanoparticles: in-situ (anomalous) small-angle X-ray scattering studies. J Appl Cryst 36:617–620CrossRefGoogle Scholar
  20. 20.
    Vad T, Hjbolouri F, Haubold HG, Scherer GG, Wokaun A (2004) Anomalous small-angle x-ray scattering study on the nanostructure of co-sputtered platinum/carbon layers. J Phys Chem B 108:12442–12449CrossRefGoogle Scholar
  21. 21.
    Brumberger H, Hagrman D, Goodisman J, Finkelstein KD (2005) In situ anomalous small-angle X-ray scattering from metal particles in supported-metal catalysts. II. Results. J Appl Cryst 38:324–332CrossRefGoogle Scholar
  22. 22.
    Yu C, Koh S, Leisch JE, Toney MF, Strasser P (2009) Size and composition distribution dynamics of alloy nanoparticle electrocatalysts probed by anomalous small angle X-ray scattering (ASAXS). Faraday Discuss 140:283–296CrossRefGoogle Scholar
  23. 23.
    Rasmussen FB, Molenbrock AM, Clausen BS, Feidenhans R (2000) Particle size distribution of a Ni/SiO2 catalyst determined by ASAXS. J Catal 190:205–208CrossRefGoogle Scholar
  24. 24.
    Bota A, Goerigk G, Drucker T, Haubold HG, Petro J (2002) Anomalous small-angle X-ray scattering on a new, nonpyrophoric Raney-type Ni catalyst. J Catal 205:354–357CrossRefGoogle Scholar
  25. 25.
    Rasmussen FB, Sehested J, Teunissen HT, Molenbrock AM, Clausen BS (2004) Sintering of Ni/Al2O3 catalysts studied by anomalous small angle X-ray scattering. Appl Catal A 267:165–173CrossRefGoogle Scholar
  26. 26.
    Zehl G, Schmithals G, Hoell A, Haas S, Hartnig C, Dorbandt I, Bogdanoff P, Fiechter S (2007) On the structure of carbon-supported selenium-modified ruthenium nanoparticles as electrocatalysts for oxygen reduction in fuel cells. Angew Chem Int Ed 46:7311–7314CrossRefGoogle Scholar
  27. 27.
    Haas S, Hoell A, Zehl G, Dorbandt I, Bogdanoff P, Fiechter S (2008) Structural investigation of carbon supported Ru-Se based catalysts using anomalous small angle X-ray scattering. ECS Trans 6:127–138CrossRefGoogle Scholar
  28. 28.
    Haas S, Zehl G, Dorbandt I, Manke I, Bogdanoff P, Fiechter S, Hoell A (2010) Direct accessing the nanostructure of carbon supported Ru-Se based catalysts by ASAXS. J Phys Chem C 114:22375–22384CrossRefGoogle Scholar
  29. 29.
    Polizzi S, Riello P, Balerna A, Benedettia A (2001) Nanostructure of Pd/SiO2 supported catalysts. Phys Chem Chem Phys 3:4614–4619CrossRefGoogle Scholar
  30. 30.
    Jokela K, Serimaa R, Torkkeli M, Eteläniemi V, Ekman K (2002) Structure of the grafted polyethylene-based palladium catalysts: WAXS and ASAXS study. Chem Mater 14:5069–5074CrossRefGoogle Scholar
  31. 31.
    Goerigk G, Williamson DL (2006) Quantitative ASAXS of germanium inhomogeneities in amorphous silicon-germanium alloys. J Appl Phys 99:084309CrossRefGoogle Scholar
  32. 32.
    Benedetti A, Bertoldo L, Canton P, Goerigk G, Pinna F, Riello P, Polizzi S (1999) ASAXS study of Au, Pd and Pd-Au catalysts supported on active carbon. Catal Today 49:485–489CrossRefGoogle Scholar
  33. 33.
    Polizzi S, Riello P, Goerigk G, Benedetti A (2002) Quantitative investigations of supported metal catalysts by ASAXS. J Synchrotron Radiat 9:65–70CrossRefGoogle Scholar
  34. 34.
    Andreasen JW, Rasmussen FB, Helveg S, Molenbroek A, Ståhl K, Nielsen MM, Feidenhans R (2005) Activation of a Cu/ZnO catalyst for methanol synthesis. J Appl Cryst 39:209–221CrossRefGoogle Scholar
  35. 35.
    Patel M, Rosenfeldt S, Dingenouts N, Pontoni D, Narayanan T, Ballauff M (2004) Analysis of the correlation of counterions to rod-like macroions by anomalous small-angle X-ray scattering. Phys Chem Chem Phys 6:2962–2967CrossRefGoogle Scholar
  36. 36.
    Dingenouts N, Patel M, Rosenfeldt S, Pontoni D, Narayanan T, Ballauff M (2004) Counterion distribution around a spherical polyelectrolyte brush probed by anomalous small-angle X-ray scattering. Macromolecules 37:8152–8159CrossRefGoogle Scholar
  37. 37.
    Goerigk G, Schweins R, Huber K, Ballauff M (2004) The distribution of Sr2+ counterions around polyacrylate chains analyzed by anomalous small-angle X-ray scattering. Europhys Lett 66:331–337CrossRefGoogle Scholar
  38. 38.
    Bota A, Varga Z, Goerigk G (2008) Structural description of the nickel part of a Raney-type catalyst by using anomalous small-angle x-ray scattering. J Phys Chem C 112:4427CrossRefGoogle Scholar
  39. 39.
    Brumberger H, Hagrman D, Goodisman J, Finkelstein KD (2005) In situ anomalous small-angle X-ray scattering from metal particles in supported-metal catalysts. I. Theory. J Appl Cryst 38:147–151CrossRefGoogle Scholar
  40. 40.
    Goodisman J, Brumberger H (1971) Scattering from a multiphase system. J Appl Cryst 4:347–351CrossRefGoogle Scholar
  41. 41.
    Pedersen JS (1997) Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting. Adv Colloid Interface Sci 70:171–210CrossRefGoogle Scholar
  42. 42.
    Hansen JP, McDonald IR (1976) Theory of simple liquids. Academic, LondonGoogle Scholar
  43. 43.
    Dingenouts N, Ballauff M (1998) Assessment of spatial order in dried latexes by small-angle X-ray scattering. Macromolecules 31:7423–7429CrossRefGoogle Scholar
  44. 44.
    Dingenouts N, Ballauff M (1999) First stage of film formation by latexes investigated by small-angle x-ray scattering. Langmuir 15:3283–3288CrossRefGoogle Scholar
  45. 45.
    Kohlbrecher J (2012) SASfit: a program for fitting simple structural models to small angle scattering data. Accessed 29 Feb 2012
  46. 46.
    Wolfram Research Inc (2010) Mathematica. Version 8.0, Champaign, ILGoogle Scholar
  47. 47.
    Boger T, Roesky R, Gläser R, Ernst S, Eigenberger G, Weitkamp J (1997) Influence of the aluminum content on the adsorptive properties of MCM-41. Microporous Mater 8:79–91CrossRefGoogle Scholar
  48. 48.
    Haubold HG, Gruenhagen K, Wagener M, Jungbluth H, Heer H, Pfeil A, Rongen H, Brandenburg R, Moeller R, Matzerath J, Hiller P, Halling H (1989) JUSIFA—a new user-dedicated ASAXS beamline for materials science. Rev Sci Instrum 60:1943–1946CrossRefGoogle Scholar
  49. 49.
    Beck JS, Vartuli JC, Roth WJ, Leonowicz ME, Kresge CT, Schmitt KD, Chu CTW, Olson DH, Sheppard EW, McCullen SB, Higgins JB, Schlenker JL (1992) A new family of mesoporous molecular sieves prepared with liquid crystal templates. J Am Chem Soc 114:10834CrossRefGoogle Scholar
  50. 50.
    Bergeret G, Gallezot P (1997) Handbook of heterogeneous catalysis, vol 2. VCH-Verlagsgesellschaft, Weinheim, pp 439–464Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Soft Matter and Functional MaterialsHelmholtz-Zentrum Berlin für Materialien und EnergieBerlinGermany
  2. 2.Institute of PhysicsHumboldt University BerlinBerlinGermany
  3. 3.Institut für Technische ChemieFakultät für Chemie und MineralogieLeipzigGermany
  4. 4.Institut für Technische Chemie und PolymerchemieKarlsruher Institut für Technologie (KIT)KarlsruheGermany

Personalised recommendations