Lattice valency model

The Lattice Valency model describes a methodology based on the modification of bulk material-based RSFs (previously defined from associated reference materials), to allow for high sensitivity/detection limit quantification over interfacial region. This was put forward to account for the variability in atomic secondary ion intensities from minor and/or trace elements with the valence stale of atoms (cations) making up the substrate (Iltgen 1997). Although trends consistent with expectations are noted within the few publications available, this method does not account for sputter rate variations, nor the impact of any segregation processes, if active. 

Within this model, the variability in the negative atomic secondary ion intensities of minor and/or trace elemental emissions is assumed to arise from variations in the concentration of highly electronegative elements (anions) within the near surface region of the substrate being sputtered. An example of this would be the effect the presence of Oxygen (the anion) has on the emissions of the Arsenic secondary ions from a Silicon (the cation) lattice (Gehre et al. 2001). 

The Lattice Valency model attempts to correct for these variations by, firstly, deriving the valency of the cations making up the lattice, and then, secondly, applying valency-specific RSFs to the respective secondary ion emissions. The cation 

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As a result, two additional methodologies describing site (depth)-specific RSF modifications were introduced allowing full utilization of the sensitivity/detection limits afforded by SIMS. These are described within the Lattice Valency model and the Point-by-point CORrection of SIMS profiles (PCOR-SIMS ) approach. These are covered in Sections A.9.3 and A.9.4, respectively. Although the former has found limited mention in the literature, the latter has become a commonly used/advertised protocol by the Evans Analytical Group (EAG). 

Figure 4. Fits of lattice strain model to experimental mineral-melt partition coefficients for (a) plagioclase (run 90-6 of Blundy and Wood 1994) and (b) elinopyroxene (ran DC23 of Blundy and Dalton 2000). Different valence cations, entering the large cation site of each mineral, are denoted by different symbols. The curves are non-linear least squares fits of Equation (1) to the data for each valence. Errors bars, when larger than symbol, are 1 s.d. Ionic radii in Vlll-fold coordination are taken from Shannon (1976).

For closest-packed oxides, a Pannetier-type cost function [58] is more robust and faster to evaluate than the lattice energy as defined earlier. Here, the bond valence model [59] is used to calculate the charge on the ions and the discrepancy with the expected value is used to measure the quality of the structure. With an additional term, the discrepancy in the expected and calculated coordination numbers, the cost function becomes... 

A fraction y of the Mn4+ ions are replaced by Mn3+. This fraction determines the average valence of the manganese atoms. For each Mn,+ there is a further OH ion in the lattice, replacing an O2 anion in the coordination sphere of the Mn3+ cation. A schematic drawing of the Rue-tschi model is shown in Fig. 4. 

Fig. 14.1 Model of a solid with cores at fixed lattice positions and valence electrons free to move throughout the crystalline solid.

The passive film is composed of metal oxides which can be semiconductors or insulators. Then, the electron levels in the passive film are characterized by the conduction and valence bands. Here, we need to examine whether the band model can apply to a thin passive oxide film whose thickness is in the range of nanometers. The passive film has a two-dimensional periodic lattice structure on... 

Classical Free-Electron Theory, Classical free-electron theory assumes the valence electrons to be virtually free everywhere in the metal. The periodic lattice field of the positively charged ions is evened out into a uniform potential inside the metal. The major assumptions of this model are that (1) an electron can pass from one atom to another, and (2) in the absence of an electric field, electrons move randomly in all directions and their movements obey the laws of classical mechanics and the kinetic theory of gases. In an electric field, electrons drift toward the positive direction of the field, producing an electric current in the metal. The two main successes of classical free-electron theory are that (1) it provides an explanation of the high electronic and thermal conductivities of metals in terms of the ease with which the free electrons could move, and (2) it provides an explanation of the Wiedemann-Franz law, which states that at a given temperature T, the ratio of the electrical (cr) to the thermal (k) conductivities should be the same for all metals, in near agreement with experiment ... 

It should be noted that, besides free electrons and holes, the role of the free valencies in the crystal may be played by the so-called Frenkel excitons. The latter are, roughly speaking, excited atoms or ions of the lattice which can transfer their state of excitation to similar neighboring atoms or ions. As an example, we may take again the CU2O lattice in which a Frenkel exciton (in the same rough model) is represented by an excited Cu+ ion with the following electronic structure ... 

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