I. Derive an equation* for the distance (X) that proeutectoid cementite will grow into austenite in time (t). Define all symbols used. 2. Using the equation from question I, determine x for t = 30 s, at a temperature of 900 C for plain carbon steel with a composition of Fe - 1.5 wt.% C. Students can take the activation energy (Qr() for diffusion of carbon in austenite as 124 kJ mol and the preexponential term (Do) as 1.23 x 106 m s' [P. Thibaux et al., Metall. Mater. Trans. A, 38A, 2007, 1169-1176]. An Fe-C phase diagram is provided in Figure I, in which m % means wt.%. R = 8.314J K' mol'. T (C) 1800 1700 1 600 1538C 1 500 1487C 1400 304" 1300 1200 1100 1000 900 12 800 a+y a 0,022 0,77 700 600 500 L+y 12 C (at%) 14 16 18 20 22 24 T(K) 25. 2.11 1153C 1148C L+ FeC 4.30 738C 727C C (m%) +FaxC + FeC 2000 1900 1 800 1 700 1 600 1227C 1 500 1 400 1 300 1 200 1 100 1000 900 800 Figure 1: Fe-C phase diagram [Drawn by C. Dang]. The hard lines are for Fe - Fe3C and should be used for answering the question (the dotted lines are for Fe - graphite). In deriving this expression, assume rate control by diffusion of carbon in austenite (although actual rate data for the growth of proeutectoid cementite suggest that the kinetics of the growth of proeutectoid cementite are more complicated than those for proeutectoid ferrite).