Alloy Theory Through the Ages
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ALLOY THEORY THROUGH THE AGES A. GONIS'
"Department
of Chemistry and Materials Science, Lawrence Livermore National Laboratory, Livermore, CA 94.550
SUMMARY Main has always been fascinated with the quest to understand the inner workings of nature at a fundamental level. According to Embedocles[1], a philosopher in ancient Greece, all material things consist of four basic elements (he called them "roots"), namely earth, water, air, and fire. Modern mail's interpretation of that statement is that earth, water and air refer to the three states of matter, i.e., solids, liquids and gasses, with fire designating a process for transforming one of those states into the other. Be that as it may, Embedocles' statement could be conceived as the first attempt to construct an alloy theory, i.e., a predictive capability of the behavior of composite systems. The attempt at the construction of such a theory has continued through the ages and it has yielded a. wealth of conicepts, as well as an ever increasing understanding of the laws of nature. For example. the attemnpts of the a.lchemnists to transform lead into gold may have failed, but they gave rise the science of chemistry. The modern era. of alloy theory, at least in the sense in which it is to be interpreted for nut" purposes begins in I,"492 when Lord ftayleigh[2] published his famous paper on the average permnitivity of a heterogeneous medium. This work ushered in the formal construct and much of the mathemnatics of what has come to be known as multiple scattering theory(MST). It is precisely the application of MST to the physics of alloys that concerns us in this session. In 1906 Einstein[3], considered the dielectric and optical properties of a suspension of small p)articles in a liquid (Brownian motion). In 1945 Foldy[4]showed how the macroscopic index of refraction of a heterogeneous medium can be related to its average forward scattering amplitude. Ilis theory was ('nolified to the strong scattering, low-concentration regime and was not selfconsistent. The first significant breakthrough in the application of MST to alloy theory occurred in 1947 when Korringa[5] applied MST to the study of the electronic states in metals. The equations that determine the electronic structure (band structure) of a material arrived at by Korringa were rederived in 1954 by Kohn and Rostoker[6]wlio used a variational formalism. The resulting theoretical construct has come to be known as the theory of Korringa, Kohn and Rostoker, or KNIt. In 1951, Lax[7] used the KKR. method (only the K method at that time!) to introduce the idea of an effective medium to describe the disordered system, and imposed a self consistency condition for the deternminatioui of that medium. llis work forms the basis for the modern self-consistent theories of the electronic structure of disordered alloys. The pace of developing a MST for alloys quickens dramatically from this point onward. In 1958 Ixorringa,[8] kitroduced the average L-mnatrix approximation (ATA) in which the true disordered material is approxi
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