4: Defects in Crystals¶

Example number 4.1, Page number 97¶

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
T1=773;     #temperature(K)
T2=1273;    #temperature(K)
n=1*10**-10;       #fraction of vacancy sites

#Calculations
X=round(T1*math.log(n)/T2,3);
x=math.exp(X);          #fraction of vacancy sites at 1000 C

#Result
print "fraction of vacancy sites at 1000 C is",round(x*10**7,4),"*10**-7"
print "answer varies due to rounding off errors"

fraction of vacancy sites at 1000 C is 8.4663 *10**-7
answer varies due to rounding off errors


Example number 4.2, Page number 98¶

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=273+25;     #temperature(K)
m=4;
n=5*10**11;    #density(per m**3)
V=(2*2.82*10**-10)**3;     #volume(m**3)
kB=8.625*10**-5;

#Calculations
N=m/V;
Ep=2*kB*T*math.log(N/n);

#Result
print "energy required is",round(Ep,3),"eV"

energy required is 1.971 eV


Example number 4.3, Page number 99¶

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
T1=273+20;     #temperature(K)
T2=273+300;    #temperature(K)
Ei=1.4;     #energy(eV)
kB=8.625*10**-5;

#Calculations
x=(1/(2*T1))-(1/(2*T2));
n=1/math.exp((Ei/(2.303*kB))*x);     #ratio of frenkel defects

#Result
print "ratio of frenkel defects is",round(n*10**3,3),"*10**-3"
print "answer in the book is wrong"

ratio of frenkel defects is 2.802 *10**-3
answer in the book is wrong