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10_2

# Materials Science and Engineering: An Introduction

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228 Now, the rate is just rate = 1 t 0.5 = 1 4.63 s = 0.216 (s) -1 10.4 This problem gives us the value of y (0.40) at some time t (200 min), and also the value of n (2.5) for the recrystallization of an alloy at some temperature, and then asks that we determine the rate of recrystallization at this same temperature. It is first necessary to calculate the value of k in Equation (10.1) as k = - ln(1 - y) t n = - ln(1 - 0.4) (200 min) 2.5 = 9.0 x 10 -7 At this point we want to compute t 0.5 , the value of t for y = 0.5, also using Equation (10.1). Thus t 0.5 = [ ] - ln(1 - 0.5) k 1/n = - ln(1 - 0.5) 9.0 x 10 -7 1/2.5 = 226.3 min And, therefore, from Equation (10.2), the rate is just
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Unformatted text preview: rate = 1 t 0.5 = 1 226.3 min = 4.42 x 10-3 (min)-1 10.5 For this problem, we are given, for the austenite-to-pearlite transformation, two values of y and two values of the corresponding times, and are asked to determine the time required for 95% of the austenite to transform to pearlite. The first thing necessary is to set up two expressions of the form of Equation (10.1), and then to solve simultaneously for the values of n and k . Rearrangement of Equation (10.1) and taking natural logarithms twice, leads to ln           ln [ ] 1 1 - y = ln k + n ln t...
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