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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 2: Bonding in Solids"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.1,Page number 62"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The binding energy of KCl = 7.10982502818 eV\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Given Data\n",
"epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m\n",
"e = 1.6*10**-19; # Energy equivalent of 1 eV, eV/J\n",
"r = 3.147*10**-10; # Nearest neighbour distance for KCl, m\n",
"n = 9.1; # Repulsive exponent of KCl\n",
"A = 1.748; # Madelung constant for lattice binding energy\n",
"E = A*e**2/(4*math.pi*epsilon_0*r)*(n-1)/n/e; # Binding energy of KCl, eV\n",
"print\"The binding energy of KCl = \",round(E,4),\"eV\";\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.2,Page number 62"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The binding energy of NaCl = 181.1005 kcal/mol\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Given Data\n",
"\n",
"epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m\n",
"N = 6.023*10**23; # Avogadro's number\n",
"e = 1.6*10**-19; # Energy equivalent of 1 eV, eV/J\n",
"a0 = 5.63*10**-10; # Lattice parameter of NaCl, m\n",
"r0 = a0/2; # Nearest neighbour distance for NaCl, m\n",
"n = 8.4; # Repulsive exponent of NaCl\n",
"A = 1.748; # Madelung constant for lattice binding energy\n",
"E = A*e**2/(4*pi*epsilon_0*r0)*(n-1)/n/e; # Binding energy of NaCl, eV\n",
"print\"The binding energy of NaCl = \",round(E*N*e/(4.186*1000),4),\"kcal/mol\" ;\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.3,Page number 62"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The nearest neighbour distance of KCl = 3.1376 angstorm\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Given Data\n",
"\n",
"epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m\n",
"N = 6.023*10**23; # Avogadro's number\n",
"e = 1.6*10**-19; # Energy equivalent of 1 eV, eV/J\n",
"E = 162.9*10**3; # Binding energy of KCl, cal/mol\n",
"n = 8.6; # Repulsive exponent of KCl\n",
"A = 1.747; # Madelung constant for lattice binding energy\n",
"# As lattice binding energy, E = A*e**2/(4*%pi*epsilon_0*r0)*(n-1)/n, solving for r0\n",
"r0 = A*N*e**2/(4*pi*epsilon_0*E*4.186)*(n-1)/n; # Nearest neighbour distance of KCl, m\n",
"print\"The nearest neighbour distance of KCl = \",round(r0*10**10,4),\"angstorm\";\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.4,Page number 63"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The nearest neighbour distance of CsCl = 3.4776 angstrom\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Given Data\n",
"\n",
"epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m\n",
"N = 6.023*10**23; # Avogadro's number\n",
"e = 1.6*10**-19; # Energy equivalent of 1 eV, eV/J\n",
"E = 152*10**3; # Binding energy of CsCl, cal/mol\n",
"n = 10.6; # Repulsive exponent of CsCl\n",
"A = 1.763; # Madelung constant for lattice binding energy\n",
"\n",
"# As lattice binding energy, E = A*e**2/(4*pi*epsilon_0*r0)*(n-1)/n, solving for r0\n",
"r0 = A*N*e**2/(4*pi*epsilon_0*E*4.186)*(n-1)/n; # Nearest neighbour distance of CsCl, m\n",
"print\"The nearest neighbour distance of CsCl = \",round(r0*10**10,4),\"angstrom\";\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.5,Page number 63"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"The repulsive exponent of NaI = 0.363\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Given Data\n",
"\n",
"epsilon_0 = 8.854*10**-12; # Absolute electrical permittivity of free space, F/m\n",
"N = 6.023*10**23; # Avogadro's number\n",
"e = 1.6*10**-19; # Energy equivalent of 1 eV, eV/J\n",
"r0 = 6.46*10**-10; # Nearest neighbour distance of NaI\n",
"E = 157.1*10**3; # Binding energy of NaI, cal/mol\n",
"A = 1.747; # Madelung constant for lattice binding energy\n",
"\n",
"# As lattice binding energy, E = -A*e**2/(4*pi*epsilon_0*r0)*(n-1)/n, solving for n\n",
"n = 1/(1+(4.186*E*4*pi*epsilon_0*r0)/(N*A*e**2)); # Repulsive exponent of NaI\n",
"print\"\\nThe repulsive exponent of NaI = \",round(n,4);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.6,Page number 63"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The compressibility of the solid = 3.329e-01 metre square per newton\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Given Data\n",
"\n",
"e = 1.6*10**-19; # Energy equivalent of 1 eV, eV/J\n",
"a0 = 2.8158*10**-10; # Nearest neighbour distance of solid\n",
"A = 1.747; # Madelung constant for lattice binding energy\n",
"n = 8.6; # The repulsive exponent of solid\n",
"c = 2; # Structural factor for rocksalt\n",
"# As n = 1 + (9*c*a0**4)/(K0*e**2*A), solving for K0\n",
"K0 = 9*c*a0**4/((n-1)*e**2*A); # Compressibility of solid, metre square per newton\n",
"print\"The compressibility of the solid = \", \"{0:.3e}\".format(K0),\"metre square per newton\";"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.7,Page number 69"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The percentage ionic character present in solid = 22.12 percent \n"
]
}
],
"source": [
"import math\n",
"\n",
"#Given Data\n",
"\n",
"chi_diff = 1; # Electronegativity difference between the constituent of elements of solid\n",
"percent_ion = 100*(1-math.e**(-(0.25*chi_diff**2))); # Percentage ionic character present in solid given by Pauling\n",
"print\"The percentage ionic character present in solid = \",round(percent_ion,2),\"percent \";\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.8,Page number 69"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The fractional ionicity of GaAs = 0.3126\n",
"The fractional ionicity of CdTe = 0.7168\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Given Data\n",
"\n",
"Eh_GaAs = 4.3; # Homopolar gap of GaAs compound, eV\n",
"C_GaAs = 2.90; # Ionic gap of GaAs compound, eV\n",
"Eh_CdTe = 3.08; # Homopolar gap of CdTe compound, eV\n",
"C_CdTe = 4.90; # Ionic gap of CdTe compound, eV\n",
"\n",
"fi_GaAs = C_GaAs**2/(Eh_GaAs**2 + C_GaAs**2);\n",
"fi_CdTe = C_CdTe**2/(Eh_CdTe**2 + C_CdTe**2);\n",
"print\"The fractional ionicity of GaAs = \",round(fi_GaAs,4);\n",
"print\"The fractional ionicity of CdTe = \",round(fi_CdTe,4);\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
