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Clusters and Nanocrystals

  • Christoph BostedtEmail author
  • Tais Gorkhover
  • Daniela Rupp
  • Thomas Möller
Living reference work entry

Latest version View entry history

Abstract

Clusters and nanocrystals constitute intermediates between molecules and condensed matter. Due to their finite size, clusters have a wide spectrum of applications ranging from building blocks for novel materials to model systems for fundamental investigations about light-matter interactions. Short-wavelength radiation from synchrotron radiation sources and free-electron lasers allows the detailed investigation of their geometric, electronic, and magnetic structure as well as dynamical processes. Conversely, clusters can serve as idealized sample systems for the development of new experimental techniques and pioneering experiments with novel x-ray sources. The chapter starts with a brief introduction to cluster physics, followed by a comprehensive overview of research performed at synchrotron light sources on van der Waals, metal, and semiconductor clusters. With the advent of short-wavelength free-electron lasers, a new research field in the x-ray peak intensity regime has opened. Experiments on single clusters, such as x-ray imaging and tracing ultrafast dynamics, now become possible.

Keywords

Clusters Free-electron lasers Imaging Spectroscopy Synchrotron radiation Nanocrystals X-ray 

Glossary

ALS

Advanced Light Source

AMO

Atomic, molecular, and optical

BESSY

Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung

CM

Condensed matter

DESY

Deutsches Elektronen Synchrotron

European XFEL

European X-Ray Free-Electron Laser Facility

EXAFS

Extended X-ray absorption fine structure

fcc

face centered cubic

FERMI

Fermi free-electron laser at Elettra

FEL

Free-electron laser

FLASH

Free-electron laser in Hamburg

ICD

Inter Coulombic decay

LCLS

Linac Coherent Light Source free-electron laser

LURE

Laboratoire pour l’utilisation du rayonnement électromagnétique

pnCCD

pn-Junction charge coupled device

SACLA

Spring-8 Angstrom compact free electron laser

SOLEIL

Source optimisée de lumiére d’énergie intermédiaire du LURE

SR

Synchrotron radiation

TOF

Time-of-flight

TTF-FEL

Tesla Test Facility-FEL

UV

Ultraviolet

VdW

van der Waals

VUV

Vacuum ultraviolet

XANES

X-ray absorption near edge structure

XAS

X-ray absorption spectroscopy

XMCD

X-ray magnetic circular dichroism

XPS

X-ray photoelectron spectroscopy

XUV

Extended ultraviolet

Preface to the Second Edition

This chapter, originally written in 2015, has been updated with recent work on clusters in synchrotron and free-electron laser light, incorporating new directions that have emerged in the last couple of years. In the first part of this chapter on clusters in synchrotron light, we included new developments in hard x-ray scattering, in the field of He clusters, on inter-Coulombic decay in neon clusters as well as a body of work on fullerenes, diamondoids, and photoemission of nanoparticles. For the second part of this chapter on clusters in intense free-electron laser pulses, we incorporated the latest work on intense x-ray cluster interaction from FLASH, FERMI, SACLA, and LCLS. We mostly rewrote the section of imaging superfluid helium nanodroplets to reflect the dynamic developments in this field. Further we added a section about clusters as holographic references and rewrote large parts of the section on diffractive imaging of dynamics. These changes went along with the implementation of new and the revision of existing figures as well as an update of the glossary and the references.

Introduction to Cluster Physics

What Is a Cluster?

Clusters and nanocrystals are assemblies of atoms or molecules that bridge the gap between atomic and molecular physics (AMO) on one hand and condensed matter (CM) on the other hand. They are intermediates between atoms and molecules with clearly defined energy states and bulk matter with energy bands. Usually it is assumed that a cluster consists of at least three subunits. The upper size limit for clusters is not well defined. Often particles with more than 104 identical units or even particles with several hundred nm radius comprising 108 atoms or molecules are regarded as clusters or as nanocrystals if they exhibit a crystalline structure.

Clusters can also be considered to constitute a new type of matter. They typically exhibit size-dependent properties which differ fundamentally from that of bulk material. Therefore they are said to extend the periodic table into the third dimension. Compared to well-established fields such as AMO or CM physics, the systematic study of clusters is a rather young research area which started to rapidly grow in the 1980s (cf. Haberland 1993, 1994, and Johnston 2002). Much information about the cluster properties could already be obtained with laboratory-based experimental techniques such as mass spectrometry and laser-based spectroscopy. The unique characteristics of short-wavelength radiation from synchrotron radiation sources (SR) or free-electron lasers (FELs) give additional insights into the properties of clusters. X-ray-based tools can yield information about their structural properties, their electronic structure with chemical sensitivity, their optical and magnetic behavior, as well as their dynamics. Both, at SR and FEL sources, endstations are available equipped with dedicated components for cluster and nanoparticle research (Strüder et al. 2010; Lyamayev et al. 2013; Kostko et al. 2017; Lau 2017; Sublemontier et al. 2014; Erk et al. 2018; Mazza et al. 2012; Ferguson et al. 2015; Osipov et al. 2018).

Questions in Cluster Research

Clusters and nanocrystals are of fundamental scientific and technological interest as they bridge atomic and condensed matter physics. Already in the early days of cluster research, the key questions in the new field were formulated:
  • How do cluster and nanocrystal properties depend on their size?

  • How many atoms are needed to form bulk properties, e.g., metallic behavior?

  • Do clusters and nanocrystals exhibit novel properties?

  • Can they be used to tailor new materials?

  • Are new concepts needed for the description of clusters?

  • How does the interaction of light with clusters differ from that with atoms?

With the development of the field, several more specific topics have been put forward, including chemical reactivity, role of surface atoms, and phase transitions to name a few. A very specific property of clusters is their shell structure. As we will see, geometric and electronic shells are observed in clusters underlining their unique position between atoms, molecules, and bulk material (Johnston 2002).

Classification of Clusters

Clusters can be classified according to their size and their chemical composition. The classification by size was originally developed for van der Waals systems by Jortner et al. (1987). For microclusters comprising 3–12 atoms, all atoms sit on the surface, and they can be described by concepts from molecular physics. Small clusters with N = 13 to ≈100 atoms are characterized by a large number of isomers. In this size regime, “every atom counts” as the properties of the clusters still depend on the exact number of atoms as depicted in Fig. 1. For large clusters with more than hundreds of atoms, a gradual transition to bulk properties can be observed. In analogy to solids, clusters can be classified according to their binding type (c.f. Table 1). The change of binding energy upon ionization (last column in Table 1) indicates whether the clusters will fragment. Large changes favor fragmentation since a large amount of energy is deposited in the ion. The binding mechanism can change with size. Probably the most prominent example is mercury (Brechignac et al. 1988). Small mercury clusters are van der Waals bonded since the outermost (5s) valence orbitals are filled. With increasing cluster size, the 5s band starts overlapping with the unoccupied 5p bands, and thus the clusters become metallic (Busani et al. 1998).
Fig. 1

Schematic representation of a generic cluster property G with cluster size (N in subunits/cluster). (Adapted from Jortner et al. 1992)

Table 1

Classification scheme of clusters. (Adapted from Jortner et al. 1987)

Type of binding

Example

Binding energy BE

Change of BE

between subunits

 

per atom

by ionization

Metallic

Na

0.5–3 eV

Small

delocalized electrons

Hg for n > 400

  

Covalent

C, Si

1–5 eV

Small

direct bonds

   

Ionic

NaCl

1.5–4 eV

Small

Coulomb interaction

   

Hydrogen bond

H2O, HF

0.15–0.5 eV

Strong

dipole interaction

   

Molecular clusters

I2, As4

0.3–1 eV

Strong

VdW and covalent

   

Van der Waals

Ar, CO2

0.001–0.3 eV

Very strong

induced dipole-dipole

Hg for n < 10

  

Cluster Generation and Cluster Sources

Clusters are usually generated in a bottom-up approach by growing them in the gas phase from single atoms or molecules. Cluster growth can be described in a macroscopic model using thermodynamic concepts or a microscopic description based on the collisions of single atoms or molecules (Haberland 1993). Condensation and cluster growth starts in the first step with a three-body collision stabilizing a collision complex. After the onset of condensation, clusters grow by addition of single atoms or molecules, while at a later stage, coagulation of clusters becomes dominant (Soler et al. 1982).

Various cluster sources have been developed for different materials (Haberland 1993). Weakly bound clusters, such as van der Waals and hydrogen-bonded clusters, are commonly produced in gas jets by expanding a gas at high pressure through a small nozzle. The average cluster size can be controlled with the gas pressure, temperature, and nozzle geometry (Hagena 1987). The resulting size distribution follows a log-normal distribution (Wang et al. 1994) with the full width at half maximum similar to the mean cluster size, with exception of beams with a very low degree of condensation and very small clusters. For systems with very low binding energy (e.g., He, Ne) cooling of the gas is required. Clusters generated from pure gases are rather warm. For rare gases their temperature is typically 80% of the melting temperature; some metal clusters are even liquid (Gspann 1986). Cold clusters can be generated by adding a seeding gas such as He or Ar. For experiments with low duty cycle, pulsed valves can be employed, but the resulting jets can exhibit a distinct time structure (Rupp et al. 2014).

For the generation of strongly bound clusters, the material needs to be first evaporated. This can be done by thermal heating in a crucible, laser vaporization or sputtering (de Heer 1993; Goldby et al. 1997). Thermal heating is limited to materials with low boiling points, but laser vaporization sources can be used for clusters of almost any material (Bondybey and English 1983; de Heer and Milani 1991). They can produce both neutral and charged clusters, but the sources are pulsed, resulting in lower average flux compared to continuous supersonic expansion even though the intensities in the pulse can be very high. Pulsed arc sources (Siekmann et al. 1991) are similar to laser vaporization sources where the laser is replaced by a strong electrical discharge. For materials with high melting points, magnetron sputter sources are very efficient, too (Goldby et al. 1997). If a large clusters are needed, gas aggregation sources are particularly efficient which allow tuning the cluster size over a large range and also cooling them to low temperature (<100 K). Finally, it is noted that small clusters can be produced by ion sputtering (de Heer 1993).

While clusters are usually produced out of the gas phase, nanocrystals are commonly grown with wet chemistry-based techniques by precipitation (Henglein 1989; Weller 1993a; Alivisatos et al. 1996). The particles consist of a crystalline core covered by a shell of ligands. The size of the particles can be controlled by the temperature of the solution, the concentrations of the compounds, and the reaction time. Since nanocrystals are usually terminated with ligands, they are rather stable and can be deposited on surfaces without damage.

Fundamental Properties of van der Waals Clusters

Van der Waals (VdW) clusters play an important role in cluster research. The first generation of Ar clusters in jets (Becker et al. 1956; Becker 1986) can be considered as one of the starting points of the field, and the concepts for condensation and particle growth were developed in the 1970s for rare gas clusters (Hagena and Obert 1972). Shortly afterwards it was demonstrated that the size distribution of clusters exhibits “magic numbers” at N = 13, 55, and 147 (c.f. Fig. 2, inset) which are signatures for geometric shell structure (Echt et al. 1981). While these numbers correspond to closed shell cubic as well as icosahedral structures, the additional intensity maxima in between the pronounced shell closings combined with results from electron diffraction yielded evidence that small clusters can also exhibit amorphous-like poly-icosahedral- or multi-icosahedral-type structures (Farges et al. 1981; van de Waal 1989). In principle small icosahedral clusters are energetically favored, but the transition to cubic bulk structure is still under discussion (van de Waal 1996; Kakar et al. 1997; Rupp et al. 2012). As argon clusters grow by fusion with increasing temperature, their structure transforms from essentially face-centered cubic (fcc) to hexagonal close packed as the cluster size approaches 10.000 atoms. The transformation involves intermediate orthorhombic phases (Krainyukova et al. 2012).
Fig. 2

Mass spectrum of Xe clusters, the magic numbers corresponding to shell closings are indicated. (Adapted from Miehle et al. 1989)

Valence Electronic Structure of van der Waals Clusters

For electronic structure investigations of rare gas clusters, short-wavelength radiation is needed, since their electronic excitations and the ionization limit are in the far UV. Initial pioneering studies on the ionization thresholds of rare gas clusters were performed with a monochromatized helium continuum lamp showing an extremely gradual ionization onset (Dehmer and Pratt 1982). For more detailed investigations, molecular beam machines were constructed and attached to synchrotron light sources at, e.g., BESSY (Ganteför et al. 1989; Kamke et al. 1989) and DESY (Stapelfeldt et al. 1989; Karnbach et al. 1993b).

Photoionization

The combination of time-of-flight (tof) mass spectrometers with coincident detection of photoexcited electrons was the prerequisite for photoionization mass spectroscopy of rather heavy molecules and clusters with the quasi-continuous SR (Cordis et al. 1986; Kamke et al. 1988; Jarvis et al. 1999). The ionization potentials of rare gas clusters (Ar, Kr, Xe, up to N ∼30) measured with such coincidence techniques (Ganteför et al. 1989; Kamke et al. 1989) exhibit a pronounced decrease toward larger particles. Further, the tof data give clear evidence that shortly after ionization, a dimer or trimer ion core is formed inside the cluster in agreement with theoretical work (Böhmer and Peyerimhoff 1989). The binding energy of the dimer and trimer ions is typically in the eV range, substantially exceeding the van der Waals binding energies. The large difference can be understood in a simple molecular orbital picture. For example, in He, the dimer ion has two bound and two unbound valence orbitals. In the neutral dimer, all four orbitals are occupied, while in the dimer ion, only one unbound orbital is occupied resulting a large binding energy of ∼2.47 eV (Maas et al. 1976) compared to a van der Waals binding energy of only 0.095 meV (Grisenti et al. 2000). The large binding energy and the short bond length of these ions are the origin of efficient fragmentation of virtually all van der Waals clusters upon ionization. Through photoexcitation the cluster ion is formed in initially highly vibrationally excited states but in the geometry of the van der Waals ground state with a rather large bond length. The vibrational excitation is then transferred to the weakly bound neighboring atoms resulting in dissociation and fragmentation. While the ionization potential drops substantially from the monomer to the dimer due to the large binding energy of the dimer ion, the steps between large clusters are with a few ten to hundred meV comparably small (Kamke et al. 1989; Ganteför et al. 1989). The size-dependent shift of the ionization potential can be mostly attributed to polarization effects (Jortner et al. 1992; Böhmer and Peyerimhoff 1989; Amarouche et al. 1988; Björneholm et al. 1996). While most initial work focused on Ar, Kr, and Xe clusters, later work on He clusters (Frochtenicht et al. 1996) attracted a lot of interest because of their unusual properties (Toennies and Vilesov 2004; Peterka et al. 2003). Ionization of He droplets proceeds by autoionization of a dense manifold of Rydberg states (Frochtenicht et al. 1996; Joppien et al. 1993a) starting ∼2 eV below the atomic ionization limit. In addition to the work on pristine rare gas clusters, also the photoionization of more complicated systems including doped rare gas and molecular clusters (Kaiser et al. 1991), or C60 and C70 has been investigated in the early days (Hertel et al. 1992; Weaver et al. 1991).

Photoexcitation

The absorption onset of rare gas clusters is often dominated by bound electron-hole pairs which can be described in the Frenkel or Wannier exciton model (Schwentner et al. 1985), a condensed matter analog of atomic Rydberg states. Since typical exciton radii from 0.2 to 10 nm are comparable to the size of small- and medium-sized clusters, an interesting interplay between their electronic structure and size as well as a strong influence of the large surface fraction can be expected.

As an example for photoexcitation, data from Ar clusters is discussed. Cluster beams are optically thin, and thus, photoabsorption cannot be measured directly in transmission. Instead, a background-free monitor such as the fluorescence yield is used. Fluorescence spectra of Ar clusters containing between 15 and 106 atoms are presented in Fig. 3. The absorption bands of large clusters in Fig. 3 (Wörmer et al. 1991) show remarkable similarity to that of solid Ar. The onset of absorption stems from Frenkel type n = 1 excitons which are split into surface and bulk states as well as different spin-orbit components. The intensity ratio between surface and bulk states reflects the ratio of surface and bulk atoms (Stapelfeldt et al. 1989) indicating that only the surface layer contributes to surface excitons. Bulk excitons and especially Wannier excitons with principal quantum numbers n > 1 can only be observed in large clusters. As a rule of thumb, Wannier excitons appear, if the cluster radius is at least three times as large as the corresponding exciton radius (Wörmer et al. 1991). It is interesting to note that in an intermediate size range (50–500 atoms), see Fig. 3 middle panel, additional cluster-specific sharp lines are observed. These “excitons” have no counterpart in the solid phase, and they develop from a broad continuum and merge into the bulk excitons (Joppien et al. 1993b). These lines are particularly pronounced in Xe clusters (compare Fig. 4c). Fluorescence spectra of different clusters exhibiting characteristic bulk and surface excitons as well as Rydberg statesare shown in Fig. 4 together with schematic illustrations depicting the corresponding radial electron distributions.
Fig. 3

Luminescence excitation spectra (dotted line) and fitted contributions (full lines) of argon clusters containing between 15 and 105 atoms. The energetic positions of the exciton bands of the solid and the bandgap Eg are indicated in the figure. Surface states are denoted by s and longitudinal exciton branches by l. (Adapted from Wörmer et al. 1991)

Fig. 4

Absorption/fluorescence yield of small Kr (a), Ar (b, d) and Xe (c) clusters, N, number of atoms per cluster. Further the radial electron density distribution of (a) surface exciton, (b) bulk exciton, (c) cluster-specific exciton, and (d) Rydberg states is sketched for the corresponding excitations marked by arrows. (Adapted from Möller 1991)

Two remarkable changes occur with cluster size. Most notably, the intensities of the absorption bands sensitively depend on cluster size (Wörmer et al. 1991; Wörmer and Möller 1991). These variations have their origin mainly in geometrical effects, such as the relationship between cluster size and the radius of the excited orbital. Further, the energies of absorption bands in the clusters are shifted with respect to their excitonic counterparts in the macroscopic solids (Wörmer et al. 1991). While the Frenkel excitons show a very complicated shift which is up to date not well understood, the energetic shift of Wannier excitons can be explained within the model of exciton confinement (Wörmer et al. 1991), originally developed for semiconductor nanocrystallites (Brus 1986). In the clusters, the transition energies are shifted to higher energies with respect to the solid, which is a consequence of the spatial restriction of the electron and the hole. The spectral shift ΔE can be approximated by
$$\displaystyle \begin{aligned} \varDelta E=\frac{h^2}{8mR^2} \end{aligned} $$
(1)
where h is Planck’s constant, m the mass of the confined particle (exciton, electron or hole), and R the cluster radius. Electron and hole can be confined separately (strong confinement limit) or as a bound electron-hole pair (weak confinement), depending on the ratio between cluster and exciton radius. The spectral shift in rare gas clusters is closer to the strong confinement limit (Wörmer et al. 1991). A better quantitative agreement can be obtained with calculations of the spectral shifts by solving the Schrödinger equationof a cluster assuming the hole fixed in the center of the cluster (Wörmer et al. 1991). The absorption spectra of the heavier rare gas clusters (Ne-Xe) follow the same concepts, and doped rare gas clusters show even more pronounced site effects (Lengen et al. 1992; von Pietrowski et al. 2006) or efficient energy transfer (Mudrich and Stienkemeier 2014; Buchta et al. 2013). In contrast, electronic excitations in He clusters differ substantially. The absorption bands of He clusters are very broad and can be regarded as perturbed atomic transitions (Joppien et al. 1993b; von Haeften et al. 2001, 2011; Closser and Head-Gordon 2010). This is closely related to the unusual structural properties of condensed He, such as its low density, small polarizability, and superfluidity of the isotope 4He.

Radiative Decay

Rare gas clusters relax from electronic excitation by emitting rather broad continua in the XUV spectral range (Müller et al. 1993) from tightly bound molecular states analog to the self-trapped excitons in rare gas solids (Joppien et al. 1991; Karnbach et al. 1993a). This indicates that the non-radiative relaxation processes are faster, taking place on a picosecond time scale. He clusters are again a special case. In addition to the broad continua, sharp, discrete lines are emitted, stemming from electronically excited He atoms and dimers in various Rydberg states that are desorbing from the clusters (von Haeften et al. 1997, 2002). Details of the complex relaxation pathways have been recently unraveled with time-resolved studies using high-harmonic laser sources (Kornilov et al. 2011).

Photoelectron Spectroscopy

Photoelectron spectroscopy is a powerful tool for the analysis of valence band and inner-shell structure. First photoemission studies on Ar clusters with a He lamp have already given evidence for the formation of tightly bound chromophores inside the clusters (Carnovale et al. 1989). While a major part of the size-dependent ionization potential shift (Carnovale et al. 1989) follows a 1∕R law and can be explained in a simple electrostatic model (“Born’s model”), the large width of the valence bands can only be understood in terms of a dimer ion, or more general, a strongly bound chromophore (also compare section “Photoionization”). Subsequent studies have shown that this holds for valence (Rolles et al. 2009; Förstel et al. 2011a) as well as inner-shell spectra (Björneholm et al. 1995, 1996). Further, the valence (Rolles et al. 2009) and inner-shell (Björneholm et al. 1995) electron spectra show clearly resolved surface and bulk contributions. A comparison of valence, inner-valence and core-level spectra shows a gradual change from a relatively localized behavior for Ar inner valence 3s, over the intermediate case of Kr inner valence 4s, to a more delocalized behavior for Xe inner valence 5s. This change correlates well with the ratio between the orbital sizes and the interatomic distances (Feifel et al. 2004). Thanks to their chemical sensitivity, inner-shell spectra have also allowed to identify interface states, e.g., phase separation in mixed clusters (Tchaplyguine et al. 2004; Lundwall et al. 2004; Pokapanich et al. 2017). Depending on their concentrations, impurities are embedded in well-defined sites in the interior (Tchaplyguine et al. 2004; Lundwall et al. 2004) or close to the cluster surface (Lengen et al. 1992; von Pietrowski et al. 2006). The structure of doped He clusters naturally differs from that of the heavier rare gases. Photoionization of pure and doped He clusters and nanodroplets has been reviewed recently (Mudrich and Stienkemeier 2014). Depending on the interaction strength, isolated atoms can, in addition to common interior and surface sites, occupy states close to the surface in dimples.

Inner-Shell Ionization and X-Ray Absorption Spectroscopy

Inner-shell ionization of clusters and nanocrystals became only possible with intense x-ray radiation from SR light sources. The great strength of inner-shell spectroscopy is its chemical selectivity. This is especially important for the characterization of rather complex materials, such as nanoparticles with core-shell structure or thin layers of nanoparticles deposited on surfaces (c.f. section “Electronic Structure Investigations of Metal Clusters and Semiconductor Nanoparticles”). Inner-shell spectroscopy can provide information on the cluster structure, chemical environment, as well as relaxation processes and charge migration. Since inner-shell spectroscopy on very dilute samples is rather challenging, the methods and tools have been developed for simple systems such as van der Waals clusters which can be produced with sufficient density (Rühl 2003; Bjorneholm et al. 2009). With x-ray absorption spectroscopy, size-dependent changes in the electronic (Rühl et al. 1993a; Federmann et al. 1994; Knop et al. 1998) and geometric structure (Kakar et al. 1997) can be investigated. Absorption spectroscopy, namely, XANES (x-ray absorption near-edge structure) (Rühl 2003) and EXAFS (extended x-ray absorption fine structure) (Kakar et al. 1997; Nagaya et al. 2002), give insight into the geometry of clusters. Various surface sites, e.g., corner and edge positions, could be identified in Kr clusters (Knop et al. 1998). Further, a size-dependent icosahedral to fcc transition was observed in Ar clusters (Kakar et al. 1997). It occurs at smaller cluster sizes than expected from energetic considerations giving evidence that the final cluster structure strongly depends on the growth process. Moreover, size-dependent changes in inner valence (Thissen et al. 1998) and inner-shell photoionization (Rühl et al. 1993a), as well as electronic and radiative relaxation (Rühl et al. 1993b) were investigated. Excitation of inner-shell levels results in complicated relaxation dynamics leading to the formation of doubly and multiply charged clusters as well to fragmentation into neutral and charged fragments (Rühl 2003). The kinetic energy of the fragments (“kinetic energy release”) provides information about the relaxation dynamics and the internuclear separation of the primary ionic species (Rühl 2003). More recently, inner-shell ionization studies have been extended to clusters containing hydrogen bonds (Björneholm et al. 1999; Ohrwall et al. 2005), as well as covalent (Teodorescu et al. 1998), ionic (Riedler et al. 2001), and metallic bond systems (Peredkov et al. 2007a). Experimental techniques range from photoelectron (Björneholm et al. 1995, 1999; Grimm et al. 2006) and Auger electron spectroscopy (Ohrwall et al. 2005) to ion-electron and ion-ion coincidence techniques (Rühl et al. 1991), momentum spectroscopy (Hoener et al. 2008a), and elastic light scattering (Shu et al. 2006). These studies on rare gas clusters and the development of experimental tools provide the basis for investigations of more complex systems (c.f. section “Wet Chemistry-Based Systems: Metal and Semiconductor Nanoparticles”).

Autoionization

Autoionization is an important pathway for the relaxation of electronically excited states. In weakly bonded matter, especially clusters, efficient autoionization channels have been found, in which not only the initially excited atom or molecule but also the neighbors participate. Shortly after the theoretical prediction of these processes (Cederbaum et al. 1997), now known as interatomic or intermolecular Coulombic decay (ICD), they were observed in small Ne clusters (Marburger et al. 2003) with photoelectron spectroscopy and in dimers using a momentum imaging experiment (Jahnke et al. 2004). Taking the neon dimer experiment as an example, in a first step, a 2s hole is created by photoionization below the atomic double ionization threshold (Fig. 5). Then the 2s hole is filled by a 2p electron and the excess energy is transferred to the neighboring neon atom (this is the ICD process) causing the ejection of one of its 2p electrons. Since the dimer now carries two charges, Coulomb repulsion leads to back-to-back emission of the charged fragments of the Ne dimer (Jahnke et al. 2004). The lifetime of the ICD in Ne2 was determined via an extreme ultraviolet pump-probe experiment (Schnorr et al. 2013). The yield of coincident Ne+Ne2+ results in a lifetime of (150 ± 50) fs, in agreement with quantum calculations.
Fig. 5

Sequence of events observed in an experiment showing ICD type autoionization. (a) Creation of a 2 s hole in a neon dimer by photoionization; (b) successive interatomic Coulombic decay: the 2 s hole is filled by a 2 p electron, the excess energy is transferred to the neighboring neon atom causing the ejection of one of its 2 p electrons; (c) back-to-back emission of the fragments due to Coulomb explosion of the Ne dimer. (Adapted from Jahnke et al. 2004)

Experiments on ICD were recently reviewed (Hergenhahn 2011). Meanwhile ICD-type processes and variants (Sakai et al. 2011) were observed in many weakly bound systems such as in water clusters (Mucke et al. 2010), solutes, and helium nanodroplets (LaForge et al. 2016). Such autoionization processes are now regarded quite common (Ouchi et al. 2011; Förstel et al. 2011b), and they may have consequences for radiation biology or could be of interest for the development of new spectroscopy techniques (Gokhberg et al. 2014).

Electronic Structure Investigations of Metal Clusters and Semiconductor Nanoparticles

In the regime of medium-sized and large clusters (more than a few hundred atoms), cluster properties vary in a smooth, continuous way with size (cf. Fig. 1), and therefore, experiments on cluster ensembles with their natural size distribution give already meaningful results. In contrast, for small clusters their properties depend on the exact number of atoms (“every atom counts”) and precise size selection is essential. Apart from special cases like C60 (Hertel et al. 1992), or diamondoids (Dahl et al. 2003), size selection can only be achieved for cluster ions, or at least to some extend for chemically inert, ligand-stabilized nanocrystals (Weller 1993a; Alivisatos et al. 1996). While experiments on cluster ions are usually performed in the gas phase, ligand-stabilized clusters can be deposited on substrates.

Wet Chemistry-Based Systems: Metal and Semiconductor Nanoparticles

Wet chemistry approaches provide a very efficient route for the generation of passivated metal (Zhang and K. Sham 2003) and semiconductor nanoparticles (Weller 1993a; Alivisatos et al. 1996). Semiconductor nanoparticles offer a large variety of very interesting properties, in particular a gradual transition from solid state to molecular structures as the particle size decreases. Their optical, electronic, and catalytic properties differ significantly from those of either the bulk materials or of the molecules. Nanometer-sized particles exhibit effects due to quantum confinement (Weller 1993b), the underlying models are the same as discussed already in section “Photoexcitation.” Especially interesting for applications is their size-dependent fluorescence (Weller 1993a). While their fluorescence wavelength can be defined quite easily with well-established quantum confinement models (Weller 1993b; Brus 1986) controlling and improving their fluorescence yield is far from being straightforward. Here, x-ray absorption (Hamad et al. 1999; Rockenberger et al. 1997), x-ray diffraction (Wickham et al. 2000), and photoemission (XPS) (Winkler et al. 1999) have considerably contributed to the characterization of the nanoparticle surface (Borchert et al. 2003a), structural disorder (Hamad et al. 1999; Winkler et al. 1999), phase transitions between different structural motifs (Tolbert and Alivisatos 1994; Wickham et al. 2000), and radial chemical composition (Borchert et al. 2003b). All of these aspects are important for the luminescence yield, and meanwhile, quantum efficiencies up to 70% have been achieved (Kompe et al. 2003). The chemical sensitivity of soft X rays and the energy-dependent escape depths of photoelectrons have played an important role for obtaining an understanding of the complicated processes controlling the luminescence yield. It turned out that the luminescence quenching is largely due to the trapping of the excited electrons at the particle surface or at interfaces. Core-shell nanocrystals consisting of a core material capped with a thin shell of another semiconductor with a larger bandgap are less affected by quenching allowing to obtain high quantum yields.

Photoemission investigations of CdSe/ZnS core-shell nanocrystals have shed some light into the relevant emission and quenching processes (Borchert et al. 2003b). The spectra indicate a rather well-ordered interface, and no evidence was found for interfacial bonds which could serve as electron trapping sites reducing the luminescence yield (Borchert et al. 2003b). Meanwhile the same technique is also applied to investigate metal (silver) nanoparticles. These studies suggest that a core-shell morphology results in metallic Ag cores surrounded by Ag2S-like phase (Battocchio et al. 2012) (see Fig. 6).
Fig. 6

Illustration of the preparation of core-shell silver Ag nanoparticles, high-resolution photoelectron spectra, and the radial composition derived from them. (Adapted from Battocchio et al. 2012)

Group IV Clusters and Nanocrystals

In this chapter, we will concentrate on the lighter elements C, Si, and Ge since Sn and Pb clusters have more in common with metal clusters.

Carbon Clusters and Fullerenes

Carbon clusters play a special role due to the carbon’s ability to form sp1, sp2, and sp3 hybrid orbitals. These clusters possess strong covalent bonds, and many have both σ and π bonding components. Probably the most famous carbon clusters are fullerenes (Johnston 2002), especially C60 and C70, which have attracted so much attention since their discovery (Kroto et al. 1985). An overview of recent work (Sattler 2010) and more general on carbon particles and nanostructures (Weltner and Vanzee et al. 1989; Shenderova et al. 2002) can be found in the literature. Here, we restrict ourselves to a few fundamental aspects, especially ionization processes which could only be addressed with the help of SR.

The closed shell nature of C60 is directly reflected in their K-shell absorption spectra. Direct comparison of C 1s absorption spectra taken in the gas phase with those from solid C60 reveals a close similarity (Krummacher et al. 1993). The hollow structure of C60 gives rise to unusual spherical shells of delocalized valence electrons with high angular momentum (Bertsch et al. 1991). The quasispherical shape of C60 suggested that the electron wave functions should be analyzed in terms of their expansion in spherical harmonics. It was found that they were dominated by a single component with angular moments from s, p, up to g (Weaver et al. 1991). The photoion yield of C60 is dominated by a strong resonance at about 20 eV with a width of ∼10 eV (compare Fig. 7) stemming from autoionization via a giant plasmon resonance (Hertel et al. 1992; Weaver et al. 1991) in agreement with theoretical work (Bertsch et al. 1991; Venuti et al. 1999). This high-frequency Mie-type plasmon has its origin in the large valence electron density in the C60 cluster and can be understood by considering a conducting spherical shell and 240 conduction electrons (Bertsch et al. 1991). The valence photoionization cross section measured over a large range up to 130 eV shows an unusual oscillation (Xu et al. 1996; Korica et al. 2005) which is a typical cluster feature resulting from interference due to electron emission from opposite sides of the hollow cage. A similar process was predicted earlier for Na clusters (Frank and Rost 1997). Related to that, experimental evidence is presented for confinement resonances associated with photoabsorption by a Xe atom in a C60 cage (Kilcoyne et al. 2010). The giant 4d resonance in photoionization of Xe at 100 eV is predicted to be redistributed into four components due to multipath interference of photoelectron waves reflected by the cage (Kilcoyne et al. 2010; Phaneuf et al. 2013). In addition to neutral carbon clusters, also the soft x-ray photoabsorption of several fullerene ions from C40 to C84 could be observed (Thomas et al. 2017). Fullerenes have been endohedrally doped by various atoms. Meanwhile the fragmentation dynamics of rather complicated systems such as Sc3N@C80 could be studied with soft x-rays (Xiong et al. 2017). Sequential emission of two out of the three Sc atoms of the encaged moiety, via Coulomb explosion in the form of Sc+ or Sc-containing ions, is significant (Xiong et al. 2017). In recent experiments on C60, previously not reported low energy electrons were observed following photoionization with photon energies significantly above – up to 60 eV – the first ionization threshold (Hansen et al. 2017). These electrons are interpreted as resulting from an indirect, quasi-thermal boiloff process after absorption of a single photon. This process is expected to be present for other molecules and clusters with a large number of valence electrons.
Fig. 7

C\(_{60}^+\) photoion yield as a function of photon energy displaying excitation of the giant plasmon resonance. (Adapted from Hertel et al. 1992)

Diamondoids

Diamondoids are perfectly sp3-hybridized carbon clusters that can be superimposed on the bulk diamond lattice, and their dangling surface bonds are terminated with hydrogen (Bostedt et al. 2012a; Dahl et al. 2003). Due to their ideal structure and surface passivation, they overcome the limitations of most other cluster studies with respect to definition of the sample. The smaller species are commercially available both perfectly size- and shape-selected.

X-ray absorption of diamondoids in the gas phase showed that their lowest unoccupied states are determined by the hydrogen surface states which are fixed in energy (Willey et al. 2005) so that all size-dependent changes in the diamondoid electronic structure stem from the highest occupied states localized in the particle core (Willey et al. 2006). Vacuum ultraviolet synchrotron radiation absorption spectra show that characteristic optical properties evolve for diamondoids as a function of their size, shape, and symmetry and that the smallest tetrahedral and highly symmetric diamondoid C26H32 exhibits optical properties that are remarkably close to bulk diamond (Landt et al. 2009a). On the other hand, diamondoids excited with vacuum ultraviolet synchrotron radiation emit strong luminescence which is surprising, as bulk diamond is an indirect bandgap material (Landt et al. 2009b; Richter et al. 2014). The emerging field of diamondoid chemistry (Schwertfeger et al. 2008) allows targeted modifications of diamondoids making them very versatile building blocks for nanomaterial design. Photoelectron spectra from diamond monolayers revealed an intense near-monochromatic emission peak near the low-kinetic energy threshold which was attributed to such films having negative electron affinity (Yang et al. 2007). Chemical modification of diamondoids allows to tune their electronic properties (Rander et al. 2013). It can induce impurity-like states within the bandgap of the pristine diamondoid (Landt et al. 2010a) and quench the luminescence for smaller particles (Landt et al. 2010b). Theoretical work has identified functionalized diamondoids as promising candidates for the tailoring of fluorescent nanomaterials, but it was found that in most systems, fluorescence is quenched. Recently, with methylated adamantanes, a class of functionalized diamondoids has been shown to fluoresce in the gas phase (Rander et al. 2017). While photoelectron spectroscopy was used to map the occupied valence electronic structure, absorption and fluorescence spectroscopies yielded information about the unoccupied electronic structure and postexcitation relaxation behavior. These results show that it is possible to overcome fluorescence quenching when functionalizing diamondoids and represent a significant step toward tailoring the electronic structure of these and other semiconductor particles in a manner suitable to applications (Rander et al. 2017).

Silicon and Germanium Nanocrystals and Nanodiamond

Silicon and germanium nanocrystals have attracted considerable interest over the last two decades. Nanometer-sized Si (Brus 1994) and Ge (Zacharias and Fauchet 1997) particles have both shown efficient luminescence at room temperature, a desirable property for optoelectronic devices. For bandgap investigations of nanoparticle films, x-ray spectroscopy provides very powerful tools. X-ray absorption and emission spectroscopy allow looking at band edges independently with large signal contrast of the thin nanoparticle films to the bulk substrates.

X-ray absorption and photoemission from deposited silicon nanocrystals have unambiguously shown that the silicon bandgap widens with decreasing particle size due to quantum confinement effects (van Buuren et al. 1998). Quantum confinement effects in the conduction band were measured to be even stronger in germanium particles compared to silicon, leading to a bandgap crossover between both elements in the nanometer size regime (Bostedt et al. 2004a). Nanodiamond itself does not exhibit appreciable bandgap opening (Raty et al. 2003), indicating that quantum confinement effects for group IV semiconductors generally become stronger for heavier elements.

Spectral fingerprints in the valence band structure of germanium nanocrystals (Williamson et al. 2004) as well as pre-edge features in the x-ray absorption spectra of nanodiamond (Raty et al. 2003) are indicative for surface reconstruction on nanoparticles in a fullerene-like manner. In concentrated assemblies of particles, surface interactions can quench the quantum confinement unless the dangling bonds are passivated (Bostedt et al. 2004b). Dedicated equipment allows the detailed investigation of various types of nanoparticles in the gas phase with photoelectron spectroscopy at SOLEIL (Sublemontier et al. 2014) and ALS (Kostko et al. 2017). Since the particle density of gas phase nanoparticles is usually low, velocity map imaging helps obtaining high quality data via the large solid angle detection. Often, aerodynamic lenses focus the gas phase nanoparticles into the x-ray beam. In initial studies the surface of oxides Si nanoparticles could be analyzed (Sublemontier et al. 2014). At the Swiss light source, electron mean path lengths could be derived from angle-dependent photoelectron spectra (Goldmann et al. 2015). The angular distribution of gas phase SiO2 particles with ≈100 nm diameter could also be used as a probe for elastic electron scattering (Antonsson et al. 2017). The photoelectron angular anisotropy is found to be lower for the nanoparticles than for isolated Si and O atoms. The reduced angular anisotropy is explained by elastic scattering of the outgoing atoms by neighboring atoms. From the comparison with Monte Carlo simulations, the number of elastic scattering events could be derived (Antonsson et al. 2017).

Metal Clusters

Pioneering experiments on metal clusters (Brechignac et al. 1988; Mason et al. 1983) were already performed in the 1980s, typically by depositing submonolayers on substrates (Mason et al. 1983). The early data provided information on the evolution of the ionization potentials with particle size. Only with the availability of intense radiation from undulator sources it became possible to study inner-shell processes of metal clusters in the gas phase without the disturbing influence of a substrate (Piseri et al. 2006). Bulk as well as surface sites could be separated in the XPS spectra of sodium clusters (Peredkov et al. 2007b) and Auger spectra allowed extracting information on the valence band (Peredkov et al. 2007b). While experiments on gas phase clusters probe the structure of isolated species, recent photoemission work on deposited noble metal clusters provides information about the interaction with a substrate (Peters et al. 2013a,b). Analysis of the photoemission shift and line shape using a dynamic electrostatic model allowed identifying initial and final state effects such as negative surface core-level shift, inhomogeneous broadening, dynamic final-state screening, and chemisorption-like interaction between cluster and support (Peters et al. 2013a).

Using Paul traps for storing cluster ions (Lau et al. 2008) at the Nanocluster Trap instrument (Lau 2017), now a permanent endstation at BESSY II, precise size selection can be achieved for metal and also semiconductor clusters (Vogel et al. 2012). The elemental specificity of x-ray spectroscopy allows addressing individual atoms in heterogeneous clusters providing information about their electronic structure including shell closings (Lau et al. 2009). XAS studies using circularly polarized light reveal information about their size-dependent magnetic properties (Lau et al. 2002). With x-ray magnetic circular dichroism (XMCD) measurements of free Co and Fe clusters (up to N ∼ 20), the intrinsic spin and orbital magnetic moments of isolated magnetic nanoparticles have been determined (Peredkov et al. 2011; Niemeyer et al. 2012). Even in very small clusters, the orbital magnetic moment is strongly quenched and reduced to a few % of its atomic value, while the spin magnetic moment remains at 60%–90%. For iron clusters the formation of bonds quenches orbital angular momenta already for coordination numbers much smaller than those of the bulk (Niemeyer et al. 2012) yielding important insight in how magnetic properties develop into that of macroscopic solids. Meanwhile the sensitivity is sufficient to determine even magnetic moments of single atoms in clusters (Hirsch et al. 2015) (c.f. Fig. 8). The size dependence of the magnetic moments of Cr-doped gold clusters gives evidence that the Anderson impurity model essentially describes finite systems comprising only a few atoms even though the discrete density of states shows a significant deviation from a bulk metal (Hirsch et al. 2015).
Fig. 8

(a) Left: linear polarized x-ray absorption spectra of \(CrAu_{n}^+\) clusters, n = 2–7, normalized to the L3 maximum intensity, overlaid with theoretical spectra resulting from charge transfer multiplet calculations (dashed line). Additionally shown are relaxed ground state structures (blue/dark atom: chromium; yellow/light atoms: gold). Middle: XMCD spectra of \(CrAu_{n}^+\) normalized to the number of unoccupied 3d states. (b) The XMCD spectra of CrAu+ n, n = 2, 5–7, are overlaid with theoretical spectra resulting from charge transfer multiplet calculations (dashed line). The weights of configurations contributing to the ground state are also given. (c) Right: measured orbital magnetization at the experimental conditions of T = (12±4) K and B = 5 T. (Adapted from Hirsch et al. 2015)

Clusters in Intense FEL Pulses

The new free-electron laser (FEL) x-ray sources open new possibilities in cluster physics. The intense FEL pulses deliver on the order of 1012 photons in 100 femtosecond pulses and in a narrow bandwidth of 0.1% of the fundamental energy. In terms of peak brightness, FELs are many orders of magnitude brighter than synchrotron sources enabling new strategies for the investigation of cluster and nanocrystal properties. In the focused beam, single-shot single-particle imaging experiments become possible giving unprecedented insight into the cluster or nanocrystal morphology and their growth processes. The pulse structure and high photon flux in each FEL pulse can be exploited to apply the powerful x-ray spectroscopy tools to ultra dilute samples such as size-selected clusters. Clusters also play an important role as “nanolab” for studying intense light-matter interaction. The ability to produce them with defined sizes in the gas phase, i.e., no interaction with a surrounding medium, is essential. By tuning the cluster size, atomic effects can be distinguished from collective effects, and the detailed study of ionization and disintegration of nanometer-sized samples in intense x-ray pulses becomes possible.

Over the past decade, a variety of free-electron laser sources have become operational and at all existing FELs cluster experiments have been a strong science driver (TTF-FEL: Wabnitz et al. 2002, FLASH: Bostedt et al. 2009, SACLA: Yabashi et al. 2013, LCLS: Bostedt et al. 2013, FERMI: Lyamayev et al. 2013). The majority of cluster experiments at FELs have focused on the fundamental physics of intense light-matter interaction in the short-wavelength regime, i.e., they have taken advantage of clusters as ideal sample systems to investigate ionization and damage processes on ultrafast time scales. However, the number of experiments employing new experimental strategies enabled by FELs to study cluster and nanocrystal properties is steadily growing and opens ample new opportunities.

Experimental Strategies for Cluster Research at Free-Electron Lasers

The experimental approaches for cluster experiments have rapidly developed over the past decade into complicated setups allowing to correlate information from many different channels. Compared to the time-stable synchrotron radiation experiments, where the experimental signal is averaged over extended periods of time, experiments at the often fluctuating FEL sources record all signals on a shot-by-shot basis. Further, extensive information from the accelerator can be added to the data stream yielding information about x-ray pulse energies, pulse length, or even photon energy jitter. In most experiments each FEL shot probes an ensemble of clusters filling the focal volume, and the data is classified according to the driving experimental parameters in the post analysis, for example, pulse energies in power density-dependent studies (Wabnitz et al. 2002; Bostedt et al. 2010a). The trend in more recent experiments is to go to even better controlled conditions and work with single clusters in the focus. This approach allows correlating all information measured in coincidence from a single particle, for example, the particle size and x-ray exposure intensity, in order to identify processes that are blurred in ensemble-averaging experiments (Gorkhover et al. 2012; Rupp et al. 2016).

An exemplary experimental setup is shown in Fig. 9. A cluster source delivers clusters in the gas phase, and multiple skimmers are used to create a defined and dilute cluster jet. Primary tools for measuring ionization dynamics are electron and ion time-of-flight spectroscopy (Bostedt et al. 2010b), but also advanced spectroscopy techniques have been adapted to the needs of FEL experiments. Reaction microscopes or Coltrims-type spectrometers have been advanced to measure the three-dimensional momentum information from cluster explosions with hundreds of fragments (Fukuzawa et al. 2009). Velocity map imaging spectrometers can very efficiently measure electron emission spectra with a large solid angle acceptance (Lyamayev et al. 2013; Johnsson et al. 2010). Fluorescence photon detection allows the detection of high charge states prior to cluster recombination which cannot be observed by ion spectroscopy (Schroedter et al. 2014). The forward scattering signal yields information about cluster size and morphology, as well as exposure intensities (Gorkhover et al. 2012; Rupp et al. 2012) and, in selected cases, transient electronic structure information (Bostedt et al. 2012b). For recording the scattering patterns, both low-cost multichannel plate-based detectors (Bostedt et al. 2012b) and advanced pixel detectors such as pnCCDs (Strüder et al. 2010) have been employed. Optical lasers can be added in (near-) collinear geometry for pump-probe experiments. X-ray-optical cross correlators provide feedback for sorting the data in the post analysis to high timing precision (Schorb et al. 2012a; Gahl et al. 2008). In most cases, the FEL pulses are focused with grazing-incidence reflective optics which are part of the beamline, but in the XUV spectral regime, very efficient multilayer optics are available that can be directly incorporated into the experimental setup (Fukuzawa et al. 2009; Rupp et al. 2012).
Fig. 9

Typical experimental setup: scattered photons and charged fragments from clusters are measured in coincidence on a shot-by-shot basis. The cluster density in the focus can be controlled with adjustable skimmers. External pump lasers can be used to trigger reactions. All experimental data including x-ray pulse characteristics and laser timing are recorded for each shot

Intense Light-Matter Interaction in the Short-Wavelength Regime

Cluster physics at FELs is often driven by fundamental questions about light-matter interaction. FELs are the most powerful sources for intense light pulses in the short-wavelength regime, and so far, each machine coming online has opened the door for investigating the fundamental physics at a new wavelength and intensity frontier. A key parameter for the interaction of intense light pulses with matter is the Keldysh parameter (Keldysh et al. 1965) approximated by:
$$\displaystyle \begin{aligned} \gamma = \sqrt{ \frac{E_{IP}}{2U_p} } \end{aligned} $$
(2)
which separates the perturbative multiphoton ionization regime (γ ≫ 1) from the non-perturbative tunneling ionization regime (γ ≪ 1). EIP is the ionization potential of the electronic levels, and Up is the ponderomotive energy that is the average kinetic energy of a free electron in an oscillating electric field. For the intensities available at the FEL sources to date, the Keldysh parameter predicts ionization dynamics well in the multiphoton regime, and ponderomotive energies are only on the order of meV (Saalmann et al. 2006; Fennel et al. 2010). However, for increasing photon energies, the residual kinetic energies of the photoelectrons can become large. In the x-ray regime, core ionization is dominant, and thus, core vacancy lifetimes and decay processes will be important.

In the optical spectral regime, extensive research on clusters in intense laser fields has been performed (Saalmann et al. 2006; Fennel et al. 2010; Ditmire et al. 1996). In short, in intense optical laser pulses, a few atoms in the cluster are ionized early in the pulse by tunnel ionization, and a nanoplasma is formed, often referred to as inner ionization (Last and Jortner 2000). The nanoplasma electrons can very efficiently absorb energy from the laser field through plasma heating processes, and the whole cluster becomes highly ionized, also referred to as outer ionization, leading to cluster disintegration in a Coulomb or hydrodynamic expansion.

Near-Threshold Ionization

Experiments with short-wavelength FELs have started in 2001 at the TTF-FEL at DESY, the machine that developed into FLASH, with a study on the ionization of Xe clusters irradiated just above the ionization threshold with intense light pulses at 13 eV and power densities up to 1013 W/cm2 (Wabnitz et al. 2002). Since the energy of one photon is larger than the ionization potential of Xe, single-photon ionization is possible, and a nanoplasma is very efficiently formed. The clusters absorb many photons per atom and completely disintegrate into singly and multiply charged atomic fragments with high kinetic energy (Wabnitz et al. 2002; Laarmann et al. 2004) and charge states up to 8+, whereas only singly charged ions from atomic gas were observed in the initial study (Wabnitz et al. 2002). It is noted that in later experiments, also higher Xe charge states were observed in atoms, however still reduced as compared to the cluster signal (Wabnitz et al. 2005). The absence of high charge states from atomic gas might be in part due to an unfavorable alignment of the time-of-flight spectrometer which allows highly charged kinetic cluster fragments to reach the detector, while ionization products from the atomic beam, initially almost at rest, will be strongly suppressed. The observation of enhanced charge states in cluster ions, however, triggered theoretical work (Santra and H. Greene 2003; Ziaja et al. 2009; Bostedt et al. 2010b; Arbeiter and Fennel 2011) which indicated that the intense radiation can very efficiently couple to the nanoplasma by inverse bremsstrahlung, leading to high charge states and kinetic energies. The high- charged states in the clusters can be formed by lowering of the ionization potentials in the nanoplasma (Siedschlag and Rost 2004) as well as collisional, i.e., electron impact ionization in the nanoplasma (Arbeiter and Fennel 2011).

Interestingly, cluster ionization can also be very efficient, if the photon energy is not sufficient for single ionization but if it coincides with a resonance below the ionization threshold (Laarmann et al. 2004; Sugishima et al. 2012). Recently, a novel, very efficient autoionization process belonging to the family of interatomic Coulombic decay (ICD) phenomena was proposed (Kuleff et al. 2010) explaining the initial results (Laarmann et al. 2004; Sugishima et al. 2012) and stimulating more experimental work (Nagaya et al. 2013; Yase et al. 2013; LaForge et al. 2014; Ovcharenko et al. 2014). When two electronically excited species are present, an ultrafast energy transfer can take place bringing one of them to its ground state and ionizing the other one (Kuleff et al. 2010), and the large majority of ions will be produced by this ICD mechanism rather than by two-photon ionization (Kuleff et al. 2010). This processes involving the absorption of at least two photons is so efficient that it can also be observed when clusters are resonantly excited with conventional SR (Buchta et al. 2013, see also section “Autoionizationł::bel sect:autoionize”). Detailed experiments on ICD-type ionization in Ne clusters performed at FERMI reveal a complex dynamics (Nagaya et al. 2016; Iablonskyi et al. 2016). Following resonant excitation, energetically considerably above the lowest n = 1 exciton state, an unusual intra-Rydberg ICD process occurs (Nagaya et al. 2016). The de-excitation of a Ne cluster atom to a close-lying Rydberg state leads to electron emission from another neighboring Rydberg atom. Similar decay processes in nanoplasma recombination also involving Rydberg-excited electrons have been studied in Xe-Ar core-shell clusters with THz-streaking (Oelze et al. 2017), indicating that low-energy-correlated electrons are emitted at least a few picoseconds after the FEL pulse has ended. Since in the case of neon, the excitons are split in bulk and surface states (as well in Ar (Wörmer and Möller 1991) and Kr clusters (Stapelfeldt et al. 1989), see also Figure 3), the effect of the environment on ICD-type ionization can be studied. While the ICD autoionization spectrum of the surface state clearly shows the prominent ICD line (see Fig. 10, Iablonskyi et al. 2016), bulk excitation results in a rather complex decay. The outgoing ICD electrons can be inelastically scattered on electronically excited Ne 2p atoms in the neighborhood, similar to the processes observed in He clusters (Ovcharenko et al. 2014).
Fig. 10

Electron emission spectra of Ne clusters (N = 5000) showing the prominent ICD line measured for surface excitations of the lowest exciton state at = 17.12 eV. The spectra were recorded at different FEL intensities as indicated. Labels on top of the spectra indicate the ICD electron energy after the excited cluster atoms relaxed to atomic 3s states. (Adapted from Iablonskyi et al. 2016)

Extreme Ultraviolet Spectral Regime

Going to shorter wavelength, away from the threshold, it is well established that plasma heating effects become negligible and that multistep photoionization is the primary pathway for energy absorption (Bostedt et al. 2008; Arbeiter and Fennel 2011). As depicted in Fig. 11, the photoelectrons are emitted in a sequential manner until the photoemission becomes frustrated in the increasingly deep Coulomb potential. As a consequence, inner and outer ionization are reversed in the short wavelength compared to the optical regime, i.e., the electrons are initially removed from the clusters, and only after the photoelectrons become trapped in the Coulomb potential, the nanoplasma develops. At high exposure intensities (Arbeiter and Fennel 2011; Bostedt et al. 2008) and for short wavelengths enabling inner-shell ionization, multiple electrons per atom are excited, and nanoplasma with supra-atomic densities are formed (Bostedt et al. 2010a; Arbeiter and Fennel 2011). Energy-exchanging electron-electron collisions in the dense nanoplasma (c.f. middle panel in Fig. 11) lead to thermalization of the plasma electrons with a kinetic energy tail exceeding the initial photo- or Auger electron lines (Bostedt et al. 2010a). Through this process many more electrons can leave the cluster Coulomb potential, and the cluster ionization is significantly enhanced. The thermal electrons lead to an exponential intensity distribution in the photoelectron spectra and creates a tail with photoelectron energies beyond the main line (Bostedt et al. 2010a; Arbeiter and Fennel 2010).
Fig. 11

Processes during cluster ionization: ionization, energy exchange, expansion, and recombination. (Adapted from Bostedt et al. 2010b, Saalmann et al. 2006, and Arbeiter and Fennel 2011)

The ion time-of-flight spectra from clusters exposed to intense extreme ultraviolet pulses with power densities in the order of 1011 – 1013 W/cm2 depend strongly on the pulse intensity, photon energy, and cluster size. In the valence ionization regime, where only a small fraction of the photoelectrons can leave the Coulomb potential, the ion spectra are dominated by monomers and larger cluster fragments (Bostedt et al. 2008; Fukuzawa et al. 2009; Iwayama et al. 2009, 2013). Highly valence-ionized van der Waals clusters have also been suggested to be metallic-like due to the large number of quasi-free electrons in the nanoplasma (Yao et al. 2011). The fragment kinetic energies increase with more intense pulses (Fukuzawa et al. 2009) or increasing cluster size (Iwayama et al. 2009). Comparing the fragmentation dynamics of Xe clusters at two wavelength of 61 nm (∼20 eV) (Fukuzawa et al. 2009) and 13 nm (∼90 eV) in the giant absorption resonance above the Xe4d inner-shell levels (Thomas et al. 2009) reveals significantly higher charge states and ion kinetic energies for the higher photon energy, underlining the importance of photon energy and target electronic structure for the energy absorption processes (Arbeiter and Fennel 2011). However, in all experiments the average cluster charge state is lower than for atoms under similar conditions, hinting at efficient charge transfer and recombination in the nanoplasma. Both effects have been elegantly shown with core-shell clusters (Sugishima et al. 2012; Hoener et al. 2008b). For Xe-Ar core-shell systems (Hoener et al. 2008b) irradiated with 13 nm (∼90 eV) photons and power densities of 1014 W/cm2, the Xe core can be highly ionized, but with increasing shell thickness, no Xe is detected in the mass spectra, and the kinetic energies of the Ar shell ions are greatly increased. Analysis of the ion kinetic energies in homogeneous clusters shows similar results (Thomas et al. 2009; Iwayama et al. 2010; Rupp et al. 2016). High charge states with high kinetic energies are associated with an exploding cluster surface, while low charge states stem from a recombining cluster core. These results have led to the following picture: the whole cluster is initially highly ionized, but only a fraction of the excited electrons can leave the cluster. Charge migration within the nanoplasma leads to a highly ionized surface shell which explodes off and leaves a quasi-neutral nanoplasma core behind. The nanoplasma core expands in a much slower hydrodynamic expansion, also proceeding via shell-by-shell ejection of partially unscreened surface layers of ions, and accompanied by efficient electron-ion recombination (Ziaja et al. 2011; Arbeiter and Fennel 2011; Peltz et al. 2014; Rupp et al. 2016). The analysis of size and intensity resolved single-cluster ion spectra (Rupp et al. 2016) reveals significantly higher ion kinetic energies than expected from simple hydrodynamic expansion models not including recombination. The energy which is liberated in the recombination process is transferred back into the nanoplasma and subsequently transformed into ion kinetic energy. This physical picture is further supported by fluorescence measurements showing that initially the whole cluster is highly charged (Schroedter et al. 2014) with emission lines that can even exceed the incoming photon energy (Iwayama et al. 2012).

X-Ray Spectral Regime

X-rays predominantly interact with inner-shell electrons ionizing atoms from the inside out. The inner-shell vacancies decay on time scales comparable to the FEL pulse length. The high x-ray photon energies lead to increased photoelectron and Auger electron kinetic energies. All these aspects are important for the ionization dynamics of clusters in intense x-ray pulses.

In a first coincident imaging and spectroscopy experiment, the ionization dynamics of large Xe clusters irradiated with power densities up to 1017 W/cm2 and photon energies of 800 eV were probed (Gorkhover et al. 2012). The diffraction images of single clusters were used to deconvolute the cluster size distribution and to determine their exposure intensity, i.e., location in the focal volume. The coincident ion time-of-flight spectra shown in Fig. 12 yielded unprecedented insight into the fragmentation dynamics of the clusters exposed to defined power densities. The stochastic sampling of the focal volume distribution with the single clusters showed that within two orders of magnitude of power density, the nanoplasma properties changed significantly. Ion spectra from clusters in the outer wings of the focal volume are dominated by the monomer signal stemming from a low temperature plasma where recombination dominates (panel (c) in Fig. 12). Clusters exposed to peak intensity in the central part of the focus are transformed to a hot nanoplasma where recombination is efficiently suppressed, and high charge states as well as high fragment kinetic energies centered around Xe26+ prevail (panel (a) in Fig. 12). The high excess energy of the trapped photo- and Auger electrons leads to the formation of a hot nanoplasma which disintegrates so rapidly that electron-ion recombination is efficiently suppressed (Gorkhover et al. 2012). In the right panel of Fig. 12, the focal volume-averaged spectra are shown in which the high-intensity information from the hottest part of the focus is hardly identifiable.
Fig. 12

Single-shot ion tof spectra of clusters irradiated with 800 eV x-ray pulses taken in coincidence with diffraction images in the center (a), outer wings (c), and in between (b) of the focus. The fragmentation dynamics depend sensitively on the exposure intensity; they are not visible in focal volume-averaged spectra. (From Gorkhover et al. 2012)

C60 plays a special role in the context of light-matter interaction with clusters since it is often regarded as a big molecule. In an experimental and theoretical study of C60 molecules interacting with intense soft x-ray pulses from the LCLS, the effect of pulse length and fluence was investigated. In contrast to large rare gas clusters, which still form a dense nanoplasma and expand in a (comparably rapid) hydrodynamic expansion, C60 clusters exposed to x-ray pulses of similar peak intensity disintegrate in a Coulomb explosion (Murphy et al. 2014) due to the accumulated positive charge. The fragmentation dynamics of these small systems with known initial geometry can be well described with classical mechanics, and it is predicted that this approach scales well to larger systems (Murphy et al. 2014).

Another interesting aspect unique to the x-ray spectral regime is that the nanoplasma formation alters the x-ray ionization dynamics. First predicted theoretically, the delocalization of the valence electrons in the x-ray-induced nanoplasma leads to the increase of the Auger lifetimes and thus changes of the inner-shell lifetimes (Saalmann and Rost 2002). This effect was demonstrated experimentally in a pulse length-dependent ionization study of small Ar clusters (Schorb et al. 2012b). The x-ray pulse lengths were controlled from 30 to 85 fs by shaping the electron bunch in the accelerator with a slotted spoiler (Emma et al. 2004). Comparing the ion spectra of clusters irradiated with the same number of photons, but different pulse length showed that shorter pulse length led to lower average charge numbers due to x-ray-induced transparency. The x-ray-induced transparency increased with increasing cluster size due to reduced Auger rates, or longer core vacancy lifetimes, in the nanoplasma. As a consequence, larger nanometer-sized samples absorb intense femtosecond x-ray pulses less efficiently than small ones – which is opposite to the ionization dynamics in the optical wavelength regime (Schorb et al. 2012b).

New Opportunities from Single-Shot Imaging in Cluster Physics

The circumstance that FEL pulses can be intense enough to generate a coherent diffraction image of nanometer-sized samples in a single shot results in new opportunities for cluster and nanocrystal research. Single-shot imaging of single particles in the gas phase allows studying the morphologies of clusters or yields detailed information about their surface and internal structure. Further, the FEL pulses can be used to take stroboscopic images of dynamics in clusters on a femtosecond time scale.

Cluster Morphology

Studying the morphology of individual clusters, each of them unique in shape and size, gives insight into their growth processes and structural properties. Conventional nanoscale-imaging methods such as electron microscopy require deposited, solid targets, but many cluster types, such as van der Waals-bound systems, cannot be landed on surfaces. Further, even for stable systems such as metal clusters, the cluster-surface interaction may change their structure (Volk et al. 2013).

The cluster shapes found with single-cluster x-ray imaging are associated with the fundamental competition between energy minimization and the kinetics of the growth process. Figure 13 displays x-ray diffraction images of two different cluster types, rare gas clusters (Rupp et al. 2012, 2014) and silver clusters (Barke et al. 2015). Early theoretical work Soler et al. (1982) predicted that clusters from supersonic gas expansion grow first by monomer addition and later on by coagulation of smaller clusters, but conventional methods are insensitive to the cluster shape. Therefore it was not known whether coalescing clusters forming a larger particle would return to a compact, almost spherical ground state. Single-cluster imaging studies on Xe clusters (Bostedt et al. 2010b; Rupp et al. 2012, 2014) revealed that for smaller particles in the size range of R = 50 nm, both spherical and nonspherical twin and triple structures coexist in the beam (c.f. upper panel in Fig. 13a). For larger clusters the freeze-out of nonspherical states continues up to μm-sized particles with a hailstone-like substructure (c.f. lower panel in Fig. 13a). The short pulses of FELs also allow to investigate the time structure of pulsed cluster jets. Scanning the FEL pulse along the cluster jet from a pulsed source showed that there is a large variation in produced cluster sizes. In particular, long after the main cluster pulse is over, extremely large clusters are produced exceeding the prediction of any scaling laws which was attributed to the closing of the valve (Rupp et al. 2014).
Fig. 13

Structure of single nanoparticles recovered from single-shot scattering patterns recorded with intense XUV or x-ray FEL pulses. Left panel (a) rare gas clusters. (Adapted from Rupp et al. 2014), right panel (b) metal clusters. (Adapted fromBarke et al. 2015)

Single-cluster imaging of metal particles with several hundreds of nm radius produced in a magnetron sputter source (Barke et al. 2015) revealed highly symmetric but diverse patterns, such as the examples in Fig. 13b. They all correspond to regular shapes, including noncrystalline motives such as icosahedra. Such geometries are energetically preferred only for small particles, and their persistence up to the μm regime shows that early formation stages are imprinted in the final distribution of particle structures. By measuring the scattered light in a wide angle around the particles, the three-dimensional shape and orientation of the clusters could be determined in a single FEL shot (Barke et al. 2015). A signature of this wide-angle limit, where full 3D information can be gained from a single scattering image, can be found in the broken point-symmetry in the upper left pattern of Fig. 13b.

In another experiment, taking advantage of the symmetry of nanocrystals, it was possible to reconstruct the 3D structure of individual gold nanocrystals deposited on a thin membrane by recording a single-shot diffraction pattern with hard x-rays (Xu et al. 2014). A resolution of 5.5 nm was achieved which can further be increased up to the atomic level by averaging a sufficient number of identical nanocrystals (Xu et al. 2014).

Superfluid Droplets

Ultrafast imaging is uniquely suited to study non-depositable fragile nanoscale objects in free flight. One prominent recent example is the pioneering study on superfluid 4He droplets of Gomez et al. (2014), which sparked a series of subsequent experimental and theoretical work on the droplets’ shapes and vorticity (Ancilotto et al. 2015; Tanyag et al. 2015; Bernando et al. 2017; Rupp et al. 2017; Langbehn et al. 2018; Ancilotto et al. 2018). In a superfluid finite droplet, any rotational motion must manifest itself in the formation of vortices. Such vortices have been observed in macroscopic amounts of rotating 4He in the so-called rotating bucket experiment (Yarmchuk et al. 1979; Bewley et al. 2006), but insight into superfluid rotational motion on the nanoscale remained elusive. Single-shot images of single superfluid 4He droplets revealed strong distortions from the spherical symmetry due to high rotational momentum (Gomez et al. 2014). In some extreme cases, patterns with sharp streaks were observed and assigned to “wheel-shaped” particles, cf. Fig. 14a. To gain more insight into the vortex formation inside the superfluid 4He droplets, they were doped with Xe atoms in a pickup cell. The Xe atoms gather along the vortex cores and act as x-ray contrast agent due to their higher scattering cross section. This way the quantum vortices can be directly imaged. For certain droplet orientations, the scattering patterns from the doped 4He droplets exhibited distinct Bragg spots in addition to the characteristic pattern of the droplet, c.f. Fig. 14b. The Bragg patterns showed that the quantum vortices form a regular lattice inside the droplets with densities up to five orders of magnitude larger than in bulk liquid helium. Other droplet orientations led to more complicated diffraction images as exemplified in Fig. 14c. They could be reconstructed via efficient iterative phase retrieval using simulated diffraction from pristine helium droplets for an input phase (Tanyag et al. 2015), revealing intricate vortex structures. Subsequent studies in the x-ray (Bernando et al. 2017) and XUV (Rupp et al. 2017; Langbehn et al. 2018) regime also showed prolate shapes in addition to the extremely oblate shapes (c.f. Fig. 14a). The studies in the xuv spectral regime (Rupp et al. 2017; Langbehn et al. 2018) took advantage of the wide-angle scattering signal, containing three-dimensional information about the droplet as demonstrated previously for metal clusters (Barke et al. 2015). The analysis of a large data set and forward modeling of the diffraction patters revealed a shape transition from spherical to oblate and triaxial prolate shapes, see Fig. 14d (adapted from Langbehn et al. 2018). These shapes resemble the evolution known from rotating droplets of classical, viscous liquids, while extremely oblate shapes as proposed previously were not observed.
Fig. 14

Single-shot diffraction images of individual helium droplets and corresponding shapes from modeling and/or reconstruction. (a) Streak patterns from x-ray diffraction were assigned to strongly deformed, classically instable oblate shapes. (Adapted from Gomez et al. 2014). (b) By doping helium droplets with Xe, quantum vortices became visible as Bragg peak-like intensity maxima. (Adapted from Gomez et al. 2014). (c) Other droplet orientations resulted in more complicated patterns (Tanyag et al. 2015). Iterative phase retrieval algorithms utilizing information on the droplets revealed intricate vortex shapes. (Adapted from Tanyag et al. 2015). (d) XUV wavelengths allowed for recording wide-angle scattering patters (Langbehn et al. 2018) which contain three-dimensional information on the droplet shapes. Forward modeling indicated a shape transition from spherical to oblate and triaxial prolate shapes, resembling rotating droplets of classical, viscous liquids, while extremely oblate shapes were not observed. (Adapted from Langbehn et al. 2018)

Clusters as Holographic References

So far we have seen that single particle imaging is a unique tool to resolve the structure of fragile nanospecimen in the gas phase, yielding insight from the fundamental growth processes of clusters to quantum vortices in superfluid 4He droplets. A fundamental limitation of the diffraction imaging approach is that during the measurement the phase information is lost. The real-space information can only be recovered through Fourier transform modeling for spherical structures (Rupp et al. 2012) or with phase-retrieval algorithms under defined boundary conditions (Aquila et al. 2015). The phase recovery from images of complex specimen requires thousands of steps, often relies on human guidance and sometimes fails to produce unique solutions for the structure, especially in the presence of background noise and dead regions on the detector.

A way around this problem is the Fourier holography approach where the phase information is recorded by means of a reference scatterer. This technique has been demonstrated in the x-ray regime with lithographic masks where a reference pinhole can be placed at a defined position with respect to the sample (Eisebitt et al. 2004). However, positioning of precise references is hardly feasible in gas-phase imaging experiments. A new approach for gas phase experiments, called in-flight holography, uses spherical clusters as holographic references, which are injected simultaneously with the sample into the FEL focus as depicted in Fig. 15a. In order to imprint the phase information with sufficient fidelity onto the coherent images of the sample while maintaining high resolution, small heavy-atom references are needed. In the first demonstration of in-flight holography, Xe clusters were combined with Mimi viruses as reproducible biological sample (Gorkhover et al. 2018). The obtained holographic images exhibit fine fringes containing the phase information (Fig. 15b). The sample shape can be reconstructed even for complex targets with inverse Fourier transforms, resulting in a unique solution of the sample as demonstrated in Fig. 15b–d (Gorkhover et al. 2018). The holographic principle can be applied even if the position, size, and number of references are initially unknown.
Fig. 15

(a) In in-flight holography, Xe clusters act as reference scatterers to a biological sample. In (b)–(d), x-ray holograms and reconstructions of complex bio specimen such as a Mimi virus (b), cluster of viruses (c), and debris (d)

Imaging Dynamics

Single-shot imaging with intense FEL pulses can also yield unique insight into ultrafast electron and ion dynamics in clusters, in addition to answering questions about their internal structure and morphology. In a sense, the diffraction patterns are more than a static structure map of the sample. They are a snapshot of complex nanoscale dynamics on the femtosecond time scale.

The scattering response of a cluster is determined by its refractive index n = 1 − δ+iβ. The real part 1-δ is a measure of the phase shift of the scattered wave and describes how efficient the whole atom scatters compared to the Thomson scattering of a single free electron. The imaginary part β describes the absorption of the system and is directly proportional to the photo absorption cross section σ. Therefore the scattering images reflect the particle’s electronic structure. This relationship has been exploited to investigate the transient electronic structure in Xe clusters during illumination with intense FEL pulses of 13.7 nm (Bostedt et al. 2012b). The scattering images showed distinct deviations from the ideal qR−4 small-angle scattering law with increasing power densities (c.f. Fig. 16a) reflecting the transient electronic structure during the light-matter interaction, on a time scale where conventional spectroscopy approaches are inherently blind (Bostedt et al. 2012b).
Fig. 16

(a) Power density-dependent changes in the scattering response of Xe clusters. With increasing power densities (top to bottom), the scattering patterns deviate from qR−4 (red line) due to transient electronic changes (Bostedt et al. 2012b). (b) Delay-dependent changes in the scattering response of laser-pumped Xe clusters. With increasing delay, the higher-order information is lost due to surface softening in the expanding nanoplasma (Gorkhover et al. 2016)

Combining ultrafast imaging with the pump-probe approach allows visualizing the structural dynamics of laser-heated clusters with femtosecond time and nanometer spatial resolution (Gorkhover et al. 2016). In a first demonstration experiment, Xe clusters were pumped with an intense near-infrared pulse into a non-equilibrium nanoplasma state, and coherent x-ray diffraction images from delayed FEL pulses shown in Fig. 16b) tracked the subsequent explosion of the cluster. Already after 100 fs and longer delays (middle panel and lower panel in Fig. 16b, respectively), the diffraction patterns lost significant contrast in the higher orders compared to a pristine particle (top panel). Modeling the delay-dependent diffraction patterns showed that the loss in contrast can be attributed to the surface softening of the clusters on the ultrafast time scale. The cluster maintains a shrinking solid core with near solid-state density during the first 500 fs. After one picosecond, the vast majority of ions are moving outward due to heat transfer from delocalized electrons. Such behavior aligns well with theoretical models of a hydrodynamic expansion into vacuum (Mora 2003; Peltz et al. 2014). In the recent years, multi-pulse and multicolor schemes have become available, in particular in the hard x-ray regime (Marinelli et al. 2015). Hard x-rays exhibit wavelength comparable to the bond length and allow ultrafast investigations of lattice dynamics via Bragg scattering. They also target the deeper core levels of heavy atoms and can deposit large amounts of energy into clusters within femtoseconds. A first hard x-ray pump-probe experiment with hard x-ray-heated Xe clusters suggests unexpected lattice contraction dynamics during the early nanoplasma stages (Ferguson et al. 2016). The powder patterns from thousands of Xe clusters witness that the initial crystalline structure slowly melts away with increasing time delay between pulses, but selected Bragg peaks from single clusters indicate a lattice contraction in parallel to the increasing disorder in the lattice (Ferguson et al. 2016). While the expansion is in line with previous knowledge, lattice compression has neither been observed experimentally nor described by any theoretical models. One possible explanation involves the delocalized valence electrons in the nanoplasma core that can lead to transient but stronger metallic-like bonding (Ferguson et al. 2016). Overall, however, the observed behavior is not yet fully understood.

Size-Selected Cluster and Same-Particle Experiments

Some experiments do not require the ultimate power density available from FELs but take advantage of their short pulse structure or high flux. One example is a photoemission study on a size-dependent metal to nonmetal transition in Pb clusters (Senz et al. 2009). Intense XUV pulses were used to remove 5d electrons from the thin target of size-selected clusters. Inner-shell photoelectron spectra were recorded for cluster containing 12–200 atoms. The size-dependent shift of the core hole binding energy substantially deviates from the expectations of the metallic droplet and jellium models, and it was concluded that the electronic shielding is reduced once the cluster size falls below about 20 atoms. This suggests a metal to nonmetal transition, in agreement with previous local density approximation calculations. This transition could only be observed using XUV radiation, since with optical or ultraviolet spectroscopy, the transition was hidden in the valence band formation (Senz et al. 2009). Meanwhile this technique has been extended to deeper core levels (Bahn et al. 2012).

A second example is ultrafast 3D imaging of the generation and evolution of acoustic phonons in individual metal nanocrystals with a comparably weak FEL beam (Clark et al. 2013). The light-induced disorder is investigated in an optical-pump/hard-x-ray-probe configuration. Time-resolved Bragg peaks were recorded with delay times up to 200 ps providing insights into the physics of coherent acoustic phonons in truncated octahedra gold nanocrystals, ≈300 to 400 nm in diameter. Oscillating regions of expansion and contraction within the nanocrystal could be resolved as spatial patterns, changing on the picosecond time scale. These results allow comparison and confirmation of predictive models based on continuum elasticity theory and molecular dynamics simulations (Clark et al. 2013) and thus contribute substantially to our understanding of dynamics on the nanometer scale.

Outlook

The 1960s mark the birth of cluster and SR research, and both fields developed rapidly and benefited each other tremendously. Today, the combination of well-defined samples, such as size-selected or even single clusters, with extremely bright light and femtosecond sources, opens up new regimes for experiments. Dedicated instruments at SR or FEL sources addressing the special needs of cluster and nanocrystal studies are now installed at many places. The combination of variable polarization undulator radiation from storage rings with advanced sample environments, especially cluster and ion beams and traps, but also well-defined substrates for cluster deposition, allows taking full advantage of the strength of short-wavelength radiation, namely, element specificity and magnetic contrast. This will help developing a deep understanding of electronic and magnetic structure on the nanoscale which is essential for many novel applications and designing new materials. While research on simple model systems, such as atomic clusters, will further address fundamental problems of size-dependent properties, there will be a growing field of studying more complex systems extending into chemistry and materials science. Often a long breath is needed before results from fundamental research bear fruits. While the concepts of quantum confinement, i.e., size-dependent electronic properties, were already developed in the 1980s, only now nanocrystals from exactly the same material but with different sizes emitting blue, green, and red light enter consumer products, such as TV screens.

With FELs, a new era has just begun. Superintense short light pulses offer new opportunities for structure determination as well as imaging nanoparticles and their dynamics. Presently investigations with these new light sources are still in the infancy of basic research. It will be exciting to follow in which direction the field will develop and if and how even shorter (attoseconds) or two-color light pulses can be used to study ultrafast dynamics and perhaps surprise us with novel unexpected phenomena. Clusters and nanocrystals will again play a prominent role. In a broader sense, as small particles with controllable properties, they are ideal test samples for investigating new phenomena in intense light-matter interaction with relevance to questions in diverse fields ranging from biology to materials sciences and at the same time bridge the gap between molecular and condensed matter physics.

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Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2019

Authors and Affiliations

  • Christoph Bostedt
    • 1
    • 2
    Email author
  • Tais Gorkhover
    • 3
  • Daniela Rupp
    • 4
  • Thomas Möller
    • 5
  1. 1.Laboratory for FemtochemistryPaul Scherrer InstituteVilligenSwitzerland
  2. 2.Institute of Chemical Sciences and EngineeringÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.Stanford PULSE InstituteSLAC National Accelerator LaboratoryMenlo ParkUSA
  4. 4.Max-Born-Institut BerlinBerlinGermany
  5. 5.Institut für Optik und Atomare PhysikTechnische Universität BerlinBerlinGermany

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