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Unformatted text preview: 9.4 In Figure 9.7, the Gibbs phase rule was applied to a hypothetical phase diagram. In a simi- lar way, apply the phase rule to a sketch of the Pb-Sn phase diagram (Figure 9.16). SOLUTION The Gibbs Phase Rule is defined on page 259 of the text. It specifies the number of degrees of freedom ( F ) that can be independently varied in a system of C components and P phases. The most general expression of Gibbs Phase Rule is equation (9.1) F = C P + 2 which applies to systems with three state variables, temperature, pressure, and composition. This problem asks for an application of the phase rule to the Pb-Sn binary phase diagram for which pressure is fixed, consequently the appropriate form of the Gibbs Phase Rule is equation (9.2), F = C P + 1 Now applying it to Figure 9.16, it is seen that all single phase fields have 2 degrees of freedom, all two-phase fields have 1 degree of freedom and at such special points as the melting points of pure Pb or pure Sn, or the eutectic point, there are 0 degrees of freedom. These are labeled on the phase diagram in the style of Figure 9.7 as instructed in the problem statement. F = 21+1 = 2 F = 22+1 = 1 F = 23+1 = 0 F = 12+1 = 0 F = 12+1 = 0 Pb 10 20 30 40 50 60 70 80 90 Sn 400 300 200 100 C wt % Sn Problem 9.4 J. F. Shackelford, Introduction to Materials Science for Engineers , 7 th Edition, Prentice Hall, New Jersey (2009) Problem 9.4 Solution Professor R. Gronsky page 1 of 1 9.13 Describe qualitatively the microstructural development that will occur upon slow cooling of a melt composed of 20 wt% Cu, 80 wt% Al (see Figure 9.27). SOLUTION Note that the problem asks only for a "qualitative" description of microstructural development. Consequently the answer does not require an application of the lever rule for quantitative amounts of the various phases emerging during melt solidification and cooling, only their de- scriptions (identity and morphology) are required. Referring to Figure 9.27 (the Al-Cu phase diagram) as instructed in the problem statement, the following description evolves. A "melt" of 20 wt% Cu and 80 wt% Al remains fully liquid until crossing the liquidus line at ap- proximately 600C. At 600C the first solid phase to appear is the aluminum-rich phase, which precipitates from the liquid as proeutectic microconstituent. On further cooling, the eutectic reaction isotherm is reached at 548C, when the remaining liquid transforms to the eutectic constituent, a lamellar composite of and phases. The final microstructure at room temperature therefore contains two equilibrium phases, and , with the phase dispersed in both proeutectic (equiaxed) and eutectic (lamellar) morphologies....
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This note was uploaded on 01/21/2011 for the course E 45 taught by Professor Gronsky during the Fall '08 term at University of California, Berkeley.
- Fall '08