The Characterization of Atomically Precise Nanoclusters Using X-Ray Absorption Spectroscopy

Abstract

The XAS toolbox (EXAFS, XANES, theoretical calculations, in situ measurements) is used in a variety of applications to determine the structure and electronic properties of atomically precise nanoclusters (APNCs). The analysis using the EXAFS part of the XAS spectrum involves models that are based on atomic packing (e.g., fcc, icosahedra) or surface effects. Theoretical methods based on DFT can improve the understanding of disorder effects on the EXAFS measurements. In comparative experiments, the effect of solvation and of the ligands (density of ligands, different ligands) is discussed. It was found that the strength of the Au–thiol bonding can lead to relaxation effects that reduce the contraction of Au–Au bonds in the core. Changes in structure could be observed for solvation and catalytic reaction with the application of in situ measurements in specifically designed reactors. Even though EXAFS is a powerful method with a number of advantages, such as that no long-range order is necessary, all kinds of materials can be investigated, nondestructively. The analysis of EXAFS data is quite challenging, however, and effects such as structural disorder, if the sample is a mixture of components (not pure) or if the APNCs have several binding ligands, can distort the results. The use of l-DOS based on theoretical XANES calculations that can give information about electronic properties of APNCs is also challenging. In complement with XPS experiments, however, consistent answers can be found.

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1 Definition of the Topic

Overview of the methods and results of the application of X-ray absorption spectroscopy characterizing atomically precise nanoclusters.

2 Introduction

Interest in catalysts such as the atomically precise nanoclusters (APNCs) is growing. Much is still to be learned about the properties of these materials, however. At what point in cluster growth does a material change from the quantum behavior of a single atom or molecule to the ensemble behavior of a bulk metal [1]? Is the transition smooth with increasing cluster size, or is there an intermediate region where the clusters have properties that are neither metallic nor due to quantum size effects [2]? Is there a relationship between the size of the clusters and their electronic, optical, and catalytic properties [3]? Is there a correlation between structure and electronic properties [4]? How are structure and electronic properties affected by a complex environment (including different temperatures, pressures, or solvation effects) [5]? Since APNCs are the focus of this book, some answers to these questions are presented in other chapters.

However, a very brief introduction shall help the reader to understand the separation of the group of APNCs from the wider group of nanoparticles (NPs). The definition of NPs as mesoscopic systems between atoms or molecules and macroscopic bulk material can apply to a good number of structures with particle sizes of ≤ 100 nm. The term APNC means that these NPs have a precise number of atoms and generally implies that they are small (below 10 nm diameter). It is reported that the atomic precision of APNCs affects catalytic and optical properties and gives exceptional stability to the APNC (e.g., [4, 6–8]). A brief history of Au APNCs is given in Schaaff et al. [7].

The first step in understanding the correlation between the structure and the chemical and physical properties (which enable tailoring of the catalytic properties of the APNC [9]) is to gain precise knowledge about the structure of the clusters. X-ray diffraction (XRD) is the best method to determine the structure of a material. For APNCs, there is a certain degree of disorder [10] and fluidity [11] on the surface due to the presence of ligands. For this reason, it is mostly not possible to grow crystals and determine the structure using XRD [12]. In order to find some understanding of the structure for these cases, certain semiempirical models have been developed [13, 14]. For example, “staple fitness,” concerning the highest structural stability of the staple motif [15], will be discussed later in this paper.

The most basic structural models were created on the basis of atomic packing structures (e.g., fcc) and are summarized by Benfield [16]. The atomic packing mode in metal NCs is in direct correlation with their size and other structural properties [4, 9, 17]. Specifically, the stability stands in direct relation to the so-called magic numbers [9]. Details will be discussed further below. New approaches using density functional theory (DFT) have made it possible to determine the structures of several clusters, e.g., Au₂₅(SR)₁₈ [18], Au₃₈(SR)₂₄ [19], and Au₁₄₄(SR)₆₀ [20]. Challenges include the determination of the cluster size (more specifically the number of atoms) from the packing mode models and the understanding why smaller clusters have icosahedral structure in one case and cuboctahedral structure in another [11].

The most studied group among the APNCs is the gold clusters (Au_x(SR)_y) with thiol capping. This is because when the gold–sulfur interface can be understood (including atomic and electronic structure, properties of signal transmittance, excitations, and electron transport), then they can be applied to fields such as nanocatalysis, molecular electronics, biolabeling, photonics, and sensing [20]. Further, the extremely high surface-to-volume ratio of these gold clusters (Au_x(SR)_y) can help with the understanding of self-organization processes in self-assembled monolayers (SAM) [7]. Solution phase investigations of Au clusters can reveal the physical and chemical properties of atomically precise Au nanoclusters [21]. In contrast to the use of thiol ligands is a new method of NC stabilization with s: These dendrimer-encapsulated nanoclusters (DENs) show quite different properties compared to thiol-stabilized NCs [22].

The second step in the understanding of the physical and chemical properties (specifically the catalytic properties) of APNCs is the determination of their electronic properties, which depend on the basic structure (size, packing) and environment. In particular, the size of a cluster will determine whether its electronic properties are discrete, i.e., atoms, molecules, and small clusters or form a band structure, i.e., bulk metals [4]. Common techniques to determine the electronic structure of materials are UV–vis spectroscopy and X-ray photoelectron spectroscopy (XPS) (which needs ultrahigh vacuum (UHV) conditions [9]). Another procedure that is used is the calculation of density of states based on quantum chemistry [23].

The goal of the generation of APNC is not only the control of the size (e.g., number of atoms) but also the distribution of metals in the case of the bimetallic NC. The determination of the distribution of the two metals is another aspect of the concept of “active sites” which includes defects, sharp corners, and atomic steps, and its understanding can help control catalytic reactions further [6].

The electronic properties can change if the two metals are distributed in the certain way [24]. For example, alloys with Pd, Ag, Pt, or Cu based on Au₂₅(SR)₁₈ and Au₃₈(SR)₂₄ NC were synthesized and investigated by both theory and experiment and showed that the content and distribution of second metal (doping) have direct effects on the geometrical structure and electronic properties (e.g., [25–28]). In the cases of Au₂₄Pt(SR)₁₈ [25], Au₂₄Ag(SR)₁₈ [26], Au₂₄Pd(SR)₁₈ [27, 28], and Au₂₄Cu(SR)₁₈ [29, 30], the dopant atoms are believed to occupy the central site of the metal core. It is the precise knowledge of the structure and electronic properties of the NCs that is important in the understanding of the catalytic properties. To achieve this goal, methods to investigate the structure and electronic properties have to be developed constantly [31].

A powerful characterization technique for many materials is X-ray absorption spectroscopy (XAS). XAS has become a very important tool among the synchrotron-based techniques for the characterization of materials, especially metal nanoparticles and catalysts [9, 32]. Because XAS is element specific, this gives a very special opportunity to observe the same sample from different points of view if several elements, e.g., metals in alloy, are used (more details below). XAS is applicable to a broad range of elemental concentrations (i.e., from tens of ppm to wt% levels) [32] for solids and liquids as well and does not require long-range order in the sample [33]. In addition to the oxidation state, the chemical environment and geometrical information can be extracted from XAS. One aspect of XAS that especially combines theoretical and experimental techniques is extended X-ray absorption fine structure (EXAFS) spectroscopy. The analysis of EXAFS can:

• Determine coordination numbers (CN) to the neighboring atoms in a NC

• Determine distances of Me–Me and Me–L bonding

• Compare structure models with experimental data

• Determine structural disorder (up to a degree)

These important structural details can even be extracted from amorphous materials [2]. The resolution of EXAFS regarding the bond distances is of the order of 0.001 Å within a distance of about 10 Å from the center to analyze the local structure [3]. In this respect, EXAFS can even extract structural information which is based on the atomic packing models above from systems that do not have a long-range order.

Using the other aspect of XAS, X-ray absorption near-edge structure (XANES, formerly called NEXAFS) spectroscopy, it is possible to:

• Analyze the electronic properties (i.e., density of electronic states above the Fermi level)

• Determine the effective oxidation state

• Determine the chemical speciation

In this review, we focus on the methods and problems that are connected with the characterization of APNCs using XAS. Correct structural models and purity of NP content are the most important aspects to highlight. Together EXAFS and XANES are very versatile (nondestructive, study both atomic and electronic structure) and can be applied to the characterization of all kinds of materials and reactions in situ, even if they require high temperatures, high pressures, or other environmental changes, e.g., solvation and vaporization [12]. XAS techniques can be combined with theoretical calculations to validate structural models [31].

Some questions that will be answered in this review are the following:

• When was EXAFS first used for the characterization of APNC?

• How is the atomic size (numbers of atoms) determined by using EXAFS?

• What is so different in the use of EXAFS to study APNC compared to normal NP?

• What is the effect of structural disorder on the EXAFS analysis technique?

• How can the electronic information contained in XANES be extracted?

This latest review focuses on the use of XAS to characterize the structure, electronic properties, and behavior of APNCs, including during heating, solvation, and catalytic activity.

Other recent reviews on related topics include the following: Bare and Ressler [32] and Frenkel et al. [34] discuss the broader field of catalysis and the application of catalytic reactors together with (in situ) XAS. A more specified discussion of the catalytic activity of metal DENs using catalytic reactors investigated with in situ XAS was published by Myers et al. [22]. The wider region of the characterization of NP using XAS was reviewed by Frenkel et al. [35], Lapresta-Fernandez et al. [36], and Modrow [9].

In the wide field of applications of EXAFS, theoretical methods especially the combination of EXAFS with other theoretical methods such as density functional theory (DFT) and molecular dynamics (MD) are progressing fast and are becoming the state of the art of the characterization techniques [34]. Some of these techniques will be discussed here later to present a complete as possible overview of the techniques currently available in the XAS toolbox.

The evolution of clusters from atomic to bulk including both theoretical and experimental discussions is found in Schmid [37]. The interplay of atomic and electronic structure from a more theoretical point of view is discussed by Hakkinen [38] and Pei and Zeng [39].

Frenkel [40] and Gao and Goodman [41] discussed the specifics of the characterization of bimetallic NP, while Jin and Nobusada [42] focused on the methods of alloying within NCs with respect to different elements. Zhang [43] summarized the research on gold APNCs that was done in his group using XAS methods in a very recent review. Zhang also sketched very briefly using excellent illustrations the advantages and results that can be drawn from XAS. There can be found many more reviews on the different aspects of APNC. However, these do not mention the characterizational strength of the XAS toolbox.

The sections of this chapter are organized as follows: A short introduction of the physics of XAS and the specifics of XANES and EXAFS is followed by a discussion of the experimental setup in the next section. The main section of this chapter discusses the techniques of the application of first, EXAFS and second, XANES that are used in order to gain structural and electronic information from investigations of APNCs and the key findings.

3 Experimental and Instrumental Methodology

3.1 The Physics of X-Ray Absorption Spectroscopy

X-ray absorption spectroscopy (XAS) is a sophisticated tool to analyze many different types of materials. It is especially useful because no long-range order is required, but only the local environment of the element of interest is significant. This qualifies XAS as an excellent tool for the investigation of noncrystalline systems. The analysis of XAS spectra can give details on oxidation state, geometry, and the kinds of neighboring atoms. The element under investigation can be chosen because of the distinct electron binding energies. There are a number of introductory texts on XAS available in the literature, for example, Bunker [44], Calvin [45], Kelly et al. [46], Koningsberger, Prins [33], and Teo [47]. In a nutshell: The law of Lambert–Beer

$$ I = {I}_0{e}^{-{\mu}_l(E)x} $$

(5.1)

describes the attenuation of radiation of initial intensity I ₀ with regard to intensity I at a distance x within a material. μ _l (E) (short, μ) is the linear absorption coefficient at energy E. For XAS experiments, bonding energies of inner shell electrons extend from UV light for light elements (≈50 eV) up to hard X-rays (≈100 keV) for heavy elements. In this typical energy range for XAS experiments, the absorption coefficient μ is dominated by the photoelectric effect. XAS involves the measurement of the absorption coefficient μ as a function of photon energy E close to the ionization energy of an inner shell electron in a material and reveals a fine structure (see Fig. 5.1). The energy at which the absorption rises abruptly is called the absorption edge, and the energetic position is denoted E ₀ . This fine structure is an oscillatory structure that modulates the (atomic) absorption coefficient of an isolated atom and originates from the interaction of an electron excited by photo absorption with the surrounding material. In the quantum mechanical picture of the photoelectron as a matter wave, the oscillatory structure can be explained as interference between waves, one wave leaving the absorbing atom and the other waves that are backscattered from the neighboring atoms according to the scattering effects of the chemical environment. Because electron binding energies are element specific, XAS is element specific.

Fig. 5.1

Fe K-XANES spectrum of metallic iron (—) and the atomic background (…)

The non-modulated absorption coefficient μ ₀ , related to an environment where no neighboring atoms are present, is called the atomic background. The atomic background can be approximated by an arc tangent curve but is, mostly, masked by the features of the main edge (cf. Fig. 5.1). Materials that can be examined with XAS are solids, fluids, or gases. XAS is divided into two aspects depending on the involvement of the type of scattering contribution and molecular orbitals to the signal. X-ray absorption near-edge structure (XANES) spectroscopy is the part of the fine structure close to the absorption edge E ₀ (typical −20 eV to 50 eV with respect to E ₀ ) showing intense features. In addition to the oxidation state, the chemical environment and geometrical information can be extracted from XANES using the fingerprinting technique. The XANES region is dominated by multiple scattering and transitions into molecular orbitals. The extended X-ray absorption fine structure (EXAFS) region extends out to 1000 eV above E ₀ and is mainly contributed by single scattering. The analysis of the EXAFS signal provides local structural information such as distance and CN of neighboring atoms. The information contained in a XAS spectrum is averaged over all atoms (of the element under investigation) that are probed (i.e., the atoms within the sample that are hit by the photon beam).

3.2 XANES

The fine structure of the near-edge (XANES, earlier NEXAFS) spectra consists of distinct characteristics such as pre-edge peaks, a white line (WL), shape resonances (SR), and the energy position of the absorption edge E ₀ (cf. Fig. 5.1). The position of the edge E ₀ is usually defined as the inflection point in the main rise of μ(E). In cases such as transition metals (Ti, Co, Fe, and so on), this position can be masked by pre-edge features. Figure 5.1 shows an example for iron metal. The position of the absorption edge E ₀ can shift due to the oxidation state of the absorbing atom or electronegativity of the neighboring atoms [48]. The white line (WL) is named after the strong feature just above the absorption edge which was observed in photosensitive films used to record spectra in early XAS experiments. Pre-edge features and WL peaks arise from transitions into unoccupied atomic or molecular orbitals (MO) above the Fermi level. All other features after the WL (up to about 50 eV) are called shape resonances (SR). SR are also characteristic features, and they have their origin in multiple scattering with neighboring atoms. Together the shape and position of each of the characteristic features in the XANES spectrum comprise a fingerprint of the electronic and geometric environment of the absorbing element. This chemical environment can be determined by comparison to XANES spectra of compounds with known structures.

Additional information contained in the XANES spectrum comes from the correlation of the WL feature to molecular orbitals and density of states [33]. The density of states (DOS) describes the number density of available states as a function of energy [49]. Further, the l-projected DOS (l-DOS) only includes the DOS for a specific quantum number (l = 0, 1, 2, etc.) which corresponds to the classification of the orbitals due to their angular momentum (s, p, d, respectively). The shape of a XANES spectrum reflects the projected electronic DOS of excited states because the XANES “function” χ(E) and the l-DOS ρ(E) share the same fine structure:

$$ \rho (E) = {\rho}_0(E)\ \left[1 + \chi (E)\right] $$

(5.2)

Here, E is the photoelectron energy, and ρ ₀ (E) is the density of states for the atomic background [50]. The XANES spectrum is derived from the reflection of transitions into unoccupied states above the Fermi level. Figure 5.2 depicts the relationship between the transitions from core states and the absorption edges (K, L, M).

Fig. 5.2

The density of states (DOS) depicted on the top reflects the transitions of electrons from core levels into unoccupied states above the Fermi energy (E_FERMI). The transitions starting from specific core levels correspond to the absorption edges of XAS (Reprinted with permission from Rehr and Albers [50]. Copyright 2000 by the American Physical Society)

To correlate the unoccupied l-DOS ρ(E) with experimental XANES, the relation

$$ \rho (E) = \left[{\rho}_0(E)/{\mu}_0(E)\right] \mu (E) $$

(5.3)

can be used, where μ ₀ (E) describes the effects of the core–hole interaction. In general, unoccupied states show up as peaks (reflecting possible transitions between molecular orbitals), and hybridization of orbitals is revealed when peaks in different orbitals have the same energy [9].

3.3 EXAFS

More than 50 eV up to 1000 eV above the absorption edge (E₀), the fine structure is much reduced in intensity but not reduced in information content. Therefore, in order to extract the information, the smooth atomic background has to be removed, and χ(E), the fine structure function (Fig. 5.3), is calculated:

Fig. 5.3

Fine structure of the Fe metal EXAFS spectrum (a) χ(k) and (b) Fourier transformed, χ(R)

$$ \chi (E) = \frac{\mu (E) - {\mu}_0(E)}{\varDelta \mu (E)} $$

(5.4)

where μ(E) is the measured absorption coefficient, μ ₀ (E) is the atomic background (a function calculated as a spline), and Δμ(E) is the edge step. Further, this function of the oscillations is converted into k-space using k ² = 2 m/ђ ² (E − E ₀ ) (with m, the mass of the electron, and ђ, the Planck constant (over 2π)) and using Fourier transformation into R-space (Fig. 5.3).

The interference between initial and backscattered waves as well as some examples for scattering paths is visualized in Fig. 5.4. Two main types of scattering paths are distinguished: single scattering and multiple scattering. Single scattering is in general sufficient to calculate the EXAFS part of the spectrum with the addition of some corrections regarding multiple scattering. Single scattering occurs only if the wavelength of the outgoing photoelectron wave λ is smaller than the interatomic bond distance R. Usually, this refers to a value of about +50 eV above E ₀ .

Fig. 5.4

(a) The interference between the outgoing wave and the backscattered waves is the source of the oscillatory structure in EXAFS, (b) examples for single scattering (red, brown) and multiple scattering paths (green, yellow, blue) in a crystal (From Ravel [51], used with permission)

The EXAFS function χ(k) is directly connected to the parameters of the environment of the absorbing atom. These parameters are described in the EXAFS equation [50]:

$$ \chi (k)={\displaystyle \sum_R}{S}_0^2{N}_R\frac{\left|f(k)\right|}{k{R}^2}* sin\left(2kR+2{\delta}_c+\varPhi \right){e}^{-2R/\lambda (k)}{e}^{-2{\sigma}^2{k}^2} $$

(5.5)

where χ(k) represents the pure oscillations in k-space. S ₀ ² is a factor that includes inelastic losses, N _R is the CN of neighbors at a certain radius, f(k) is the scattering amplitude, R is the distance to the neighboring atoms, δ _e is the phase shift, λ is the mean free path for inelastic losses, and σ ² is the Debye–Waller factor which relates to thermal and structural disorder. In order to extract the contributions of different backscattered waves, a Fourier transformation is performed, usually denoted FT χ(k) or just χ(R). From these parameters, bond lengths and coordination numbers can be extracted.

At present, EXAFS data are analyzed by refining the theoretically calculated EXAFS spectra of single paths using the sum of path rule:

$$ \chi (k)={\displaystyle \sum_P}{\chi}_P(k) $$

(5.6)

where χ _P denotes each path contributing to the spectrum.

The modern analysis of EXAFS data is done with programs such as Artemis (Demeter/Ifeffit) [52], WinXAS [53], or GNXAS [54]. The details of the application of these methods are described there. Briefly, the EXAFS spectrum in k-space is fitted using theoretically calculated scattering amplitudes and phase shifts from reference compounds with known structure. The parameters of the EXAFS equation are set as a relation to the structural values given for the known compounds. For the analysis of the EXAFS data, especially in the case of NCs, it is very important that the samples are 100 % NC and not containing by-products or precursors that contain the element under investigation [55]. For an EXAFS fit, it is important to have a model for the structure that is to be characterized. In the case of metallic NC, this model as a first-order approximation can be the metallic bulk structure. With a fit, distance and CNs with the first neighbors (up to five shells) are determined with the use of information about the Au–Au distance and CNs derived from the metal bulk. The number of SS paths (also coordination numbers) and the number of multiple scattering paths are intercorrelated and depend on the size and shape of the crystallites (i.e., the NC).

For the EXAFS fitting approach for NP, the following constraints have been proposed previously [35, 56–59]:

• 1. The degeneracy of multiple scattering paths has to be optimized within a range obtained by the measured size distribution of the nanoparticles.

• 2. Due to the presence of surface, i.e., ill coordinated, atoms in NP systems, the bond distance and bond–angle distributions are affected; therefore, it must be possible to determine the bond distances separately from the bulk metal system.

• 3. Because the background is the same as in bulk crystalline metal foil, nonstructural parameters are fixed to the values obtained for bulk metal within their estimated uncertainty (S _O ² , ΔE ₀ ).

The EXAFS analysis of bimetallic APNCs is even more challenging [55]. For alloy nanoclusters, the further following constraints are used on the heterometallic bonds based on Nashner et al., Frenkel, and Knecht et al. [40, 60–62]:

• 1. The CNs (N _Me1-Me2 and N _Me2-Me1 are heterometallic coordination numbers) of the Me–Me bonds for the two different metals (Me1 and Me2) have to relate to their concentration c: ${N}_{Me1- Me2}/{N}_{Me2- Me1}={c}_{Me2}/{c}_{Me1}$

• 2. The distances R between atoms of the two metals in each shell have to be the same: ${R}_{Me1- Me2}={R}_{Me2- Me1}$

• 3. The disorder parameters (Debye–Waller factor, σ ²) for both metals in each shell have to be the same: ${\sigma^2}_{Me1- Me2}={\sigma^2}_{Me2- Me1}$

3.4 The XAS Experiment

Synchrotron radiation is monochromatized using a set of parallel crystals in a double crystal monochromator applying Bragg’s law:

$$ n\cdot \lambda = 2\cdot d\cdot \sin \theta $$

(5.7)

with n being the order number, λ the wavelength of the reflected light, d the spacing of the crystal, and θ the Bragg angle. Slits are used to collimate and mirrors to focus the incoming beam onto the sample position.

A double crystal monochromator with parallel crystal setup is preferred for XAS experiments because the incoming and exiting beams are parallel to each other [63]. This way the monochromatized beam is fixed on the sample position, while the energy is scanned. The rest of this experimental setup consists of ionization chambers to measure the photon current before and after the sample and of an energy-dispersive semiconductor detector, positioned at a 90° angle with respect to the incoming beam, to measure fluorescence photons coming from the sample. The layout is displayed in Fig. 5.5.

Fig. 5.5

Experimental setup of a XAS experiment

After monochromatizing, the photons pass through the two ionization chambers and the sample to measure μ(E). For concentrated samples, the absorption μ can be measured indirectly by applying the law of Lambert–Beer (cf. Eq. 5.1) – transmission mode:

$$ \mu (E)\propto ln\left(\frac{I_0}{I_1}\right) $$

(5.8)

The absorption coefficient μ(E) is determined by measuring the photon current before the sample (I ₀ ) and behind the sample (I ₁ ). If another ionization chamber (I ₂ ) is installed behind I ₁ , a standard (e.g., metal foil) can be measured at the same time with the sample. This standard is used for energy calibration purposes.

Diluted samples with less than 1 % concentration of the absorbing element are measured in fluorescence mode where the semiconductor detector collects the fluorescence photons (I _f ) that are emitted as response to the absorption of the incident beam (I ₀ ) by the sample. Fluorescence and Auger electrons are the two relaxation mechanisms of atoms excited by X-ray radiation. For fluorescence detection, the absorption coefficient μ(E) is described by

$$ \mu (E)\propto \left(\frac{I_f}{I_0}\right) $$

(5.9)

Equation 5.9 is an approximation and only valid if the sample is thin and diluted so that no self-absorption occurs. Also, the sample should face in the direction of 45° with respect to the incoming beam (and therefore also the semiconductor detector) [44].

The sample preparation can have significant effects on the measurement. It is important that the samples are of the right average thickness and are homogeneous. The thickness of the sample determines the total absorption, which ideally should be about 1. Homogeneity of the sample is important because a nonhomogeneous sample will have a distribution of absorption coefficients instead of a well-characterized single value. As discussed by Lee et al. [64] and Stern and Kim [65], if samples have, for example, little holes, the absorption coefficient cannot be the same at each point (see Eq. 5.1). Therefore, if the absorption coefficient μ is not measured correctly, the data evaluated from those measurements cannot be reliable, especially for the increased distortions in monocrystalline materials due to higher surface-to-volume ratio [66, 67].

4 Key Research Methods and Findings on APNCs Characterized Using XAS

4.1 EXAFS

The EXAFS analysis method is very important for the characterization of metal clusters and catalysts. EXAFS analysis is used to determine specific information about materials including the chemical identity, average bond lengths for the different shells, and ensemble-average CN of atoms in each shell around a central atom. To date, only APNCs containing Au, Pd, Pt, and some alloys (e.g., Au–Cu, Au–Pd, and Au–Pt) have been characterized by EXAFS. The literature reporting EXAFS used for the characterization of APNCs together with the details of the EXAFS analyses is summarized in Table 5.1.

Table 5.1 Summary of EXAFS data on APNCs

4.1.1 Simple Structural Models

The first reports of the characterization of APNCs with EXAFS, i.e., Au₅₅ clusters made by the Schmid [68] process by Cluskey et al. [69], Fairbanks et al. [70], and Marcus et al. [71], used early EXAFS analysis techniques where experimental phase shifts and amplitude of reference materials were compared with those of the unknown sample, and the software to make use of the EXAFS equation was just beginning to be developed. With time, a more complete understanding of the various effects that impact the spectra and the improvement of the analysis software has made possible a much more sophisticated approach to the analysis of EXAFS spectra. Better understanding of the effect of multiple scattering and curved wave effects [72] has improved the characterization of APNC with EXAFS. Early EXAFS results on Pd₅₆₁ [72] and also Au₅₅ [10] were revised and refined.

Several papers on the characterization of nanoparticles (not APNC) using EXAFS [17, 57–59, 73] form the basis for reliable results derived from EXAFS. In these publications, Frenkel and coworkers discuss the importance of multiple scattering effects [58] on the EXAFS analysis and models regarding the structural geometry of the nanoclusters [17, 59, 73], summarized in Frenkel et al. [35]. Together with the development of the FEFF code (specifically version 6), the calculation of multiple scattering paths became possible. This big improvement boosted the development of analysis software (e.g., WinXAS [53], Ifeffit, and Demeter [52]). The analysis of EXAFS spectra can only provide CN, bond distances, and disorder correlations. If a model provides predictions for these values, the validity of the model can be tested.

Specifically for the characterization of APNCs, basic structural models are important tools to determine the structure of the NCs with EXAFS. These models essentially derived from the fcc structure that is inherent to many metals in their bulk form. For their analysis of Au₅₅ [10, 70], Pd₅₆₁ [72], and Pt₃₀₉ [2], they used the cuboctahedron (fcc) model and based the verification of the model on the comparison of the CN of the first-shell Me–Me bonding. This method is discussed extensively in Benfield [16] where a formula for the mean CN is derived. For each model system (cuboctahedron (fcc, hcp), icosahedral), the CNs of the atoms in the first shell close to the center atom are distinct. However, in some reports [2, 10, 70, 72], the CNs were always too low compared to the fcc model. The development in the understanding and description of the model system, specifically fcc vs. icosahedral, made it possible to include other features into the analysis. The Me–Me bond distances of the first shell in an icosahedral structure should show splitting of about 0.2 Å into two subshells, but Benfield et al. [10] could not resolve these subshells in their data.

In another early approach, Benfield et al. [2] and Vargaftik et al. [74, 75] used the ratios of the Me–Me distances for the first three shells derived from EXAFS in comparison with these ratios in cuboctahedral and icosahedral models. Vargaftik et al. [75] determine an icosahedral structure for the Pd₅₆₁ cluster they reported, and Benfield et al. [2] reported that the Pt₃₀₉ cluster has fcc structure.

This technique using the CNs of the first shell of the EXAFS analysis comparing to the fcc model was typically used in early EXAFS analyses [12]. Later this technique was expanded to the cubic (fcc) model with different shapes (such as spherical, hemispherical, rod, etc.) [59, 76], to hcp and icosahedral models [73], and to other structures [77]. Figure 5.6 shows the correlation between cluster size and CN of the first nearest neighbor for several structures. The packing structure of these models also implies distinct numbers of atoms in the clusters [16, 78]. An example of these “magic numbers” for a cuboctahedral structure (hcp packing) is shown in Fig. 5.7.

Fig. 5.6

The relation between number of atoms in a cluster and first-shell coordination number for a cuboctahedron, an hcp cluster, and a truncated octahedron (Based on data from Glasner and Frenkel [73])

Fig. 5.7

Overview of structures and magic numbers of cuboctahedral clusters of different sizes (Reproduced from Schmid [79] with permission of the Royal Society of Chemistry on behalf of the Centre National de la Recherche Scientifique (CNRS) and the RSC)

4.1.2 Nanoscale Structural Distortions

4.1.2.1 Coordination Number Truncation

The coordination number truncation model (CNT) demonstrates that atoms on the surface of the particle are surrounded by fewer neighbors than those in the bulk, and, hence, the average coordination number of the first nearest neighbors decreases [57]. This model was also discussed in Benfield et al. [10] explaining the lower CNs for NCs compared to bulk metal. Using this model, the size of APNCs can be determined by comparison with the coordination numbers of several first shells by assuming specific polyhedral shapes [12]. This CNT method was used by Frenkel [58] for nanoparticles using a hemispherical fcc structure and by Frenkel et al. [12] for APNCs using a spherical fcc structure to determine the cluster size of NCs. More extensive applications of the CNT model including cuboctahedral, icosahedral, and hemispherical cuboctahedral structures by Glasner and Frenkel [73] and pyramidal structures by Beale and Weckhuysen [77] have been reported.

4.1.2.2 Surface Tension

The surface-tension (ST) model was developed by Mays et al. [80]. Here the stress of the surface tension induces compression on the lattice which can be measured (in EXAFS) through the distances of the Me–Me coordination in the first shells if the data for the compressibility K and surface stress f _rr are available:

$$ d=\frac{4}{3}\frac{f_{rr}K}{\alpha }, $$

(5.10)

where d is the particle diameter and α = ΔR/R is the relative lattice contraction.

Me–Me bond length contraction that is directly related to this lattice contraction was observed not only by Frenkel et al. [12] but previously also by Benfield et al. [2, 10, 72] and Cluskey et al. [69]. Benfield et al. [2] found there to be different contraction rates for Au (4 %), Pt (1 %), and Pd (0.4 %) and related these to the results of differential scanning calorimetry measurements. They observed that bonding for Au–Au in NCs compared to bulk Au is stronger, while for Pd–Pd in NCs bonding is weaker than for bulk Pd. However, it was established by Häberlen et al. [81] and Kruger et al. [82, 83] using DFT calculations that the bond distances in small metal clusters (e.g., Pd, Au) are in direct and nearly linear relation to the mean nearest-neighbor CN and that the bond distances increase with cluster size. Later it was determined that as the particle size increases, the contraction decreases [12]. Further, it was found by Christensen et al. [25] that doping with Pt increased the Au–Au and Au–S contraction in the Au₂₄Pt(SR)₁₈ NC compared to the not doped Au₂₅(SR)₁₈.

Contraction of the first-shell Au–Au distance was observed by Menard et al. [3] for Au₁₃ NCs. The contracted bond length was then used for geometrical calculations in order to determine the bond length of another Me–Me distance in accordance with a structural model, i.e., the distance to the third Au–Au shell which is on the surface of the cluster in an Au₁₃ icosahedron. The discrepancies of their model with the experimental data led to the assumption that due to the ligands, there is a relaxation effect and therefore reduced contraction of this third shell distance. One of the objectives of the investigations by Simms et al. [84] was to understand the influence of the thiol ligand structure on the staple motif in Au₂₅ NCs and the relationship of this structure toward physiochemical properties. The gigantic bovine serum albumin (BSA) molecule with tertiary structure as a ligand affects the structure of the Au₂₅ NCs directly via contraction of the Au–S and Au–Au bonds: The Au–S bonds are shorter than in the theoretical model, while the Au–Au bond lengths agree with the model.

MacDonald et al. [5, 85] studied the effects of temperature and solvation of Au₂₅(SR)₁₈ and Au₃₈(SR)₂₄ nanoclusters. They observed that although the first two core shells were possibly contracted at lower temperature relative to room temperature, the third shell was expanded. On the other hand, although the nanoparticles solvated in toluene and acetonitrile (ACN) also had the first two core shells contracted, only the nanoparticles solvated in toluene showed an expansion (relaxation), and the Au–Au distance of the third shell solvated in ACN was the same as the solid. The effect that relaxation is sometimes observed for longer Au–Au distances with regard to the ligands is due to surface stabilization [86].

4.1.2.3 Self-Consistent Analysis

Frenkel et al. [12] were the first to characterize APNCs by applying the two above models (CNT and ST) independently. This self-consistent analysis uses the comparison of results from two independent methods to give more reliable results than the use of a single model alone when applying a fitting procedure. A spherical fcc structure was used to determine the cluster size for the CNT model. Then, using the EXAFS data from their own experiment and experimentally determined values for f _rr and K from the literature, Frenkel and coworkers [12] determined the cluster size of thiol-stabilized gold nanoparticles according to the ST model. These findings by use of the ST model together with EXAFS are in agreement with the works by Zanchet et al. [87] and refined by Zhang and Sham [88] who used the same synthesis method as Frenkel et al. [12] but with different Au/thiol ratios. The work of these three groups did not include specification of the actual numbers of Au atoms determined by other methods such as MALDI-MS and qualify as borderline between studies of regular nanoparticles and studies of specific APNC.

Using these two methods (CNT and ST), Frenkel et al. [12] were able to determine the number of atoms in the core and particle diameters of several thiol-protected very small NCs (close to Au₅₅, Au₁₄₇, and Au₅₆₁). The EXAFS results were internally consistent, while the TEM and XRD measurements showed some discrepancies. These differences show that while methods such as TEM and XRD have problems resolving nanoclusters of this size (TEM, poor sensitivity to very small NCs smaller than 2 nm; XRD/Scherrer analysis: When the samples are dispersed in size, higher values for the particle diameter are assumed), this is not the case for EXAFS spectroscopy. However, the size dispersity of the sample does affect the reliability of the EXAFS analysis. The average particle size may be underestimated using the CNT method for size-dispersed samples. This is not the case when the ST model is used because both the mean bond length and its standard deviation (Gaussian distribution, which is the static contribution of the Debye–Waller factor in EXAFS) are involved in the determination of the size [12]. Frenkel et al. [12] concluded that the Au clusters investigated had a cuboctahedral fcc structure (using the CNs of several shells together instead of just the first shell) and that the synthesis methods (with one step or two steps) had an effect on the size of the clusters for the same Au/thiol ratios.

Frenkel and coworkers also used this self-consistent model investigating the geometry of Au₁₃ NCs capped with mixed ligands [89]. The EXAFS-derived CN for three shells resulted in an icosahedral structure of the Au₁₃ NCs where the number of atoms in the cluster was determined with high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). Contraction of Au–Au bonds was measured by EXAFS and compared with ideal icosahedral structures. The differences in contraction (5 % ideal vs. 3 % EXAFS) seem to indicate that a relaxation of the strain is related to the capping ligands [89]. Even though this self-consistent method is very reasonable, it is only not often used.

However, these studies show the importance of using several models for the characterization of APNCs because each method includes some disadvantages.

4.1.3 Synergy of Multiple Techniques: The Use of Complementary Experimental Methods

There are many different techniques for the characterization of materials, such as TEM (transmission electron microscopy), UV–vis (optical spectroscopy), FTIR (Fourier-transformed infrared spectroscopy), XAS, XPS, MALDI-MS (matrix-assisted laser desorption/ionization mass spectrometry), theoretical calculations, and others. It is desirable when possible to use more than one of these techniques for the characterization of APNCs, especially when XRD, which is the major tool for structure determination, is not applicable. In some cases, the different methods complement each other and increase the level of understanding of the system, while in other cases, the results can confirm each other or point out possible problems.

Weir et al. [90] used additional TEM, UV–vis, XPS, and XANES for their in situ EXAFS investigations on Pt₂₄₀ dendrimer-encapsulated nanoclusters (DENs). The details of the in situ EXAFS analysis are discussed in Sect. 4.1.5. UV–vis and TEM results were not discussed as these results were in agreement with previous studies. However, these techniques confirm some properties of the material under investigation. The interrelations of EXAFS with XANES are significant for this analysis. Because the XANES spectra show an oxidized species for one of the experiments, the question of including Pt–O scattering paths in the fitting procedure of the EXAFS analysis can be answered positively. This detail was crucial in the understanding of the effect of the reactions (application to the electrode, with potential, CO adsorption, and CO desorption).

In the work of Simms et al. [84] investigating Au₂₅ encapsulated in bovine serum albumin (BSA), a sulfur-rich protein, TEM, EXAFS, XANES, XPS, and l-DOS were used. Here, regular TEM (compared to high-resolution TEM (HRTEM) and HAADF-STEM) is presented and shows one of the drawbacks of this method which is due to the fact that the resolution of the TEM results can be obscured by the enveloping protein. The correlation of XPS, XANES, and l-DOS is discussed in Sect. 4.2. The comparison of these results using different techniques including EXAFS, TEM, and XRD shows that the limitations of the resolution (sizes below 2 nm) of TEM and XRD lead to an overestimation of the cluster size [12]. EXAFS (CNT method) tends to underestimate the size, and EXAFS (ST model) is more accurate [12]. However, TEM can give information about the dispersity of sizes which EXAFS and XRD cannot [12]. In most cases, TEM is employed to monitor the size distribution during a reaction or comparative experiments (e.g., [21, 31]) to observe if the APNCs show changes.

Multiple techniques were used by Menard et al. [3]. To overcome the poor contrast in TEM between the smallest metal nanoparticles and the support films on which they are deposited, high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was employed. Using HAADF-STEM, it was possible to determine the number of atoms in the core as a size distribution showing a homogeneity of the small Au clusters with a ca. 13 Au atom core. This information was important to confirm that the EXAFS-derived results of the coordination numbers had no error. Wrong determination of CNs from EXAFS analysis can arise from a significant presence of other larger clusters (in this case with fcc structure). Due to the precise results from HAADF-STEM, this scenario could be ruled out which again supported that the Au₁₃ clusters have icosahedral structure.

Using HRTEM electron diffraction techniques, Menard et al. [3] were able to observe the fcc pseudo-spherical structure of the Au₁₄₇ MPCs, while HAADF-STEM showed a much wider atom number distribution of the core. Detailed modeling showed that the coordination numbers (including CN for Au–S) and distances derived from the EXAFS analysis comply with a truncated octahedral core (which includes that a path for the second single scattering shell is applied). Altogether, in their report, Menard and coworkers [3] show how important are the careful application of models for the EXAFS analysis and the involvement of multiple scattering paths.

Frenkel et al. [89] used the same methodology (HAADF-STEM, TEM, MS EXAFS analysis, and XANES (see Sect. 4.2) as Menard et al. [3] to investigate Au₁₃ NCs with a multi-ligand shell. Applying this method, they could characterize the nanocluster sample extensively – since it was both homogeneous in size and of high purity. They determined an icosahedral structure for the Au₁₃ clusters, where two thiolates are bound at on-top sites, two thiolates at bridge sites, and four phosphines at on-top sites.

Vargaftik et al. [75] used TEM and SAXS to determine the cluster size of the different Pd NCs investigated. Testing the agglomeration was done with TEM and ED, while NMR, MS, FTIR, and EXAFS were used to determine the structure when XRD was not possible (because no crystal could be grown).

Benfield et al. [10] used wide-angle X-ray scattering (WAXS) as complimentary technique to EXAFS and XANES (which will be discussed in detail in Sect. 4.2) comparing bond distances and crystallite size with the EXAFS-derived results. The results from WAXS measurements are systematically larger than from EXAFS. Longer bond distances (WAXS) can be explained twofold: (a) The WAXS measurements were conducted at room temperatures and EXAFS measurements at 80 K and (b) by aggregation of NCs. The WAXS spectra (being a method similar to XRD) of the NCs are rather broad due to their more amorphous long-range structure.

In other cases [21, 91], the synergetic use of several techniques (Raman, FTIR, MALDI-MS, DFT, HAADF-TEM) was focused on the in situ application of these techniques and will be discussed in Sect. 4.1.5.

4.1.4 Combining EXAFS Analysis with DFT and MD, DFT Modeling Methods, and EXAFS Simulations

4.1.4.1 EXAFS Simulations on the Basis of DFT-Calculated Structures

Theoretical EXAFS methods, i.e., simulations of EXAFS spectra, are an effective characterization technique. These methods are based on density functional theory (DFT) calculations, and this technique became possible after structural models on the basis of DFT methods of the APNCs Au₁₄₄(SR)₆₀, Au₁₀₂(SR)₄₄, Au₃₈(SR)₂₄, and Au₂₅(SR)₁₈ were developed by Lopez-Acevedo et al. [20], Jadzinsky et al. [92], Qian et al. [19], and Heaven et al. [18], respectively.

For the Au₁₄₄ cluster, with well-established synthesis practices, MacDonald et al. [93] investigated the agreement of EXAFS in experiment and theory. In the theoretical structure model of the Au₁₄₄(SR)₆₀ cluster, the Au atoms are distinguished with regard to their bonding environment. Lopez-Acevedo et al. [20] proposed that the Au atoms occupy five different sites in this cluster, each of which represents a different environment for the Au atoms within the cluster. The details are shown in Fig. 5.8.

Fig. 5.8

Overview of Au sites (1–5) for the Au₁₄₄(SR)₆₀ NC (Reprinted with permission from MacDonald et al. [93] after Lopez-Acevedo et al. [20]. Copyright 2010 American Chemical Society)

One central feature to the structure of Au_x(SR)_y NCs is the so-called staple motif (Fig. 5.9). Two sulfur atoms of the thiol ligand lift a Au atom up out of the surface of the cluster like in a staple. This was proposed first by Jadzinsky et al. [92]. The staple motif is responsible for the structural stability of Au_x(SR)_y NCs and can occur as monomer (RS–Au–SR) and dimer (RS–Au–(SR)–Au–SR) making Au NCs highly symmetrical [94]. The staple motif model was extended to “staple fitness” by Jiang [15] using combinatorics, and it was observed that the arrangement of the staple motifs on the surface of the NC affects the structure of the core and that the most stable configuration also protects a highly symmetrical core.

Fig. 5.9

Visualization of the “staple motif” as the thiolate ligand (here R = methanethiol) lifts one Au atom out of the surface (Reprinted with permission from Jiang et al. [94]. Copyright 2008 American Chemical Society)

Because there are different sites for the Au atoms in the Au_x(SR)_y NCs, theoretical investigations (by MacDonald et al. [93]), which were performed as simulations of EXAFS spectra (in k-space) using this structural information, have to be site specific. This means that for each site, a separate EXAFS spectrum has to be calculated, and these spectra averaged with regard to their number of degeneracy. The site-specific EXAFS spectra calculated using this method and the experimental spectrum are shown in Fig. 5.10a. The correlation of the simulated EXAFS spectra with the experimental EXAFS spectra, i.e., χ(R) in R-space, is an important feature of this work [93]. Clearly, the feature around 2 Å (pink spectrum in Fig. 5.10a) is related to Au–S bonding at site 5 (staple motif), and the next feature (in the other spectra in Fig. 5.10a) at about 2.5 Å is related to the first-shell Au–Au bonding (e.g., in the core or on the surface). This knowledge is used in all other reports for Au–thiol NCs based on the usual EXAFS fitting methods employing theoretical standards such as metal bulk. However, Fig. 5.10a with the EXAFS simulations showed this effect more visually and directly applied to the NCs. XPS results support this site-specific view of the Au₁₄₄(SR)₆₀ NC where Au atoms in the core show metallic features, Au atoms in the staple show nonmetallic features, and Au atoms on the surface of the NC show mixed features [93]. In addition, these data show that the whole cluster overall exhibits metallic behavior which is supported by the rather high intensity of the Au–Au first-shell peak in the EXAFS spectrum in Fig. 5.10b. Using the model structure of Au₁₀₂(SR)₄₄ [92] for the EXAFS fitting procedure (as standards) gives results for average Au–Au and Au–S CN that agree with the theoretical model of Au₁₄₄(SR)₆₀ from Lopez-Acevedo et al. [20].

Fig. 5.10

(a) Examples of simulated EXAFS spectra for the five different Au sites from bottom to top (site 1–5) of the Au₁₄₄(SR)₆₀ NC, (b) experimental EXAFS spectrum and fit of the Au₁₄₄(SR)₆₀ NC (Reprinted with permission from MacDonald et al. [93]. Copyright 2010 American Chemical Society)

Site-specific EXAFS simulations using the structure model of Au₂₅(SR)₁₈ cluster, proposed by Qian et al. [19], can show specifically that the first Au–Au shell in the core is split into three subshells. This splitting into subshells is a distinct feature for icosahedral structures, and it was observed in the experimental EXAFS spectra. The EXAFS results of Au₂₅(SR)₁₈ for the different environmental conditions show firstly that although the Au–Au bond length for the first Au–Au subshell decreases at low temperature, the Au–Au bond length for the third shell increases. This behavior is also observed in the solvation environments but only for toluene, with no change being observed for acetonitrile. The Au₂₅(SR)₁₈ NC is very special compared to the other Au_x(SR)_y NCs. This cluster is characterized by six dimeric staple motifs [5], and these are expected to show significant changes in different solvation environments. For the Au–S bond length, no change can be observed in all cases which means that this stiff SR–Au–SR dimer is less responsive to the changes in the environment making this material (i.e., Au₂₅(SR)₁₈) more stable. Secondly, the Debye–Waller factor is much lower at lower temperature (which is to be expected) and also lower for the solvation environment (which is rather unexpected). And thirdly, upon solvation, the structural changes for the Au₂₅ are not the same as observed for the Au₃₈ cluster. For the Au₃₈ cluster, all distances are longer (Au–S and Au–Au), and even splitting of the first Au–Au shell into two subshells for the solvated cluster was observed. The structural changes of Au₂₅ are in agreement with the interactions between the aromatic solvent (i.e., toluene) and the ligand tailgroup vs. the polar solvent (i.e., acetonitrile) with the tailgroup. For the second interaction of the polar solvent with the ligand tailgroup, the ligand-induced strain on the core is not reduced as much compared with the results for toluene. There is a relaxation of the Au–Au bond distance in the third shell (and a slight lengthening for Au–S bonds) for the toluene-solvated Au₂₅ only compared to the acetonitrile-solvated sample but on the other hand contraction of the first-shell Au–Au bond distance for both solvation environments. These observations confirm that there is an interplay between the Au–S bonding structure in the staple motif and the Au–Au bonding structure in the core [5]. These reports show the capabilities of EXAFS in distinguishing between the different (liquid vs. solid) environmental conditions due to the structural changes that have been observed with regard to tuning the properties of NCs.

Chevrier et al. [95] investigated Au₁₉(SR)₁₃ in comparison with Au₂₅(SR)₁₈ using EXAFS, XANES, l-DOS, and XPS. Again, XANES, l-DOS, and XPS are discussed in Sect. 4.2. The structure of Au₁₉(SR)₁₃ was reported by Jiang [15] (using DFT and XRD methods). Following the above technique of using this structural information from theory, the number of Au atoms in the core was varied in order to understand the structural evolution of NCs and structural stability. First, the EXAFS data were fit using only two shells in order to determine the CN for the Au–S and Au–Au coordination and to identify which of two structural scenarios agrees with the experiment. This step was necessary because the Au₁₉(SR)₁₃ cluster was shown to have 11 isomers [15]. Scenario 1 is that the center Au atom has a surface of only ten Au atoms (Au₁₁ core) and eight Au atoms coordinate the S atoms in the staple motif (two monomers and three dimers). In scenario 2, the Au₁₂ core does not have a center atom, and only seven Au atoms coordinate the S atoms in the staple motif (five monomers and one dimer). The EXAFS fitting procedure of the experimental data agreed better with scenario 1. For the refinement of the structural information, a multishell fitting where the CNs were calculated and fixed based on the Au₁₉(SR)₁₃ model (scenario 1) was performed. The Au–S and first Au–Au distance were found to be the same as for Au₂₅, and the second Au–Au distance was a bit longer. While the Au–S and the Au–Au bond distances for the center–surface bonding and surface–surface bonding agree very well with the fit, the long-range aurophilic distances do not. The Au–Au third shell was overestimated (meaning that the fixed CN was too high compared to the experimental data), and an incorrect Debye–Waller factor (being too large) was derived. The comparison with the Au₂₅(SR)₁₈ data discussed above shows the differences in the core structure (defective icosahedral) and higher structural disorder especially mixed (monomer and dimer) staple motifs [95]. This report shows that there are limitations of the EXAFS fitting technique in the presence of highly disordered system (in this case only for the long Au–Au bonds), but because of the systematic approach, reasonable conclusions still can be derived.

Exchanging the thiolate ligands for selenolate ligands, the structure of Au₂₅(SeR)₁₈ NCs was investigated by Chevrier and coworkers [96] based on the same multishell (three Au–Au shells) approach similar to their previous work discussed above. In addition, the analysis of Se K-edge data was included, which helped enhance the understanding of the Au–Se bond. Also, data on Au₂₅(SR)₁₈ were collected, reported, and analyzed again (compare [5]) to ensure consistency, which is very important. A Au–Se distance of 2.42 Å determined by Chevrier et al. was in agreement with the data from Kurashige et al. [97]. The Au–Se distance is longer than for Au–S in Au₂₅(SR)₁₈, which is presumed to be due to a larger covalent radius for the Se atom. The temperature dependence of the structure of Au₂₅(SR)₁₈ and Au₂₅(SeR)₁₈ was studied for 50 and 300 K. Strong contraction for the three Au–Au shells was determined for Au₂₅(SeR)₁₈ NCs for 300 K. This negative thermal expansion behavior was supported by DFT calculations (details for DFT calculations are discussed in section “The Relationship of DFT-MD Calculations and DFT Bases EXAFS Calculations”), and it was determined that the angle between the surface and the Au–Se–Au staples as well the angle of Au–Se in the staples changed due to the temperature change [96].

This same EXAFS approach (theoretical model vs. experimental data) was used in the structural determination of Au₃₆(SR)₂₄ in comparison with Au₃₈(SR)₂₄ by Chevrier et al. [98]. They find that the Au₃₆ clusters have an fcc-like core structure and bridging S atoms and four dimeric staple motifs compared to Au₃₈ (icosahedral) with only staple motifs. Historically, investigations on the structure of the Au₃₆ cluster exist because it is one of the few APNCs that can be grown into crystals and the structure resolved using XRD methods. The fcc-like structure of Au₃₆ was verified with EXAFS using a new strategy: From a theoretical model with fcc core structure (Au₂₈), the EXAFS spectrum was simulated (k-space), and then Fourier transformed (R-space) and then backtransformed (k-space) calculated in order to compare this model data with the experimental data (isolated backtransformed signal for Au–Au bonding in the core only). These backtransformed spectra are an astonishingly good match.

Next to the Au–S shell, two Au–Au shells could be determined from the experimental EXAFS analysis. Again the CNs were fixed from the theoretical model, in this case a Au₂₈ fcc core with 12 bridging and 8 Au atoms in staple motifs. For the first shell of Au–Au bonding, a much shorter distance compared to the Au₃₈ cluster was observed. This experimental EXAFS data (see Fig. 5.11) show how well the scattering peaks at high R (>3.5 Å) are resolved for the low-temperature EXAFS spectra, which is directly correlated to precise (low Debye–Waller factors) values for the bond distances (when the k-range can be extended to about 16 Å⁻¹), and that the structural disorder increases quite much for room-temperature measurements (the Debye–Waller factor increases with temperature, and the shells are featured with much lower intensity and broadening in the R-space EXAFS spectra). It also shows that high purity of the samples is crucial for the reliability of the analysis. However, the two different Au–S bonding types (bridging and staple) did not result in different Au–S bond distances in this report [98].

Fig. 5.11

FT-EXAFS data (black dots) and fit (red line) of the Au₃₆(SR)₂₄ NC at (a) room temperature and (b) low temperature. All peaks in the FT-EXAFS spectrum at low temperature are more intense and well resolved (Reprinted with permission from Chevrier et al. [98]. Copyright 2013 American Chemical Society)

The importance of the Au₄ units for the structure of the fcc-like Au₂₈(SR)₂₀ NCs was investigated in comparison with other Au_x(SR)_y NCs in a very recent study by Chevrier et al. [99]. It was shown that site-specific EXAFS simulations can very well agree with experimental EXAFS results.

In another investigation, solely theoretical considerations of Au₂₅ and Au₁₀₂ NCs using site-specific EXAFS and l-DOS calculations were reported by Christensen et al. [100]. Due to size differences of the two NCs, the Au–Au coordination environments and also the electronic characters were found to be different. This pure theoretical discussion is important and can lead to valuable information about NC in the transition zone between atomic and bulk materials. In addition to the constant improvement of experimental techniques, the improvement of theoretical techniques is equally important. However, if these theoretical models are not compared with experiment, this information has to be regarded with caution.

4.1.4.2 The Relationship of DFT-MD Calculations and DFT Bases EXAFS Calculations

In another step to enhance the quality of EXAFS analysis and modeling, Yancey et al. [31] combined them with molecular dynamics (MD) and density functional theory (DFT). In this study, dendrimers were used to synthesize Au₁₄₇S_n (NC with Au core and thiol shell where n gives Au/thiol ratio, also called thiol capped Au DEN). A similar system (Au–Pt DENs) was discussed in a theoretical way defining the DENs as a model system that is well defined, stable, homogeneous in size, and relatively simple (because they are not on a support) [101]. Yancey et al. [31] used the model system Au₁₄₇S_n DEN to study the effects of different densities of the thiols on the Au surface (surface ligand density) on the structural disorder of the NCs. Along with EXAFS measurements of the Au₁₄₇S_n DENs, theoretical EXAFS spectra were calculated based on DFT-MD simulations of the structure of the DENs as well as separate DFT-MD simulations of pair distribution functions (PDF). These methods were also reported by Yevick and Frenkel [102] and Roscioni et al. [103]. The simulated EXAFS spectra were fit using the same modeling strategy as for the experimental EXAFS spectra. More information was included by use of UV–vis and TEM. The size homogeneity was confirmed by TEM for all samples.

The EXAFS analysis shows that the CNs for Au–Au decrease and for Au–S increase when the surface density of thiols increases. This decrease in Au–Au CN with increasing surface density of thiols is in agreement with other results reported for disordered nanoparticle systems (e.g., Myers et al. [104], Price et al. [105]). For the Au–Au distances, a slight increase with higher thiol density was found which relates to a relaxation of the Au–Au bond length as discussed above. On the other hand, the increasing thiol density on the surface results in a decreasing Au–S bond length. This trend is consistent with the existence of the staple motif where the bonding of Au–S is stronger (and thus shorter). If we compare the Au–S bond in a Au–S lattice, the Au–S bond length is longer due to the fact that each S atom is pulling on several Au atoms isotropically (stellate) and vice versa in the three-dimensional lattice. Therefore, a shorter Au–S distance is highly correlated with the formation of staple motif on the surface of the DENs which is more likely for higher Au/thiol ratios. Finally, the Debye–Waller factors increase with increased surface thiol density [31]. The effects of structural disorder are discussed in detail below.

Among their results, Yancey et al. [31] find that using this method, the CNs, average bond lengths, and Debye–Waller factors are in agreement for the theoretical and experimental EXAFS data. Only in the results where the MD-derived parameters from the PDF are compared with the EXAFS-derived parameters (average bond lengths and Debye–Waller factors), there are some discrepancies. The main result of the study is that DFT-MD calculations can simulate complex experimental systems with control over structural disorder in nanoparticles and that this can improve EXAFS fitting methodologies for NC characterization. This combined technique using experimental and theoretical XAS with DFT was also used by Behafarid et al. [106]. Integrating different electron microscope techniques, they characterized Au NCs of different sizes prepared by their new synthesis method employing an inverse micelle encapsulation method with polymers. Distortions of the core structure (e.g., bond length contraction) were found to be size dependent for the ligand-protected NCs. Oyanagi et al. [107] also combined experimental and theoretical XAS with DFT to characterize Cu₁₃ NCs synthesized using a new strategy of synchrotron radiolysis together with wet chemistry. Ahmadi et al. [108] also used DFT calculations, in this case on Ag and Cu NCs with cuboctahedral or Marks decahedral structure to determine lattice contraction and coordination. These calculations were though not accompanied by experimental EXAFS results.

4.1.5 In Situ EXAFS

Fast scanning techniques make it possible to observe reactions with EXAFS as they proceed (in situ). The strategic approach of using in situ EXAFS for temperature and extensive catalysis experiments consists of (1) gathering basic structural information about the system using EXAFS and (2) correlating this knowledge with chemical and structural changes of the APNCs during catalytic reactions [21]. UV–vis, MALDI-MS, TEM, and EXAFS together were applied in the examination of Au₂₅(SR)₁₈ MPCs on carbon support by Shivhare et al. [21] to determine that heating resulted in the removal of all of the thiolate stabilizers, while cluster integrity was maintained or until higher temperatures. The use of two different ligand thiols (phenylethanethiolate and hexanethiolate) for the experiments showed that higher activity was observed for phenylethanethiolate MPCs. A separate analysis of the Au₂₅(SR)₁₈ MPCs on the carbon support confirmed that the cluster kept structural integrity during the transfer process and bond lengths (Au–S and Au–Au) were not temperature dependent. However, the CNs changed (decrease for Au–S, increase for Au–Au bonds). There is a significant increase of the Au–Au CN, and the three Au–Au subshells that are characteristic for the Au₂₅ cluster are not separated any longer. This is related to an increase in structural disorder and growth of the clusters, which was confirmed by TEM observing a small growth in the structures with increasing temperatures. Catalytic activation tests were performed with similar experimental conditions showing that the highest catalytic activity were observed at 250 °C where nearly all thiols have been removed from the surface [21].

Wu et al. [91] reported in situ EXAFS on Au₂₅(SR)₁₈ supported on CeO₂ including CO oxidation. Other methods used were UV–vis, FTIR, Raman spectroscopy, MALDI-MS, quadrupole-MS, DFT calculations, and HAADF-TEM methods. While UV–vis, MALDI-MS, and HAADF-TEM were used to confirm the successful synthesis and loading on CeO₂ rods, the CO oxidation treatment was investigated in situ with MS, FTIR, Raman, XAS spectroscopy, and DFT calculations. In this report [91] with huge effort (many techniques) focusing on the CO oxidation effect on the Au₂₅ NCs on CeO₂ support, unfortunately, no EXAFS fitting plots and/or table including fitting results were shown or discussed. Even the experimental EXAFS spectra before heating of the Au₂₅ NCs on CeO₂ were not discussed. The only focus of the EXAFS analysis was a change in the Au–S bond distance (which did not occur) and the Au–S CN (a decrease was observed with heating). Since no values for Au–Au bonding and no Debye–Waller factors were given, the results derived from this EXAFS analysis can only qualitatively describe the reaction.

The structure of Pt₂₄₀ DENs (on electrode support) during electrocatalytic oxidation of CO was investigated with in situ EXAFS, UV–vis, XPS, and TEM by Weir et al. [90]. UV–vis, XPS, and TEM results were used to confirm either data from previous reports or confirm the XAS data. Using only the CN of the first shell of the EXAFS results, the size of the Pt DENs was estimated to be about 240 atoms in agreement with TEM. After the first application of an electrical potential to the electrode, the Pt DENs were determined to be reduced. Weir et al. [90] observed that the Pt DENs were metallic (reduced) all further reactions. Especially important from this report is that the stability of the Pt DENs was not disrupted during the adsorption and subsequent oxidation of CO. The objective of this study is to understand if the catalyst (Pt DEN) can remain unchanged during the catalysis, which was successfully observed due to the stabilizing effect of the DENs. Immobilization on an electrode prevented agglomeration.

Myers et al. [104] report the in situ investigation of Pt₂₂₅ DENs during electrocatalytic oxygen reduction reaction using EXAFS, XANES, TEM, and UV–vis. They successfully demonstrated the use of an in situ cell (like Weir et al. [90]) for electrometric experiments while recording EXAFS. Applying different potentials and gas conditions, the changes in the structure (Pt–Pt distances and CNs from EXAFS analysis) were observed but could not be fully explained. The structural disorder of the Pt NCs in these experiments can describe the discrepancy of low experimental CN compared to higher theoretical CN (fcc model clusters, size determined by TEM). This correlates well with EXAFS results, specifically multiple scattering contributions, if the core is ordered and the shell disordered. A rather fluid surface behavior for APNC was proposed by Schmid [11] using NMR techniques. This XAS cell and experimental method is promising for the analysis of such in situ experiments using EXAFS analysis. However, better quality and repeatable data is important which can be achieved by repeating measurements at the same conditions in order to make use of the correlation of electrical potential with structural effects.

4.1.6 Bimetallic APNCs

Bimetallic APNCs are discussed in Knecht et al. [62]. Using established synthesis procedures, bimetallic NCs were characterized using EXAFS. Here the synthesis employs dendrimers to form alloyed Au–Pd NCs and dodecane thiols for the extraction and stabilization of the NCs to form monolayer-protected clusters (MPCs). Bimetallic NCs were generated in different Au/Pd ratios. EXAFS analysis is used to understand the structural changes before and after extraction for all (5) Au/Pd ratios. In their EXAFS analysis, the model for bimetallic NPs (see Sect. 3.3) was applied. Increasing CNs for Pd with increasing Pd concentration for the Au–Pd DENs show that these NCs are partly random alloy and partly in a core–shell structure (with Au in the core and Pd in the shell). For the Au–Pd MPCs, the CNs change drastically, which indicate a clear core–shell structure, where the Pd shell thickness increases with increasing Pd concentration. Additionally, coordination with sulfur was only observed for Pd atoms unless the Pd concentration was very low (Au₁₁₈Pd₂₉). However, the coordination numbers found for Pd–S bonding were much higher than anticipated for the NC model. This indicates the presence of small Pd–thiol complexes as a result of the high excess of thiol addition in the synthesis. The distances for the Au–Au, Pd–Pd, and Au–Pd bonds in the Au–Pd DENs are in agreement with other examples of binary alloys. However, for the Au–Pd MPCs, some distances (Pd–Pd) show some anomalous behavior. This behavior is either caused by relaxation effects in the Pd–S shell or due to misinterpretation cause by the presence of small Pd–S complexes that were found earlier. Detailed interpretation of UV–vis spectra supports the transformation of Au–Pd DENs into Au–Pd MPCs including the formation of a Pd–thiol compound. The analysis of bimetallic EXAFS spectra is very challenging not only because of the higher structural disorder of the system but also because these syntheses often involve the formation of a thiol species that masks the results of the bimetallic sample.

Anderson et al. [109] using in situ EXAFS, complemented by DFT calculations, XPS, UV–vis, XANES, and HRTEM and electrochemical experiments, monitored the three-step synthesis of DENs: (1) formation of a Pd core (Pd₁₄₇ DEN), (2) deposition of a Cu shell (Pd₁₄₇Cu₁₆₂), and (3) galvanic exchange of Pt for Cu in the shell (Pd₁₁₄₇Pt₁₆₂). The summarized result of this synthesis is instead structural inversion: The DENs with Pd–Cu core–shell structure change into a Pt-rich core and Pd-rich shell structure (Pt₁₄₇ (core) Pd₁₄₇Pt₁₅ (shell)). DFT calculations were employed to help determine the structure of the Pt₁₄₇ (core) Pd₁₄₇Pt₁₅ (shell) DENs after step 3.

Another approach based on site-specific structural considerations (such as in section “The Relationship of DFT-MD Calculations and DFT Bases EXAFS Calculations”) can only be applied on very small NCs with only one doping atom. Investigations on Au₂₄Pt(SR)₁₈ are reported by Christensen et al. [25] using EXAFS, XPS, and l-DOS. The clusters were analyzed using Pt and Au L₃-edge EXAFS as well as previously published experimental data and theoretical knowledge about Au₂₅(SR)₁₈. The analysis of Au L₃-edge EXAFS spectra of the bimetallic cluster showed the contraction of Au–S and Au–Au bond distances in comparison with previous Au₂₅ data. Using the Pt L₃-edge EXAFS data, the location of the doped Pt atom was determined to be in the center of the Au₁₃ core. The presence of a second Pt species was determined by XPS compositional analysis. This unreacted Pt–thiolate oligomer present in the sample was also observed in the Pt L₃-EXAFS spectrum and causes a very intense Pt–S peak compared to the Pt–Au peak. This would not be possible for Pt in the center of an Au core. Further, while MALDI-MS can in theory be a great tool to determine the cluster composition, a drawback here is that the Pt–S compound was not detected with MALDI-MS because the molecular mass of this compound was below the detection range of this device. In order to resolve this issue, instead of purifying the sample (which may not possible), Christensen et al. [25] used a theoretical approach to determine the possible CN for this mixture and, therefore, the position of the Pt atom within the Au cluster. Even though the EXAFS analysis was performed without the constraints for bimetallic clusters (as described in Sect. 3.3) and a short k-range only up to 8.8 Å⁻¹ (which prevented them from resolving Au–Au vs. Au–Pt distances), this report shows that by use of several complementary methods, reasonable information for a complicated system can be derived.

Site-specific EXAFS simulations together with Mössbauer and EXAFS spectroscopy were used by Negishi et al. [28] in their report of bimetallic Au₂₄Pd(SR)₁₈ NC. Only EXAFS measurements at Pd K-edge are reported so only Pd–Au bonding can be discussed. The comparison of experimental with simulated EXAFS spectra of this cluster for Pd at different sites (center of the core, surface, staple) and the very high Pd–Au CN support the notion that the Pd atom is found mainly in the center of the core of the cluster. While no fits for the EXAFS analysis are shown (and the reported R-factor is 10 %, which is too high), this group makes an effort to determine the degree of purification of the synthesized clusters and improve the synthesis until the sample is purified. These findings show that effective use of EXAFS can give clear results even for the more complicated bimetallic system if great care is taken in confirming the purity of the sample and good EXAFS measurements.

4.1.7 EXAFS Analysis Is Not a Black Box

EXAFS analysis has a steep learning curve which is obvious if one watches the instruction videos or attends an EXAFS training workshop. The fitting technique using the analysis software is not “intuitive.” At the same time, it is not enough to just press some buttons and the result is given. In these fast times where too much stress is laid on the number of publications, there seems to be not enough time to learn this technique by training to fit already-understood data. In this following section, a couple of problems are discussed to point out the difficulties of an EXAFS analysis that are rarely discussed.

4.1.7.1 Variety of Capping Ligands

One problem in the characterization of APNC by applying EXAFS fitting analysis, which is discussed in Menard et al. [3], is related to different and mixed ligands that are used for the stabilization of the NCs. Next to thiols (e.g., [3, 5, 89, 90, [93, 95, 98]), also phosphines [3, 89], acetates [75], selenides [97], and unoxidized tellurates [110] have been used in the literature reviewed. Also, chlorine can act as ligand as well if it is not carefully removed [69–71]. Specifically for the Au₅₅ Schmid cluster, the gold atoms can have several different bonding partners in addition to gold (i.e., chlorine, triphenylphosphine, or nothing) [68]. The overview for this rather complex system is given in Table 5.2.

Table 5.2 Overview of Au sites and bonding ligand for the Au₅₅(PPh₃)12Cl₆ cluster

The scattering amplitudes and phases that are calculated from theory (specifically by use of crystal structures of bulk compounds as an input for the FEFF calculations) are equivalent for elements such as P, S, Cl [3], N, C, O [90], and other elements that have similar atomic masses. The basis of the EXAFS single scattering model is that the backscattering of elements with similar atomic masses cannot be resolved within the EXAFS fitting analysis. This is connected to the principle of transferability of photoelectron phase shifts [111]. In the everyday typical EXAFS analysis, this means that a theoretical compound such as Au₂S can serve as a joint model for the determination of, for example, S and P contributions together or by themselves. It also means that S and P contributions cannot be separated. A complicated set of sites such as the Au₅₅ NCs with Au–Cl, Au–P, and Au not bound (as in Table 5.2) cannot be completely specified with EXAFS. This is even more true when the surface is rather fluidic (Schmid [11]) causing structural disorder.

4.1.7.2 The Effect of Structural Disorder

Within the EXAFS data analysis technique as can be seen from the EXAFS equation (Eq. 5.5), structural disorder is parameterized in the form of the Debye–Waller factor (σ ²) (e.g., Calvin [45]). This total Debye–Waller factor includes thermal dynamic and static components that in turn represent changes in the configuration of the metal and ligand atoms in the NCs with time due to size dispersity [12]. EXAFS is only able to derive results for bond distances and bond length disorders from accurate structural and dynamic characteristics if the underlying distribution is quasi-Gaussian [31]. The effect of increased structural disorder for high temperatures as compared to low temperatures is discussed in Benfield et al. [2, 72], Chevrier et al. [98], and Shivhare et al. [21], specifically employing low temperatures (80 K). However, only in some cases, lower values for the Debye–Waller factor at low temperatures are reported [2, 72, 98]. Another aspect of this comparison is that the quality and reliability of the EXAFS analyses can be improved by taking data for the same sample at different temperatures [2, 21, 72]. The reliability of the EXAFS analysis technique can be tested observing certain ranges for the Debye–Waller factor values. For a reliable EXAFS analysis, σ ² values for Au–Au bonding (most Me–Me bonding) need to be between 0.005 and 0.01 for the first shell and up to 0.02 for higher shells.

The effects of static structural disorder beyond the Gaussian case that are correlated to symmetric bond length distributions in the NCs are due to different bond lengths in the core and on the surface of the NCs. This feature is called asymmetric bond length or the anharmonicity of the effective pair potential. This is reflected in the third cumulant parameter [3], a parameter included with modern EXAFS analysis software packages. The role of the third cumulant during the fitting procedure is to give an assessment of the significance of anharmonicity [12]. Symmetric bond length distributions are usually observed in bulk materials (i.e., without surface effects).

In the reports by Frenkel et al. [12], Menard et al. [3], and Yancey et al. [31], it was found that the role of the third cumulant was small. The main issue with this finding, addressed by Yancey et al. [31], is that EXAFS spectra provide only averaged information about the structure and dynamics of the environment of all absorbing atoms of the NC. If this “average” configuration is assumed to be the actual configuration, the EXAFS analysis cannot provide correct structural results. Specifically, this means that a broad distribution of sizes, shapes, crystal structures, and states of order will lead to misinterpretation of the EXAFS spectra. This effect of structural disorder on the EXAFS fit results was investigated in detail in the study by Yancey et al. [31]. One main result of this study is that the EXAFS fitting method which is based on the Gaussian bond length distribution is not able to describe highly disordered systems very well. Such systems can be described better in the PDF extracted from DFT-MD calculations, which can be asymmetric. In a report by Price et al. [105], experimental EXAFS and EXAFS simulations were combined with DFT-MD calculations for small Pt NPs in order to determine how the size determination for small NPs is affected by anharmonicity. They modeled the contraction of the surface layer was well as anisotropic disorder. In many cases, the use of the third cumulant, which should address this issue in the EXAFS fitting procedure, is not applicable because the Au–Au and Au–S bonding features (peaks) overlap and mask possible asymmetry. While it seems that this parameter does not “do” anything for some groups, it is important that it is reported together with errors and with a picture of the fit in k- and R-space in order to verify the reliability of the results.

4.1.7.3 The Importance of the k-Range and the Limitations of the Resolution of EXAFS

The limitations of the resolution of the EXAFS analysis are discussed in the report by Menard et al. [3]. While an EXAFS analysis can deliver results with a resolution of 0.001 Å for bond distances, this depends on the quality of the data measured. The knowledge that can be gathered from the EXAFS analysis can be limited when the k-range that is measured is too short or noise in high k region shortens the k-range. This results in the limitation of the spatial resolution of the EXAFS data (cf. Fig. 5.12). For example, because of the icosahedral structure of the Au₁₃ NC, the Au atoms are distributed in two shells closest to the core (i.e., subshells). This multishell or splitting arises from a 5 % difference of the Au–Au distances in the distance range for the first shell [12] and could not be resolved by Menard et al. [3]. However, this group used a trick to overcome this problem: By calculating the ratios of the distances of the different shells (i.e., R _3NN /R _1NN third shell vs. first shell), the icosahedral structure for Au₁₃ NCs and fcc structure for the Au₁₄₇ MPCs could be determined. Additionally, the fact that in the FT-EXAFS R-space spectra no single scattering for a second shell was observed helped with this assessment.

Fig. 5.12

FT-EXAFS spectra in R-space derived from the same EXAFS data (Au–S site in Au₁₀₂(SR)₄₄) for different k-ranges (from bottom to top, 2.5–8, 2.5–12, 2.5–16, and 2.5–20) (Structural data used from Jadzinsky et al. [92])

As a positive example where subshells could be observed in the experimental EXAFS spectra, the report by MacDonald et al. [5] is mentioned: The first Au–Au shell in the core is split into three subshells for the Au₂₅(SR)₁₈ icosahedron (determined by theoretical EXAFS). There is a discussion about the standardization to report XAS data among the XAFS community (cf. refs: IXS committee [112, 113]) ongoing. However, no agreement has been found yet.

4.1.7.4 The Requirement of Sample Purity

Menard et al. [3] also discuss discrepancies between the model (truncated octahedron) and the experimental EXAFS results (CN for Au–S) for the Au MPCs they investigated. These discrepancies are possible if the sample contains a thiolate precursor or if the NCs in the sample have degraded. Additional investigations by this group show that there are similarities in the EXAFS data between pure monomer gold (I) thiolate and the thiolate-protected Au MPCs. Menard et al. [3] point out that the EXAFS analysis technique is based on mass-weighted signals (which is nonstatistical). Therefore, with increasing metal cluster size, the CNs increase hyperbolically, and there is a higher sensitivity toward smaller clusters or low-coordination organometallic species. This means that suspiciously high Au–S and low Au–Au scattering magnitudes are related to the presence of a gold (I) thiolate species, making EXAFS uniquely sensitive to this impurity. Menard et al. [3] point out further several reports where the EXAFS data is attributed to pure NC samples; this data is actually identical to the EXAFS data of gold (I) dodecane thiolate and not NCs. The comparison of Au NCs with different cluster size (Au₁₄₄ Au₃₈ Au₂₅) by MacDonald et al. [93] confirms the sensitivity of EXAFS to the low-Z elements because of the quite slow reduction in intensity of the Au–S peak in the EXAFS spectrum of the experimental samples.

The effect of mixed samples on EXAFS analysis is discussed extensively by Frenkel and coworkers, specifically in [55]. The importance (and verification) of the purification of the samples was shown by Negishi et al. [28]. This means that it is important to employ other techniques (e.g., XPS elemental analysis, ICP, EXAFS simulation) to confirm the purity of the sample or that the model applied agrees with the experimental data.

4.2 XANES

4.2.1 Experimental XANES and the Fingerprint Analysis

The measurement of XANES spectra can take less time than the measurement of EXAFS spectra, and more noise is acceptable for the data analysis using the fingerprint method (see Sect. 3.2). In order to gain structural information using the fingerprint method, effort has to be taken to find adequate reference spectra. In the case of APNCs, this is not always possible. In the studies when XANES data of APNCs have been reported, they were mainly shown compared with the bulk metal data (e.g., [28, 71, 84, 91, 93, 114]), which is always measured with the APNC sample simultaneously. Marcus et al. [71] used this comparison to confirm the fcc structure for the Au core in the Au₅₅(PPh₃)₁₂Cl₆ NCs since all the features of the bulk metal were observed in the XANES spectrum of the NC. The features (e.g., maxima) in the XANES spectrum were broadened and reduced in intensity which is known to be normal for nanoparticles [9]. Also, in MacDonald et al. [93], the metal character and fcc structure were observed for the Au₁₄₄(SR)₆₀ NCs by comparing the XANES spectra of bulk gold and the NCs. The metallic character of the one Pd atom in the bimetallic cluster Au₂₄Pd(SR)₁₈ was observed using Pd K-edge XANES spectra [28].

Another useful approach was reported by Frenkel et al. [89]. They acquired XANES spectra taken from the point of view of the ligand (in this case S and P K-edge) instead of metal core atoms (Au L₃-edge). The change in the chemical environment and, thus, the formation of the Me-ligand bond were confirmed because the features in the XANES spectra (at S or P K-edge) of the Au₁₃[PPh₃]₄[S(CH₂)₁₁CH₃]₂Cl₂ NCs were shifted to different energies compared to the pure ligand spectra. This approach was also used by Liu et al. [115]. Using also the ligand “point of view” using S K-edge XANES spectra, the increase in S–Au bonding with increasing cluster size was observed for several Au_xSR_y NCs [93].

Only in the report by Benfield et al. [10], quite a number of reference compounds for Au are presented. This group used the comparison of the XANES fingerprints to determine the metal-like chemical environment and oxidation state of the Au atoms in the Au₅₅(PPh₃)₁₂Cl₆ NCs. In addition to the standard reference compounds for the initial solution (KAuCl₄), ligand reference (PPh₃AuCl), and bulk gold, several NC and NP are collected in Fig. 5.13 showing how the features of the XANES spectra of the NCs (especially Au₅₅(PPh₃)₁₂Cl₆) are broadened as discussed above.

Fig. 5.13

XANES spectra at Au L₃-edge for different Au NP samples and reference compounds (Reprinted with permission from Benfield et al. [10]. Copyright 2001 American Chemical Society)

Even though not precisely about APNCs, Ohyama et al. [116] reported in situ XANES during the formation of (naked) Au NCs. This series of Au L₃-XANES spectra shows how the cluster formation starts with the precursor aurochloric acid (Au³⁺) after addition of NaBH₄, reduction to Au(0), and formation of NP and how aggregation ends with the formation of Au bulk (Fig. 5.14). When the process starts, a broad peak at about 11,929 eV appears (characteristic for KAu(III)Cl) and is reduced in intensity during the reduction. An increase in WL intensity for Au L₃-edge XANES spectra at about 11,929 eV is reported for small NCs [3, 5, 28, 84, 85, 93, 95–98]. This feature is used quite extensively for the analysis of APNCs to determine the catalytic activity. The small difference of the intensity in the Au L₃-edge WL compared to bulk gold is used to indicate an increase in d-hole population.

Fig. 5.14

XANES spectra at Au L₃-edge during the formation of Au NPs (Reprinted from Ohyama et al. [116]. Copyright (2011) with permission from Elsevier)

However, caution must be applied when dealing with small differences. Although experimental XANES spectra are usually less affected by noise (because of the much more intense nature of the WL and SR) than EXAFS spectra, both EXAFS and XANES spectra always contain experimental errors that must be considered when making conclusions from the data. Firstly, there is an experimental error in the energy (E). If the energetic position of a peak maxima/minima (e.g., WL) or edge E ₀ differs by more than the minimum step size (which was used for the measurements), this difference is significant [117]. Therefore, an edge shift of 0.2 eV at Au L₃-edge (11,919 eV) for XANES spectra of two different samples (e.g., at different temperatures) [96] cannot be significant because the minimum step size at Au L₃-edge is at least 0.2 eV (more likely 0.5 eV). Secondly, there is an experimental error in the absorption coefficient (μ) or line intensity. This was discussed in Benfield et al. [2, 10] where the differences in the intensity of the peaks were more than 5 %. An experimental error analysis is always necessary, and this is especially true when trying to make conclusions based on intensity differences of only a few percent. This was crucial, e.g., in the analysis of plant samples by Bovenkamp et al. [118] at Pb L₃-edge using a method to analyze the error contribution to XANES spectra by Bovenkamp et al. [119]. The XAFS community is working toward the implementation of standards for XAS measurements for the last 20 years [112] in order to raise awareness of the effect of the experimental error on the analysis of XAS experiments. If small variations are reported, it should be self-evident to report the error bars of this measurement.

L₃-edge XANES measurements are usually reported for transition metals such as Au and Pt. The L₃-edge XANES spectra for these elements probe the transition 2p → 5d_5/2 (or 6 s). Correspondingly, for the L₂-edge, the transition 2p → 5d_3/2 (6 s) is probed as discussed in Sect. 3.2. For the transition metals Au and Pt, the L_3,2-edge spectra are quite sensitive to electronic changes of the d-band which is especially observed in the WL region. These changes directly correlate to the oxidation state and d-band population of the material. In transition metals such as Pt and Au, the 5d-bands are filled in the metal state, and the XANES spectra (at L_3,2-edges) of these metals do not have a WL. For example, in the case of Au(III) compounds (with oxidation state 3+), the WL increases drastically due to the decrease in the occupancy of the d-orbitals (as d-electrons are transferred to the ligand) (Fig. 5.13: KAuCl₄). On the other hand, the Au(I) dodecane-thiolate polymer does not exhibit a strong white line even though the oxidation state of Au is 1+ [3]. This shows that the intensity of the WL does not solely depend on the oxidation state but also on the hybridization of the orbitals [3]. Additionally, stronger d–d interactions in Au NCs that increase the d-charge of Au atoms – as a “nanosize effect” [88] – might result in lower WL intensity compared to that for the bulk. Work by Zhang and Sham [120] shows also a more intense WL for Au NCs capped with thiols compared to capping with weakly interacting dendrimers (the clusters had identical size). The explanation for these effects lies in the difference in charge transfer for Au–S due to the different surface-to-volume ratios for small NCs compared to bigger ones [88] and that the size of the particle does influence this intensity due to broadening [33] as was discussed above.

In order to extract significant information from the shape (e.g., intensity differences of the WL) of the XANES spectrum, several methods intending to estimate densities of unoccupied 5d states around the Fermi level have been developed. These approaches do not just use the comparison of the intensity of the WL per se but the comparison of the intensity of the absorption edge calculated as the area under the peak [121–127]. According to Benfield and coworkers [10], only the method by Mattheiss and Dietz [125] as well as Tyson et al. [127] gives reliable semiquantitative estimates, whereas the others do not. Therefore, in two reports by Benfield et al. [2, 10], a method was used where the L₃-edge and L₂-edge spectra are compared with each other. This method employs the spin–orbit splitting effect between d_5/2 and d_3/2 orbitals to gain information on the occupancy of the d_5/2 orbital. The basis of this method is measurements of L₃-edge XANES spectra of gold, platinum, and iridium by Lytle et al. [128] showing WLs for compounds with metal oxidation state > 0, and band calculation measurements by Mattheiss and Dietz [125] show that spd hybridization causes unoccupied states in the d_5/2 and d_3/2 orbitals at the vicinity of the Fermi level.

In Benfield et al. [2], the L₃ to L₂ comparison is used to determine if Pt in the Pt₃₀₉ NCs has molecular (oxidation state > 0) or metallic (oxidation state = 0) behavior. For this specific Pt₃₀₉ NC, the comparison of the different area values for Pt foil, K₂PtCl₄, and Pt₃₀₉ NCs resulted in the observation that the Pt atoms in the Pt₃₀₉ NC have metallic character. In their report, Benfield and coworkers [10] investigate the oxidation state of Au in Au₅₅ NCs with the same method. However, the area values for the Au₅₅ NCs were smaller than those for Au bulk. The small cluster size resulting in stronger d–d interactions was the reason given why this method did not work for gold. This method was not used in any of the later reports. Possibly due to the extra time needed to measure both L₃-edge and L₂-edge XANES.

4.2.2 Theoretical XANES, l-DOS Calculations, and Charge Transfer

In a number of reports [5, 25, 84, 85, 93, 95, 98], mainly on Au APNCs, calculations of the projected DOS and charge transfer of electrons between orbitals have been discussed. The application of l-DOS and charge transfer calculations is useful because the knowledge about the DOS above and around the Fermi level makes it possible to probe the electronic structure dependent on the size of the NCs [3]. L-DOS and charge transfer calculations are used by more researchers because of the development of the theoretical description of XAS ab initio and the FEFF code as a program using those principles.

Without getting into much detail about the theory, which is covered by the literature (e.g., [9, 33, 50]), a short overview is presented here. Version FEFF6 made possible the successful calculation of EXAFS spectra based on single scattering and selected multiple scattering paths. The first time the multiple scattering expansion [129] was used to calculate XANES was in FEFF7, but only with the development of FEFF8 did the self-consistent (SCF) calculations of the scattering potential allow the determination of the Fermi energy and charge transfer. Since version FEFF8 with the development of better algorithms to calculate the matrix elements for the multiple scattering expansion and the development in computer capacity simulations of XANES spectra, l-DOS and charge transfer became easily calculable. Further, the multiple scattering calculations were extended to a real-space full multiple scattering routine [130] to prevent the divergence of the path expansion at low photon energy (which is exactly around the absorption edge). This important feature (real-space full multiple scattering) is crucial in any XANES calculation and, thus, l-DOS and charge transfer calculations. The real-space multiple scattering approach [130], which makes the FEFF8 (and later versions) code so user friendly (i.e., not difficult to use), needs the input of cluster data (of any compound or NC) in real space (xyz). This input can be derived from different atomic programs based on crystal structure.

Using the FEFF code to get a XANES spectrum is not too difficult. However, if something that looks somewhat like (the) data is calculated (and electron counts and l-DOS is calculated in any case), it is important to test its validity. These tests would include:

• Convergence of the SCF calculations (to determine the stability of the Fermi energy and thus electron transfer)

• Convergence of the full multiple scattering calculations (to determine the necessary cluster size)

• Agreement with the experimental data (to determine the validity of the cluster used and thus the l-DOS curves)

For typical compounds, it has been shown that 5–6 shells of atoms around the absorbing atom are required for a multiple scattering calculations in the full multiple scattering module so that the cluster can reproduce a XANES spectrum for that compound [131]. For more complicated structures such as NCs where the cluster size of one particle is effectively too small for the full multiple scattering calculation (e.g., with < 100 atoms in a cluster such as the Au₂₅ or Au₃₈ NCs), the convergence of the full multiple scattering calculations cannot be reached which means that the calculated XANES spectrum is not correct. This was described by Soldatov et al. [132] for small clusters at the Au L₃-edge.

The development of XANES features for small Au clusters was studied by Chen et al. [133] applying the XANES simulation tool of FEFF8 using a simple model of fcc gold. Figure 5.15 shows the simulated XANES spectra for several Au clusters created by restricting the cluster size for the full multiple scattering calculation (to shells 1–4) in comparison with the experimental XANES spectrum. Broadening washes out the features (e.g., maxima) of the XANES spectra for NCs (and other small nanoparticles, as was discussed above) similar to the effect of the different Au–Au bonding structure for the surface sites on NCs. Further, theoretical XANES investigations of small metal clusters were also done by Bazin and Rehr [1]. They find that the inner structure as well affects the XANES spectrum [1].

Fig. 5.15

XANES spectra at Au L₃-edge of Au₁₃, Au₄₃, Au₅₅, and Au₇₈ clusters calculated with FEFF (Reprinted with permission from Chen et al. [133]. Copyright (2007) American Chemical Society)

However, in the above report by Chen et al. [133], the XANES calculations are not completely correct, since the cluster size used was too small. The application of the full multiple scattering module, which is crucial for the XANES calculations, involves the inclusion of all multiple scattering contributions. Together with the muffin tin approximation, the center of the potential calculations, it is necessary to use large clusters for the calculations where the contributions of surface atoms can be neglected [1]. For a small cluster, this means that the contributions of (a) the Au–S staple motif atoms and (b) other nearby clusters have to be included.

There are discrepancies between experiment and FEFF calculations that are due to approximations. This fact is known, and the need for improvement of the FEFF code for XANES calculations is discussed by the developers of FEFF (e.g., [130, 134, 135]). Including full potential calculations instead of spherical muffin tin calculations is necessary to accurately model for anisotropic systems. Also, better treatments of inelastic losses, self-energy, many-body corrections, and core–hole effects need to be implemented. These factors are rarely discussed within the community (because they know about it), but the new user might not be aware of these limitations and the connections between XANES and l-DOS. In a sequence of studies by Soldatov and coworkers [136–139], other software codes not using the muffin tin approximation were compared to FEFF for small clusters of Ti, Cu, and Nb. Oyanagi et al. [107] also used other software codes beyond the muffin tin approximation for their time-resolved characterization of radiolysis-irradiated Cu samples. These studies show the above-stated points.

To better understand the following discussions about l-DOS and charge transfer, some basics about Au are mentioned first. The electronic structure of Au was reported by Coulthard et al. [140] and Kuhn and Sham [141]: Due to the configuration of Au (as [Xe]4f¹⁴5d¹⁰6s¹), the d-band in metallic Au is nominally full. However, d and non-d (sp) rehybridization is possible and can create d-band holes where the Fermi level is then somewhere in the middle of the d-band 0.4 of the population for Au [88, 125]. Even for alloy formation, this rehybridization showed a significant effect in XPS and XANES [141]. Therefore, the first peak of the Au L₃-edge XANES spectrum (the WL, transition 2p → 5d_5/2) is related to the presence of d-holes [125, 140] (see Fig. 5.13) which, in turn, is related to a peak in the d-DOS. However, caution is necessary when interpreting features of the l-DOS curves as contributions to the XANES spectrum; not in all cases mixing (e.g., p–d mixing results in L₃ features [118]) is possible.

MacDonald et al. [5, 85, 93] used EXAFS, XANES, and XPS, and, in addition, l-DOS and charge transfer calculations, to study Au thiolate APNCs. The XANES spectra of the simulations were found to show features similar to those in the experimental spectra (Fig. 5.16a and b). However, it is not discussed why the experimental data shows a better resolution/less broadening compared to the simulations (usually it is reversed, and additional broadening has to be introduced with the simulated spectra). The strong S–Au/S–C (A and B) line in the S K-edge spectrum was inspected further. The l-DOS calculations here confirm that feature A originates from S–Au bonding and feature B originates from S–C bonding. The features a and a’ in the simulated spectrum (Fig. 5.16c) are not resolved in the experimental spectrum (Fig. 5.16a). The discussion of similarities between calculated and experimental spectra in relationship to the presence and absence of S–C bonding is quite useful to confirm the bonding-type information reported by Chaudhuri et al. [142] and Zhang and Sham [88].

Fig. 5.16

Experimental and theoretical XANES spectra of Au₁₄₄(SR)₆₀ at (a) S K-edge, (b) S L_3/2-edge, and (c) calculated l-DOS of the S, Au, and C atoms of Au₁₄₄(SR)₆₀, with simulated XANES spectra of Au₁₄₄(SR)₆₀ (black line) compared to Au₁₄₄S₆₀ (red dotted line), over only about 2470–2476 eV (Reprinted with permission from MacDonald et al. [93]. Copyright 2010 American Chemical Society)

L-DOS and charge transfer calculations can be complemented with XPS and can extend the understanding of electronic properties [84]. XPS can also support the other results from MacDonald et al. [93] where the d-DOS of Au–S and Au–Au bonding shows the same behavior (molecular/nonmetallic = sharp singlet, metallic = wide doublet). Similar effects were observed by MacDonald et al. [85] for an Au₃₈ cluster, by Chevrier et al. [95] for Au₁₉ and Au₂₅ clusters, and by Simms et al. [84] for Au₂₅ clusters.

Site-specific d- and s-electron occupancy was used by MacDonald et al. [5, 85] to show similar properties of similar atomic sites for Au₃₈ and Au₂₅ NCs including charge transfer for Au in staple sites compared to Au in core sites. This is in agreement with a hypothesis of donation (3 s to Au 6 s) and back donation (Au 5d to S 3p) by Park and coworkers [143]. Also in this report, a theoretical model was used to represent solvation effects. The d-DOS curves of both the solid and the modeled (solvated) Au₃₈ NC show that next to the narrowing of the d-band in the staple motif (as above) a shift to higher (closer to Fermi level) energies can be observed for the solvated model [85]. This hypothesis should be investigated more closely.

Chevrier et al. [95, 96, 98] compare the l-DOS curves (site specific) of Au₁₉(SR)₁₃ vs. Au₂₅(SR)₁₈, also Au₂₅(SeR)₁₈ vs. Au₂₅(SR)₁₈, and Au₃₆ vs. ideal Au₂₈ core, respectively, similar to the work by MacDonald et al. above. For the comparison of the Au₁₉ vs. Au₂₅ NCs, the d-band for Au surface and Au center sites is broadened for Au₂₅. XPS results agree with this observation indicating that the Au₁₁ core of Au₁₉ has defects and has fewer Au–Au bonding interactions compared to the Au₁₃ core of Au₂₅ [95]. For the Au₂₅(SeR)₁₈ vs. Au₂₅(SR)₁₈ NCs, the 5d-band of the selenolate NCs shows higher electron counts compared to the 5d-band of the thiolated NCs which is linked to less charge transfer and more covalent behavior of the Au–Se bond [96]. The investigation of the electronic behavior of Au₃₆(SR)₂₄ and Au₃₈(SR)₂₄ resulted in the finding that for the Au₃₆ cluster, the Au–Au bonding is more molecular compared to a rather metallic Au–Au bonding in Au₃₈ NCs [98].

5 Conclusion and Future Perspectives

The quite young field of atomically precise nanoclusters started in the 1980s and was first addressed by the technique of EXAFS in 1985 [74] with early forms of analysis software. The boost of synchrotron radiation facilities and theoretical developments subsequentially has led to greatly improved analysis software and strategies to apply EXAFS to all kinds of systems.

One of the main uses for EXAFS became the determination of the size (number of atoms) of the APNCs. This was implemented using structural models based on atomic packing (e.g., fcc) and the proportionality of size and CN within these models. The successful application of this strategy made it possible to compare TEM, XRD, and EXAFS results.

The EXAFS strategies that were developed for the characterization of NP can be applied similarly to APNCs. However, improvements in EXAFS, such as the CNT model or the surface-tension model, were necessary due to the small size of the NCs. One important feature of all nanoparticle investigations is that the amplitudes of the EXAFS signals (in k-space and R-space) of the nanoparticles compared to the bulk metal are always reduced and in XANES even broadened. It has been shown that a self-consistent approach for the EXAFS analysis, using different models within the same technique, is a good method in order to validify the results characterizing the NCs.

Since XAS is a technique based on the average configuration of the sample under investigation, disorder within this configuration (more precisely disorder in the structure due to different bond distances) can lead to EXAFS analysis results that can be misleading.

XANES and EXAFS are not black boxes where a button just has to be pressed to measure the samples and spit out the results. Some understanding of the underlying physics of both methods (which includes an understanding of the errors involved) and a deeper understanding of the methods which are the basis of the technique have to be developed [144].

The techniques and methods that are presented here give a brief overview of the models that EXAFS analysis can use and how XANES and l-DOS calculations can be applied.

The application of complementary techniques (including HRTEM and HAADF-STEM to determine size homogeneity) is important to help validify the EXAFS results. Even more so can theoretical calculations using different techniques (DFT-EXAFS, DFT-MD) help to determine effects of structural disorder on the EXAFS analysis of experimental spectra.

The extraction of electronic information about APNCs from XAS can be done through L-DOS calculations based on FEFF. However, this has to be set in perspective with previous DOS calculations or XPS results to make proper analyses.

In conclusion, we find that a number of groups are using XAS techniques, especially EXAFS analysis for the characterization of APNCs. These reports are not just about understanding the structure of the NCs any longer but more so about tuning the properties of these NCs by varying the ligands. A particular driving force in these reports has been the understanding of the effect of the staple motif. EXAFS is a very powerful tool to study the changes in structure including bond length, coordination environment, and disorder that can be examined very powerfully. This use of the XAS toolbox (theoretical, experimental, in situ EXAFS and XANES, and l-DOS calculations) in its variety does help to gain more accurate information about the structural and electronic properties of APNC and their catalytic application.

Further improvements in the application of EXAFS/XANES in the characterization of APNCs lie in the development of reactors that can be installed in the XAS beamline to collect X-ray absorption spectra in situ as temperature and pressure are varied or other environmental conditions are needed or to observe the synthesis or a catalytic reaction itself. Such reactors to observe the synthesis can be, for example, milli-fluidic reactors (e.g., [145]) which bring the possibility of spatially resolved observation of the reaction. X-ray fluorescence mapping and X-ray microscopy using micro-focused beams are also useful.

Summarizing, we find that EXAFS and XANES are exciting and versatile techniques in the study of APNCs and their use in catalysis. The analysis of XAS data can be quite challenging, however, and it is important to have a thorough knowledge of the physics and possible sources of error involved and, in many cases, combine the EXAFS and XANES analyses with other techniques, and theoretical modeling, to produce the best understanding of the system under investigation.