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CHAPTER 10 PHASE TRANSFORMATIONS IN METALS PROBLEM SOLUTIONS 10.1 The two stages involved in the formation of particles of a new phase are nucleationand 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 This problem calls for us to compute the length of time required for a reaction to go to 99% completion. It first becomes necessary to solve for the parameter kin Equation (10.1). Rearrangement of this equation leads to k =−ln (1−y)tn=−ln (1−0.5)(100 s)1.7= 2.76 x 10-4Now, solving for the time to go to 99% completion t = −ln (1−y)k⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 1/n=−ln (1−0.99)2.76 x 10−4⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1/1.7= 305 s10.3 This problem asks that we compute the rate of some reaction given the values of nand kin Equation (10.1). Since the reaction rate is defined by Equation (10.2), it is first necessary to determine t0.5, or the time necessary for the reaction to reach y= 0.5. Solving for t0.5from Equation (10.1) leads to t0.5=−ln (1−y)k⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 1/n1
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