Binary materials reconsidered

Equations (15.2b) and (15.6b) show a denominator containing the term 2j (bK + a K% where eqn. (14.9b) has only 2j K. The separateness of K and in this chapter sheds light on the question of what K actually represents in Chapter 14—a question that was left in an unsatisfactory state in that chapter. The purpose of this section is to review ideas about forming K from and in a simple binary system. 

The picture from which K and emerge is the mixed compound (A, B)X, on which a stress fluctuation has two effects. Consider a site where the compressive stress is at a local maximum, with a local minimum or sink-region somewhere nearby. The two stress-driven diffusion effects are 

The answer is that two comparable effects can certainly be separated by an algebraic step or trick but the step is more than merely a trick, and does indeed resolve some of the uncertainty as to whether a material can be represented both as a continuum and as particles (see Chapter 14, last paragraph of the Summary). 

The conclusion is that even for a simple binary material, we should not look for a single factor K constructed from and K as in eqn. (14.9). 

The behavior of a material of composition (A, B)X contains two parts (i) behavior shown by the ensemble and (ii) behavior that involves atoms of A exchanging position with atoms of B. 

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This chapter has two purposes, one limited and one more extensive. The limited purpose is to reconsider simply binary materials like ideal alloys, where two components A and B or copper and tin mix with each other in any proportion without being encased in a matrix of a third species X. 

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