Chemical Physics 40 (1979) 145-152 @ North-Holland Pub!ishing Company

MATRIX ISOLATION/AGGREGATION OF SODIUM ATOMS AND MOLECULES FORMED IN A SUPERSONIC NOZZLE BEAIM

Manfred HOFMANN, Samuel LEUTWYLER Insriczccfiir Anorgunische, Anolytische rrnd Physikulische Chemie der Uniaersitiir Bern,

CH-3000 Bern 9. Switzerland

and

Wilfried SCHULZE

Fritz-Hnber-Institut der Mas-PlunckGesellschaft, D-1000 Berlin 33, Germany

Received 13 November 1978

Preformed sodium molecules and atoms from a supersonic nozzle beam were deposited in krypton matrices on a sapphire window at 4 K. Matrix absorption spectroscopy was performed in the wavelength range 400-800 nm using a double-beam arrangement. Simultaneously the relative concentrations of molecules and atoms in the molecular beam were determined by mass spectrometry. Matrix/guest ratios were varied between 150: I and 30 000 : 1 and a lower bound of -20 000 : I was found necessary to prevent matrix aggregation processes. The atomic transitions were identified at around 590 nm and absorption bands at 655 nm and 473 nm assigned to the Na2 A + X and B .- X transitions, respectively. Further bands of Na, and Na, appear between 630 and 780 nm in partial agreement with the gas phase spectra. Spectroscopic changes during matrix annealing indicate growth of sodium aggregates via small clusters. Correlation of the optical and mass spectrometric measurements proves that preformed Na, molecules can be matrix isolated as such.

1. Introduction

Alkali atoms in rare gas matrices have been repeatedly studied by various investigators from the early days of matrix spectroscopy up to the present [I&]. Most experiments were concerned with the spectral shifts and splittings of the lowest resonance absorption line (n P,,,.,,, + n S,,,) of the isolated alkali atom induced by matrix effects. In all of these experiments the metal was vaporized at low pressures in a Knudsen cell and deposited in almost purely monoatomic form in the matrix, the equili- brium vapour pressure of the alkali dimers being usually < 1% as compared to the atom at the temperatures used, the vapour concentration of larger molecules being negligible. Nevertheless, distinct dimer absorption bands were found and the work of Andrews and Pimentel[3] has shown that

very high M/R ratios and low condensation temperatures are needed to effectively isolate the alkali atoms.

By adiabatic expansion of alkali metal vapours at high source pressures (50-700 Torr) it is possible to generate intense supersonic alkali beams containing a high proportion of dimers (30-40 %) and a noticeable concentration of trimers and higher polymers (0.2-I %), which can be studied by mass- spectrometry and laser spectroscopy [7-9, 131.

On the other hand, careful annealing of metal-

doped rare gas matrices leads to a weakening of the atomic absorption lines with new lines and bands belonging to aggregates appearing at the same time. In favourable cases these new abiorptions can be plausibly assigned to distinct Me, species.

We have recently combined the molecular beam clustering method with the low temperature matrix

145

146 Al. Hofntmtn et al./h~fatrix isolution ojsodiwn utom and molecules

technique, thereby isolating a mixture of small metal clusters from the beam in amounts large enough to be detected by normal absorption spectroscopy. Sodium atoms and molecules from a supersonic nozzle beam were deposited in krypton matrices on a sapphire target at 4 K and absorption spectra in the w&length range 400-800 nm were measured using a dual-beam arrangement.

* Most of the work reported here is centered on the following three problems:

(1) The low temperature spectra of sodium measured by different authors are not completely identical; indeed some of the data is contradictory. We have therefore remeasured the absorption spectrum of the isolated Na atom, at the lowest condensation temperature possible using a very high M/R ratio.

(2) With the knowledge of operating parameters gained from the isolation of atoms, we deposited mixtures of atoms/molecules at different oven pressures and molecular concentrations. The appearing molecular absorptions can be partially correlated to the molecular concentrations in the beam, which were determined by mass spectrometry.

(3) The formation of higher clusters in the matrix by annealing and temperature cycling was studied starting either with isolated atoms or a mixture of atoms/molecules as deposited from the beam.

2. Experimental

Detailed descriptions of both the molecular beam apparatus and the liquid helium cryostat have been given e!sewhere [9, lo]. Fig. 1 shows a diagram of the experimental setup.

The sodium used was analytical grade (Merck) containing less than 0.01% of potassium. The stainless steel oven cartridge was loaded under a nitrogen atmosphere in a glove box. Depending on the molecular concentration required in the beam, the oven was heated to between 850 K and 1170 K (equivalent to source pressures between 30 and 1000 Torr). Relative concentrations of Na/Na,/Na,/Na, were measured with a quadrupole mass spectrometer using a 1000 W Hg/Xe high-pressure arc as photoionization light source.

Total beam intensity was measured using both a

55 166

r

_L 17 11

r r ?-I

0 Co Ch

Fig. 1. Schematic diagram of the apparatus: view from above. (0 = moleculltr beam oven, Co = collimating slits,

Ch = tuning-fork chopper. Q = quadrupole mass spectrometer, LT = Langmuir-Taylor detector. Cr = con- tinuous-flow cryostat with sapphire window, T = quartz crystal microbalance, L = halogen lamp (100 W). M = monochromator, P = photomultipliers (RCA 4832). (All distances in centimeters).

Langmuir-Taylor hot-wire detector employing a rhenium lilament positioned in front of the cryostat and a thin film thickness monitor of the quartz oscillator type (Kronos Model QM-311) mounted behind it. Normally the beam intensity was measured with the surface-ionization detector because it could be easily and reproducibly positioned in the beam. It was calibrated against the quartz oscillator during several experiments and good agreement was found if the detector efficiency was taken as 10 %. Total beam intensities at the cryostat window ranged between 4 x IO”-4 x 10” particles cm-’ s- l. The highest fluxes had to be reduced by introducing narrower collimating slits in the source chamber so as to be able to keep the M/R ratio high enough. Total matrix deposition times were between 3 and 12 min depending on beam flux. The beam intensity measurements are estimated to be accurate within + 5 %_

The matrix gas (krypton) was directed onto the sapphire window where it was condensed quantita- tively_ The gas flux was measured outside the vacuum chamber by making use of a capillary. It seems worthwhile mentioning that an increase of the residual pressure in the chamber above 10e6 Torr could only be observed for gas fluxes higher than z 7 x 10” s-l_ Thus even at the highest M/R values used in these experiments, the intensity of the metal beam was not reduced by scattering with the matrix gas. The uncertainties of the M/R ratios

are probably less than k 10 %_

The experimental wavelength resolution was 4.2 nm; the wavelength readout of the spectrometer was calibrated using mercury, sodium and neon

spectral reference lines.

The absorption spectra were hand digitzed, corrected for baseline slope and plotted using a desk computer/digitizer/plotter system. The overall

wavelength accuracy is &3 nm.

3. Results

3.1. Variatiotl of M/R

Earlier work has shown the prime importance of sufficiently high M/R ratios when trying to matrix

isolate alkali atoms [3]_ We have therefore carefully studied the concentration dependence of the

absorption spectra in order to be sure to reach dilutions necessary to completely isolate the species

present in the molecular beams. The results for

krypton matrices are shown in fig. 2. Care was taken to ensure closely similar beam conditions

(oven temperature, nozzle diametei) and beam intensity for this series of experiments. Beam parameters are listed in table 1.

The progressive changes from a completely featureless broad absorption band centered at 577.5 nm (hl : R = 150 : 1) to the clearly separated

atomic and molecular absorption bands at

M : R = 25700 : 1 show that high dilutions are

indeed necessary to keep the dopant species from aggregating during the deposition process. No further changes were observed at higher M : R ratios

as a comparison between the spectra for the two highest dilutions clearly demonstrates. All further work was therefore performed at M : R ratios of (25000-30000) : 1.

The strong central absorption band is assigned

to the atomic 2P,,,.,,2 c ‘S,,, transition_ At our experimental resolution the transition is split into two or three components centered at 585 nm, the

“blue” band at 574 nm and two red bands at 593

and 602.5 nm. The absorption bands at 655 nm and 473 nm are

definitely assigneable to the Naz (‘Z: + ‘E,‘) and

B t X (‘II, c ‘Cl) transitions. The maximum

1 LOO iO0 600

7001nmI *’ IC

Fi_g. 1. Concentration dependence of Na/Kr matrix spectra at 4.2 K. The respective M/R ratios are indicated in the ligure. The molecular beam parameters were kept as similar as possible (stagnation pressure = 1 IO-180 Torr. nozzle diameter = 0.25 mm, beam inlensity at the sapphire window = 1.3 x lWJcm-‘s- I). The deposition time was 240 s. Zero absorbance is at the long-wavelength limit except for 150: I sample.

absorption value in the matrix compared to the maximum of the Franck-Condon distribution in the

gas-phase is blue-shifted by z 12 nm for the B + X and red-shifted by z 17 nm for the A t X system. Additional absorptions at 525 nm and 745-765 nm

are due to sodium aggregates and will be discussed

below. The peaking of the M :R = 150: 1 spectrum at

577 nm is characteristic of a large number of over- lapping absorption bands of medium-to-large sodium

clusters. Obviously in the limit of large Na, particles (x > 50) it is no longer meaningful to speak of specific molecular absorption bands; optical transitions between surface states of small metal

particles (optical plasmon excitations) are known

to lie in the visible and near UV regions [ 12, 181.

3.2. Variution ofmoleculur beum composition

Once ‘the conditions for effective isolation of

sodium atoms and molecules have been found, one can use the matrix spectra as a diagnostic tool to

determine relative concentrations of the different

148 fil. Hofmunn et ai.fMatrix isolation of sodium atoms und mol~~les

sodium species and to detect previously unknown absorption bands of sodium clusters. By variation of the oven temperature one can change the relative concentrations olthe molecular beam constituents:

the results are gathered in table 1 and fig. 3.

Fig. 3a reproduces the matrix optical spectrum corresponding to a molecular beam generated at low stagnation pressure (p = 42 Torr). The molecular content of the beam is Iow: the NaJNa ratio inside the oven is z 7.5 % (equilibrium vapour pressure).

The mass-spectrometric Na,/Na ratio in the molecular beam is slightly higher (8.3 %), indicating enhanced dimer formation during the adiabatic

expansion. The NaJNa ratio in the Kr matrix was

measured by using the integrated peak areas of the

Na, (B + X) absorption band and the peak areas of the Na atomic absorptions at 574,593 and

603 nm. Equal oscillator strengths for both the

atomic and the dimer transition are assumed. An

intriguing detail in fig. 3a is the sm&l absorption peak at 500 nm which continues as a barely discernible shoulder on the intense 473 nm absorption band. We believe that this absorption is due to a second Na, (B - X) absorption site; the site splitting is 30 nm, which is comparable to the splitting of the atomic absorption (25-30 nm).

Table I Beam parameters and Na, concenrrarions in beam and matrix (ligs. 3-5)

Fig. Stagnation Absorption Mass spectromctry no. pressure spectrometry in the

(Torr) in Kr matrices molecular beam ___. -

Na Naz”’ Na NC;’ Na 3E) Nad’

3a 42 100 7.5 100 8.3 0.3 0.06 3bf4 185 100 18.1 100 21.5 1.4 0.9 3c/5 984 100 55 100 50 2.2 1.8

” Peak area of the Na2 (B t X) absorption band (473 nm) divided by the total peak area of the Na absorption al 574.593 and 602.5 nm. Equal oscillator strengths are assumed for atom and dimer.

” Calibrated at equilibrium Nal/Na ratios under effusive flow conditions (p = O-I-O.3 Torr, Knudsen number =z I).

” Uncorrected roar photoionization cross section, wmsmission factor and electron multiplier discrimina- tion.

!- - LOO 500 600 700 inrn, 800

Fig. 3. Variarion ofreIarive molecular concenrraCon by changing the stagnation pressure(p) in the oven: (a) p = 42 Torr, M/R = 30 000 : 1: (b) p = 18.5 Torr, M/R = 25 600: 1; (c) p = 984 Torr, M/R = 23 600: 1. Note the marked development of the Na, B + X and A + X bands at 490 nm and 670 nm. Measured NaJNa ratios are given in table 1. Samples were deposited in a krypton matrix at 4.2 K. Zero absorbance for all samples is af the short-wvavelen_eth limit.

The sample whose spectrum is shown in fig. 3b was prepared using medium stagnation pressure (185 Torr). The dimer concentration is increased by

a factor of 2.5 by mass spectrometric analysis as well as by integrated absorption peak area. In fig. 3c at the highest source pressure (z 1.3 bar) attainable with our present oven system, the NaJNa ratio reaches a value of 50-55 %- A new absorption system arises with two maxima at 736 nm/747 nm, probably due to Na, and/or Na,. In this case there is a large discrepancy between the optical and the mass-

spectrometric measurements, which is presently not well understood.

3.3. Warming of deposited samples

Controlled annealing of deposited NajKr

samples was performed by warming to a delined temperature and quenching by rapid retooling to 4 K. The absorption spectra show characteristic and irreversible changes indicating growth of sodium aggregates. Two warm-up sequences are shown in figs. 4 and 5.

Fig. 4 shows a molecular beam sample with

M. Hojnonn et al/Matrix isolation ofsodium aroms and rnolec&s 149

I-_----__I

LOO 500 600 700 800 [nml

Fig. 4. Annealing of a sample with medium NaJNa ratio (see fig. 3b) in a krypton matrix.

medium molecular content with a Na/Na#as ratio of approximately IOO/ZO/lS. The characteristic trends on warming are:

(I) A strong decrease in the atomic absorption

peaks at 593/602 nm (the “red triplet” [ 1, 3-61) indicating diffusion/reaction of Na atoms in this thermally labile site. The “blue” site at 574 nm is much more stable to annealing as the peak intensity

decreases only slowly up to 20 K. (2) Structured absorption appears around 530 nm

and develops into three almost equidistant peaks at .529/538/546 nm. This absorption may be due to

LOO 5w 600 7oo [nml 8C0

Fig. 5. Annealing of a sample with high NaZ/Na ratio (see lig. 3c) in a krypton matrix.

Na, or Na,, but is definitely not the same species that absorbs in the far-red part of the spectrum

(736/747 nm). This follows from the spectrum in fig. 3c, which corresponds to the direct deposition of a high-molecular-content beam at 4 K and shows

only the far-red but no yellow-green absorption bands. An assignment of the far-red bands to Na, implies that the yellow-green bands are due to Na, or a higher cluster.

(3) Unstructured absorption reaching from 780 nm up to the Na2 (A c X) band; these absorptions are only partly due to the tentative Na, 7361747 nm absorption.

(4) The shoulder on the Na, (B 6 x) band

attributed to site splitting develops with increasing temperature indicating a site redistribution or site rearrangement for the dimer.

Fig. 5. shows a similar sequence for a high molecular content sample with Na/Na@a, = 100 : 50 : 2.5.

On warming, the spectrum shows a similar drastic decrease in the red part of the atomic absorption at z 600 nm. The pattern of intensity

growth is however different: - the main growth in absorbance is between the

Na, A + X band and the (Na,.,?) absorption at

7241747 nm; - the structured yellow-green absorption also

appears, but is much weaker than in fig. 4. The peak positions are slightly blue-shifted by 2 nm relative to fig. 4. A common feature of both warm-up sequences is

the very slight sensitivity of the Na, B + X and A + X bands to annealing up to about 25 K.

4. Discussion

4.1. Isolability ofsodium atoms and molecules

Since alkali atoms have been studied in low temperature rare-gas matrices for almost twenty years now, the description of isolation conditions

would perhaps seem inappropriate. In our experience however, several stringent conditions have to be met:

(a) Temperature: as Weyhmann and Pipkin [2] have shown, alkali-atom spectra are extremely

150 M. Hojinum~ et al./Mutrix isolation of sodim atoms und moleades

sensitive to deposition temperatures, as exemplified by the large decrease in the intensity of the so-called “blue” triplet [I] on improving thermal contact between the cryostat and the deposition substrate (optical window). We have studied the changes in absorption spectra on raising the deposition temperatures a few degrees above 4 K (5-8 K). The resulting spectrum is shown in fig_ 6. A significant rise in the Na,lVa absorption ratio and the appearance of new absorption bands in the red at 67&750 nm are signs of increased cluster formation. Only by lowering the deposition temperature to z 4 K is it possible to obtain an absorption spectrum where the different spectral features correspond to the specific composition in the sodium beam used for deposition. This is especially true if a molecular beam is used.

On the other hand, the isolation of heavier metal atoms, e.g. silver [l l] is much less sensitive to deposition temperature and metal concentration than for the alkali atoms. .The different behaviour of these metal atoms can either be explained by assuming a more effective energy transfer (thermal and binding energy) of the heavier atoms condensing at the matrix surface, drastic differences in the reactivity - being stronger in the case of the alkali

atoms - and/or a better incorporation of the silver atoms in a substitutional matrix site. The lirst two arguments_ given above, would result in a longer diffusion path for the alkali metal atoms until complete thermalization is achieved, thus favouring aggregation. As the thermal energy of the super-

too ml 600 700 Inml ‘Cl’

Fig. 6. Absorption spectrum of a Na/Kr matrix deposited at 7 K window temperature (M/R = i9 000: 1). Note the additional bands at 678/714 nm as compared to the lowest trace of fig. 4. which was deposited at 4 K under otherwise similar conditions.

sonic sodium beam (Z 1200 K) is not much higher than the energy of the silver atoms evaporated from a Knudsen cell (1200-1300 K), a noticeable influence of this parameter can be ruled out.

(b) Corrcerltration: the influence of concentration on the absorption spectrum is nicely demonstrated in fig. 2. We believe that much work that was done at low M/R ratios [l. 4,6J is partially inconclusive because aggregate formation, especially of the species absorbing around 530-560 nm has led to erroneous assignments. An example is the complete absence in our spectra of two peaks belonging to the “blue” atomic triplet at 559 nm and 568 nm reported by Meyer Cl].

We believe that a M/R ratio of 25000-3OUOO is adequate for a reasonable isolation of Na atoms and molecules in krypton matrices. This value will have

to be adjusted for other matrix gases or if other spectroscopic methods more sensitive to long-range interactions (such as luminescence measurements) are used.

Andrews and Pimentel [3] have carefully analyzed the concentration dependence of Li in Ar, Kr and Xe matrices and arrive at two conclusions: (i) the oscillator strength of the atom is 300 times greater than that for the dimer; (ii) as a consequence the degree of isolation of lithium atoms is very low as calculated from the areas under the atomic and molecular absorptions, the Li/Li2 ratio being between 2-15 % at M/R’s of 18000: 1. We believe this is an unfortunate conclusion from otherwise excellent experimental work. From gas-phase and molecular-beam lifetime measurements the oscillator

strengths of the alkali dimers are known to be within a factor of 2 of the atomic values+. There is no a priori reason for the oscillator strength of a molecular transition to change more than that of an atomic transition upon deposition in a low-

temperature rare-gas matrix (except for the

occurrence of excimer formation in emission; here we are only concerned with absorption). A reexamination of their data with the assumption of equal extinction coefficients for Li and Li, leads to

t Oscillator strength:/,, = 2 - - y, Zne’r’ T2,’

N~I’P,,~.,,~ + ‘S,,=. r= 16ns Na :‘fl r=7.2+0.2ns.ref.~14]:Na2:‘~~$‘Z,’,

+‘I+ E’

* = IZ f 1 ns, ref. [IS].

M. Hojr?wnn et al./Macrix isolariott of sodium atoms crud rmleculrs ISI

the very reasonable conclusion that the Li/Lil ratio for a M/R of 18000 in Xe is 100: 1, the ratio calculated for equilibrated vapour at the Knudsen-cell tempera- ture used being 500 : 1 [ 161. The use of higher M/R’s seems to enhance the Li/Li, ratio; this is, however, partially due to a lower Liz concentration

in the lithium vapour as the Knudsen cell was operated at lower temperature for these experiments.

We find in our experiments that the -‘optical” Na/N+ ratio (by integrated areas of the absorption bands) corresponds very well to the ratio measured by mass spectrometry (see table 1). Hence it is evident that aggregates from molecular beams can be matrix isolated without change.

The Na atomic absorption is not homogeneous

as shown by the warm-up studies. Careful annealing

leads to a rapid decrease in absorption of the red part (around 600 nm) indicating an unstable site.

The “blue“ part at 573 nm is quite stable up to 20 K, confirming the observation of earlier authors

Cl, 341.

The Na2 absorption bands show very little change during annealing, apart from the appearance of the previously mentioned shoulder at 500 nm. This seems to indicate that the Na, species is relatively stable with respect to matrix aggregation.

The characteristic spectral changes during matrix annealing are, although weak, found to be at the wavelengths corresponding to molecular absorp- tions produced by depositing a high molecular content beam. This suggests that the thermal aggregation taking place does proceed via very sma!l sodium molecules (e.g. NaZ, Na,, Na,). The general picture evolving from the annealing studies is the following: the Na atoms in the sites causing the “red” absorption are rapidly mobilized and diruse leading to formation of several stable aggregates Na, (x >, 2) characterized by extended and probably overlapping absorption bands. Which of the molecular aggregates will grow, depends strongly on the size of the aggregates already present in the matrix. Generally it is found that the larger the aggregate size the larger wil: be the size of the aggregates which will increase by annealing. This result is in good agreement with results on the

growth of silver molecules grown by annealing [ 121. The formation of Na, clusters was also noted by

Andrews [17] in the course of an experiment designed to study the formation ofNaiO; species in an Ai matrix. No analysis of these absorptions

was undertaken.

\ve believe that a soundly based assignment of absorption bands to higher sodium molecules is not possible on the basis of absorption spectroscopy in matrices_ Further progress can be made by using Raman, lluorescence and EPR techniques, and especially by correlations with the results coming

out of laser two-photon-ionization spectroscopy

c131-

Acknowledgement

This work was financed in part by grant NQ. 2.919-0.77 of the Swiss National Science Foundation_ We shou!d like to thank Professor H. Gerischer and Professor E. Schumacher for their contribution to this research and Dr. L. Wiiste for advice during the early planning stage. We also wish to thank Professor G. Ozin at the Universily of Toronto for correspondence concerning his recent experimental results on sodium cluster matrix spectroscopy.

References

[I] B. Meyer, J. Chem. Phys. 43 (1965) 2986. [z] W. Wiyhmann and F.M. Pipkin, Phys. Rev. 137

(1964) A490. [31 L. Andrews and G.C. Pimentel, J. Chcm. Phys. 47 _-

(1967) 2905. [4] D. Nagel and B. Sonnta_r. Ber. Bunsen~es. Physik

Chem. 82 (1978) 38. [S] A.A. Bclyaeva, Y.B. Prcdtechncnskii and L.D.

Shcherba, Opt. Spec:ry. (USSR, English Transl.) 24 (1968) 233: 34 (1973) 21.

[6] R.B. Merrithew, G-V. Marusak and C.E. Blount, J. Mol. Spectry. 29 (1969) 54.

[7] R.J. Gordon. Y.T. Lee and D.R. Herschbach, J. Chem. Phys. 54 (1971) 2393.

[8] A. Herrmann, E. Schumacher and L. Wiiste. J. Chem. Phys. 68 (1978) 2327, and references therein.

[Y] A. Herrmann, S. Leutwyler, E. Schumacher and L. Waste, Helv. Chim. Acta 61 (1978) 453.

152 M. Hofmonn et ol.fMotrix isolation of sodium atoms and molecules

[IO] W. Schulze. H.-U. Becker and D. LeutloK J. Phys. (Paris) Colloq. (2) (1977) Z-10.

[ 1 I] W. Schulze, H--U. Becker and H. Abe, Ber. Bunsen- ges. Physik Chem. 82 (1978) 138.

[12] W. Schulze, H.-U. Becker and H. Abe, Chem. Phys. 35 (1978) 177.

[13] A. Herrmann, S. Leutwyler, E. Schumacher and L. W&e, Chem. Phys. Letters 52 (1977) 418; D.L. Feldmann, R.K. Lengel and R.N. Zare. Chem. Phys. Letters 52 (1977) 413.

[ 141 W. Demtriider, W. Stetzenbach, M. Stock and J. Witt, J. Mol. Spectry. 61 (1976) 382.

[15] T.W. Ducas, M.G. Littman, M.L. Zimmermann and

D. Kleppner, J. Chem. Phys. 65 (1976) 842. [ 161 D.R. Stull and G.S. Sinke, Thermodynamic

properties of the elements, Advan. Chem. Ser. No. I8 (1956): W.H. Evans, R. Jacobson, T.R. Munson and D.D. Wagman, J. Res. Nat. Bur. Stds. 55 (1955) 83; I. Barin and 0. Knacke, Thermodynamic properties of inorganic substances (Springer, Berlin, 1973) p. 397/398.

[ 171 L. Andrew, J. Mol. Spectry. 61 (1976) 337. [IS] U. Kreibig, Conference Internarionale sur les

petites particules et amas inorganiques, Lyon, 1976 (and references therein).