Collective-electron models

2 ORIGINS OF RADIATION SENSITIVITY 1.2.1 Collective-electron models 

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According to the collective-electron model developed in the last paragraph, each state is filled with two electrons, one of each spin,... 

The LDOS-based frontier orbital model is different from the simpler collective-electron model, in which all local information is averaged out. In the context of alloys. Ponec and Bond (23. p. 451). stated that it must be clear to the reader that (the collective electron model of catalytic activity of alloys] has now been consigned to the trash can of science. . . [because of] the discovery that, more in tune with chemists intuition, the atoms in an alloy retain their identity more or less completely. Such local properties disappear from the collective-electron model in which it was supposed that the available electrons were equally shared by aU the atoms present, and that. .. the density of states at the Fermi surface or some related... 

A very clear distinction between the total DOS D s) and the LDOS D e,t) is shown by calculations on binary alloys [51]. Look, e.g., at the (partly hypothetical) series of isoelectronic 1 1 alloys TcTc, MoRu, NbRh, ZrPd, YAg, where the alloying partners have nominal valence differences between 0 (for pure Tc) and 8 (for YAg). As shown in Figure 5, the overall density of states curves look more or less alike for all five alloys, but the partial densities on the sites of the individual partners are very different. Such curves also show why the so-called collective electron model does not work for catalytic activity [52, p. 458], or even for alloy properties in general. 

In collaboration with Wavefunction we have created a cross function CD ROM that contains an electronic model building kit and a rich collection of molecular models that reveal the interplay between electronic struc ture and reactivity m organic chemistry... 

A Del Electronics, Model ESP-100A, electrostatic precipitator was used for sample collection. Cigarette smoke particles were found to give approx the same particle distribution pattern on the collection filter paper as the gunshot residue, and since the smoke stains the paper, this provided a v rapid technique for optimizing operation conditions. With a flow rate of 15cfm and a corona current of 125 uA, the residue collects primarily on a narrow band across the sample paper. Samples were collected on Whatman No 1541 filter paper which lined the inside of the sample collection tube. The presence of this paper allowed air to flow only thru the center of the tube, so particle collection was made upon the filter paper exclusively. The filter paper samples were pelletized prior to neutron activation analysis... 

We know that not all solids conduct electricity, and the simple free electron model discussed previously does not explain this. To understand semiconductors and insulators, we turn to another description of solids, molecular orbital theory. In the molecular orbital approach to bonding in solids, we regard solids as a very large collection of atoms bonded together and try to solve the Schrodinger equation for a periodically repeating system. For chemists, this has the advantage that solids are not treated as very different species from small molecules. 

The position of a nickel Auger peak superimposed on the N(ls) photoelectron peak was detected when spectra of coated nickel samples were collected on the Physical Electronics Model 5300 ESCA system using Mg Ka X-rays. Therefore, XPS spectra of nickel samples were obtained using a Surface Science Instruments SSX-100-03 instrument equipped with a monochromatic A1 Ka source. The N(ls) high-resolution spectra obtained from polished nickel which had been coated with y-APS from a 1% aqueous solution at pH 10.4 are shown in Fig. 8. 

The chemist is accustomed to think of the chemical bond from the valence-bond approach of Pauling (7)05), for this approach enables construction of simple models with which to develop a chemical intuition for a variety of complex materials. However, this approach is necessarily qualitative in character so that at best it can serve only as a useful device for the correlation and classification of materials. Therefore the theoretical context for the present discussion is the Hund (290)-Mulliken (4f>7) molecular-orbital approach. Nevertheless an important restriction to the application of this approach must be emphasized at the start viz. an apparently sharp breakdown of the collective-electron assumption for interatomic separations greater than some critical distance, R(. In order to illustrate the theoretical basis for this breakdown, several calculations will be considered, the first being those for the hydrogen molecule. 

B. BAND MODEL FOR COLLECTIVE ELECTRONS 1. Major A ssumptions... 

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