Essentials Of Materials Science And Engineering
Essentials Of Materials Science And Engineering
4th Edition
ISBN: 9781337385497
Author: WRIGHT, Wendelin J.
Publisher: Cengage,
Question
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Chapter 12, Problem 12.3P
Interpretation Introduction

Interpretation:

The value of constants n and c for the given equation needs to be calculated.

Concept Introduction:

At constant temperature, the determination of solid phase transformation is done by using the Avarmi equation. Generally, it is used to describe the rate of kinetic crystallization.

This equation is also known as the JMAK equation as it was founded by Johnson-Mehl-Avrami-Kolmology. This equation was first found in the year 1937 by Kolmogorov. And the first paper was published by Melvin Avrami during the years 1939 and 1941 in the Journal of chemical equations.

Expert Solution & Answer
Check Mark

Answer to Problem 12.3P

The constant value of c = 8.9×10-6 and n = 2.81.

Explanation of Solution

Given:

Eqauation: f=1-exp(-ctn)

Temperature = T =140 K

Essentials Of Materials Science And Engineering, Chapter 12, Problem 12.3P , additional homework tip  1

Assume:

Elapsed time − t

Temperature constants - and n

From the given equations of curves, the values of f and time are:

fTime (min)
0.128
0.237
0.344
0.450
0.555
0.660
0.767

Table 1

To calculate the constants value of c and n by using the below formula,

  f=1-exp(-ctn)

  1-f = exp( -ctn)ln(1-f)= -ct

Taking natural logarithm on both sides,

  ln[-ln(1-f)]= ln(c)+n×ln(t)

ft (min) ln(t)ln[-ln(1-f)]
0.1283.332.2504
0.2373.611.4999
0.3443.781.0309
0.4503.910.6717
0.5554.010.3665
0.6604.090.0874
0.7674.20.1856
0.8734.290.4759
0.9864.450.8340

Table 1

From the above table, the solpe of the graph is plotted as:

Essentials Of Materials Science And Engineering, Chapter 12, Problem 12.3P , additional homework tip  2

Fig. 2 Slope graph

From graph ,

  n - temperature constant

  n = 2.81

Then to find value of c, we can use −

  ln[-ln(1-f)]= ln(c)+n×ln(t)

  ln[-ln(1-0.2)]= ln(c)+2.81×ln(37)ln(c)=-11.64c = e-11.64c=8.9×109

Conclusion

Thus, the value of c = 8.9×10-6 and n = 2.81 which are obtained by using the slope of graph.

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Chapter 12 Solutions

Essentials Of Materials Science And Engineering

Ch. 12 - Prob. 12.11PCh. 12 - Prob. 12.12PCh. 12 - Prob. 12.13PCh. 12 - Prob. 12.14PCh. 12 - Prob. 12.15PCh. 12 - Prob. 12.16PCh. 12 - Prob. 12.17PCh. 12 - Prob. 12.18PCh. 12 - Prob. 12.19PCh. 12 - Prob. 12.20PCh. 12 - Prob. 12.21PCh. 12 - Prob. 12.22PCh. 12 - Prob. 12.23PCh. 12 - Prob. 12.24PCh. 12 - Prob. 12.25PCh. 12 - Prob. 12.26PCh. 12 - Prob. 12.27PCh. 12 - Prob. 12.28PCh. 12 - Prob. 12.29PCh. 12 - Prob. 12.30PCh. 12 - Prob. 12.31PCh. 12 - Prob. 12.32PCh. 12 - Prob. 12.33PCh. 12 - Prob. 12.34PCh. 12 - Prob. 12.35PCh. 12 - Prob. 12.36PCh. 12 - Prob. 12.37PCh. 12 - Prob. 12.38PCh. 12 - Prob. 12.39PCh. 12 - Prob. 12.40PCh. 12 - Prob. 12.41PCh. 12 - Prob. 12.42PCh. 12 - Prob. 12.43PCh. 12 - Prob. 12.44PCh. 12 - Prob. 12.45PCh. 12 - Prob. 12.46PCh. 12 - Prob. 12.47PCh. 12 - Prob. 12.48PCh. 12 - Prob. 12.49PCh. 12 - Prob. 12.50PCh. 12 - Prob. 12.51PCh. 12 - Prob. 12.52PCh. 12 - Prob. 12.53PCh. 12 - Prob. 12.54PCh. 12 - Prob. 12.55PCh. 12 - Prob. 12.56PCh. 12 - Prob. 12.57PCh. 12 - Prob. 12.58PCh. 12 - Prob. 12.59PCh. 12 - Prob. 12.60PCh. 12 - Prob. 12.61PCh. 12 - Prob. 12.62PCh. 12 - Prob. 12.63PCh. 12 - Prob. 12.64PCh. 12 - Prob. 12.65PCh. 12 - Prob. 12.66PCh. 12 - Prob. 12.67PCh. 12 - Prob. 12.68PCh. 12 - Prob. 12.69PCh. 12 - Prob. 12.70PCh. 12 - Prob. 12.71PCh. 12 - Prob. 12.72PCh. 12 - Prob. 12.73PCh. 12 - Prob. 12.74PCh. 12 - Prob. 12.75PCh. 12 - Prob. 12.76PCh. 12 - Prob. 12.77PCh. 12 - Prob. 12.78PCh. 12 - Prob. 12.79PCh. 12 - Prob. 12.80PCh. 12 - Prob. 12.81PCh. 12 - Prob. 12.82PCh. 12 - Prob. 12.83PCh. 12 - Prob. 12.84PCh. 12 - Prob. 12.85PCh. 12 - Prob. 12.86PCh. 12 - Prob. 12.87PCh. 12 - Prob. 12.88PCh. 12 - Prob. 12.89PCh. 12 - Prob. 12.90PCh. 12 - Prob. 12.91PCh. 12 - Prob. 12.92PCh. 12 - Prob. 12.93PCh. 12 - Prob. 12.94PCh. 12 - Prob. 12.95PCh. 12 - Prob. 12.96PCh. 12 - Prob. 12.97PCh. 12 - Prob. 12.98PCh. 12 - Prob. 12.99PCh. 12 - Prob. 12.100PCh. 12 - Prob. 12.101PCh. 12 - Prob. 12.102PCh. 12 - Prob. 12.103PCh. 12 - Prob. 12.104PCh. 12 - Prob. 12.105PCh. 12 - Prob. 12.106PCh. 12 - Prob. 12.107PCh. 12 - Prob. 12.108PCh. 12 - Prob. 12.109PCh. 12 - Prob. 12.110PCh. 12 - Prob. 12.111PCh. 12 - Prob. 12.112PCh. 12 - Prob. 12.113PCh. 12 - Prob. 12.114PCh. 12 - Prob. 12.115PCh. 12 - Prob. 12.116PCh. 12 - Prob. 12.117PCh. 12 - Prob. 12.118DPCh. 12 - Prob. 12.119DPCh. 12 - Prob. 12.120DPCh. 12 - Prob. 12.121DPCh. 12 - Prob. 12.122CPCh. 12 - Prob. K12.1KPCh. 12 - Prob. K12.2KP
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