Origin of Metallicity – Photoelectron Spectroscopy of Copper Clusters

ShakuntalaCY01C019

Experiment:

Generation of large clusters- cluster source nozzle.

Requirements of the source: Should make large clusters Clusters should be vibrationally cold

Results:

Fig 1- 4 Show the UPS data.

UPS taken with 7.9 eV photons from an F2 excimer laser.

EA for each cluster chosen by drawing a straight line along the signal onset and adding a constant value of 0.2 eV to compensate for hot bands.

EA for d electrons obtained by taking the binding energy value which corresponds to ½ the distance between the large peak and valley in the region of interest.

Analysis:

A. Shell ModelElectrons are assumed to move in a perturbed harmonic potential of a

modified Nilsson Hamiltonian.

Hn = (1/2) (pk2 / 2m + mωk

2qk2) – Uo(h/2π) ωo(L2 _ < L2 >n)

Where, ωk are the frequencies of motion along the three coordinates; qkpk are the corresponding conjugate momenta, h/2πL is the pseudo angular

momentum operator.

The three frequencies were allowed to vary independently subject to the constraint that ω1 ω2 ω3 = ωo

3

Where ωo is the frequency of the spherical limit

Comparison of Shell Model and Experimental Data

1) For small clusters, the correspondence between EA and shell model is poor.

2) Clusters in the size range 8-40 atoms show good correspondence.

Dips in EAs at values of 8,34, 40 and 58 mark closing of shells.

3) At larger clusters- 50 atoms or more- even-odd oscillations of the electron affinities washed out.

B. Even-odd alternations and metals

Smaller sized clusters (<30 atoms) show even odd oscillation oscillation of EA values

Even numbered clusters have lower EAs.

In even numbered clusters, HOMO is occupied by two electrons.

Odd numbered clusters, are open shell species and have a hole inthe HOMO.

As size of the cluster increases the even odd oscillations diminish as density of electronic states increases.

C. Evolution of the d bands

At 2 eV higher than onset of of the UPS, a large peak moves smoothly with cluster size.

For larger clusters it can be extrapolated to the sharp onset of d bands.

This can be attributed to photoemission from d electrons in the clusters .

D. Convergence to bulk properties

Electrostatic spherical drop model.

EA = WF – A e2 / R

R – effective radius of the cluster

R = N 1/3 r + d r - bulk density, d - spillout of the electronic charge of the cluster

Conclusion:

Starting from size of about twenty atoms the clusters can be regarded as small metallic pieces

The general features of the UPS are similar to those of the bulk materials.

The boundary conditions give rise to shell structure.

The even-odd alterations of EAs is due to sparseness of energy levels.

These effects erode as clusters grow.

References:

1) C. L. Pettiette, S. H. Yang, M. J. Craycraft, J. Conceicao, R. T.Laaksonen, O. Cheshnovsky and R. E. Smalley. Journal of Chemical Physics, 88, 5377-5382 (1988).

2) O. Cheshnovsky, K. J. Taylor, J. Conceicao and R. E. Smalley. Physical Review Letters, 64, 1785-1788 (1990).

3) K. J. Taylor, C. L. Pettiettehall, O. Cheshnovsky and R. E. Smalley. Journal of Chemical Physics, 96, 3319-3329 (1992).