Short range order hardening with second neighbor interactions in fcc solid solutions
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I.
INTRODUCTION
THEidea that local order can contribute to the hardening of a solid solution was first proposed by Fisher,2 and its mathematical analysis was subsequently performed by Flinn. 2 These authors attributed the hardening effect, called short range order hardening (SROH), to the partial destruction of equilibrium short-range order across a slip plane due to a motion of a dislocation line. Flinn calculated the number of ordering pairs before and after a dislocation passage and estimated the hardening effect for a C u 3 A u crystal, finding the effect to be quite appreciable. Although the basic ideas of Fisher and Flinn were certainly valid, their pair interaction model should be reexamined in the light of modem treatments of local order. Such is the object of this paper. It is important to specify what kind of atomic interactions stabilize the local order of the system. If multibody interactions are important, changes of multiatom atomic configurations associated with a dislocation slip should be taken into consideration in addition to changes due to pairs. Even if pair interactions are dominant, which pair interactions (first neighbor, second neighbor... ) should be involved in the estimation of the SROH is another important issue. In this study, we shall investigate the effects of first and second neighbor pair interactions in fcc solid solutions. The reason for selecting these interactions is provided by ground state analysis of the fcc lattice: 3-6 rigorous results indicate that most experimentally observed fcc-based ordered structures (superstructures) can be stabilized by 1st and 2nd n.n. pair interactions only. In fact, eight stable superstructures have been thus determined, the stability of each depending on the concentration and on the ratio a of 2nd to 1st n.n. pair interactions. In the light of these resuits, it can be reasonably assumed that the SROH of fcc solid solutions, whose ground states contain these ordered phases, can be evaluated by a 1st and 2nd n.n. pair interaction model. Since Flinn's original calculation was limited to 1st n.n. pair correlations, it is important to extend his analysis to include at least 2nd n.n. pair correlations.
T. MOHRi, formerly with the University of California-Berkeley, Berkeley, CA, is Assistant Professor, Department of Metallurgical Engineering, Hokkaido University, Sapporo, Japan. D. de FONTAINE is Professor of Materials Science, Department of Materials Science and Mineral Engineering, University of California-Berkeley, Berkeley, CA 94720. J. M. SANCHEZ is Professor of Materials Science, Henry Krumb School of Mines, Columbia University, New York, NY 10027. Manuscript submitted December 21, 1984. METALLURGICAL TRANSACTIONS A
The calculation of pair correlations depends largely on the thermodynamic model used. Flinn's calculation was based on the Bragg-Williams (BW) approximation which is the simplest one available and which is known as a single site approximation. In order to properly evaluate pair probabilities, however, it is indispensable to emplo
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