Lecture note 13 (10-18-2011)

Lecture note 13 (10-18-2011) - MAE 581 Advanced Materials...

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1 MAE 581 Advanced Materials Science Lecture note 13 Phase equilibrium and structure Free energy and composition Of considerable importance in metallurgical practice is the increase in entropy associated with the formation of a disordered solid solution from the pure components. This arises because, over and above the entropies of the pure components A and B, the solution of B in A has an extra entropy due to the numerous ways in which the two kinds of atoms can be arranged amongst each other. This entropy of disorder or mixing is of the form shown in Figure 2.9a. As a measure of the disorder of a given state we can, purely from statistics, consider W , the number of distributions which belong to that state. Thus, if the crystal contains N sites , n of which contain A atoms and ( N n ) contain B atoms , it can be shown that the total number of ways of distributing the A and B atoms on the N sites is given by This is a measure of the extra disorder of solution, since W =1 for the pure state of the crystal because there is only one way of distributing N indistinguishable pure A or pure B atoms on the N sites.
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Lecture note 13 (10-18-2011) - MAE 581 Advanced Materials...

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