Alloys theoretical models

Figure 2 Residual isotropic resistivity p of disordered Co Pdi- (open symbol.s) and CoiPti i (full symbols) alloys. Theoretical results obtained in a fully relativistic way and using the two-current model are given by up and down-pointing triangles, re- spectively. All other symbols represent experimental data taken from various sources [13, 14, 15, 16].

In the Introduction the problem of construction of a theoretical model of the metal surface was briefly discussed. If a model that would permit the theoretical description of the chemisorption complex is to be constructed, one must decide which type of the theoretical description of the metal should be used. Two basic approaches exist in the theory of transition metals (48). The first one is based on the assumption that the d-elec-trons are localized either on atoms or in bonds (which is particularly attractive for the discussion of the surface problems). The other is the itinerant approach, based on the collective model of metals (which was particularly successful in explaining the bulk properties of metals). The choice between these two is not easy. Even in contemporary solid state literature the possibility of d-electron localization is still being discussed (49-51). Examples can be found in the literature that discuss the following problems high cohesion energy of transition metals (52), their crystallographic structure (53), magnetic moments of the constituent atoms in alloys (54), optical and photoemission properties (48, 49), and plasma oscillation losses (55). 

Abstract The focus of this chapter is primarily directed towards nanocrystalline soft magnetic materials prepared by crystallization of amorphous precursors. The key elements involved in the development of this class of materials are three-fold (i) theoretical models for magnetic softness in nanostructures (ii) nanostructure-property relationships and (iii) nanostructural formation mechanisms. This chapter surveys recent research on these three areas with emphasis placed on the principles underlying alloy design in soft magnetic nanostructures. 

This comprises both new catalysts and new alloys. Here, new fundamental knowledge is needed in order to fully understand the catalyst mechanism and, more importantly, hydride destabilization. Further discussions on some new directions are the subject of other chapters of this book (complex hydrides, amides, destabilized systems, aluminum hydride, nanoparticles and theoretical modeling). 

Problems of current interest to which we draw attention in this review are (1) the nature of adsorbed hydrogen, (2) the possibility of weak adsorption in excess of a monolayer and its influence on surface area determinations, (3) the adsorption/ absorption transition and the mechanism of absorption, and (4) the selectivity of H for special sites in alloys and the structural modifications in alloys caused by H. Finally, we shall comment briefly on the extent to which existing theoretical models can account for some of these features. 

The absorption of H by alloys poses even more complicated and less well understood problems. None of the theoretical models currently available can account satisfactorily for the fact that H can distinguish between interstitial sites surrounded by different types of metal atoms, although Switendick has commented on the need to allow for substantial local effects in calculations of the band structure of alloy hydrides. 

Figure 15 Comparison between theoretical (left) and experimental (right) results for diffraction patterns obtained at four different kinetic energies 60, 66, 80, and 94 eV. The diffraction patterns are from Mn emitters in a c(2 x 2) MnNi surface alloy. The model structure used for the theoretical results was a substitutional alloy with the Mn atoms buckled out of the surface layer.

Systems of randomly oriented magnetic nanoparticles randomly dispersed in a supporting medium or matrix and that interact via dipole-dipole forces (last subsection) are systems having several energetically equivalent supermoment orientational states, at given temperatures and applied fields. As such, it is relevant to compare their magnetic behaviors with both the observed behaviors of canonical SG systems (dilute magnetic alloys such as MnCu) and the theoretical predictions from overly simple SG models. This has lead to a productive examination of the effects of dipolar and other inter-particle interactions in synthetic nanoparticle model systems that is reviewed below. Hopefully, this will in turn motivate the development of more realistic theoretical models of disordered dipolar systems. 

Electronic properties such as electrical conductance, magnetic behaviour and band structure typically show dramatic changes with alloy composition, especially where the electronic structures of the pure components differ greatly, as happens for example when the d-shell is filled. Alloys of this type (Ni-Cu, Pd-Ag, Pd-Au) were the subject of intensive research in the period 1945-1970, as it was believed that the presence of an incompletely-filled d-shell was an important feature in determining catalytic activity, and that filling would occur at some composition that could be deduced from electronic properties. The experimental results and the theoretical models that form our present state of understanding of the behaviour of electrons in alloys will be considered in the following section. 

The mechanical properties and glass transition behavior of these polymer alloys were compared. The kinetics of polymerization of the component pol3rmers were measured and varied by changing the concentration of catalysts in order to determine the effect of polymerization rates on the morphology of the IPN s. Electron microscopy and dynamic mechanical spectroscopy were also carried out. Several theoretical models predicting the modulus of... 

The measurement of the metallic surface area in a multi-component system as a bimetallic supported catalyst or an alloy is feasible by selective chemisorption on the metallic phase. The chemisorption stoichiometry is defined with reference to the adsorbate related to the metallic element [8]. Therefore, the chemisorption process is very different if the adsorbed gas molecule is dissociated or not. The two kinds of chemisorption involve different energetic behaviours and different theoretical models define them associative and dissociative adsorption. In the first case, the gas is adsorbed without fragmentation in the second case, the gas molecule is adsorbed after its decomposition in one or more fragments. Hydrogen, for example, is always adsorbed in its dissociated form. 

Depth-profile analysis is also possible, as the sample is ablated layer-by-layer with a penetration rate of 1 - 3 pm/min. Here, the intensities of the analyte lines are measured as a function of time. However, the sputtering rates of alloys with varying composition must be known to convert the time scale into a depth scale. The intensities must be related to concentrations, which can be done by using theoretical models and sputtering constants [291]. The power of detection may be quite good and depth resolution is of the order of 5 nm, when elemental concentrations >0.1% are monitored. Depth profile analysis is now a main field of application of glow discharge emission spectrometry in the metals industry (Fig. 42) [291]. 

It is also observed that activation energies of amorphous alloys calculated by means of the different theoretical models differ substantially from each other. This difference in the activation energy as calculated with the different models may be attributed to the different approximations used in the models. 

In this section, we introduce computational methods employed in surface adsorption studies. Examples of theoretical studies of the adsorption of molecular oxygen and ORR intermediates on transition metals and alloys will be provided. Insights and findings from theoretical modeling will also be discussed. 

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