Chapter 7: Phase Diagram

Example 7.2 Page 190

In [3]:
#initiation of variable
#alpha phase
#from diagram
Sn=10;
Pb=100-Sn;

#result
print "In alpha phase % of tin is",Sn,"and % of lead is",Pb,"in the alloy"

#beta phase
#from diagram
Sn=78
Pb=80-Sn;

#result
print "In alpha phase % of tin is",Sn,"and % of lead is",Pb,"in the alloy"

In alpha phase % of tin is 10 and % of lead is 90 in the alloy
In alpha phase % of tin is 78 and % of lead is 2 in the alloy

Example 7.3 Page 191

In [4]:
#initiation of variable
C1=40.0  # Overall alloy composition
Cb=98.0
Ca=10.0
rho_Sn=7.24 #  density in g/cm^3  density of tin
rho_Pb=11.23  # density in g/cm^3  density of lead
Ca_Sn=10.0
Ca_Pb=90.0
Cb_Sn=98.0
Cb_Pb=2.0

#part A
#calculation
Wa=(Cb-C1)/(Cb-Ca)
Wb=(C1-Ca)/(Cb-Ca)

print" Mass fraction for alpha and beta phases is %.2f" %Wa,"and %.2f respectively" %Wb;

#partB
rho_a=100.0/((Ca_Sn/rho_Sn)+(Ca_Pb/rho_Pb));
rho_b=100.0/((Cb_Sn/rho_Sn)+(Cb_Pb/rho_Pb));
Va=Wa/(rho_a*((Wa/rho_a)+(Wb/rho_b)));
Vb=Wb/(rho_b*((Wa/rho_a)+(Wb/rho_b)));

#result
print" Density of alpha phase is : %.2f g/cm^3" %rho_a;
print" Density of beta phase is : %.2f g/cm^3" %rho_b;
print" Volume fraction of alpha phase : %.2f" %Va;
print"Volume fraction of beta phase : %.2f" %Vb;

 Mass fraction for alpha and beta phases is 0.66 and 0.34 respectively
 Density of alpha phase is : 10.64 g/cm^3
 Density of beta phase is : 7.29 g/cm^3
 Volume fraction of alpha phase : 0.57
Volume fraction of beta phase : 0.43

Example 7.4 Page 217

In [5]:
#initiation of variable
C0=0.35 # given composition
C_a=0.022 # given composition
C_Fe3C=6.7 # given composition
C_p=0.76 

#partA
W_a=(C_Fe3C-C0)/(C_Fe3C-C_a)
W_Fe3C=(C0-C_a)/(C_Fe3C-C_a)

#result
print" Mass fraction of total ferrite phase  is %.2f" %W_a
print" Mass fraction of cementide phase is %.2f" %W_Fe3C

#part B
Wp=(C0-C_a)/(C_p-C_a)
W_a1=(C_p-C0)/(C_p-C_a)

#result
print" Mass fraction of Pearlite is %.2f" %Wp
print" Mass fraction of proeutectoid ferrite is %.2f" %W_a1

#partC
Wae=W_a-W_a1

#result
print" Mass fraction of eutectoid ferrite : %.3f" %Wae
print "Answer in book is 0.39. It is due to considering different number of significant figure at intermediate steps"

 Mass fraction of total ferrite phase  is 0.95
 Mass fraction of cementide phase is 0.05
 Mass fraction of Pearlite is 0.44
 Mass fraction of proeutectoid ferrite is 0.56
 Mass fraction of eutectoid ferrite : 0.395
Answer in book is 0.39. It is due to considering different number of significant figure at intermediate steps