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and the vacancy mechanism being equivalent to the two "chemical reactions" A + V~&~A~+ V and B + V~~B~+V . The reaction rates in these models are derived in terms of the fundamental parameters of atom movements, and are themselves order-dependent.(6) The vacancy-interchange model has been applied to the case of Cu3Au, which has been studied experimentally by Burns and Quimby. A Bsymmetry was assumed, an activation energy and a pre-exponential factor were taken from the measurements of self-diffusion in pure copper and pure gold, and the remaining parameter of the theory was adjusted to produce agreement with the known critical temperature for ordering in this system. The theory then gives reasonably good agreement with relaxation times observed by Burns and Quimby over the temperature range of the experiments, 338'C to 388'C. (7) The developments outlined above have been concerned with homogeneous systems. The basic apparatus of multiparticle distribution functions and their equations of motion is equally applicable to inhomogeneous systems, including cases of domains of order in a disordered matrix, domains of antiphase order, and diffusion in alloys. 9. ACKNOWLEDGMENTS The writer is indebted to G. J. Dienes for numerous discussions and some important suggestions in the course of this work, and to S. L. Quimby for supplying information about his Cu3Au experiments.It is known that the free energy of an imperfect semiconductor or insulator crystal contains terms which arise from the ionizability of these imperfections and which represent chemical interactions between imperfections of the same and different kinds. We show that these ionization terms, which involve the Fermi level and the parameters of the energy band model, explain the systematic differences between eand p-type semiconductors in lattice vacancy concentration, in substitutional atom diffusion coe%cients, and in amphoteric impurity behavior. The ionization terms also explain the variation of solid-liquid impurity distribution coefficients with the crystal growth rate of certain semiconductors, and also the well-known "charge balance" effect in insulators.

Pressing changes are needed in the administration of real estate taxation that will not only ensure that all properties be assessed accurately and equitably, but will enable taxpayers to perceive that they are being treated fairly. In this paper, we examine what properties an automated mass appraisal system should exhibit so as to meet efficacy, equity and public acceptability criteria. A new automated system designed on the basis of these properties which utilizes feedback control and pattern recognition concepts is presented. Results of an empirical study using Pittsburgh data supports the feasibility of the proposed system.