Question

For some metal alloy it is known that the kinetics of recrystallization obey the Avrami equation, and that the value of k in the exponential is 2.60 x 10-6, for time in seconds. If, at some temperature, the rate of recrystallization is 0.0013 s-1, what total time (in s) is required for the recrystallization reaction to go to 90% completion?

Answer 1

Answer:

t = 1456.8 sec

Explanation:

given data:

contant k = 2.60*10^{-6}

rate of crystallization is 0.0013 s-1

rate of transformation is given by

$r = \frac{1}{t_0.5}$

use specifies value to solve $t_0.5$

it is ime required for 50% tranformation

$r = \frac{1}{.0013}=769.2 sec$

Avrami equation is given by

$y = 1 - e^{-kt^n}$

$0.5 = 1 - e^{-kt_0.5^n}$

$1-0.5 = e^{-kt_0.5^n}$

$ln (1 - 0.5) = -kt_0.5^n$

$ln \frac{ln (1 - 0.5)}{-k} = nln t_0.5$

$n = \frac{ ln \frac{ln (1 - 0.5)}{-k}}{ln t_0.5}$

$n = \frac{ ln \frac{ln (1 - 0.5)}{-2.60*10^{-6}}}{ln 769.2}$

n = 1.88

second degree of recrystalization may be determine by rearranging original avrami equation

$t = [\frac{-ln(1-y)}{k}]^{1/n}$

for 90%completion

$t = [\frac{-ln(1-0.9)}{2.60*10^{-6}}]^{1/1.88}$

t = 1456.8 sec