Chapter 2: Bonding in Solids

Example 2.1,Page number 62

In [1]:
import math 

#Given Data
epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m
e = 1.6*10**-19;   # Energy equivalent of 1 eV, eV/J
r = 3.147*10**-10;     # Nearest neighbour distance for KCl, m
n = 9.1;    # Repulsive exponent of KCl
A = 1.748;  # Madelung constant for lattice binding energy
E = A*e**2/(4*math.pi*epsilon_0*r)*(n-1)/n/e;     # Binding energy of KCl, eV
print"The binding energy of KCl = ",round(E,4),"eV";

The binding energy of KCl =  7.1098 eV

Example 2.2,Page number 62

In [3]:
import math

#Given Data

epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m
N = 6.023*10**23;     # Avogadro's number
e = 1.6*10**-19;   # Energy equivalent of 1 eV, eV/J
a0 = 5.63*10**-10;      # Lattice parameter of NaCl, m
r0 = a0/2;      # Nearest neighbour distance for NaCl, m
n = 8.4;    # Repulsive exponent of NaCl
A = 1.748;  # Madelung constant for lattice binding energy
E = A*e**2/(4*math.pi*epsilon_0*r0)*(n-1)/n/e;     # Binding energy of NaCl, eV
print"The binding energy of NaCl = ",round(E*N*e/(4.186*1000),4),"kcal/mol" ;

The binding energy of NaCl =  181.1005 kcal/mol

Example 2.3,Page number 62

In [4]:
import math

#Given Data

epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m
N = 6.023*10**23;     # Avogadro's number
e = 1.6*10**-19;   # Energy equivalent of 1 eV, eV/J
E = 162.9*10**3;  # Binding energy of KCl, cal/mol
n = 8.6;    # Repulsive exponent of KCl
A = 1.747;  # Madelung constant for lattice binding energy
# As lattice binding energy, E = A*e**2/(4*%pi*epsilon_0*r0)*(n-1)/n, solving for r0
r0 = A*N*e**2/(4*math.pi*epsilon_0*E*4.186)*(n-1)/n;     # Nearest neighbour distance of KCl, m
print"The nearest neighbour distance of KCl = ",round(r0*10**10,4),"angstorm";

The nearest neighbour distance of KCl =  3.1376 angstorm

Example 2.4,Page number 63

In [5]:
import math

#Given Data

epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m
N = 6.023*10**23;     # Avogadro's number
e = 1.6*10**-19;   # Energy equivalent of 1 eV, eV/J
E = 152*10**3;  # Binding energy of CsCl, cal/mol
n = 10.6;    # Repulsive exponent of CsCl
A = 1.763;  # Madelung constant for lattice binding energy

# As lattice binding energy, E = A*e**2/(4*pi*epsilon_0*r0)*(n-1)/n, solving for r0
r0 = A*N*e**2/(4*math.pi*epsilon_0*E*4.186)*(n-1)/n;     # Nearest neighbour distance of CsCl, m
print"The nearest neighbour distance of CsCl = ",round(r0*10**10,4),"angstrom";

The nearest neighbour distance of CsCl =  3.4776 angstrom

Example 2.5,Page number 63

In [6]:
import math

#Given Data

epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m
N = 6.023*10**23;     # Avogadro's number
e = 1.6*10**-19;   # Energy equivalent of 1 eV, eV/J
r0 = 6.46*10**-10;     # Nearest neighbour distance of NaI
E = 157.1*10**3;  # Binding energy of NaI, cal/mol
A = 1.747;  # Madelung constant for lattice binding energy

# As lattice binding energy, E = -A*e**2/(4*pi*epsilon_0*r0)*(n-1)/n, solving for n
n = 1/(1+(4.186*E*4*math.pi*epsilon_0*r0)/(N*A*e**2));   # Repulsive exponent of NaI
print"\nThe repulsive exponent of NaI = ",round(n,4);

The repulsive exponent of NaI =  0.363

Example 2.6,Page number 63

In [7]:
import math

#Given Data

e = 1.6*10**-19;   # Energy equivalent of 1 eV, eV/J
a0 = 2.8158*10**-10;     # Nearest neighbour distance of solid
A = 1.747;  # Madelung constant for lattice binding energy
n = 8.6;    # The repulsive exponent of solid
c = 2;  # Structural factor for rocksalt
# As n = 1 + (9*c*a0**4)/(K0*e**2*A), solving for K0
K0 = 9*c*a0**4/((n-1)*e**2*A);        # Compressibility of solid, metre square per newton
print"The compressibility of the solid = ", "{0:.3e}".format(K0),"metre square per newton";

The compressibility of the solid =  3.329e-01 metre square per newton

Example 2.7,Page number 69

In [8]:
import math

#Given Data

chi_diff = 1;   # Electronegativity difference between the constituent of elements of solid
percent_ion = 100*(1-math.e**(-(0.25*chi_diff**2)));  # Percentage ionic character present in solid given by Pauling
print"The percentage ionic character present in solid = ",round(percent_ion,2),"percent ";

The percentage ionic character present in solid =  22.12 percent

Example 2.8,Page number 69

In [9]:
import math

#Given Data

Eh_GaAs = 4.3;       # Homopolar gap of GaAs compound, eV
C_GaAs = 2.90;      # Ionic gap of GaAs compound, eV
Eh_CdTe = 3.08;      # Homopolar gap of CdTe compound, eV
C_CdTe = 4.90;      # Ionic gap of CdTe compound, eV

fi_GaAs = C_GaAs**2/(Eh_GaAs**2 + C_GaAs**2);
fi_CdTe = C_CdTe**2/(Eh_CdTe**2 + C_CdTe**2);
print"The fractional ionicity of GaAs = ",round(fi_GaAs,4);
print"The fractional ionicity of CdTe = ",round(fi_CdTe,4);

The fractional ionicity of GaAs =  0.3126
The fractional ionicity of CdTe =  0.7168
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