Thermodynamics of segregation in alloys
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I.
INTRODUCTION
SEGREGATION plays a very important role in many processes of interest to metallurgists and chemists. Experimental measurements of segregation have now been possible for over 20 years using Auger electron spectroscopy. Theoretical models are, however, still needed to understand better the segregation process. Many theoretical models have been proposed in the literature. t~-m Most of these models are either simplified to the point that they can be applied only to some simple dilute and regular solutions or are too complex to be useful with the available data. A more useful but somewhat empirical model was recently proposed by Miedema which appears to be applicable to a number of dilute alloy solutions. 16'7] In many situations of interest to metallurgists, it is important to know the segregation behavior of elements that form strong chemical compounds, such as sulfides, borides, and phosphides. There are no theoretical models available to describe the segregation in such situations. The primary purpose of this study was to develop approximate thermodynamic equations, based on first principles, that can be used in a wide variety of situations, including those where the segregating element forms strong chemical compounds. This has been achieved using the concepts of excess free energies and activity coefficients. Although both of these functions have been used extensively in the literature to describe bulk solutions, their use in surface segregation processes has been rather limited. IJ4'2~ We first discuss (in Section II) some of the basic relations for segregation. Most of these relations are given in the literature, in particular in Reference 1, and are included here for the sake of completeness. The general segregation equations developed here are given in Section III. These equations are then used to derive segregation equations for elements that form strong chemical compounds (such as sulfur, phosphorus, and boron) in Section IV. Finally, in Section V, the validity of our equations is tested by comparing the calculated segregation effects with those observed experimentally I~2'~31 on the surface of NiCrAI(Y) alloys containing sulfur impurities.
K.L. LUTHRA and C.L. BRIANT are Staff Scientists with General Electric Company, Research and Development Center, P.O. Box 8, Schenectady, NY 12301. Manuscript submitted June 5, 1987.
METALLURGICALTRANSACTIONS A
II.
BASIC RELATIONS
The segregation of elements from a bulk phase to its surface can be considered by treating two solutions--the bulk phase and the surface--in equilibrium. The chemical potential of all elements should then be equal in both the locations. The chemical potentials can be expressed in terms of the free energies of dissolution of each of the elements, except that those in the surface phase would be modified by the surface tension of the solid. It is, therefore, useful to consider the relations describing the chemical potentials and total free energies of each of the solutions. (A detailed description of the basic free energy rela
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