MECH530MaterialScience_PhaseTransformationMetalsChp10ProbSolutions

MECH530MaterialScience_PhaseTransformationMetalsChp10ProbSolutions

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CHAPTER 10 PHASE TRANSFORMATIONS IN METALS PROBLEM SOLUTIONS The Kinetics of Phase Transformations 10.1 Name the two stages involved in the formation of particles of a new phase. Briefly describe each. Solution The two stages involved in the formation of particles of a new phase are nucleation and growth . The nucleation process involves the formation of normally very small particles of the new phase(s) which are stable and capable of continued growth. The growth stage is simply the increase in size of the new phase particles. 10.2 (a) Rewrite the expression for the total free energy change for nucleation (Equation 10.1) for the case of a cubic nucleus of edge length a (instead of a sphere of radius r). Now differentiate this expression with respect to a (per Equation 10.2) and solve for both the critical cube edge length, a* , and also ΔG*. (b) Is ΔG* greater for a cube or a sphere? Why? Solution (a) This problem first asks that we rewrite the expression for the total free energy change for nucleation (analogous to Equation 10.1) for the case of a cubic nucleus of edge length a . The volume of such a cubic radius is a 3 , whereas the total surface area is 6 a 2 (since there are six faces each of which has an area of a 2 ). Thus, the expression for G is as follows: G = a 3 G v 6 a 2 Differentiation of this expression with respect to a is as d G da = d ( a 3 G v ) da d ( 6 a 2 ) da
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  • Fall '11
  • Zanuzi
  • Phase transition

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