Study of electronic structure of carbon and silicon particles

  
intermediate size have received a great deal of attention for the promising technological 
applications in optoelectronics.  
The present dissertation is focused on studies of physical properties of size-selected carbon 
and silicon clusters. The research work is experimental - the electronic structure of small clusters 
has been investigated employing photoelectron spectroscopy. Fragmentation spectroscopy has 
been performed as well for a better comprehension of the photoelectron results.  
1.1 The systems: Carbon and silicon clusters 
Although carbon and silicon belong to the same group (IV) of the periodic table of the 
elements, they represent a particularly interesting sequence. They show slightly different properties 
which are attributed to the decreasing importance of pi bonding with increasing atomic 
dimensions. This leads to the formation of a large variety of single and multiple bonding structures 
in the case of carbon while mostly single bonding structures for silicon.  
In crystals, the nature of their bonding is intermediate between metals and insulator – carbon 
and silicon crystals are covalent materials. In chemical terminology this means that each atom of 
the covalent material participates in four covalent bonds by sharing two electrons with each of its 
four neighbours in the typical crystal structure of diamond. Significant covalent bond strength 
arises if hybrid bond orbitals are formed from linear combinations of low-lying atomic s- and p-
orbitals. The highly directional sp3 hybrid bonds that result determine the diamond and zincblende 
crystal structures of most common semiconductors. Overlapping hybrid orbitals on neighboring 
tetrahedral coordinated sites produce bonding and antibonding levels which ultimately broaden 
into the semiconductor valence and conduction band, respectively, of the band model theory.  
Although the common nature of the bonds, the physical properties of carbon and silicon bulk 
show some differences generally related to the resistivity: 
• The most covalent carbon crystal - diamond - is an insulator; 
• The hexagonal lattice form of bulk carbon - graphite - is a semimetal; 
• Silicon, with the same crystal structure of diamond, is a semiconductor. 
• There is no evidence of the existence of a graphitic form of silicon. 
The atomic arrangement on the surface of covalent bonded materials is often different from 
that in the bulk. The modification of the crystal lattice at the border is known as surface 
reconstruction. In the electronic density of states (DOS) the surface states are defects of the band 
structure which can be clearly distinguished from the other states only in presence of a band gap. 
The study of the electronic properties of carbon and silicon particles provides a clue to the 
origin of the band structure and surface reconstruction.  
The information that can be gained by spectroscopic investigation is explained in the chapter 
“Experimental Setup”. There the techniques treated are exclusively those employed in our 
experimental work. 
  
 
2 STATE OF THE ART: CARBON 
Carbon clusters are fascinating examples of the richness and variety of carbon chemistry. Due 
to the enormous bonding flexibility of carbon, viz. its unique ability to form stable single, double, 
or triple bond, carbon clusters appear in a wide range of structural forms that are synthesised 
spontaneously in hot carbon plasmas produced during the energetic processing of carbon-rich 
materials. Such natural environments include the atmospheres surrounding carbon stars, 
interstellar dust clouds irradiated by intense UV radiation, and terrestrial sooting flames [Ger87, 
Her83]. The most widely used laboratory technique for producing carbon clusters is laser ablation 
or arc-discharge vaporisation of graphite followed by supersonic expansion into an inert carrier 
gas, usually helium or argon. Neutral, anionic, and cationic carbon clusters grow directly from the 
plasma with the sizes ranging from one to hundreds of atoms. The size distribution produced in 
this way can be controlled by varying such experimental parameters as laser power, gas pressure, 
and the geometry of the supersonic nozzle. Elucidating the evolution of carbon cluster structure, 
from linear chains to rings to closed spheroidal cages to nanotubes, that takes place as the cluster 
size increases, constitutes a major scientific challenge and requires an intimate interplay of state of 
the art experimental and theoretical techniques. In this chapter the literature on carbon clusters is 
reviewed for two groups of clusters: the fullerenes and the other geometrical structures of carbon 
clusters. This classification is based on the peculiarity of the cage clusters among all the possible 
single-element clusters - fullerenes are the only atomic clusters which crystallise in new solids. 
Low mass fullerenes are of particular interest because their high curvature and increased strain 
energy owing to adjacent pentagonal rings could lead to solids with unusual intermolecular 
bonding and electronic properties. The aim of this research project is to demonstrate the 
existence of the smallest possible fullerene C20. 
2.1 Particular class of clusters: Fullerenes 
In 1985 Kroto and Smalley [Kro85], producing carbon clusters by a laser graphite-
vaporisation source have observed, for the first time that, under certain source conditions, the 
intensity of C60 could be made to fully dominate the mass spectrum. The recognition of the unique 
stability of the cluster with 60 carbon atoms has induced the researchers to propose a highly 
symmetric truncated icosahedral structure (“football or soccerball”) for this molecule. It was 
christened with the name “Buckminster fullerene”, or more commonly fullerene, in recognition of 
  
the structure of Buckminster Fuller’s geodesic domes. Such a geometrical arrangement involves 
no dangling bonds and has been calculated to be very stable with pi-electrons delocalised over 
the outer and inner surfaces of the spheroidal structure. 
An sp3-hybridized array of carbons is three-dimensional (e.g. diamond) but has a surface with 
attendant (destabilising) dangling bonds. Similarly an sp2-hybridized planar fragment of a graphite 
sheet has a reactive edge with dangling bonds. In C60, however, the incorporation of pentagons 
into the hexagonal graphite planes allows the sp2-hybridized structure to bend around and form a 
cage, thus removing any dangling bonds and being further stabilised due to the overlap of adjacent 
pi-electrons. Each carbon atom has all valences satisfied by two single bonds and one double 
bond. A C60 has many resonance structures, and appears to be aromatic. This kind of structure 
has, in fact, been predicted on a number of occasions before the Smalley/Kroto experiments 
were carried out. Simple geometrical considerations show that it is possible in principle to 
envisage similar cage structures for all of the even carbon clusters with 20n ≥ , with the 
exception of n = 22. The structural peculiarity is the presence of an even number of three-
coordinated sp2 carbon atoms that arrange themselves into 12 pentagonal faces and any number 
(except 1) of hexagonal faces. Odd-numbered clusters will always have at least one atom with a 
remaining dangling bond and will thus be very reactive and unstable. The cage should be stable if 
the curvature related strain is symmetrically distributed (geodesic structure) and if the pentagons 
are isolated as much as possible by the hexagons in order to avoid the inherent instability of 
fused-pentagon configurations (see “isolated pentagon rule” in Kro87). The unique stability of C60 
can thus be understood since it is the only 5/6-ring cage for which all the atoms are equivalent (i.e. 
the strain is perfectly distributed) and it is the smallest fullerene for which all pentagons can be 
isolated. The next fullerene which is able to avoid abutting pentagons is C70, which is observed 
also to be particularly stable. 
While great progress has been made in recent years in understanding the physical and 
chemical properties of this new class of clusters, many unanswered questions still remain. For 
example: 
• The mechanism of formation of fullerenes is not yet well understood since their formation 
does not require extreme plasma conditions – it accompanies soot formation by burning 
candles [Sma90]. A pentagon road accretion as been proposed as mechanism for 
fullerene formation [Kro88]. 
• The stability of small cage structures like C20, which is the smallest carbon cluster that can 
exist as fullerene, is still an open question since different studies show conflicting 
predictions concerning the relative energies of the possible isomers. 
• The whole question of energy storage and conversion within C60 and the other fullerenes 
is topical. Thermionic emission has been observed to occur from neutral fullerenes 
[Cam91], giant (n = 150 – 600) positively charged fullerenes and negatively charged C60- 
[Sma91] on a time scale of microseconds.  
  
 
2.1.1 C20: Cage, bowl and ring structure 
A dodecahedron consisting of 12 pentagons whose vertexes are occupied by 20 carbon 
atoms is topologically the smallest possible fullerene. Its structure is shown in the left side of figure 
2.1. Kroto [Kro87] has underlined that the existence of such a structure with adjacent pentagons 
would be unfavorable for a cage structure. His theory is known as the “isolated pentagon rule”. 
He formulated the hypothesis that curved graphitic networks, like bowl C20 (see the relative 
structure in the middle of figure 2.1), are intermediates in the growth mechanism which produces 
buckminsterfullerene and larger closed cages [Kro88]. This further theory is known as the 
“pentagon road” in the formation of fullerenes. In laser ablation experiments of graphite under 
conditions that produce fullerenes for clusters bigger than C30
-
 [Han95a], only a monocyclic ring 
isomer (see the right picture in figure 2.1) is produced containing 20 carbon atoms. The structure 
has been assigned on the basis of the agreement between experimental and theoretical electronic 
structures [Sai00]. 
In calculation, a bowl-shaped isomer which minimizes the number of dangling bonds in a 
graphite-type structure, has been found to be competitive in energy with the fullerene and ring 
isomers [Gro95, Jon97, Scu96]. In figure 2.1 the structures of the three candidates for the ground 
state geometry are shown: cage (three dimensional), bowl (two dimensional) and ring (one 
dimensional). 
 
 
 
 
Figure 2.1: The three most probable isomeric form of C20. From the left to the right are 
shown cage, bowl and ring. 
Empirical and semiempirical previsions are of little help in predicting the most stable structure 
of C20. The ring, bowl, and fullerene isomers contain different types, as well as different number 
(20, 25, and 30 respectively) of bonds.  
Entropic factors greatly favor the ring isomer over the bowl and fullerene isomers at high 
temperature.  
  
The relatively low energy of the bowl isomer is consistent with an accretion mechanism 
(pentagon road) of fullerene formation [Kro88] in which the growing carbon sheets have enough 
time to anneal to their lowest energy forms, simultaneously minimizing the number of dangling 
bonds. The absence of the bowl isomer in mobility experiments may simply be related to entropic 
and kinetic (high-reactivity) factors. 
 
Figure 2.2: The relative energy differences for the ring, bowl, and cage C20 isomers. For 
each theory the lowest energy structure is taken as a reference. LDA (Local Density 
Approximation), HF (Hartree-Fock), DMC (Diffusion Monte Carlo), BLYP (Becke-Lee-
Yang-Parr functional) [Mit00]. 
The striking feature about this problem is the enormous discrepancy between the various 
theoretical methods. The graph below shows the relative energies of these three clusters 
calculated following four different methods: Local Density Approximation, Hartree-Fock, 
Diffusion Monte Carlo, Becke-Lee-Yang-Parr functional (figure 2.2). The data are obtained by 
[Gro95] and are corrected with respect to the performed last calculation [Mit00]. Therefore, a 
relative energy scale of the different structures cannot be established and thus the ground state 
geometry cannot be predicted. Furthermore, stability alone does not determine which isomer 
actually is formed preferentially. 
  
 
Galli et al. [Gal98] have calculated the density of the occupied valence states of C20 for the 
three isomeric structures. The results for the anion and neutral samples are shown in figure 2.3. 
The dotted line is relative to the anions, the straight line is relative to the neutrals. 
 Figure 2.3: Density of valence occupied states (arbitrary units) 
of the three C20 Isomers. Solid and dotted lines indicate the results 
for neutral and negatively charged clusters, respectively. The 
bottom of the valence bands of the neutral and charged clusters has 
been arbitrarily aligned for each isomer [Gal98].  
 
The features at binding energies higher than 10 eV distinguish the 
three isomers. Large intervals between the peaks characterises the 
DOS of the cage isomers. Conversely, for electron binding energy 
lower than 10 eV, the electronic structure does not allow to 
distinguish the three isomers from each other. The peaks are just of 
different intensities. Therefore the theory predicts difficulties in the 
assignation of the structures by performing PES with conventional 
either visible or near-ultraviolet excitation sources.  
In the particular case of the cage structure, the energy 
thresholds of neutral and anion is the same. Therefore, Galli’s 
calculation predicts no band gap between HOMO and LUMO of 
C20 fullerene, which is in contrast with the observed behaviour of 
larger fullerenes. 
The investigation of allowed vibrational modes is more promising for the identification of the 
atomic structures. In experiments involving transitions between electronic states, oscillation 
frequencies peculiar of each structure can be excited which are related to the nature and 
symmetry of the involved molecular orbitals. 
The vibrational frequencies of C20 cage, bowl and ring have been investigated by Seifert 
[Sei99]. His molecular dynamic calculations are relative to the electron emission process from the 
anion to the neutral C20 and, in particular, the results predict the vibrational modes excited during 
the emission process for samples at 0 K.  
In a private communication, Seifert refereed us the results of the calculated vibrational spectra: 
• The spectrum of the ring isomer shows exclusively a vibrational mode at 2000 cm-1. It is 
attributed to the stretching of the acetylenic bond. 
• The spectrum of the bowl is more complex than the ring. Several vibrational modes have 
been predicted. However, the most intensive peak in the spectra corresponds to 2200 
cm-1. The relative vibrational mode is attributed to an acetylenic stretching as well.  
• No high-energy vibrational modes have been predicted for the cage isomer. This result is 
expected since no triple bond are present in this structure. The spectrum relative to the 
cage shows a large number of peaks. The most intensive ones appear at 700 cm-1 and 
  
500 cm-1 wave numbers. In this case the attribution is not simple since the relative 
vibrations can be due to different kinds of stretching and bending of carbon bonds. 
2.1.2 Chemical synthesis to generate structural precursors 
of the smallest fullerene: C20 
To investigate the existence of the smallest possible fullerene, consisting of 20 carbon atoms 
posed at the vertices of 12 pentagons forming the surface of the cage structure, a dodecahedral 
parent is synthesised in Prof. H. Prinzbach’s laboratory [Pri94]. The research project is aimed to 
verify the existence of the dodecahedral fullerene by studying the fragmentation pattern of the 
structural parent, as well as the spectroscopic properties of the C20 fragment. The parent is 
dodecahedrane with molecular formula C20H20. It was firstly synthesised by Paquette and co-
workers [Paq83]. Prinzbach has started out the synthesis from the former insecticide C12-isodrin 
and followed the multi-step sequence ultimately based on C5 (cyclopentadiene) and C2 
(acetylene) building blocks. The synthesis has been highly optimised and is known as “isodrin-
pagodane” route [Pri94]. 
The highly symmetric structure of the dodecahedrane has been unequivocally established by 
1H NMR and X-ray spectroscopies [Ber97, Paq83]. The carbon atoms are all tetra-coordinated 
in a slightly distorted tetrahedron geometry, the cage structure is stabilised by the presence of the 
outer-cage carbon-hydrogen bonds and therefore the strain energy is minimised. However, the 
dodecahedrane has been proved to be a very stable molecule. In order to make the 
transformation of the precursor into the fullerene possible, the strongly bound hydrogen had to be 
replaced by more weakly bound atoms. The research group of Prof. Prinzbach has produced two 
halogen-functionalised dodecahedrane: A chlorinated and a brominated derivative. As is 
extensively discussed in the next paragraph, mass spectroscopic results have induced to opt for 
the bromide [Ber97, Sch98]. For an extensive treatment of the bromination process see [Lan00]. 
An oxygen-insensitive product of average [C20HBr13] elemental composition was obtained 
and was spectroscopically and chemically identified as a multitude of primarily isomeric C20H0-
3Br14-11 trienes. Catalytic reduction back to dodecahedrane proved the cage skeleton to have 
survived the bromination [Ber97].  
In order to exclude the isomerisation of the cage into the bowl structure during the 
debromination, the latter generated independently was pursued. This was likewise achieved by 
gas phase debromination of a brominated precursor with average [C20HBr9] elemental 
composition. The bowl precursor C20H10, better known as corannulene, was synthesised and 
brominated by Prof. Scott and co-workers [Sco97]. 
  
 
3 STATE OF THE ART: SILICON 
Silicon is currently the preferred material for electronic devices. Due to its superior material 
and processing properties it is the most useful and exploited material in modern technology. 
However, silicon is an extremely inefficient light emitter and for this reason its optical applications 
are few. This optical behaviour can be microscopically explained: Silicon is a semiconductor with 
an indirect band gap in the electronic structure due to the symmetry of its crystal lattice. The 
indirect band gap energy is Eg = 1.17 eV. The presence of this indirect gap makes the optical 
properties of silicon different from those of direct gap semiconductors. In fact, each electron 
transition between the bottom of the conduction band and the top of the valence band in direct 
gap semiconductors requires an electron-photon interaction. Instead, in an indirect gap 
semiconductor the interaction of at least three particles is necessary to conserve the momentum: a 
phonon, a photon and an electron. Therefore, radiative recombination (i.e., luminescence) is a 
very improbable process and the time scale for the photon emission (~ 10 µs) is slow if 
compared with that of direct gap semiconductors. Other relaxation processes requiring no photon 
emission are therefore faster and more probable than luminiscence. For this reason, silicon is not 
used in the generation of optical signals. 
Due to the reduced dimension, it is expected that silicon nanocrystals have completely 
different optical and electronic properties. The luminescence should become more allowed in 
small crystallites as translational symmetry is broken.  
One experimental evidence is the measured visible fluorescence of porous silicon [Ram91]. 
The energy of the emitted radiation is higher than the energy gap of bulk silicon. This effect is due 
to the presence of fused nanometer-diameter silicon wires or particles in the sample. This 
enhancement of the energy of the emitted photon in small systems can be explained as follows: the 
electron and hole acquire in small crystallites (quantum crystallites) a significant “quantum energy” 
of localisation which increases the recombination energy. The effect known as quantum 
confinement is extensively discussed in the literature. For a deeper comprehension of this effect, 
we suggest to read the explanation of Brus in [Bru94] and the review of Yoffe on the behaviour 
of semiconductor microcrystallites [Yof93]. 
Surface effects can affect as well the electronic structure of small silicon clusters since 
covalent bonds favour the reconstruction on the surface of the particles. 
The luminescence of silicon nanocrystals is a topical research field. A lot of studies, both 
theoretical and experimental, have tried to explain it [Ali96, Bru84, Xia99, Bru91, Wil93, 
Wol99]. For example, the results of tight-binding cluster model calculations qualitatively unify the 
  
quantum confinement model and the surface-localised-state model for the luminescence 
mechanism [Xia99]. In accordance with the quantum confinement effect, Xia’s calculations 
predict the increase of the energy gaps for decreasing diameter. Furthermore, the results of the 
calculations indicate that the energy gap becomes smaller in case of incomplete saturation of 
surface bonds. 
A systematic experimental investigation of the electronic structure of silicon clusters is missing. 
The main goal of this research project is to investigate the ground and excited electronic structure 
of silicon clusters. We have started with very small particles, but following experiments will be 
performed in the mesoscopic range (quantum dots). The question we hope to answer in the 
present work is whether the properties of small silicon clusters are extensively determined by 
quantum size effects or by the formation of covalent bonds on the surface. 
3.1 Ground electronic states  
Cheshnovsky et al. [Che87] measured anion photoelectron spectra of Sin- ( 13n ≤ ) clusters, 
yielding electron affinities and a qualitative picture of the electronic states of the neutral clusters. 
The spectra are shown in the right side panel of figure 3.1. The experimental resolution was 
insufficient to observe any vibrational structure, and no assignments of the electronic states were 
attempted. Neumark et al. [Kit90, Kit91] later measured vibrationally resolved anion 
photoelectron spectra of Sin
-
 in the range 3 < n < 7 and zero electron kinetic energy (ZEKE) 
spectra. These spectra show well-resolved vibrational progressions for several electronic states, 
yielding vibrational frequencies and electronic term values for some of the low-lying electronic 
states. 
Chelikowsky et al. [Bin95] calculated the electron binding energies for the highest occupied 
orbitals of small silicon clusters whose geometries are shown in the left panel of figure 3.1. They 
investigated Sin
-
, 7n4 ≤≤ , at finite temperature (500 K and 1500 K), via ab initio Langevin 
molecular dynamics simulations. The results of their calculation are shown in the left side panel of 
figure 3.1. Furthermore, they compared the calculated Density of States (DOS) with 
photoelectron spectra on cluster anions. The comparison demonstrates that the atomic 
environment in small silicon clusters and the coexistence of more stable isomers have considerable 
effects on the distribution of the electron binding energies. 
  
 
 
Figure 3.1: Calculated density of states for the Sin- n = 4 to 7 clusters as obtained from 
Langevin simulations at T = 500 K (left side panel) and T = 1500 K (central panel). The 
spectrum indicated by the dashed curve and shaded area corresponds to the distorted 
octahedron isomer of Si6-. The experimental photoelectron spectra are shown on the right 
side panel. The calculated spectra for Si6 have been reported in the right side for 
comparison with experiment. Data from [Bin95, Che87]. 
Experimental results on the electronic structure of bigger silicon clusters are missing. 
Theoretical predictions on the development of the band gap were formulated. 
The electronic properties of semiconductor particles with perfect crystal structure (quantum 
dots), were studied by Brus [Bru83, Bru84, Wil93, Bru94]. The predictions are the following: 
Due to a pure quantum confinement effect, the splitting of the valence band and conduction band 
becomes larger and the electron affinity decreases for decreasing cluster size. 
For studying metal clusters the simple classical model of a spherical metal droplet is used 
extensively. This simple model predicts the decrease of the electron affinity for decreasing cluster 
size. This behaviour was observed for copper [Pet88, Che90] and silver clusters [Gan88] which 
are elements with s electrons in the valence shell. However, open shell transition metal clusters 
with valence d electrons show electron affinity values lower than those predicted by the model of 
the metal droplet.  
  
Since silicon has more delocalised p valence electrons, it can be expected that this model 
does not predict the electron affinity values of silicon clusters. 
Recently, Delerue et al. [Wol99] have investigated the electronic state in silicon nanocrystals 
as a function of cluster size and surface passivation. The results of their calculation are plotted in 
figure 3.2. There, the energy of the electronic states is as a function of the diameter of the 
particles. The figure shows a behaviour of the band gap as predicted on the basis of the quantum 
confinement effect.  
The effect of passivation due to oxygen bound to the cluster surface is shown as well. The 
related electronic states are inside the band gap. 
 
Figure 3.2 Dependence of the energy of the electronic states of silicon particles on the 
diameter of the clusters. Electronic states of the bottom of the conduction band (o) and of 
the top of the valence band () are shown. The effect of passivation due to oxygen bonding 
is shown as well. The symbol H is relative to electrons trapped in a p-state localised on the 
Si atom of the Si=O bond. The trapped hole states � are p-states localised on the oxygen 
atom [Wol99]. 
Recent calculations of tight-binding type have been performed by Xia et al. for understanding 
the size effect and the effect of surface-bond saturation [Xia99]. Once more the prediction due to 
the quantum confinement turned out to be correct. In addition, they have found that the energy 
gap becomes smaller in the case of incomplete saturation of surface bonds. 
  
 
3.2 Motivation for the experiments 
Small silicon clusters display a rich variety of structures. These structures are neither open 
(chains, rings, and fullerene), like those of small carbon clusters, nor fragments of the most stable 
bulk (diamond) silicon phase, like those of metal clusters. Instead, the most stable Sin are usually 
compact, but they are not always quasispherical and/or high-symmetric structures.  
Related to these peculiar symmetries and to the reduced dimension, the electronic properties 
of silicon clusters are different to those of the bulk, as demonstrated by the fluorescence of 
porous silicon. 
The modifications of the electronic structure due to the surface reconstruction and quantum 
confinement have been theoretically predicted.  
Experimental investigations are thus necessary to test the theories. 
  
CONCLUSIONS OF OUR EXPERIMENTS 
The present research work has investigated the electronic properties of size-selected silicon 
and carbon clusters.  
The experiments demonstrate that electronic structures of small clusters of these two elements 
cannot be understood taking the bulk as the reference and explained by the band model theory. 
Basically, the strong type of atomic bond – covalent bond – is assumed to determine the unique, 
molecule-like structures of these small clusters in order to minimise the number of dangling bonds.  
The reached results on carbon and silicon clusters can be summarised as follows: 
• For the first time, the existence of the fullerene at 20 carbon atoms has been 
demonstrated by comparing PE spectra of C20- isomers produced in different ways. It is 
not easy to achieve this fullerene. However, an opportune precursor can be synthesised 
whose fragmentation does not destroy the carbon cage structure. We suggest that the 
electronic properties of this fullerene are different than those of larger fullerenes. The 
existence of the bowl isomer has been proved as well. The vibrational frequencies and the 
electron affinities of these two isomers have been measured and compared with those of 
the ring isomer. The experimental results are in line with theoretical predictions. The 
lifetime of these C20- carbon isomers has been estimated to be longer than 0.4 ms.  
• For negatively charged silicon clusters in the size range 60n3 ≤≤ , the electronic 
structure does not show the band gap predicted by quantum confinement. We explain this 
as due to the occupation of surface states. The existence of excited states of different 
nature has been demonstrated. Their lifetimes have been found to vary in the range from 
few hundreds of fs to ns. The involved relaxation processes are supposed of at least three 
types.  
Furthermore, a new experimental method to investigate photofragmentation has been 
proposed. For the first time, pump-probe-type photoelectron spectroscopy has been used to 
study the fragmentation pattern. This technique allows one to make a time-resolved measurement 
of the fragmentation process. The achieved information are of static and dynamic type - 
fragmentation behaviour and velocity of the process.