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Cluster Beam ChemistryЧfrom Atoms to Solids.

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Volume 25 . Number 3
March 1986
Pages 197-296
International Edition in English
Cluster Beam Chemistry-from Atoms to Solids
By T. Patrick Martin*
How do the properties of a solid gradually evolve as atoms are brought together to form
increasingly larger units? In order to answer this question one must study aggregates of
atoms too large to be called molecules but still too small to have even the structure of a
crystal. Recent advances in both theory and experiment have made possible some first explorations in this long neglected but fascinating field of study. This review will emphasize
the generation, growth, and properties of homo- and heteronuclear clusters in the vapor
phase, particular attention being paid to mass spectrometric investigations.
isolated clusters or even as clusters of clusters in the vapor
1. Introduction
Recently it has become possible to produce and detect
aggregates of atoms varying continuously in size from two
to several hundred atoms. Because these aggregates have
attracted wide-ranging attention, a colorful but confusing
array of terms has been used to describe them, including
small particles, microclusters, grains, oligomers, specks,
and microcrystals. Considering this state of affairs it is best
to define several terms as they will be used in this article. A
ring of eight sulfur atoms or a tetrahedron of phosphorus
atoms cannot with good conscience be called a cluster.
Such stable units exist in the vapor, liquid, and solid
phases and have long been called molecules. Because molecules are readily available, their proerties are usually well
investigated. The term cluster will be reserved for atom aggregates that are not found in appreciable numbers in an
equilibrium vapor. Clusters therefore represent new objects for investigation (Fig. l).1'-41
Clearly this use of the word cluster differs from that employed for many years to describe several classes of new
crystalline cluster
However, one of the objectives of cluster beam research is to determine whether
these units, already identified in solids, can also exist as
('1 Dr. T. P. Martin
Max-Planck-Institut fur Festkorperforschung
Heirenbergstrasse I. D-7000 Stuttgan 80 (FRG)
Angeu Chem. Inr. Ed. Engl. 25 (19861 197-211
Fig. 1. Moleculea, cluaters, and a microcrystal. Clusters do not exist in equilibrium vapors. Microcrystals have the symmetry of the crystalline bulk substance.
After a cluster reaches a critical size, it is no longer free
to rearrange its structure each time a new atom is added. A
final lattice structure becomes frozen into the cluster. This
crystallization may occur for aggregates containing less
than 100 atoms. Still it is convenient and meaningful to
give these aggregates a new name, microcrystals, because
deviations from the bulk structure can be described as a
surface relaxation.
Why are the properties of clusters of interest? We would
like to understand the crystal growth process on a microscopic level. Everytime a new atom or molecule condenses
0 VCH Verlagsyesellschaft mbH. 0.6940 Weinheim. 1986
0570-0833/86/0303-0197 $ 02 SO/#
onto a cluster, the atoms in the cluster completely rearrange themselves; the cluster "reconstructs." We would
like to know the sequence of structures a cluster assumes
as it grows from a molecule into a crystal.
Another reason for studying clusters is to learn how the
electronic band structure of a solid develops. This is represented in Figure 2 by a simple Hiickel calculation of the
electronic energy levels of silicon clusters with increasing
size. It is of interest to observe how the discrete levels coalesce to form bands and at what stage a distinct gap appears between filled and unfilled states.
L I atom
LI crystal
Li microcrystal
Fig. 3. Absorption of light h) lithium
Fig. 2. ('alculated electronic energy levels of SIatoms and clusters.
A question often asked is, how many metal atoms are
required to form a cluster that has metallic properties?
One characteristic property of a metal is its optical response, i.e., its interaction with light. A single Li atom has
a very simple absorption spectrum, consisting of essentially one line in the visible (Fig. 3). This absorption can be
well described as a one-electron transition from a 2 s to a
2p state. A lithium crystal, on the other hand, has a completely different absorption spectrum. The absorption is
strong in the far-infrared, goes through a minimum in the
visible, and rises again in the ultraviolet (Fig. 3). The reason for the strong far-infrared absorption is that very low
energy photons can excite electrons from the continuum of
states just below the Fermi energy to states just above the
Fermi energy. The strong UV absorption is caused by interband transitions. Suppose we chip off a small corner of
the crystal, producing a microcrystal that contains only 50
atoms. The absorption spectrum changes completely. A relatively broad absorption maximum appears in the visible
(Fig. 3). This absorption is due to a plasmon excitation,
i.e., a collective excitation of outer electrons. The Li crystal also exhibits plasmon excitations, but these excitations
have a longitudinal chacacter and d o not couple to transverse light waves. In the microcrystal one can consider a
plasmon as a collective sloshing motion of the electrons
from one side of the microcrystal to the other. Obviously,
such a motion has a strong dipole moment, thus giving rise
to the strong absorption band in the visible. The absorp198
Li cluster
various stages 01 dggrcgatiuri
tion of light by a Li atom is well described within the oneelectron picture. However, this picture cannot describe
even qualitatively the plasmon excitations that dominate
the optical response of a 50-atom cluster. Between a few
atoms and 50 atoms, we must completely change our way
of looking at optical response. Clusters offer us the opportunity of studying this transition.
Another reason for studying clusters is that the technique of cluster-beam mass spectrometry offers a new and
convenient method of allowing elements to react in a controlled manner and of determining the stability of the reaction products.['] This topic will be the main theme of this
article, which will begin with a very brief review of work in
the field of cluster preparation.
2. Four Case Studies
Four case studies will first be presented, each representing a different method of cluster preparation, a different substance, and a different level of interpretation.
2.1. Water Clusters Produced by Gas Expansion
It has been known for several decades['"."' that when a
gas under relatively high pressure (1 bar) expands into a
vacuum through a small (0. I-mm) nozzle, clusters condense out of the cooled gas. The size distribution of the
clusters can be controlled by varying the expansion parameters. This technique has been used to study a large variety
of gas-phase and vapor-phase clusters, including those of
hydrogen,"21 ~ a t e r , [ ' ~ - ~' ' ~
o d i u m , ~ ~ inert
t e t r a ~ e n e . ' Figure
~ ~ . ~ ~4 ~shows the mass spectrum of water
clusters formed by expanding a mixture of H 2 0 (4.6 torr)
in argon through a 0.22-mm nozzle. The average cluster
size increases with increasing total pressure and the mass
peak corresponding to the cluster [H(H20)21]+stands out
particularly strongly. This finding is usually interpreted to
indicate an enhanced stability for the 21-molecule water
cluster. What does this cluster look like? Ice has a wurtzite
Angew. Chem. In,.
Ed. Engl. 25 (1986) 197-211
1 5 1.2 torr
ntug 4. Or.pcndt.ricc. 0 1 the
of uclter clusters on total pressure (determined
by mass spectrometry). The water clusters were produced by expanding a
mixture of H 2 0 vapor and argon at the indicated pressure through a 0.22-mm
orifice into a vacuum "41. n=number of water molecules per cluster; ]=relative amount of cluster.
NaC1[4'-431and CUB^^^^^ have also been shown to have an
enhanced stability. Since this cluster is too small to be observed directly, theoretical considerations are required in
order to determine its structure. Stable cluster configurations can be calculated at widely varying levels of sophistication. The simplest method uses a model involving the
packing of hard spheres. At the other end of the scale, stable structures can be determined by elaborate configuration interaction calculations of the total energy. Such calculations are appropriate for all types of clusters but are
limited in practice to very small clusters of light atoms. The
total energy of clusters with either purely
purely van der W a a l ~bonding
~ ~ ~ ] can be determined much
more simply. It is possible to define a size-independent,
structure in which each oxygen atom is surrounded tetrahedrally by four other oxygen atoms. One hydrogen atom
is found between each pair of oxygen atoms. It is not possible to find a highly symmetric arrangement of 21 H 2 0
molecules within the wurtzite structure. However, the tetrahedral bonding scheme may be used to construct a dodecahedral cage consisting of 20 H,O molecules. In fact,
such a cage has been identified in many clathrate compounds. The stability of the dodecahedron could explain
the strength of the n = 2 1 peak in the mass spectrum (i.e.,
the 20 molecules comprising the dodecahedron surround a
central, charged molecule).
0 .
Fig. 6. Size distribution of [Cs(CsI),,]' clusters determined h! wcondary
mass spectrometry (SIMS). The numbers in parentheses indicate the sizes of
perfect, rectangular clusters. I is a measure of the intensity of the mass peak
(lg counts per second) [37].
two-body interatomic potential. By summing this potential
over all atom pairs, a multidimensional total energy surface is obtained. Each minimum on this surface corresponds to a stable cluster configuration. The main computational difficulty is not to define the surface but to find all
true minima without getting trapped at a saddle point with
a low curvature.
Such total energy calculations indicate that [Nal,ClI3J+
has more than the usual binding energy. The reason for
this is quickly seen by looking at the structure of this cluster (Fig. 7). [Na,,CI,,]+ is highly symmetric, resembling a
Fig. 5. Clathrale cage composed 01 twenty hater molecules.
2.2. Alkali Halide Clusters Produced by Ion
If an intense beam of high-energy (5-keV) xenon ions
(Xe') is directed against a solid surface (e.g., CsI), secondary ions are ejected from the surface and can be detected in mass spectrometer. These secondary ions include
not only simple, ionized molecules but also large clusters
containing hundreds of atom^.[^^-^" A mass spectrum of
[Cs(Csl),]' clusters produced in this way is shown in Figure 6. The peak corresponding to the cluster [CsI4II3]+is
particularly strong. Analogous clusters produced from
A n g e n . Chem Int. Ed Engl. 2 5 0 9 8 6 ) 197-211
zinc blend
Fig. 7. The most stable form ol'thi. metal hdlrde clu,ter J M , , X , , J ( I e l l ) and
the crystal structures of NaCI, Csl, and CuBr (right, top to bottom).
portion of the rock salt structure. Calculations with parameters appropriate for the compounds CuBr and CsI indicate that the cubic cluster [Mi4Xr3]+is responsible for the
strong peaks in the mass spectra of these substances also.
This is quite surprising because CuBr and CsI condense to
form crystals of the zinc blende (coordination number
(CN) 4) and cesium chloride type (CN 8), respectively.
Thus, the rock salt form (CN 6) appears to be energetically
favored in the early stages of growth of not only NaCl but
also CsI and CuBr.
peak for x = 14 (Fig. 9). In this respect tin resembles
lead.[531That tin should more resemble lead than germanium can be seen already in the solid state. Although tin
does have a low-temperature semiconducting crystalline
modification with the diamond structure (a-Sn),at room
2.3. Quenching of Ge and Sn Vapors in Helium Gas
Most substances when heated to a sufficiently high temperature in an inert-gas atmosphere produce a dense
smoke composed of r n i c r o ~ r y s t a l s . [ ~
~ - ~linear
~ ~ dimension of the microcrystals varies from 10 to 1000 A depending on experimental conditions. Recently, a time-of-flight
mass spectrometric study showed that the technique of
inert-gas evaporation produces not only microcrystals but
also clusters containing fewer than 100
Not all elemental vapors produce a detectable number
of clusters when quenched in helium gas. Germanium and
tin, however, form clusters readily and are particularly interesting because a transition from covalent to metallic
bonding occurs in the solid forms. Perhaps this transition
is reflected in the cluster mass spectra. Mass peaks of the
Ge;’ clusters (Fig. 8) are strong for x = 6 , 10, 14, 15, and 18
I 4
200 400 600 800 1000 1200 1400 1600 1800
Fig. 9. Mass spectrum of clubters formed bq quenching Sn \iipor
temperature it is a metal with the b-Sn structure (CN 6).
Once again we can only speculate as to the cause of the
instability of the cluster ion Sn A. There are several closepacked structures corresponding to Sn & consisting of a
central atom surrounded by a complete shell of twelve
outer atoms.[“] An additional atom, which lies on the surface of such a highly symmetric, compact core, could be
expected to be weakly bonded.
2.4. Carbon Clusters by Laser Evaporation
I 4
A pulsed cluster source has been developed which uses a
focused laser beam for v a p o r i z a t i ~ n .The
[ ~ ~vaporization
is timed to occur at the peak of a high-pressure He pulse.
Such a source is particularly appropriate for time-of-flight
mass spectrometry. It has the advantage that essentially
any material can be vaporized, even carbon.[561The mass
spectrum of C,’ clusters has a bimodal size distribution.
For x < 30, clusters containing both even and odd numbers
of atoms have been observed. The peaks corresponding to
x=3, 11, 15, and 19 are particularly strong. For x>30,
however, only clusters containing even numbers of atoms
have been observed. Recently, a c60 cluster was generated
and found to be particularly stable.[56b1This cluster, named
“Buckminsterfullerene,” is assumed to owe its stability to
its highly symmetric, spherical structure.[56C1
800 1000 1200 1400 1600
Fig X M a s s hprctrum 01 clusters Ioormed by quenching Cie vapor in He gas.
Peaks corresponding to clusters with x=6, 10, 14, 15, and 18 Ge atoms are
particularly strong. Two structures having bond angles of nearly 109” are
and particularly weak for x = 13, 17, 20, and 24. A discussion of the structures of these stable clusters should be
based o n total energy calculations. However, such calculations have only been made for very small G e clusters.[”]
Therefore, we will limit the discussion to pointing out several atomic arrangements within a Ge crystal. The basic
structure in such a crystal is a six-membered ring in the
chair conformation; this structure can form the basis of an
adamantane system, which can in turn be enlarged still further. In this way a sequence of closed polycyclic Ge, structures is formed corresponding to x = 6 + 4a where a is an
integer. A plausible structure may also be formulated for
the GeA cluster ion (Figure 8).
The dominant feature of the mass spectrum of the Sn,’
clusters is the weakness, or in this case the absence, of the
3. Heteronuclear Clusters
Heteronuclear clusters, i. e., clusters composed of more
than one element, can be produced by allowing the elements to react in the vapor phase.[91The composition of
the clusters can be determined by mass spectrometry. By
varying the partial pressures of the two elements, the stability of clusters having all conceivable compositions can
be tested in just one experiment. Various combinations of
elemental vapors (Ge, Sn, Pb, Ga, In, Cs, Rb, Sr, Tm, Eu,
CI, 0, S, and P) have been allowed to react in the vapor
Angew. Chem. In!. Ed. Engl. 25 (1986) 197-211
phase and then thermally quenched in cold He gas. Heteronuclear clusters condensed out of the vapor and were
identified using a quadrupole mass spectrometer. The average cluster composition could be changed by varying the
partial pressure of the two elements. Of particular interest
are mass peaks having unusually strong or weak intensities, because such peaks allow clusters of unusually high or
low stability to be identified.[41Also significant in such experiments is the observation of a sequence of strong mass
peaks corresponding to clusters with the cornposition
This identifies the unit A,B, as a building block
for cluster construction and for possible use in the synthesis of new solids.
3.1. Experimental Procedures
Elemental vapors are produced in ovens of various design and allowed to react in a chamber containing from
0.7- to 5-mbar He gas. The outer mantel of the reaction
chamber is cooled with liquid nitrogen. The kind of oven
used depends on the element to be evaporated. For S, Rb,
Cs, and P, the oven consists of a resistively heated quartz
crucible (1 cm in diameter and 8 cm long) with a pocket at
the bottom to hold a thermocouple. The crucible fits
snugly into an A1203 cylinder grooved and wrapped with a
Ta coil. This unit is inserted into a closely fitting second
cylinder (also made of A1203).This is followed by several
layers of radiation shielding. The outermost cylinder is a
stainless steel jacket having good thermal contact with a
water-cooled electrode. The same unit can be used for
evaporation of Pb, In, and Ga, except that in these cases a
graphite rather than a quartz crucible is required. A stainless steel crucible is used for Tm and Eu. The high temperatures necessary for the evaporation of Sn require that the
oven length be scaled down by a factor of almost 2. Ge is
evaporated from a resistively heated graphite tube.
The reaction chamber contains two of these ovens. The
vapors from the ovens are mixed and cooled. Heteronuclear clusters condense out of the supersaturated vapor
and pass through a 3-mm diameter hole into an intermediate chamber where the excess He gas is pumped off with
a turbopump (150 L/s). The cluster beam then passes
through a 1-mm diameter hole into a high-vacuum chamber containing a quadrupole mass spectrometer (pumped
with a 360-L/s turbopump). The cluster beam intersects
the axis of the spectrometer, where the clusters are ionized
with 80-eV electrons. The spectrometer can be operated in
the range from 1 to 2000 amu. A quartz-film thickness
monitor, located on the farside of this chamber, allows the
total mass flux in the cluster beam to be measured. A schematic drawing of the apparatus is shown in Figure 10.
3.2. The Cesium-Sulfur System
3.2.1. Sulfur Clusters
The cesium-sulfur system is of particular interest since it
permits the investigation of an entire range of cluster compositions from pure sulfur to pure cesium. The mass spectrum of a mixture of clusters formed by quenching pure
sulfur vapor in He gas is shown in Figure 11, top. Clusters
containing from 2 to 56 sulfur atoms are easily identified.
Fig. 1I . Mass spectra of a mixture of clusters formed by quenching various
mixtures of sulfur vapor and cesium vapor in He gas. Pure sulfur clusters are
constructed out of Ss rings (top). Clusters with composition [CsS,,]' seem to
be stable against fragmentation (middle). At increased partial pressure of Cs,
polysulfide clusters composed of Cs+ ions and S:- and S i - ions (bottom)
Fig. I U Experimental apparatus (schematic) for the formation, reaction, and
mass spectrometric analysis of clusters.
Angew. Chem. Int. Ed. Engl. 25 (1986) 197-211
The mass peaks corresponding to clusters containing 8, 16,
24, 32, and 40 sulfur atoms are particularly strong. Apparently sulfur clusters have a tendency to be constructed out
of eight-atom building blocks, presumably ring molecules.
In large clusters the molecules are bonded together by
means of weak van der Waals forces. Orthorhombic sulfur
is constructed in exactly the same way (i.e., Sx rings are
stacked one on top of another). Thus, the cluster mass
spectrum appears to reflect the initial growth of a sulfur
crystal. This is somewhat surprising since the clusters are
all positively charged. In fact, the removal of a lone pair
electron from one of the sulfur rings does appear to affect
the overall stability of the cluster. Although the clusters
S & are represented by strong peaks (Fig. 11, top), neighboring peaks corresponding to the loss of one to seven
atoms are almost as strong. This gives the spectrum a steplike appearance.
Doubly positively charged sulfur clusters S',+ appear
for n = 2 0 or 21. The uncertainty in this value arises from
the fact that S:; is superimposed on S;. The existence
of a critical size for the appearance of doubly ionized clusters has been substantiated in a number of systems[601and
is thought to reflect the instability of small clusters in
which two positive charges are forced to exist in close
3.2.2 Cesium Polysulfide Clusters
A mass spectrum of clusters produced by mixing a small
amount of cesium vapor with sulfur vapor is shown in Figure 11, middle. The spectra of the Cs-S system must be
analyzed carefully since four sulfur atoms (128 amu) are
distinguishable from one Cs atom (133 amu) only in high
resolution mass spectra. Fortunately, the required resolution lies just within the specifications of our quadrupole
analyzer. The series of peaks in Figure 11, middle, due to
pure sulfur clusters is very strong. The unusual strength of
peaks corresponding to S& is once again noteworthy.
However, the strongest peaks in the spectrum belong to the
series [CsSsn]+.Apparently, only one Cs atom is bonded to
each sulfur cluster. Presumably, the positive charge on
each cluster tends to be localized on the Cs atom. Removal
of even a lone pair electron from a sulfur ring apparently
leads to considerable fragmentation (see Section 3.2.1). A
sulfur cluster containing one Cs atom, on the other hand,
can be ionized with only a small amount of fragmentation.
This is reflected in the mass spectra by the presence of a
clear maximum in the series of peaks at [CsSsn]+ rather
than a step. Presumably, Cs is located on the central axis
of a stack of S8 rings and is bound to the rings through a
point charge-induced dipole electrostatic interaction.
One might expect that by increasing the partial pressure
of Cs vapor, additional metal atoms would be incorporated into the Ssnclusters. But this is not what happens
(Fig. 11, bottom). An entirely new type of cluster appears,
in which the S8 rings are broken up into smaller chains
(S:- and S:- ions). We can gain insight into the structure
and bonding of polysulfide clusters by considering the results of investigations o n Bas, and Bas, crystals, which
contain the same polyatomic anions.f6'.621Bas, crystals are
made up of Ba2+ and S$- dianions. The exact structure
of this crystal is rather complicated, the lattice being monoclinic with four Bas, formula units per unit cell. However, if one considers an idealized crystal constructed by replacing the S:- ions by single anions located at the centers of the dianions, the picture simplifies considerably.
The idealized crystal has a slightly distorted rock salt structure: each Ba2+ ion is surrounded by six S$- units and
vice versa. Apparently, the bonding between Ba2+ and
S$- is essentially ionic. The same conclusion can be drawn
from the results of investigations on Bas, .f611 This crystal is
tetragonal, each unit cell containing two formula units.
The sulfur is solely in the form of trisulfide units with an
angle of 114.9" and an S-S bond length of 2.076
However, the essentially ionic nature of the bonding between
Ba2+ and S:- is revealed by the observation that the two
units are arranged in a slightly distorted CsCl type structure.
3.2.3. Cesium Sulfide and Subsulfide Clusters
Increasing the Cs partial pressure still further results in
the formation of cesium sulfide clusters [Cs(Cs,S),]+ (see
Fig. 12, top). These clusters are built out of Cs+ and S2ions. No strong intensity anomalies were observed for
clusters with n = 1-6. The possible structure of these sulfides will be discussed below in connection with cesium
oxide clusters for which explicit calculations have been
made (see Section 3.4).
Fig. 12. Mass spectrum of cesium:cesium sull'lde cluster5 (composed ol c's
and 5'- ions) (top) and of cesium/cesium subsulfide clusters (below). The
mass peaks due to [Cs,S]+ clusters (connected) alternate in intensity (bottom).
If sulfur is evaporated at a very low oven temperature
(53 "C), it is possible to produce cesium-rich subsulfide
clusters (see Fig. 12, bottom). In the mass spectrum the
peaks of the pure Cs clusters are each followed by an intense cesium sulfide peak (which are joined by lines for
clarity). Exactly halfway between each Cs; and [Cs,S]+
peak, additional weaker peaks appear which are due partly
to cesium oxide clusters and partly to doubly ionized cesium sulfide clusters. The intensities of the Cs peaks alternate and that of [Cs6S]+is particularly weak.
3.3. The Cesium Chloride and Rubidium Chloride Systems
Alkali clusters have been intensively studied both experimentally and t h e ~ r e t i c a l l y . ' ~In~ 'the experiments carAngew. Chem. Inr. Ed. Engl. 2S 11986) 197-21 1
ried out until now a solid salt was used as the source for
the production of cluster^."^-^^.^^^ By using cesium metal
and gaseous chlorine we are able to study Cs-CI clusters
deviating strongly from the normal stoichiometry.
3.3.1. Cesium Subchloride Clusters
The relative yields of clusters formed when only a small
amount of chlorine gas is introduced into the system is
shown in Figure 13. The top curve indicates that if only
one CI atom is incorporated into the cluster, mass peaks
corresponding to [Cs2Cl]+, [Cs4CI]+,[Cs,CI]+, [Cs,CI]+,
etc., are particularly strong. However, if two C1 atoms are
incorporated into the cluster, an odd number of Cs atoms
are preferred, i. e., the peaks [Cs3Cl2]', [Cs5CIz]+,
etc., are strong. Inspection of the entire series of
curves in Figure 13 reveals that, if the number of Cs atoms
2 4 6 81012
Fig 13. I'he yield of cesium subchloride clusters formed by quenching Cs
vapor in a mixture of He and CI2. Noteworthy is the vertical and horizontal
alternation in the amount of cluster formed. The filled circles correspond to
clusters containing ions with rare gas electronic configurations.
plus the number of CI atoms is odd, the peak in the mass
spectrum is strong. This result can be understood if all
electrons are required to occur in pairs. Each Cs atom and
each CI atom has one unpaired electron. Therefore, the total number of atoms must be odd, since one electron is removed upon ionization. This effect has already been observed for pure alkali metal c l ~ s t e r s . The
[ ~ ~rule
~ ~ can
~ ~ be
stated more generally; a highly stable cluster, either charged
or neutral. must contain only paired electrons. The same
rule will be seen to apply also to oxide, sulfide, and phosphide clusters.
3.3.2. Rubidium Chloride Clusters
As the partial pressure of chlorine is increased, the cluster mass spectrum simplifies considerably. A series of very
strong peaks emerges corresponding to clusters with the
composition [M(MX),]+. Because of this simplification in
the spectrum, a lighter altxli metal can be used without
causing confusion due to overlapping peaks. Figure 14
shows the results for the Rb-CI system for which mass
Anyew. Chem. Int. Ed. Engl. 25 (1986) 197-211
Fig. 14. Mass spectrum o1 rubidium chloride clublerb formed by qurtiChing
Rb vapor in a mixture of He and CI2. Noteworthy is the intense peak
[Rb(RbCI),,]' and the relatively high intensities in the [(RbCI),]+ series
( n = 3 , 6 , 9 , 12,and IS).
peaks can be observed for clusters containing u p to 30
The peaks for the clusters [Rb(RbCl),]+ with n equal to
6, 9, and 13 are particularly strong. A second series of
peaks, each peak occurring exactly halfway between peaks
of the principal series, is due to doubly ionized clusters
[Rb2(RbC1)JZ+.A third series corresponds to clusters with
composition [(RbCI),]'. Peaks in this series stand out
strongly for x=3, 6, 9, 12, and 15.
Clusters in the principal series d o not contain equal
numbers of rubidium and chloride atoms. This fact reflects
the strongly ionic character of the clusters and can be explained as follows: Mass selection is possible only if a
cluster is charged. If all electrons in the cluster are localized and paired, the electrons most easily removed belong
to the chloride ions. After ionization, the neutral chlorine
atom is bonded to the remaining ions in the cluster only
through a monopole-induced dipole interaction. This interaction is weak compared with the large amount of energy that is converted into vibrational motion during the
ionization. Therefore, the neutral chlorine atom is lost, resulting in the formation of a cluster with composition
The intensity of a given line in a mass spectrum is influenced by many factors; the stability of the neutral clusters entering the ionization chamber, the cross section for
ionization, the probability of fragmentation, and finally
the stability of the ionized products. The relative stability
of clusters can be determined by minimizing the total energy, which is given by the sum of all two-body interactions.146. 471
V,J =
i-A exp( - r z J / p )
The symmetries of the most stable configurations depend on the form of the two-body interaction.[631Nonetheless, Figure 15 gives a fairly good representation of the
stable forms of alkali halide clusters [MnXn-,]+.
The calculated energy per MX unit for the most stable
form of RbCl clusters with rock salt structure, ranging in
size from 6 to 3 2 atoms, is shown in Figure 16. The binding
energy for neutral clusters is particularly large for n = 6, 9,
12, and 15, because stacked six-membered rings and sixatom rectangles are the favored structures. The curve for
3.4. The Cesium-Oxygen System
The elements cesium and oxygen combine to form a bewildering array of crystalline compounds (Cs,O, Cs40,
C s 2 0 2 ,Cs,03, CsO, , and G O 3 ) .The structures of
the suboxides Cs70, Cs,O, and C s I I 0 3are particularly intersting and unusual.[29'Crystallographic investigations indicate that these compounds are composed of C s I I 0 3clusters having strongly ionic character.165-681However, the
bonding between the clusters is metallic. This bonding
model is supported by comparison of the interatomic distances in the suboxides with the corresponding distances
in normal oxides and pure metals. The metal-oxygen distances in the suboxide clusters are nearly the sum of the
ionic radii, whereas the metal-metal distances between
clusters are nearly those found in the pure alkali metal.
The superoxides owe their formation to the ability of oxygen to appear as O ; - , OF, or 0; ions.'6x8'Cesium oxide
clusters of all possible compositions were produced by
evaporating cesium metal into a He-0, gas mixture containing a n increasing amount of oxygen.
3.4. I . Cesium Clusters
Almost no clusters could be detected in the mass spectrometer if oxygen-free helium was used as the quenching
gas. Upon addition of 0.01% oxygen
mbar), the cluster signal rose three orders of magnitude (Fig. 17). The intensity of the peaks of the pure Cs clusters also increased
Fig. 15. Calculated stable configurations of alkali halide clusters
I, l
charged clusters with composition [Rb,CI,_,J+ is rather
smooth except for [Rb14C1,3]+,which appears to have
more than the usual binding energy. The reason for this is
quickly seen by looking at the structure of this cluster (Fig.
16). [Rbl4ClI3]+is highly symmetric, resembling a portion
of the rock salt structure.
-f 6.0
5.5 -
nFig. 16. Ihiiding energy per
charged and neutral clusters.
800 1000
Fig. 17. Mass spectrum of a mixture 01lightly oxidired Ca clusters. The mass
peaks of the pure cesium clusters Cs,' and Csi+ have been labeled explicitly. Each subsequent peak indicates the addition of one or more oxygen
u n i t ( o r the most stable forms
of positively
dramatically, indicating that these clusters may be fragments created during the ionization process. The first peak
in every group corresponds to a pure Cs cluster containing
the indicated number of atoms. The following, closely
spaced peaks correspond to clusters containing one or two
additional oxygen atoms. The intensities of the peaks of
the pure metal clusters alternate. Peaks corresponding to
clusters containing an odd number of Cs atoms are stronger. Since the clusters are positively charged, an odd number of atoms means a n even number of valence electrons.
Apparently, Cs clusters containing paired electrons have
an enhanced stability.
After the group marked n =9, new peaks appear exactly
halfway between the pure Cs peaks. This new series correAngew. Chem Int. Ed. Engi. 25 (1986) 197-211
sponds to doubly ionized cesium and cesium oxide clusters. For large clusters the individual peaks in each group
have merged together. This is not due to a worsening of the
mass resolution at high masses but to the newly emerging
doubly ionized oxides, which are now separated by only 8
The intensity of the doubly ionized, pure metal clusters
rises sharply at n = 19. Configuration i n t e r a ~ t i o n ' ~ and
density f ~ n c t i o n a l ' calculations
~ ~ - ~ ~ ~ have shown that small
metal clusters d o not necessarily have closed-packed structures. Still it is worth pointing out that there exist two
highly symmetric arrangements of 19 spheres/'] a large octahedral structure and a double icosahedron.
ICS(CS,O), I +
Fig. 19. Mass spectrum 01 il inixture 0 1 cesium oxide clusters formed by
quenching Cs vapor in a mixture of He and O2 gas.
3.4.3. Cesium Oxide Clusters
3.4.2. Cesium Suboxide Clusters
Increasing the amount of oxygen in the He buffer gas to
0.1% results in the formation of metal-rich suboxide clusters (Fig. 18). In order to observe irregularities in the intensities more easily, it is convenient to make comparisons between clusters containing the same number of oxygen
atoms. The peak corresponding to the cluster [Cs60]+ is
particularly weak.
If the concentration of 0, in helium is raised to O.6%, a
mixture of clusters is obtained, the mass spectrum of which
is shown in Figure 19. Certain clusters containing an odd
number of cesium atoms are represented particularly
strongly. These clusters have the composition
[Cs(Cs,O),]+, two Cs atoms for each oxygen and one extra
Cs atom for the positive charge. Each of the ions in these
clusters has a rare gas electronic configuration. In this respect they might he regarded as normal oxides. The distribution of charge between the ions is therefore unambiguous, namely, Cs' and 02-.Therefore, Equation (a) may
be used to calcuIate the structures of the stable configurations. The parameters, A=4000 eV and l/p=3.03 A-',
were chosen so that the C s - 0 distance in [Cs502]+is that
observed for crystalline CszO.
[Cs,O]' has only one stable configuration, a planar
structure with a binding energy of 119.46 eV with respect
to dissociation into ions. The dimer has two stable configurations. The symmetric dimer with a threefold symmetry
axis (Fig. 20, top right) has 0.6 eV more binding energy
than the unsymmetric dimer. Larger clusters with a threefold axis are also energetically favored over less symmetric
structures. The cluster [Cs703]+consists of a C s 3 0 3 ring
ntig. i x . C omposition of'
mixture of cesium-rich suboxide clusters (see
The strongest peak in each series corresponds to the normal oxide [Cs(Cs,O),]' (solid circles in Fig. 18). As more
cesium atoms are added to the normal oxide cluster, the
peak intensities tend to alternate. However, the alternation
is in the horizontal direction (Cs) only and not in the vertical direction (anions) as was the case for the halides (Fig.
13). The different behavior of the oxides and halides supports, nonetheless, the same rule (Section 3.3.1): stable
clusters prefer to have paired electrons. Strong peaks are
found not only for [Cs,O]+, [Cs,O]', [Cs,O]+, etc., but
also for [Cs30z]+,[CssOz]+,[Cs702]+,etc.
Electron correlation calculations for Li40 offer some insight into the bonding of suboxide cluster^.^;'^."^ The most
stable form, even for the positive ion, seems to have tetrahedral geometry. Although the central oxygen atom acquires a negative charge of 0.87, Li-Li bonding makes a
large contribution to the total energy.
Angrn,. Chem. Int. Ed. Engl. 25 (1986) 197-211
38 29eV
38 90 eV
57 L6 eV
5813 eV
76 2 5 eV
7731 eV
Fig. 20. The most stable configurations of (C's:,, ,O,,] ' clu\ter\ contatning
ions with rare gas electronic configurations. The total binding energy is given
below each structure.
along with one central and three terminal Cs atoms. The
most stable form of [Csg04]+has 77.31 eV of binding energy, 1 eV more than its closest competitor.
3.4.4. Cesium Superoxide CIusters
The character of the mass spectrum changes again as the
oxygen concentration is increased to about 40% (Fig. 21).
nected the peaks corresponding to clusters containing
eight atoms, starting with Inx and ending with Pb8. Clusters containing an odd number of In atoms, i. e., containing
an even number of electrons (in the ion), appear to be particularly stable. [Pb,In6] is an exception.
FIE. :I. Muss spectrum ofil mixture 01 cesium oxide and cesium hyperoxide
clusters. Each group of peaks begins with clusters containing 0 2 -ions, goes
through a maximum for clusters containing 0:- ions, and ceases abruptly
at clusters containing 0, ions.
In addition to clusters containing 02-and 0:- ions, the
which contain 0; ions,
oxygen-rich clusters [Cs(CsO,),] +,
are formed. Thus, as expected, clusters containing an even
number of oxygen atoms show u p more strongly in the
mass spectrum. Although no calculations are available for
the structure of large superoxide clusters, LCAO-MO S C F
calculations indicate that Li20z is planar with D2,,symmetry.17'l
3.5. Lead-Indium Clusters
If the elements in a heteronuclear cluster are chemically
equivalent and the vapors of the two elements are mixed
together in a ratio of about 1:1, then clusters having all
possible compositions should appear in the mass spectrum. The probability of finding a cluster with a given size
and composition should follow a binomial distribution.
Lead and indium have nearly the same electronegativity
and mix very well; the mass spectrum of a mixture of clusters is correspondingly complicated (Fig. 22). Rather than
trying to label all peaks in this spectrum, we have con-
3.6. Cesium-Lead Clusters
When two metals are mixed together, the properties of
the mixture usually d o not change continuously with con~entration.['~
I n the solid state the discontinuities are due
to the formation of well-defined intermetallic compounds.[61 Strong evidence exists that such compounds
form even in the liquid ~tate.['~.'*~
Here we present evidence for the existence of analogous heteronuclear clusters
in the vapor phase.
Intermetallic compounds are particularly stable if the
two metals are characterized by a large electronegativity
difference. A classic example is C S A U . ~When
~ ~ ~Cs
~ 'and
Au are mixed in the ratio 1:1, a compound is formed with
an ionic character similar to that of CsCI. I n fact, CsAu
crystallizes in the CsCl structure. Even though Cs and Au,
separately, are excellent electrical conductors, the 1 :I mixture is nonmetallic in both the liquid and solid phases.
The Cs-Pb system is particularly interesting because of
the large electronegativity difference between its two components. In an early study of a solution of this alloy in
liquid NH3, Zintl and c o - ~ o r k e r s [ came
to the conclusion
that there was polar bonding between the Pb$- anions
and the alkali metal ions. The obvious question is therefore
whether evidence can be found in cluster mass spectra for
the existence of Pb9 groups and for charge transfer between Cs and Pb. A mass spectrum of a mixture of Cs-Pb
clusters is shown in Figure 23. Pb9 is just light enough to
400 600
800 I000 1200 1400 1600 1800 2000
Fig. 23. Mass spectrum of a mixture of Cs-f'b dusters. Peakz corresponding
to [Cs3Pb2]+and [Cs,Pb5]+ are particularly strong.
1200 1400 1600
mlz A
Fig. 22. Masa spectrum 01.d mixture of Pb-In clu\ter\ The peaks of the pure
Pb clusters have been labeled (3.0; 4,O; 5,O; etc.). Each immedlately follow-
ing peak corresponds to the removal of one Pb atom and the addition of two
In atoms. The peaks corresponding to eight atom clusters (0,s; 1,7; 2,6; etc.)
have been connected.
fall within the mass region (1-2000 amu) accessible with
our mass spectrometer. However, the cluster we are looking for is [Cs(Cs,Pb,)]+, since, in addition to nine Pb
atoms, four C s + ions are needed to compensate the charge
on Pb$-, and one additional Cs+ is required to provide
the overall positive charge on the cluster. This cluster has a
mass of 2529 amu, well above the mass limit. We solved
this problem by investigating a system with lighter elements (see Section 3.7). First, however, there are several
features of the Cs-Pb mass spectra that must be pointed
Angew. Chem. Inr. Ed. Engl. 25 (1986) 197-211
out. Two of the strongest peaks in the spectrum correspond to the clusters [Cs3Pb2]+ and [Cs3PbS]+.As discussed below, evidence exists'"I that Pb, is a very stable
polyanion and has the exact charge required to explain the
mass peak, i.e., Pbz-.
Although Zintl was able to identify many polyanions in
solution, these ions did not prove to be sufficiently stable
to act as building blocks for the construction of crystals
when the solvent was evaporated. This problem was solved
by Corbett and c o - ~ o r k e r s [ 'who
~ ~ stabilized the sodium
salts of the polyanions in crystals by complexation with
4,7,13,16,2 1,24-hexaoxa-1,1O-diazatricyclo[8.8.8]hexacosane (2,2,2-crypt). In this way they were not only able to
grow the salt [2,2,2-crypt Na]:[Pb5]2- but also to determine the structure of the P:- polyanion (trigonal bipyramidal).
Thus, the strongest peak in the mass spectrum (for a
cluster containing more than two atoms) corresponds to
[Cs3Pb5]+.The structure can probably be described as a
cluster within a cluster; that is, a covalently bonded, trigonal bipyramid of five Pb atoms ionically bonded to three,
symmetrically placed, outer Cs ions.
and [Cs,Sn,]+ appear to be particularly stable (intense
mass peaks). The first cluster type was already observed in
the Cs-Pb system; the last cluster was expected from earlier ~ o r k . ' ~ , ' ~ ~
The cluster [Cs,Sn9]+ supports the existence of the polyanion Sn;-. Although this polyanion has never been observed for Sn, a Ge analogue has been stabilized[s31as part
of a complicated solid, [(2,2,2-crypt K)6 Gels.2.5 en],
which contains Ge:- and Ge;- anions. The structure of
Ge;- is probably similar to that of SnG- (Fig. 25).
3.7. Cesium-Tin Clusters
The Cs-Pb system has the advantage that the small number of isotopes present results in sharp mass peaks. However, Pb is so heavy that the stability of two important clusters, the Zintl cluster [Cs5Pb9]+and the cluster [CssPblo]+,
cannot be checked with our spectrometer. What is the significance of this second cluster? We stated in the introduction that two types of information concerning stability can
be obtained from the mass spectra of clusters. A single, intense, isolated mass peak indicates a highly stable cluster;
a periodicity in the mass spectrum means that this cluster
can be used as a building block to construct larger cl'usters.
Since [Cs(Cs2Pb5)] is stable, the question arises whether
the next cluster in the series [Cs(Cs2Pb5),]+ is also stable.
In order to determine the stability of such clusters we turn
to the analogous system containing the lighter element Sn.
This change has the disadvantage, however, that, because
Sn has many more isotopes, the mass peaks are broader. A
mass spectrum of a mixture of Cs-Sn clusters is shown in
Figure 24. Although the mass peaks are broad, pure Sn
clusters containing as many as ten atoms can be identified.
Among the heteronuclear clusters, [CsiSn,] +, [Cs3Sn9]+,
Fig. 25. The structure of several polyanions (empty circlea) I24 ?hi .ind [he
probable distribution of alkali metal ions (filled circles) in the corresponding
Cs-Sn clusters.
Not found in the mass spectrum of Cs-Sn clusters (Fig.
24) is a strong peak corresponding to [ C S ( C S ~ S ~ ~That
is, the Snz- polyanion does not act as a building block for
larger clusters and is therefore less likely to be found as a
unit in pure crystals.
Increasing the Cs partial pressure results in the cluster
mass spectrum shown in Figure 26. All peaks due to pure
Sn clusters are absent. Two series of peaks emerge-one for
clusters containing three Cs atoms and the other for clusters
containing five Cs atoms. This selectivity reflects the
strong tendency to form clusters with paired electrons
only. Sn atoms contain an even number of valence electrons, Cs atoms an odd number. However, one Cs electron
is ejected on cluster ionization. Therefore, an odd number
of Cs atoms leads to an even number of electrons in the
cluster ion.
1000 1200 1400 1600 1800 2000
Fig. 24. M a s s a p w t r u r n 01 d mixture 01 C Sn clusters. The peaks are broad
due to the large number of Sn isotopes. The clusters [Cs,Sn5]+ and [CssSnq]+
are particularly stable.
Angew. Chem. In!. Ed. Engl. 25 (1986) 197-211
1000 1200 1400
Fig. 26. Mass spectrum of a mixture 01. C
1800 2000
Among clusters having a higher Cs content, [Cs5Sn4] is
unusually stable. This may indicate the presence of the polyanion Sni-. Since this anion is isoelectronic with p,, it
would be expected to have a tetrahedral structure. In fact,
tetrahedral G e i - units have been observed in lithium and
sodium germanide ~ r y s t a l s . [ ~ ~[Cs5Sn4]+
could also be
described as [ C S ( C S ~ S ~ ~The
) ~ ] mass
+ . peak corresponding
to the first member of this sequence, [Cs(CszSn2)]', is also
served in this case are [K(K2P4),]+. Also easily identified
are the mixed clusters [K(K2P4)n(K3P7)m]+.
The polyanion
P2- may have the butterfly configuration (Fig. 28), already
observed'''' in R2P4 ( R = (Me3Si),N, 2,4,6-tBu3C6H2).
3.8. Indium-Phosphorus Clusters
InP is a good semiconductor. However, the InP molecule is not found in the vapor phase. O n evaporation, InP
dissociates into In atoms and P4 and P2 molecules. Therefore, we would not have been surprised to find that In and
P d o not react in the vapor phase-but they do. A mass
spectrum of the mixture of clusters is shown in Figure 27.
The shaded peaks correspond to pure In clusters. The
peaks immediately following each shaded peak correspond
to clusters containing one or two P atoms. Clusters containing three P atoms are also present but they are one order of magnitude weaker. In Figure 27 we have joined with
a short vertical bar the peaks of clusters containing one o r
two P atoms but the same number of In atoms. The peak
corresponding to [ln,P]+ is stronger than that of [In,P,]+,
whereas the peak identified as [In,P]+ is weaker than that
of [In,P,]'. In general, [In,P]+ clusters are more stable for
even values of x and [In,PZ]+ clusters are more stable for
odd values of x. This is another manifestation of the rule
that stable clusters prefer to have an even number of electrons. [In,P]+ is an exception to this rule. Two other clusters that stand out from the rest are [In,P,]+ and
1800 2000
Fig 27. Md\s spectrum o l d mixture o f In-P clusters formed by combining
red phosphorus vapor (390 "C) with indium vapor (970 "C). Black peaks correspond to pure In clusters. Each subsequent peak corresponds to the addition of one more P atom. Clusters containing an odd number of atoms tend
to be more stable.
3.9. Potassium-Phosphorus Clusters
A mass spectrum of clusters formed by quenching the
mixed vapors of red phosphorus and potassium is shown
in Figure 28. Analysis of this spectrum reveals a double
periodicity; that is, two highly stable building blocks exist.
One series corresponds to the clusters [K(K,P,),]+. P:- is
polyanion of phosphorus occurring in seva
eral compounds, including K3P7.The other series indicates
the existence of a new polyanion, P:-. The clusters ob208
Fig. 28. Mass spectrum of a mixture of K - P clusters formed by cornhmng
potassium vapor (230 "C) with red phosphorus vapor (390 "C) in cold He gas.
The clusters contain the phosphorus polyanions P:- and Pi-.
3.10. Clusters Prepared from Elements of the 5th and 6th
Main Groups
Arsenic and sulfur combine to form a rich variety of
compounds. As4S4 (realgar) is composed of eight-atom
molecules weakly bonded to one another by van der Waals
forces. As,& has a polymeric layer structure (orpiment).
Finally, molten As-S can be quenched to form a glass. One
motivation for studying the relative stability of As-S clusters is the identification of other highly stable building
blocks, which could lead to the synthesis of new compounds. Moreover, information concerning the stability of
cluster ions in the vapor phase could shed light on the
structure of glasses.
Before examining the results of experiment, it is useful
to first consider qualitatively what types of clusters might
be expected in quenched vapors containing various As:S
ratios. Pure arsenic vapor is known to contain As, molecules. On quenching the vapor, these molecules would presumably condense into As4" clusters composed of tetrahedral units weakly bonded to one another. The first sulfur
atoms to be incorporated into the As, tetrahedral unit can
be expected to bridge As atoms. This will be possible until
all six edges of the tetrahedron are occupied by S atoms.
High stability is expected for the symmetric molecules
As4S3,As,S,, and As4& (Fig. 29). Pure sulfur has two crystalline forms, which consist of ordered arrays of Ss rings.
These rings can persist even into the melt. Therefore, clusters composed of Ss rings weakly bonded together would
not be unexpected. On the other hand, sulfur also forms
polymer chains. Addition of a small amount of As to the
vapor could result in the linking of rings and chains together. Two of the bonds to arsenic are required in order to
incorporate the As atom into the ring. The remaining valence is available for branching (Fig. 29, top right), or it
can form a n As-As bond with a second arsenic atom in the
same ring o r in another sulfur ring.
Before analyzing the relatively complex mass spectra of
As-S clusters, it is instructive to first consider the spectra
of two seemingly closely related materials, phosphorus sulAngew. Chem. Int. Ed. Engl. 25 (1986) 197-211
The mass spectrum of clusters formed by quenching the
vapor of As203 in helium is also easy to interpret (Fig.
31).[8y1The mass peaks of the clusters [As,O,]: (n = I , 2,
3, ...) are strongest. As406 is a building block in two mod-
1000 1200 14C
Fig. 31. Mass spectrum of cIusler\ formed h j quenching 01 A a 2 0 , vapor.
big. 2Y. Some probable dructures of As& molecules and clusters. Filled
circles are As atoms, empty circles are S atoms.
fides and arsenic oxides. The mass spectrum of a mixture
of clusters formed by quenching the vapor of P4S3 in helium gas is shown in Figure 30. The analysis of this spectrum is made difficult by the similarity of the atomic
masses of the two component atoms, 31Pand 32S.In principle, we can determine from a low-resolution mass spectrum only the total number of atoms in a cluster. Each
big. 30 Mass spectrum oTclusters lbrmed by quenching 0 1 P S I vapor.
strong line in the spectrum is separated from the other
strong lines by a distance corresponding to seven atoms.
Since P4S3 is a stable molecule,~s81the strong lines most
likely correspond to the clusters [P4S3]: (n= 1-9). The
next strongest lines occur exactly halfway between the
strongest lines and are, therefore, probably due to the doubly ionized clusters [P4S3]:+. Double ionization without
fragmentation appears to be more probable in large clusters, where the excess positive charge can occupy a greater
volume, thus reducing the energy of the species. The
weaker lines correspond to fragments. The most important
feature of the mass spectrum of the P-S clusters can be
seen at first glance: it is extremely simple. Singly and doubly charged clusters of only one type are observed. These
clusters are constructed from P4S3 building blocks. Presumably, these units are only weakly bonded to one another, as is the case in the molecular crystal. This simplicity is in sharp contrast to the mass spectrum of As-S clusters (see below).
Angew Chem Inr. Ed. Engl 25 (1986) 197-211
ifications of arsenic oxide, arsenolite and claudetite. The
As406 units are weakly bonded to one another to form
cubic and monoclinic structures in the crystal. Since the
most intense lines in the cluster mass spectrum belong to
As4@,, AssOI2, AS,^^]^, AsIbOZ4,
and AS^^^^^, it is clear
that stable As406 units are also building blocks in the formation of clusters. The next strongest peaks occur exactly
halfway between the strongest peaks and are therefore
probably due to either [As40&+ or [AszO3];. This ambiguity did not exist for the corresponding peaks of the P-S
clusters. In that case they were identified as doubly ionized
Figure 32 shows the mass spectrum of clusters formed
by the evaporation of As2S3 glass.[8y1The spectrum contains many lines, but all can be assigned to [As,S,]+ clusters. The peaks corresponding to n = 4 , 6 , 8, and 10 have
been labeled explicitly. The remaining peaks are due to
clusters with odd values of n. Particularly strong lines are
observed, for example for [As4S3]+, [As4S4]+, [ASd&]+,
and [ A s ~ ~ S , ~It]would
not be proper
[As6S9]+, [As8SI3]+,
to conclude that these clusters necessarily occur in the
beam of neutral clusters, because relatively high energy
(70-eV) electrons have been used for ionization. This results in high sensitivity but also in a high degree of fragmentation. It is valid to assume, however, that a strong line
in the mass spectrum indicates the existence of a highly
stable cluster of the same mass, be it neutral cluster or ionized fragment. The fragmentation, far from being a hindrance, allows us to examine the stability of a larger variety of clusters than is found in the beam of neutral clusters.
Fig. 3 2 . Mass spectrum
clu~terhlornicd by quenching As&% iapor
Although many As-S clusters can be identified as being
highly stable, only As& is observed to act as a building
block in the formation of larger van der Waals clusters.
Many of the other clusters, such as [As7SI3J+are probably
stable only in the ionic form and are therefore not suitable
as building units in the absence of charge compensating
anions. On the other hand, these stable ions could be of
interest in the synthesis of ionic cluster compounds.
As2S3condenses into a glassy state. As,S, glass prepared
from the melt is thought to contain almost exclusively AsS bonds.[”l As2& condensed from the vapor phase, o n the
other hand, seems to contain a large fraction of homonuclear bonds. Assuming that As,& glass has the same local
composition as these clusters, we can draw the following
conclusions: The molecule As4S6 plays no important role
in the structure of As& glass. Our mass spectra suggest
that the first stable building block with composition
As2&, is the molecule As,&. In addition, excess sulfur
does not result in the formation of S-S bonds but rather in
fourfold-coordination of As atoms by terminal sulfur
4. Concluding Remarks
Not all elements are equally suited for the type of investigation reported in this article. The ideal element has the
following properties: a high vapor pressure at low temperature; only one isotope; high reactivity; not too large but
not too small atomic mass. If a n element is too heavy, large
clusters cannot be observed in the mass range available to
us (0-2000 amu). If the element is too light, the masses of
the reaction products overlap one another, making it difficult to assign mass peaks.
It would appear from these findings that a strong peak
in a mass spectrum usually reflects a high stability of the
corresponding charged cluster. This is true not only for
cluster ions, for example [Rb,,Cl,,]+, but also for the more
covalently bonded suboxides and subhalides for which the
total electron spin seems to play a decisive role. The question arises to what extent the stability of the neutral parent
cluster influences the mass spectra. The results for the pure
sulfur clusters and for As-0, As-S, P-0, and P-S clusters
indicate that very stable neutral clusters (S8, Asq06, P4S3)
can indeed be observed as positive ions by mass spectroscopy even though the removal of an electron decreases
their stability. However, these “neutral clusters’ are so
strongly bonded that they appear in the solid, liquid, and
vapor phases and are therefore more appropriately called
molecules. In summary, neutral clusters composed of exceptionally highly stable units (molecules) can appear as
strong peaks in mass spectra. However, in general, the
character of a mass spectrum is determined by the stability
of charged fragments.
Although the stable clusters M,Oz and M 1 , 0 3found in
cesium and rubidium suboxide crystals can be thought of
as being constructed from face-sharing M 6 0 octahedra,
our mass spectrometric study shows that the clusters
[M60]+ and [M6S]+ are particularly unstable. Therefore,
this cluster probably does not act as a building block for
the growth of larger clusters.
An important finding of our investigations is the rule
that stable clusters contain an even number of electrons.
This rule is particularly valid for subhalide and suboxide
clusters and indicates that a strong covalent contribution is
made to the bonding of metal-rich clusters. The normal
halides, for which each ion has a rare gas electronic configuration, can be well described by a purely ionic model of
the bonding.
Mass spectrometry of clusters formed by the reaction
and quenching of elementary vapors should prove to be of
value in the search for new compounds. The composition
of the clusters can be changed quickly and continuously by
adusting the oven temperature of each of the elements. The
relative stability of each cluster can be immediately determined from the mass spectrum. However, it is important to
remember that it is usually the stability of a charged fragment that is being measured.
Mass spectra are capable of indicating two different degrees of cluster stability. An isolated, intense mass peak
indicates a high stability for a particular cluster. A periodic
appearance of intense peaks indicates that a cluster is stable not only as an isolated unit but can be used as a building block in the construction of larger clusters. It should be
possible to synthesize solids from the same unit. The two
kinds of stability are illustrated by clusters containing the
two polyanions Sn:- and Pz-. Although [Cs(Cs,Sn,)]+ is
stable as an isolated cluster, it does not appear to have a
strong tendency to build larger units [Cs(Cs2Sn5),]+. The
tetraphosphorus dianion does occur in the sequence of
mass peaks [K(K2P4),J+ and is therefore a candidate for a
new solid compound.
Many stimulating discussions with H . G . von Schnering
and A. Simon are gratefully acknowledged.
Received: April 23, 1985 [A 568 IE]
Geman version: Angew. Chem. 98 (1986) 197
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