Energetics of alloys

Alloy Research Center and Department of Physics, Florida Atlantic University, Boca Raton, FL 33431. 

Yang Wang, Nassrin Moghadam, and G. M. Stocks Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830. 

Certain properties of the disordered alloy are qualitatively different from the properties of an intermetallic compound. A simple example of a property that demonstrates this qualitative difference is the finite residual resistivity of the disordered alloy, which is the resistivity in the limit as the temperature approaches zero. An ordered intermetallic compound will have a resistivity at T=0 that is essentially zero or infinity. A less simple example is Anderson localization.  

In the early days of alloy theory, Lifshitz argued on intuitive grounds that one can calculate the properties of a disordered alloy from one sufficiently large sample, and referred to this property of a large sample as self-averaging. It can be seen most easily in exact 

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. 

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Fig. 6.18. Schematic of the low-order clusters considered in the treatment of the energetics of alloys built on a host fee lattice (adapted from Lu et al. (1991)).

Recently, a method has been proposed to overcome the problems associated with calculating forces in both VMC and DMC [122], It has been suggested that the use of QMC in the near future to tackle the energetics of systems as challengmg as liquid binary iron alloys is not unthinkable [123],... 

A stated objective of many of the reported studies of the catalytic properties of alloys has been to elucidate the significance of the band structure of the metallic phase (i.e., the energy levels of the d electrons) in determining the energetics of reaction (i.e., the value of E). While significant correlations of the values of E with band structures have been found in several instances [e.g., (25,255)], the interpretation of results is not always straightforward (237) and it may be necessary to incorporate due allowance for other factors that may exert some control over the mechanisms of reactions. Such factors include the possible presence of more than one alloy phase (207), dissolution of hydrogen in the alloy (207), and the composition and disposition of elements in the active outer surface of the alloy under reaction conditions (28,113,208). 

Several groups have ascribed this irreversible Cd stripping to the formation of an alloy with the Au [136-138], as does this author. If UPD can be thought to result from the energetics of compound formation, it may also result from alloy formation. Evidently, the Cd atoms are able to diffuse into the Au, exposing more surface Au atoms, to react with more Cd. Subsequent stripping then requires the Cd atoms to diffuse to the surface before they can oxidize, resulting in the observed irreversibility in the voltammetry [138]. 

Nitric acid reacts energetically at ordinary temperatures, with formation of the nitrate and of the oxides of nitrogen. The behaviour of the metal with hydrochloric acid is similar to that of lead. The action of concentrated sulphuric acid and of nitric acid finds application in the separation of alloys of gold and silver. The corrosive effect of acids is accelerated by the presence of an oxidizer.5... 

In this work, we summarized recent progress in the modeling of surface alloys by linking, via a number of selected examples, the different tools available for a comprehensive analysis of such systems a powerful and versatile quantum approximate method for the energetics of the system, appropriate and efficient use of experimental input for its parameterization and, perhaps more importantly, an approach for dealing with the multitude of issues characteristic of such complex systems. 

In a staged multi-scale approach, the energetics and reaction rates obtained from these calculations can be used to develop coarse-grained models for simulating kinetics and thermodynamics of complex multi-step reactions on electrodes (for example see [25, 26, 27, 28, 29, 30]). Varying levels of complexity can be simulated on electrodes to introduce defects on electrode surfaces, composition of alloy electrodes, distribution of alloy electrode surfaces, particulate electrodes, etc. Monte Carlo methods can also be coupled with continuum transport/reaction models to correctly describe surfaces effects and provide accurate boundary conditions (for e.g. see Ref. [31]). In what follows, we briefly describe density functional theory calculations and kinetic Monte Carlo simulations to understand CO electro oxidation on Pt-based electrodes. 

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