1: Bonding in Solids

Example number 1.1, Page number 1.11

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

#Variable declaration
e=1.6*10**-19;   #charge of electron(c)
epsilon0=8.85*10**-12;    #permittivity(C/Nm)
r0=236*10**-12;     #seperation(m)
IE=5.14;     #ionisation energy of Na(eV)
Ea=-3.65;     #electron affinity(eV)

#Calculation
V=-e**2/(4*e*math.pi*epsilon0*r0);     
BE=IE+Ea+round(V,2);       #bond energy(eV)

#Result
print "bond energy is",round(BE,1),"eV"

bond energy is -4.6 eV

Example number 1.2, Page number 1.11

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

#Variable declaration
e=1.602*10**-19;   #charge of electron(c)
epsilon0=8.85*10**-12;    #permittivity(C/Nm)
r0=0.314*10**-9;     #seperation(m)
A=1.75;    #madelung constant
n=5.77;    #repulsive exponent value
IE=4.1;     #ionisation energy of K(eV)
Ea=3.6;     #electron affinity(eV)

#Calculation
E=-A*e**2*(1-(1/n))/(4*e*math.pi*epsilon0*r0);      #energy(eV)
Ce=E/2;      #cohesive energy per atom(eV)
x=IE-Ea;     #energy(eV)
CE=Ce+(x/2);    #total cohesive energy per atom(eV)

#Result
print "total cohesive energy per atom is",round(CE,4),"eV"
print "answer varies due to rounding off errors"

total cohesive energy per atom is -3.0684 eV
answer varies due to rounding off errors

Example number 1.3, Page number 1.12

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.602*10**-19;   #charge of electron(c)
epsilon0=8.85*10**-12;    #permittivity(C/Nm)
r0=0.281*10**-9;     #seperation(m)
alpham=1.748;    #madelung constant
n=9;    #repulsive exponent value

#Calculation
E=-alpham*e**2*(1-(1/n))/(4*e*math.pi*epsilon0*r0);      #cohesive energy(eV)

#Result
print "cohesive energy is",round(E,3),"eV"

cohesive energy is -7.965 eV

Example number 1.4, Page number 1.12

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;   #charge of electron(c)
epsilon0=8.85*10**-12;    #permittivity(C/Nm)
r0=2.5*10**-10;     #seperation(m)

#Calculation
PE=e**2/(4*e*math.pi*epsilon0*r0);     #potential energy(eV)

#Result
print "potential energy is",round(PE,3),"eV"

potential energy is 5.755 eV

Example number 1.5, Page number 1.13

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=1;
n=9;     #repulsive exponent value
a=1.748*10**-28;     
r0=0.281*10**-9;     #seperation(m)

#Calculation
Ur0=-a*(1-(m/n))/(e*r0**m);    #cohesive energy(eV)

#Result
print "cohesive energy is",round(Ur0,2),"eV"

cohesive energy is -3.46 eV

Example number 1.6, Page number 1.13

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;   #charge of electron(c)
epsilon0=8.85*10**-12;    #permittivity(C/Nm)
r0=0.281*10**-9;     #seperation(m)
IE=5.14;     #ionisation energy of Na(eV)
Ea=-3.61;     #electron affinity(eV)

#Calculation
V=-e**2/(4*e*math.pi*epsilon0*r0);     
CE=IE+Ea+round(V,2);       #cohesive energy(eV)

#Result
print "cohesive energy is",CE,"eV"

cohesive energy is -3.59 eV