Electronic-Structure-Based Design of Ordered Alloys
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Introduction For decades there has been rapid growth in the availability of computational power. In parallel, constantly improving algorithms for accurate electronic structure calculations of ever more complex materials have been developed.1 The combination of available computer power and improved algorithms is leading to rapidly decreasing costs for calculations of the electronic structure of materials at acceptable levels of accuracy. The experimental methodology in materials design has also improved significantly through the introduction of high-throughput synthesis, characterization, and testing. The decrease in the cost of experimental synthesis and testing of a given material, however, has not been quite as impressive as that of computing electronic structure, and the costs of developing new materials are in many cases still overwhelming. The reductions in computation costs relative to the cost of experiments is changing the level of ambition of computational researchers from merely rationalizing known experimental facts to actively participating in the materials design process.2–7
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An extrapolation of the advances in the past suggests that electronic structure theory in the relatively near future might become a competitive tool in the design process for a wider range of materials. One issue that needs to be addressed in order to design or search for new materials with special properties is the choice of screening strategy: how does one determine for which structures it would be interesting to perform electronic structure calculations?
Screening Strategies Today we are beginning to be able to calculate the electronic structure of tens of thousands of materials, at least ones with simple structures.8 We are, however, not close to being able to computationally design new materials from a random trialand-error approach. Nor is it desirable to do so—the number of distinct possibilities for a particular class of materials will generally be much too large. It is necessary to employ methods that aim at the most interesting materials while utilizing a limited number of electronic structure calculations.
Three useful strategies are global search algorithms, database construction and mining, and hierarchical screening methods. Global search algorithms are systematic methods to investigate a given search space for optimal solutions. The global optimization problems relevant for materials design are often dependent on a number of parameters that can be varied individually. For such problems, no method can in general be sure to find the optimal solution, but reasonable algorithms exist. As an example of a global optimization algorithm with satisfactory convergence, we describe an evolutionary algorithm for alloy design in the next section. As an illustration of a fruitful data mining algorithm, we shall describe the use of the concept of “Pareto-optimality” to determine the most interesting materials in a given database. Finally, we discuss a hierarchical approach to alloy catalyst design that involves a hybrid betw
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