Essentials of Materials Science and Engineering, SI Edition
Essentials of Materials Science and Engineering, SI Edition
4th Edition
ISBN: 9781337672078
Author: ASKELAND, Donald R., WRIGHT, Wendelin J.
Publisher: Cengage Learning
Question
Book Icon
Chapter 12, Problem 12.4P
Interpretation Introduction

Interpretation:

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

Concept Introduction:

At constant temperature, the determinationof 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 12.4P

The value of c = 6.18×10-4 and n = 3.19.

Explanation of Solution

Given:

Eqauation: f=1-exp(-ctn)

Temperature = T=135°C

Essentials of Materials Science and Engineering, SI Edition, Chapter 12, Problem 12.4P , additional homework tip  1

Assume -

Elapsed time − t

Temperature constants - and n

The effect of temperature on crystallization is:

Essentials of Materials Science and Engineering, SI Edition, Chapter 12, Problem 12.4P , additional homework tip  2

Fig. 2 The effect of temperature on crystallization

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)

From the given equations of curves, the values are:

ft (min) ln(t)ln[-ln(1-f)]
0.151.612.25
0.26.61.891.50
0.37.72.041.03
0.48.52.140.67
0.592.200.37
0.6102.300.09
0.710.52.350.19
0.811.52.350.48
0.913.72.620.83

Table 1

From above table, plot the solpe of the graph:

Essentials of Materials Science and Engineering, SI Edition, Chapter 12, Problem 12.4P , additional homework tip  3

Fig. 2 slope of calculated values

Equation of a straight line −

  y = mx+c

Then to find the value of n,

  n = 0.83(1.50)2.621.89

  n = 3.19

Then to find value of c,

  ln[-ln(1-f)]= ln(c)+n×ln(t)

  ln[-ln(0.5)]= ln(c)+2.81×ln(9)ln(c)= -7.39c=6.18×104

Conclusion

The value of c and n are 6.18×104 and 3.19 respectively and are obtained by using the slope.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A weight (W) hangs from a pulley at B that is part of a support frame.  Calculate the maximum possible mass of the weight if the maximum permissible moment reaction at the fixed support is 100 Nm.  Note that a frictionless pin in a slot is located at C.
You and your crew have made it through the night and the day has brought more warmth.  After searching the industrial site, you find an abundant amount of fuel to run the generators to keep you warm.  You also find a memory card labelled “cure”, but your cell phone battery is dead.  First things first, you will need to stay safe as the zombies continue to hunt you in your current location.  The industrial site is surrounded by a metal chain-link fence.  You decide you will electrify the fence to keep the zombies from scaling it.  But the output voltage from the generators is not high enough to really deter them.  You would like to apply around 10 kV to the fence (AC or DC, at that voltage it doesn’t really matter).  You find a transformer that you can use but it only has a turn ratio of 10.  You find some diodes and capacitors and construct the circuit shown in Figure 3 with the intention of hooking Vout to the fence.   Perform a simulation, displaying the voltage Vout using a scope.…
Part F: Progressive activity week 7 Q.F1 Pick the rural location of a project site in Victoria, and its catchment area-not bigger than 25 sqkm, and given the below information, determine the rainfall intensity for ARI 5, 50, 100 year storm event. Show all the details of the procedure. Each student must propose different length of streams and elevations. Use fig below as a sample only. Pt. E-nt 950 200 P: D-40, PC-92.0 300m 300m 000m PL.-02.0 500m HI-MAGO PLA-M 91.00 To be deemed satisfactory the solution must include: Q.F1.1.Choice of catchment location Q.F1.2. A sketch displaying length of stream and elevation Q.F1.3. Catchment's IFD obtained from the Buro of Metheorology for specified ARI Q.F1.4.Calculation of the time of concentration-this must include a detailed determination of the equivalent slope. Q.F1.5.Use must be made of the Bransby-Williams method for the determination of the equivalent slope. Q.F1.6.The graphical display of the estimation of intensities for ARI 5,50, 100…

Chapter 12 Solutions

Essentials of Materials Science and Engineering, SI Edition

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
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Engineering
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Essentials Of Materials Science And Engineering
Engineering
ISBN:9781337385497
Author:WRIGHT, Wendelin J.
Publisher:Cengage,
Text book image
Industrial Motor Control
Engineering
ISBN:9781133691808
Author:Stephen Herman
Publisher:Cengage Learning
Text book image
Basics Of Engineering Economy
Engineering
ISBN:9780073376356
Author:Leland Blank, Anthony Tarquin
Publisher:MCGRAW-HILL HIGHER EDUCATION
Text book image
Structural Steel Design (6th Edition)
Engineering
ISBN:9780134589657
Author:Jack C. McCormac, Stephen F. Csernak
Publisher:PEARSON
Text book image
Fundamentals of Materials Science and Engineering...
Engineering
ISBN:9781119175483
Author:William D. Callister Jr., David G. Rethwisch
Publisher:WILEY