# Chapter 9 : Alloys Systems Phase Diagrams and Phase Transformations¶

## Example 9.1 Page No : 317¶

In [2]:

import math

# Calculation
#Fulcrum is at 0.5% carbon
#from lever rule
Pro_f = ((0.80-0.5)/(0.80-0.0))*100;			# % Proeutectoid ferrite
Pea_f = 100-Pro_f;			# % Pearlite ferrite

# Results
print 'Proeutectoid ferrite = %.1f %%'%Pro_f
print 'Pearlite ferrite = %.1f %%'%Pea_f

Proeutectoid ferrite = 37.5 %
Pearlite ferrite = 62.5 %


## Example 9.2 Page No : 317¶

In [2]:

import math

# Variables
N = 2;
C = 2;
#F = C-P+N
P_1 = 1;
P_2 = 2;
P_3 = 3;
P_4 = 4;

# Calculation
F_1 = C-P_1+N;
F_2 = C-P_2+N;
F_3 = C-P_3+N;
F_4 = C-P_4+N;

# Results
print 'Degrees of freedom for 1 phase = ',F_1
print 'Degrees of freedom for 2 phases = ',F_2
print 'Degrees of freedom for 3 phases = ',F_3
print 'Degrees of freedom for 4 phases = ',F_4

Degrees of freedom for 1 phase =  3
Degrees of freedom for 2 phases =  2
Degrees of freedom for 3 phases =  1
Degrees of freedom for 4 phases =  0


## Example 9.3 Page No : 318¶

In [3]:

import math

# Variables
P = 4;			#Number of phases exhibit by a material
F = 0;			#Minimum degrees of freedom

# Calculation
#modified form of the phase rule F = C-P+1
C = F+P-1;			#minimum number of components in the system

# Results
print 'the minimum number of components in the system = ',C

the minimum number of components in the system =  3