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9.order_disorder - T Y Tan 9 ORDER-DISORDER TRANSITIONS IN...

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T. Y. Tan 1 9. ORDER-DISORDER TRANSITIONS IN ALLOYS For alloys consisting of completely mutually soluble component atoms, at certain specific compositions the alloys exist as ordered solid solutions at low temperatures and as a single phase disordered solid solution at high temperatures. The Cu-Au system exhibits such a behavior, as can be seen from its phase diagram shown in Fig. 9.1. The Cu and Au atoms form a disordered solid solution at any composition when the temperature is higher than ~400 o C, while at lower temperatures ordered solid solutions Cu 3 Au, CuAu, etc. form in the appropriate alloy composition ranges. Here the terms order and disorder are not referring to the structures of the solutions, which are crystalline and are the same for both solutions, e.g., face centered cubic (fcc), but to the arrangement of the relative positions of atoms of the different components. For example, in the ordered Cu 3 Au alloy, it may be viewed that Au atoms are occupying the corner positions of a unit cell and Cu atoms are occupying the face-centered positions, see Fig. 9.2, while in the disordered alloy the Cu and Au atom positions are random. Phase changes associated with most alloys are first order transformations that are characterized by a sharp transition temperature T c . The order to disorder (upon heating) and disorder to order (upon cooling) transitions are, however, second order phase transformations that occur over a range of temperature below a "critical" temperature T c , see also Fig. 9.1. Above T c , only a short-range ordering phenomenon can exist. 9.1 Physical Basis of the Order-Disorder Transition The basic reason that the order-disorder transition occurs is that, at low temperatures, Gibbs free energy of the ordered alloy is lower than that of the disordered alloy. The reverse is true at high temperatures. For the two component system at any temperature, G AB = H AB - TS AB . (9.1) Postulating the existence of a perfectly ordered (stoichiometric) alloy and a completely disordered alloy of the same chemical composition and structure, we can find the basic reason (which also constitutes some necessary conditions) for this to occur. For the ordered alloy G AB (O) = H AB (O) - TS AB (O) , (a) and for the completely disordered alloy
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T. Y. Tan 2 G AB (D) = H AB (D) - TS AB (D) . (b) Consider S AB as that due to mixing only, S AB (O) = 0 (c) holds for the perfectly ordered alloy, and S AB (D) = - k B N A ln N A N + N B ln N B N (d) holds for the completely disordered alloy. By Eqs. (6.26), H AB of the disordered alloy is H AB (D) = 1 2 zN A h AA + 1 2 zN B h BB + z N A N B N h 12 - 1 2 h 11 + h 22 . (e) H AB of the ordered alloy is structure dependent and can therefore not be arrived at in the same way as for (e). For this reason, we shall consider the example of CuAu for which N A =N B =N/2 and the structure is fcc. In this ordered structure each Cu atom has 12 Au atoms and no Cu atom as nearest neighbors, and the analogous situation holds for the Au atoms. Therefore, H AB (O) = 6 Nh AB . (f) For this example, (d) and (e) respectively reduce to S AB (D) = 0.693Nk B , (g) H AB (D) = 3 N h AB + 1 2 h AA +h BB . (h)
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