2.2 Cluster Growth and Statistical Principles
19
M
∗
n + L → M n + L
( 2 . 2 )
Evidently, the efficiency of this process also varies with the collision gas itself and
the pressures. The cluster growth can continue via cluster-cluster collisions when the
ratio of monomers to large clusters reaches a certain point, resulting in a twin-peaked
mass distribution [112, 115].
The growth mechanism to form a dimer based on three-body collisions may also
be assisted by a heavy inert carrier gas (e.g. argon instead of helium), but this is not
recommended for a LaVa source to avoid possible formation of argon additions on
the metal clusters [2, 116]. It is worth mentioning that rare gas atoms in plasma may
also become ionized or electronically excited, and then their collisions with metal
atoms or clusters may cause electronic excitation [15, 117].
M n + L
∗
→ M
∗
n + L
(2.3)
In general, as the rare gas bear relatively higher ionization energies (He: 24.6 eV;
Ne: 21.6 eV; Ar: 15.8 eV) than metals (typically 5–9 eV) [118], there are little chances
for direct ionization of these rare gases. But the energies at metastable excited states
could be comparable to metal ionization potentials, which allow penning ionization
being efficient and exothermic enough to cause fragmentation of the growing clusters
[15].
M n + L
∗
→ M
∗
n−X + x M + L
( 2 . 4 )
In addition to the nascent neutral atoms/clusters, experimental results have demonstrated that both positive and negative ion clusters are produced by variation of
the laser plasma conditions. Moreover, the electron attachment to neutral clusters
contributes to producing anion clusters, which can be promoted in case of the addition
of an electron source [15, 55].
M n + e
−
→ M
−
n
(2.5)
Following these origins in forming clusters in a LaVa source, further insights into
the LaVa sources shed light on the statistical principles. In general, the evaporation of
atoms/clusters into vacuum is dependent on the element studied, but can be broadly
represented by the following equation where clusters with a diameter smaller than
d
* will evaporate while the larger will grow:
d
∗
=
4σ m
kT
·
1
ln(Φ k )
(2.6)
In this equation, σ is the surface tension of the liquid cluster, m is the mass of
the monomer, k is Boltzmann’s constant. T and are the temperature and density of
the cluster respectively. Φ k is the supersaturation level of the liquid/vapor interface,
represented by the ratio of the partial pressure of the monomer over the vapor pressure
19
M
∗
n + L → M n + L
( 2 . 2 )
Evidently, the efficiency of this process also varies with the collision gas itself and
the pressures. The cluster growth can continue via cluster-cluster collisions when the
ratio of monomers to large clusters reaches a certain point, resulting in a twin-peaked
mass distribution [112, 115].
The growth mechanism to form a dimer based on three-body collisions may also
be assisted by a heavy inert carrier gas (e.g. argon instead of helium), but this is not
recommended for a LaVa source to avoid possible formation of argon additions on
the metal clusters [2, 116]. It is worth mentioning that rare gas atoms in plasma may
also become ionized or electronically excited, and then their collisions with metal
atoms or clusters may cause electronic excitation [15, 117].
M n + L
∗
→ M
∗
n + L
(2.3)
In general, as the rare gas bear relatively higher ionization energies (He: 24.6 eV;
Ne: 21.6 eV; Ar: 15.8 eV) than metals (typically 5–9 eV) [118], there are little chances
for direct ionization of these rare gases. But the energies at metastable excited states
could be comparable to metal ionization potentials, which allow penning ionization
being efficient and exothermic enough to cause fragmentation of the growing clusters
[15].
M n + L
∗
→ M
∗
n−X + x M + L
( 2 . 4 )
In addition to the nascent neutral atoms/clusters, experimental results have demonstrated that both positive and negative ion clusters are produced by variation of
the laser plasma conditions. Moreover, the electron attachment to neutral clusters
contributes to producing anion clusters, which can be promoted in case of the addition
of an electron source [15, 55].
M n + e
−
→ M
−
n
(2.5)
Following these origins in forming clusters in a LaVa source, further insights into
the LaVa sources shed light on the statistical principles. In general, the evaporation of
atoms/clusters into vacuum is dependent on the element studied, but can be broadly
represented by the following equation where clusters with a diameter smaller than
d
* will evaporate while the larger will grow:
d
∗
=
4σ m
kT
·
1
ln(Φ k )
(2.6)
In this equation, σ is the surface tension of the liquid cluster, m is the mass of
the monomer, k is Boltzmann’s constant. T and are the temperature and density of
the cluster respectively. Φ k is the supersaturation level of the liquid/vapor interface,
represented by the ratio of the partial pressure of the monomer over the vapor pressure