Modern Physical Metallurgy and Materials Engineering Part 3

Tham khảo tài liệu 'modern physical metallurgy and materials engineering part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Structural phases their formation and transitions 51 Figure Free energy-temperature curves for a f and liquid phases. 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 . 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 Figure Variation with composition of entropy a and free energy b for an ideal solid solution and for non-ideal solid solutions c and d . atoms on the N sites is given by N W -7- -n N n 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. To ensure that the thermodynamic and statistical definitions of entropy are in agreement the quantity W which is a measure of the configurational probability of the system is not used directly but in the form S k ln W where k is Boltzmann s constant. From this equation it can be seen that entropy is a property which measures the probability of a configuration and that the greater the probability the greater is the entropy. Substituting for W in the statistical equation of entropy and using Stirling s approximation1 we obtain S kln N n N - n k NlnN n lnn N n ln N n for the entropy of disorder or mixing. The form of this entropy is shown in Figure where c n N is the atomic concentration of A in the solution. It is of particular interest to note the sharp increase in entropy for the addition of only a small amount of .

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