Polarizabilities of Isolated Silicon Clusters

Abstract

Dedicated to Prof. Dr. E. Wicke on the occasion of his 80th birthdayThe static electric polarizabilities a of silicon clusters with up to 60 atoms have been measured employing a mass selective molecular beam deflection method. The polarizability per atom aN = ol/N of the Sijy-clusters has been investigated for Siu and the size ranges N = 14-28, 22-34, 28-44, 34-50, 41 -58, and 42-68. The results show that the polarizability per atom decreases from N = 11 until a minimum at N « 28 is reached. The polarizability per atom increases for N > 28, passes through a maximum at N « 36 and finally converges between N « 50-70 against the value a.N = 1.9 A3. If the model of a homogeneous dielectric sphere is applied to the larger clusters one calculates that the value a.N = 1.9 Ä3 corresponds to a dielectric constant of e = 3.2. This value is significantly smaller than the dielectric constant of bulk silicon eb = 11.8.The present paper focuses on the maximum in the polarizability at N » 36. This effect is discussed with special emphasis to recent Car-Parinello calculations which have predicted cage-like silicon structures that enclose a core of several highly coordinated atoms. This structure suggests an im proved dielectric sphere model where the core is represented by a smaller sphere with its own dielectric constant ec. It is shown within this model that the observed maximum in polarizability is due to a significant enhancement of the core dielectric constant to a value of ec « 50. This enhance ment is related by means of a simple model to the effect that silicon becomes metallic under high pressure.

New Molecular Cage Clusters of Pb by Encapsulation of Mg

“…However, from the symmetry of the predicted deltahedral cage structures one expects a nonvanishing dipole moment for MgPb 11 and MgPb 13 . The experiments on MgPb 11 display a small but detectable broadening of the molecular beam in combination with a slightly enhanced polarizability and point to the existence of a small dipole moment, consistent with the structure of an octadecahedral lead cage (C 2v ) resembling (BH) 11 2À . But from the molecular-beam profiles of MgPb 13 there is no experimental support for the presence of a permanent dipole moment.…”

“…This is particularly striking for MgPb 12 and MgPb 14 , in contrast to the significant dipole moments of Pb 12 and Pb 14 . The measured polarizabilities of the MgPb [10][11][12][13][14][15][16] are slightly larger than that of a small, ideally metallic sphere with the properties of bulk lead (solid curve in Figure 5). [26,27] But for the doped lead clusters it is expected that the polarizabilities will be increased by an additional amount of about 0.…”

“…[11] For that purpose, either a pure lead rod or lead rods doped with 10, 20, 40, and 50 at. % magnesium were used.…”

“…, one can speculate that MgPb 11 and MgPb 13 are composed of deltahedral lead cages Pb 11 2À (C 2v ) and Pb 13 2À (C 2v ) with a Mg 2 + cation at the center, which resemble the structure of (BH) 11 2À and (BH) 13 2À , respectively.…”

“…Detection of the Mg-doped lead clusters took place within a photoionization mass spectrometer. [11] These experiments allowed us to study the size requirements of the Pb cage that have to be met for the uptake of one or two Mg atoms. To obtain information concerning the structure of the clusters, their dielectric properties were studied with a molecular-beam electric deflection experiment.…”