Walter D. Knight

Electronic Shell Structure and Metal Clusters

Publisher Summary The chapter presents a study on electronic shell structure and metal clusters. Unlike the “macroscopic” atoms, the metallic clusters described from both experimental and theoretical viewpoints in this chapter come far closer to having bulk properties, because they are 10–100 times bigger. The science of clusters is a rapidly growing interdisciplinary field with great promise for the production of new ideas and physical systems. Its ideas are relevant to related problems in the physics of atoms, molecules, condensed matter, and transitions among these systems. The chapter presents a review emphasizing on the electronic shell model, which is elegant and simple, avoids the complexity of elaborate quantum chemical computer calculations for clusters containing large numbers of atoms, and possesses the power of predictability. The study of the physical properties of states intermediate between the atom and the solid is called cluster physics. Lacking a precise definition, it is said that a cluster is a stable group of a few or a few hundred identical atoms or molecules. This chapter mainly discusses metal clusters. Atomic theory depends on the application of angular momentum conditions in the Coulomb field.

A Radiofrequency Spectrograph and Simple Magnetic‐Field Meter

A simple oscillating circuit with a special feed‐back circuit is employed as a tool for the search for and detailed analysis of nuclear paramagnetic absorption lines. The sensitivity approaches the optimum for a given noise band width and particularly useful is the ease of conducting slow, continuous changes of frequency while recording the output data. Spectra having several components at scattered frequencies are thus displayed. Line shapes are unambiguously recorded because of the absence of sensitivity to dispersion. Using protons in water, or solutions containing Li7, the device can be used as a versatile and extremely precise meter for measuring magnetic field strengths in the range from about 100 to 25,000 oersteds with a minimum of auxiliary equipment.

Electronic shell structure in potassium clusters

Abstract Mass spectra of potassium cluster beams show electronic shell structure like that recently reported for sodium clusters, with peaks or steps for those clusters which contain N = 2, 8, 20, and 40 atoms. The potassium contained sodium impurities, which produced satellite peaks corresponding to the substitution of one Na atom for a K atom in each cluster. The satellite peak structure for these mixed clusters of total valence electron number N also corresponds to the above sequence of numbers.

Nuclear resonance in solid and liquid metals: A comparison of electronic structures

Abstract The electronic structures of ten solid and liquid metals are investigated experimentally and theoretically, and the results of recent nuclear resonance measurements are correlated with already published data concerning magnetic susceptibility, electrical conductivity and atomic arrangement. It is concluded that the electronic structure of each of the metals investigated, with the notable exceptions of Bi and Ga, does not change appreciably at the melting point. Moreover, in Ga and Bi there is a correlation between a change in the electronic structure and structural rearrangements of neighboring atoms at short range; the other metals considered show neither sort of change. A principal conclusion is that a liquid metal possesses a band structure which is very like that of its solid, provided the short-range structure is not altered during melting. Included are hitherto unpublished values for the nuclear magnetic resonance line shifts in liquid Al, Sn, In, and Bi, and the nuclear spin relaxation times in solid and liquid Ga. The nmr shifts in solid and liquid Al are equal within experimental error. The same is true for Sn. This is in agreement with published results on the alkali metals and Hg, where the corresponding changes are known to be small, suggesting that the electronic structures of the respective solids and liquids are the same. The large quadrupole coupling in Ga, In, and Bi prevents observation of the nmr in the solid state. However, the value of the nmr shift in liquid In is consistent with values of the hyperfine coupling constant and the electronic specific heat at low temperatures, a situation which is true for most of the other metals. Ga and Bi are the exceptions for which the nmr shift in liquids is much larger than the hyperfine and low-temperature data would lead one to expect. This is taken as evidence for a reduced density of states at the Fermi surface in solid Ga and Bi. Confirmation is provided by the fact that the nuclear spin relaxation time of Ga increases sharply when the metal freezes. The measurement of relaxation in solid Ga is significant because the nuclear quadrupole resonance is directly observed and the relaxation process is of the same type, so that a change in its magnitude may also be related to a density of states.

Nuclear magnetic resonance in intermetallic compounds

The Nuclear Magnetic Resonance is observed in a series of intermetallic compounds of structure type NaTl, including NaTl, LiAl, LiGa and LiIn. Motional narrowing of the dipolar part of the Li resonance line is observed in all the compounds from which the activation energy of diffusion of Li is estimated to be 0.15 eV. The low value of the activation energy in this defect lattice is associated with a 3 per cent vacancy concentration in the lithium sublattice. Motional averaging of quadrupole interactions is observed for both the Li and Al lines in LiAl. The magnitudes of the quadrupole couplings e2qQ/h produced by a nearest-neighbor vacancy are 0.36 Mc for Li7 and 29 Mc for Al27. Second-order broadening obliterates the Ga and In resonances in LiGa and LiIn below 200°K. It is estimated that the quadrupole couplings are of order or greater than 30 Mc and 80 Mc for Ga71 and In115, respectively. The size of the quadrupole interaction is consistent with a high degree of covalency in these crystals. The frequency shifts, relative to diamagnetic chemical compounds, are found to be (in per cent): Li (< 0.005), Al (<0.01), Ga (0.09), In (0.13), Na (−0.016), Tl (−0.50).

Alkali metal clusters and the jellium model

Abstract The application of the jellium model and the resulting quantum shell structure for metal clusters is examined in the light of theoretical calculations and experimental observations. Objections to the jellium model by Kappes, Schar, Radi and Schumacher appear to be based on misunderstandings of the model and on inadequate experiments.

The Physics of Metal Clusters

Scientists often set the stage for their most productive advances by first developing simple models, even when sophisticated first‐principles tools are available. These models usually originate from the necessity to explain experimental observations. If the models are robust, then a variety of data fall into place, and successful predictions are made. If a model is “correct,” it is eventually found to be consistent with or derivable from fundamental theory. The Bohr model for atoms is a prime example. Ernest Rutherfords experiments showed that J. J. Thomsons “plum pudding” model of an atom, consisting of a positive spherical “pudding” embedded with negative electron “plums,” had to be replaced by Rutherfords nuclear picture, and subsequent optical data led to the Bohr model. Eventually quantum theory confirmed that the Bohr model is an excellent rudimentary representation for an atom. Although it has been superseded by more elaborate quantum theoretical approaches, this model is still taught to student...

Shell Structure and Response Properties of Metal Clusters

Electronic shell structure, which was first recognized in sodium clusters, has been observed in alkali and noble metals, as well as in divalent and trivalent metals. Shell structure with modifications is expected to be broadly applicable to most metals. Features in the cluster abundance spectra and in the experimental dipole polarizabilities and ionization potentials correlate well with predictions of electronic level filling in spherical and spheroidal potential wells. The lack of precise quantitative agreement between experiment and theory for the response properties indicates necessary refinements in the self-consistent uniform background jellium model for clusters.

Optical spectra of sodium microclusters

Photoabsorption spectra have been measured for free neutral sodium clusters containing fromN=3 to 40 atoms. In the size range ofN≈3 to 5, a transition occurs from molecule-like absorption to collective excitations of the valence electrons. ForN≈6 to 12, the data are well described by an ellipsoidal shell model. In open-shell clusters, the multiple surface plasma resonances expected for spheroidal or ellipsoidal shapes are observed. The experimental resonance positions provide a sensitive measurement of the cluster distortions. ForN≳13, the per atom strength of these collective resonances is reduced; this may be due to peak fragmentation caused by interaction between the surface plasmon and nearby single-electron resonances. In three distinct wavelength regions, one of which corresponds to the position of the Na atom “D-lines”, additional absorption is seen in the spectra of all investigated clusters.

Measurement of Electronic Susceptibilities by Means of Nuclear Resonance Absorption

The proton nuclear magnetic resonance is observed in two crossed capillary tubes embedded in a paramagnetic material in a constant external field. The resonance frequencies from the two capillaries depend on the respective demagnetizing factors. For Mn2O3 the two resonance lines are separated by 13.0 kc at 22.3 Mc, giving a mass susceptibility of 65×10−6 cgs, in agreement with values obtained by other methods. For a magnetic field homogeneity of about one part in 107 over the sample, the ultimate sensitivity of the method would be 10−7 to 10−8 susceptibility unit. Measurements can be made at low temperatures.