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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 1: Bonding in Solids and Crystal Structures"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.10: spacing_between_the_nearest_neighbouring_ions.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//variable declaration\n",
+"n=4 \n",
+"M=58.5 //Molecular wt. of NaCl\n",
+"N=6.02*10**26 //Avagadro number\n",
+"rho=2180 //density\n",
+"\n",
+"//Calculations\n",
+"a=((n*M)/(N*rho))**(1/3) \n",
+"s=a/2\n",
+"\n",
+"//Result\n",
+"printf('a=%0.3f*10**-9 metre\n',(a/10**-9))\n",
+"printf('spacing between the nearest neighbouring ions =%0.3f nm',(s/10**-9))"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.11: lattice_constant.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//variable declaration\n",
+"n=4 \n",
+"A=63.55 //Atomic wt. of NaCl\n",
+"N=6.02*10**26 //Avagadro number\n",
+"rho=8930 //density\n",
+"\n",
+"//Calculations\n",
+"a=((n*A)/(N*rho))**(1/3) //Lattice Constant\n",
+"\n",
+"//Result\n",
+"printf('lattice constant, a=%0.3f nm',(a*10**9))"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.12: Density_of_iron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//variable declaration\n",
+"r=0.123 //Atomic radius\n",
+"n=4\n",
+"A=55.8 //Atomic wt\n",
+"a=2*sqrt(2) \n",
+"N=6.02*10**26 //Avagadro number\n",
+"\n",
+"//Calculations\n",
+"rho=(n*A)/((a*r*10**-9)**3*N)\n",
+"\n",
+"//Result\n",
+"printf('Density of iron =%0.3fkg/m**-3',rho)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.1: Calculation_of_youngs_modulus.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Initialisation of variables\n",
+"clc\n",
+"//Variable declaration\n",
+"a=7.68*10**-29; \n",
+"r0=2.5*10**-10; //radius(m)\n",
+"\n",
+"//Calculation\n",
+"b=a*(r0**8)/9;\n",
+"y=((-2*a*r0**8)+(90*b))/r0**11; \n",
+"E=y/r0; //young's modulus(Pa)\n",
+"\n",
+"//Result\n",
+"\n",
+"printf('youngs modulus is %0.2f GPa',(E/10^9))\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.2: Find_the_Effective_charge.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Initialisation of variables\n",
+"clc\n",
+"\n",
+"d=((1.98)*10**-29)*1/3; //dipole moment\n",
+"b=(0.92); //bond length\n",
+"EC=d/(b*10**-10); //Effective charge\n",
+"\n",
+"//Result\n",
+"printf('Effective charge =%0.2f *10**-29 coulomb',((EC*10**19)))"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.3: Find_the_Cohesive_energy.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Initialisation of variables\n",
+"clc\n",
+"\n",
+"A=1.748 //Madelung Constant \n",
+"N=6.02*10**26 //Avagadro Number\n",
+"e=1.6*10**-19\n",
+"n=9.5\n",
+"r=(0.324*10**-9)*10**3\n",
+"E=8.85*10**-12\n",
+"//Calculations\n",
+"U=((N*A*(e)**2)/(4*%pi*E*r))*(1-1/n) //Cohesive energy\n",
+"\n",
+"//Result\n",
+"printf('Cohesive energy =%0.2f *10**3 kJ/kmol \n',(U/10**3))\n",
+"printf('//Answer varies due to rounding of numbers')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.4: Find_the_Coulomb_energy.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//variable declaration\n",
+"I=5; //Ionisation energy\n",
+"A=4; //Electron Affinity\n",
+"e=(1.6*10**-19)\n",
+"E=8.85*10**-12 //epsilon constant\n",
+"r=0.5*10**-19 //dist between A and B\n",
+"\n",
+"//Calculations\n",
+"C=-(e**2/(4*%pi*E*r*e))/10**10 //Coulomb energy\n",
+"E_c=I-A+C //Energy required\n",
+"\n",
+"//Result\n",
+"printf('Coulomb energy =%0.2f eV\n',C)\n",
+"printf('Energy required =%0.2f eV',E_c')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.5: Find_the_Distance_of_separation.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//variable declaration\n",
+"I=5.14; //Ionization energy\n",
+"A=3.65; //Electron Affinity\n",
+"e=(1.6*10**-19);\n",
+"E=8.85*10**-12; \n",
+"//calculations\n",
+"E_c=I-A //Energy required\n",
+"r=e**2/(4*%pi*E*E_c*e) //Distance of separation\n",
+"\n",
+"//Result\n",
+"printf('Energy required=%0.2f eV \n',E_c)\n",
+"printf('Distance of separation =%0.2f Angstrom',r/10**-10)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.6: Find_the_Bond_Energy.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//variable declaration \n",
+"I=5.14; //Ionization energy\n",
+"A=3.65; //Electron Affinity\n",
+"e=(1.6*10**-19);\n",
+"E=8.85*10**-12; \n",
+"r=236*10**-12;\n",
+"\n",
+"//Calculations\n",
+"E_c=I-A //Energy required\n",
+"C=-(e**2/(4*%pi*E*r*e)) //Potentential energy in eV\n",
+"BE=-(E_c+C) //Bond Energy\n",
+"//Result\n",
+"printf('Energy required= %0.2f eV\n',E_c)\n",
+"printf('Energy required =%0.1f eV\n',C)\n",
+"printf('Bond Energy =%0.2f eV',BE)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.7: Find_the_density.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//variable declaration\n",
+"d=2.351 //bond lenght\n",
+"N=6.02*10**26 //Avagadro number\n",
+"n=8 //number of atoms in unit cell\n",
+"A=28.09 //Atomin mass of silicon\n",
+"m=6.02*10**26 //1mole\n",
+"\n",
+"//Calculations\n",
+"a=(4*d)/sqrt(3)\n",
+"p=(n*A)/((a*10**-10)*m) //density\n",
+"\n",
+"//Result\n",
+"printf('a=%0.2fAngstorm\n',a)\n",
+"printf('density =%0.2f kg/m**3\n',(p*10**16))\n",
+"printf('//Answer given in the textbook is wrong')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.8: Find_the_radius_of_sphere.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Variable declaration\n",
+"\n",
+"\n",
+"//Calculation\n",
+"a1=4/sqrt(3);\n",
+"R1=(a1/2)-1; //radius of largest sphere\n",
+"a2=4/sqrt(2);\n",
+"R2=(a2/2)-1; //maximum radius of sphere\n",
+"\n",
+"//Result\n",
+"printf('radius of largest sphere is %f*r\n',R1)\n",
+"printf('maximum radius of sphere is %f*r',R2 ) "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.9: increase_of_density_or_the_decrease_of_volume.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//variable declaration\n",
+"r1=1.258 //Atomic radius of BCC\n",
+"r2=1.292 //Atomic radius of FCC\n",
+"\n",
+"//calculations\n",
+"a1=(4*r1)/sqrt(3) //in BCC\n",
+"b1=((a1)**3)*10**-30 //Unit cell volume\n",
+"v1=(b1)/2 //Volume occupied by one atom\n",
+"a2=2*sqrt(2)*r2 //in FCC\n",
+"b2=(a2)**3*10**-30 //Unit cell volume\n",
+"v2=(b2)/4 //Volume occupied by one atom \n",
+"v_c=((v1)-(v2))*100/(v1) //Volume Change in % \n",
+"d_c=((v1)-(v2))*100/(v2) //Density Change in %\n",
+"\n",
+"//Results\n",
+"printf('a1=%0.3f Angstrom\n\n',(a1)) \n",
+"printf('Unit cell volume =a1**3 =%0.3f *10**-30 m**3\n',((b1)/10**-30))\n",
+"printf('Volume occupied by one atom =%0.2f *10**-30 m**3\n',(v1/10**-30))\n",
+"printf('a2=%0.2f\n Angstorm\n',(a2))\n",
+"printf('Unit cell volume =a2**3 =%0.3f *10**-30 m**3\n',((b2)/10**-30))\n",
+"printf('Volume occupied by one atom =%0.3f*10**-30 m**3\n',(v2/10**-30))\n",
+"printf('Volume Change in percentage =%0.3f\n',(v_c))\n",
+"printf('Density Change in percentage =%0.3f\n',(d_c))\n",
+"printf('Thus the increase of density or the decrease of volume is about 0.5 percentage')"
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2025-03-12 01:55:02 +0000