Calculations on alloys

Part of my work has been performed at the laboratory of the National Research Council (NRC) of Canada in Ottawa and at the Kamerlingh Onnes Laboratory in Leiden, and I owe my sincere thanks to my colleagues at these institutions as well as to those at my home base Risj6. I am especially grateful to J.-P. Jan at NRC who, from a desire to interpret his pioneering de Haas-van Alphen measurements on intermetal 1ic compounds, helped perform the first LMTO calculations on alloys in 1975, and who continued to be a true collaborator until his untimely death in 1981. 

A number of attempts have been made to quairtify this model by means of fundamental quantum-mechanical calculations on the free electron transport in metals and alloys, but at dre present time, the qualitative data presented in Table 5.1 will suffice to indicate the U eirds. 

In this paper, the electronic structure of disordered Cu-Zn alloys are studied by calculations on models with Cu and Zn atoms distributed randomly on the sites of fee and bcc lattices. Concentrations of 10%, 25%, 50%, 75%, and 90% are used. The lattice spacings are the same for all the bcc models, 5.5 Bohr radii, and for all the fee models, 6.9 Bohr radii. With these lattice constants, the atomic volumes of the atoms are essentially the same in the two different crystal structures. Most of the bcc models contain 432 atoms and the fee models contain 500 atoms. These clusters are periodically reproduced to fill all space. Some of these calculations have been described previously. The test that is used to demonstrate that these clusters are large enough to be self-averaging is to repeat selected calculations with models that have the same concentration but a completely different arrangement of Cu and Zn atoms. We found differences that are quite small, and will be specified below in the discussions of specific properties. 

The specific capacity obtained in such Ams, actually corresponds to near theoretical limit of 372 mA-h/g, as calculated on a basis of classical LiC6 stoichiometry). Further increase of capacity is possible only via switching to new or modified materials, composites or alloys, which are capable for reversible and stable intercalation of lithium. 

Surface tension and density of liquid alloys have been studied by Moser et al. (2006). Measurements by maximum bubble pressure and dilatometric techniques were carried out in an extensive range of temperatures on liquid alloys close to the ternary eutectic Sn3 3Ag0 76Cu with different Sb additions, which decrease surface tension and density. The experimental data were discussed in comparison also with values calculated on the basis of different models. 

The Hume-Rothery phases constitute an interesting and ubiquitous group of binary and complex intermetallic substances it was indeed Hume-Rothery who, already in the twenties, observed that one of the relevant parameters in rationalizing compositions and structures of a number of phases is the average number of valence electrons per atom (nJnM). An illustration of this fact may be found in Table 4.6, where a number of the Hume-Rothery structure types have been collected, together with a few more major structure types relevant to transition metal alloys. For each phase the corresponding VEC has been reported as njnai ratio, both calculated on the basis of the s and p electrons and of s, p and d electrons. 

Clearly CALPHAD has now come of age and is at a watershed where complex phase equilibria calculations can now be performed as a routine operation and yet have also been placed on a sound physical basis. Computer programmes exist which can perform complex calculations on a PC and which can therefore be operated at any location without extensive prior expertise. Furthermore, it is possible in many cases to predict phase equilibria in multi-component alloys to a degree which is close to that expected from experiment (see Chapter 10). It is therefore a branch of science that is mature and, indeed, has already entered the next stage of development, which emphasises the need to concentrate on extending its range of applicability. 

Table 10.3. Composition of candidate alloys and results of calculations on toughness, weldability and corrosion resistance. Calculation was conducted assuming an annealing temperature of 1050°C, 0.8%Mn, 0.7%Si and 0.024%C (wt%). PRE value in the heading of the table indicates value for SAF2205 (from Lee 1995)...

In the field of alloy surface composition, both theory and experimental determination achieved much progress in recent years. The present state of the art does not, unfortunately, allow one to predict quantitatively the surface composition from the bulk concentrations, but calculations on models allow one to estimate various effects and to make interesting conclusions and sometimes even semiquantitative predictions. 

From calculations on quasi-infinite lattices it was found that there is a distinct difference between initial changes in heat of chemisorption due to the presence of a surface layer of inactive atoms and changes induced by alloying in several outer layers (136). 

Stoichiometry is the series of calculations on the basis of formulas and chemical equations and will be covered in Chapter 4. The use of conversion factors is common even when the relative proportions are not fixed by a chemical formula. Consider a silver alloy used for jewelry production. (Alloys are mixtures of metals and, as mixtures, may be produced in differing ratios of the metals.) A particular alloy contains 86 percent silver. Factors based on this composition, such as... 

National Bureau of Standards (NBS) alloys with certified compositions were used as standards along with Centre Technique des Industries de la Fonderie (CTIF) standards. These standards cover a fairly wide range of tin and lead concentrations. When no standards were available that had compositions close to those of the coins, corrections for the effect of lead and tin contents were calculated on the basis of the presence of these elements in various standards. 

Bimetallic alloys have modified electronic structures on the surface, and so adsorption energy changes of certain intermediates may enhance the overall catalytic activity. Zhang et al. have performed periodic DFT calculations on a Pt monolayer on Au(lll), Rh(lll), Pd(lll), Ir(lll), and Ru(OOOl) substrates." Zhang and coworkers have also undertaken simulations on mixed Pt-M (80 20) monolayers (M = Ir, Ru, Rh, Pd, Au, Re, or Os)... 

To quantily the metal dissolution trends, and to offer comparisons of the stability of surface Pt atoms in different environments, we reported the development and application of a computational approach based on first-principles calculations on metal slabs, using the methodologies explained in this chapter. The method allows us to evaluate the electrochemical potential shift AU (V) for the dissolution of Pt atoms in an alloy surface, relative to the potential at which the same reaction would take place on pure Pt(lll) surfaces. Recent investigations in our lab have found interesting correlations between the potential shift for the onset of surface oxidation of Pt in Pt-based alloys with respect to the same potential in pure Pt surfaces and the d-band shift of the surface atoms, reflecting the changes in the electronic structure due to alloying. The results will be published elsewhere. 

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