# Chapter 8: Phase transformation¶

## Example 8.1 Page 236¶

In :
#initiation of variable
from math import pi
Hf=-1.16*10**9  #  Latent heat of fusion in J/m^3
Y=0.132  #   Surface energy in J/m^2
Tm=1064+273.0  # Melting point of gold in K
T=1064+273-230.0  #  230 is supercoiling value in K
a=0.413*10**-9  #  Unit Cell edge length in m
n = 4.0 # Number of atoms in a FCC unit cell

#part A
#calculation
r=-2*Y*Tm/(Hf*(Tm-T));
G=16*pi*Y**3*Tm**2/(3*Hf**2*(Tm-T)**2);

#result
print" Critical Radius is : %.2f nm" %(r/10**-9);
print" Activation free energy is : %.2e J" %G
print "Answer in book is 9.64e-19 J. It is due to approximation at intermediate stage"

#part B
u_c=4*pi*r**3/(3*a**3)
tot_uc = n*int(u_c) # Total no. of atoms per critical nucleus

#result
print" Unit cells per paricle are : %d" %u_c;
print" Total no. of atoms per critical nucleus are : %d" %tot_uc;

 Critical Radius is : 1.32 nm
Activation free energy is : 9.68e-19 J
Answer in book is 9.64e-19 J. It is due to approximation at intermediate stage
Unit cells per paricle are : 137
Total no. of atoms per critical nucleus are : 548


## Example 8.2 Page 252¶

In :
#initiation of variable
#part A
t1=10
print " At 350C the isothermic reaction begins time",t1, "s and reaches completion of about 500s completion time"

#partB
t2=150
print " In this case it takes about time",t2,"s for the reaction to begin and so, at 100s the specimen is 100% austenite"

#partC
t3=7
print "In this case reaction begins after time",t3,"s and at about 20s 50% of reaction is complete"

 At 350C the isothermic reaction begins time 10 s and reaches completion of about 500s completion time
In this case it takes about time 150 s for the reaction to begin and so, at 100s the specimen is 100% austenite
In this case reaction begins after time 7 s and at about 20s 50% of reaction is complete