summaryrefslogtreecommitdiff
path: root/Engineering_Physics_by_D_K_Bhattacharya/6-Conducting_materials.ipynb
diff options
context:
space:
mode:
Diffstat (limited to 'Engineering_Physics_by_D_K_Bhattacharya/6-Conducting_materials.ipynb')
-rw-r--r--Engineering_Physics_by_D_K_Bhattacharya/6-Conducting_materials.ipynb486
1 files changed, 486 insertions, 0 deletions
diff --git a/Engineering_Physics_by_D_K_Bhattacharya/6-Conducting_materials.ipynb b/Engineering_Physics_by_D_K_Bhattacharya/6-Conducting_materials.ipynb
new file mode 100644
index 0000000..b48b626
--- /dev/null
+++ b/Engineering_Physics_by_D_K_Bhattacharya/6-Conducting_materials.ipynb
@@ -0,0 +1,486 @@
+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 6: Conducting materials"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.10: calculate_electrical_conductivity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6.10 , pg 175\n",
+"lam=4*10^-8 //maen free path of electrons (in m)\n",
+"n=8.4*10^28 //electron density (in m^-3)\n",
+"Vth=1.6*10^6 //average thermal velocity of electrons (in m/s)\n",
+"e=1.6*10^-19 //charge of electron (in C)\n",
+"Me=9.11*10^-31 //mass of electron (in Kg)\n",
+"sigma=(n*e^2*lam)/(Vth*Me) //conductivity\n",
+"printf('Electrical conductivity (in /(ohm*m))')\n",
+"disp(sigma)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.11: calculate_electrical_and_thermal_conductivities.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6.11 , pg 176\n",
+"Tr=10^-14 //relaxation time (in s)\n",
+"T=300 //temperature (in K)\n",
+"n=6*10^28 //electron concentration (in /m^3)\n",
+"Me=9.11*10^-31 //mass of electron (in Kg)\n",
+"e=1.6*10^-19 //charge of electron (in C)\n",
+"k=1.38*10^-23 //Boltzmann constant (in J/K)\n",
+"sigma=(n*e^2*Tr)/(Me) //Electrical conductivity \n",
+"K=(3*n*k^2*Tr*T)/(2*Me) //Thermal conductivity \n",
+"L=K/(sigma*T) //Lorentz number\n",
+"printf('Electrical conductivity (in /(ohm*m))')\n",
+"disp(sigma)\n",
+"printf('Thermal conductivity (in W/(m*K))')\n",
+"disp(K)\n",
+"printf('Lorentz number (in(W*ohm)/K^2)')\n",
+"disp(L)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.12: find_relaxation_time.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6.12 , pg 177\n",
+"n=5.8*10^28 // electron concentration (in /m^3)\n",
+"e=1.6*10^-19 // charge of electron (in C)\n",
+"rho=1.54*10^-8 //resistivity of metal (in ohm*m)\n",
+"M=9.11*10^-31 //mass of electron (in Kg)\n",
+"T=M/(n*e^2*rho) //relaxation time\n",
+"printf('Relaxation time(in s)')\n",
+"disp(T)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.13: calculate_drift_velocity_and_mobility_and_relaxation_time.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6.13 , pg 177\n",
+"rho=1.54*10^-8 //resistivity (in ohm*m)\n",
+"E=100 //electric field intensity (in V/m)\n",
+"n=5.8*10^28 //electron concentration (in /m^3)\n",
+"e=1.6*10^-19 //charge of electron (in C)\n",
+"Me=9.11*10^-31 //mass of electron (in Kg)\n",
+"T=Me/(rho*n*e^2) //relaxation time\n",
+"Vd=(e*E*T)/Me //drift velocity\n",
+"U=Vd/E //mobility\n",
+"printf('Relaxation time (in s)')\n",
+"disp(T)\n",
+"printf('Drift veloity (in m/s)')\n",
+"disp(Vd)\n",
+"printf('Mobility(in m^2/(V*s))')\n",
+"disp(U)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.14: calculate_drift_velocity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 14 , pg 178\n",
+"T=300 //temperature (in K)\n",
+"l=2 //length (in m)\n",
+"R=0.02 //Resistance (in ohm)\n",
+"u=4.3*10^-3 // (in m^2/(V*s))\n",
+"I=15 //current (in A)\n",
+"V=I*R //voltage drop across wire (in V )\n",
+"E=V/l //electric field across wire (in V/m)\n",
+"Vd=u*E //drift velocity (in m/s)\n",
+"printf('Drift velocity (in m/s)')\n",
+"disp(Vd)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.15: calculate_Fermi_energy_and_Fermi_temperature.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 15 , pg 179\n",
+"m=9.11*10^-31 //mass of electron (in Kg)\n",
+"k=1.38*10^-23 //boltzmann constant (in J/K)\n",
+"e=1.6*10^-19 //electronic charge(in C )\n",
+"Vf=0.86*10^6 //Fermi velocity of electron (in m/s)\n",
+"Ef=(m*Vf^2)/(2*e) //Fermi energy (in eV)\n",
+"Tf=(Ef*e)/k //Fermi temperature\n",
+"printf('Fermi energy=')\n",
+"printf('Ef=%.1f eV \n',Ef)\n",
+"printf('Fermi temperature =')\n",
+"printf('Tf=%.0f K',Tf)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.16: calculate_Fermi_velocity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 16 , pg 179\n",
+"Tf=2460 //Fermi temperature (in K)\n",
+"m=9.11*10^-31 //mass of electron (in Kg)\n",
+"k=1.38*10^-23 //boltzmann constant (in J/K)\n",
+"Vf=sqrt((2*k*Tf)/m) //Fermi velocity\n",
+"printf('Fermi velocity (in m/s)=')\n",
+"disp(Vf)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.1: calculate_Fermi_energy.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 1 , pg 170\n",
+"Vf=10^6 //Fermi velocity (in m/s)\n",
+"m=9.11*10^-31 // mass of electron(in Kg)\n",
+"Ef=(m*Vf^2)/2 //Fermi energy (in J)\n",
+"printf('Fermi energy for the electrons in the metal=')\n",
+"printf('Ef=%.1f eV',(Ef/(1.6*10^-19))) //converting J into eV"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.2: calculate_Fermi_energy.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 2 , pg 170\n",
+"Ef0=7.04*1.6*10^-19 // Fermi energy at 0 K (converting eV into J)\n",
+"T=300 //temperature (in K)\n",
+"k=1.38*10^-23 //boltzmann constant (in (m^2*Kg)/(s^2*K^-1))\n",
+"Ef=Ef0*(1-(%pi^2*(k*T)^2)/(12*Ef0^2)) //Fermi energy at 300 K (in J)\n",
+"printf('Fermi energy at 300 K =')\n",
+"printf('Ef=%.4f eV',(Ef/(1.6*10^-19))) //converting J into eV"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.3: calculate_conductivity_and_relaxation_time.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6.3 , pg 171\n",
+"d=2.7*10^3 //density (in Kg/m^3)\n",
+"Ma=27 //atomic weight\n",
+"Me=9.11*10^-31 //mass of electron (in Kg)\n",
+"e=1.6*10^-19 //charge in electron (in C)\n",
+"T=10^-14 //relaxation time (in s)\n",
+"Na=6.022*10^23 //Avogadro constant\n",
+"N=3*10^3 //number of free electrons per atom\n",
+"n=(d*Na*N)/Ma //(in /m^3)\n",
+"sigma=(n*e^2*T)/Me //conductivity\n",
+"printf('Conductivity of Al (in /(ohm*m))')\n",
+"disp(sigma)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.4: calculate_Lorentz_number.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 4 , pg 171\n",
+"sigma=5.87*10^7 // electrical conductivity (in /(ohm m))\n",
+"K=390 //thermal conductivity (in W/(m K))\n",
+"T=293 //temperature (in K)\n",
+"L=K/(sigma*T) //Lorentz number by wiedemann-Franz law\n",
+"printf('Lorentz number (in W*ohm /K^2)')\n",
+"disp(L)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.5: calculate_electrical_conductivity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 5 , pg 172\n",
+"d=8900 //density (in Kg/m^3)\n",
+"M=63.5 //atomic weight \n",
+"T=10^-14 //relaxation time(in s)\n",
+"N=6.022*10^23 //Avogadros constant\n",
+"N1=10^3 //number of free electrons per atom\n",
+"e=1.6*10^-19 //electronic charge (in C)\n",
+"me=9.11*10^-31 //mass of electron (in Kg)\n",
+"\n",
+"n=(N*d*N1)/M \n",
+"sigma =(n*e^2*T)/me //electrical conductivity\n",
+"printf('Electrical conductivity(in ohm m)=')\n",
+"disp(sigma)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.6: EX6_6.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 6 , pg 172\n",
+"rho=1.54*10^-8 //resistivity (in ohm*m)\n",
+"Ef=5.5 //Fermi energy (in eV)\n",
+"E=100 //electric field intensity (in V/m)\n",
+"n=5.8*10^28 //concentration of electrons (in atoms/m^3)\n",
+"e=1.6*10^-19 //charge in electron (in C)\n",
+"Me=9.11*10^-31 //mass of electron (in Kg)\n",
+"T=Me/(rho*n*e^2) //relaxation time\n",
+"Un=(e*T)/Me //mobility of electron\n",
+"Vd=(e*T*E)/Me //drift velocity\n",
+"Vf=sqrt((2*Ef*e)/Me) //Fermi velocity\n",
+"lam_m=Vf*T //mean free path\n",
+"\n",
+"printf('Relaxation time of electron (in s)')\n",
+"disp(T)\n",
+"printf('Mobility of electron (in m^2/(V*s))')\n",
+"disp(Un)\n",
+"printf('Drift velocity of electron (in m/s)')\n",
+"disp(Vd)\n",
+"printf('Fermi velocity of electrons (in m/s)')\n",
+"disp(Vf)\n",
+"printf('Mean free path(in m)')\n",
+"disp(lam_m)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.7: calculate_thermal_conductivity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 6 , pg 174\n",
+"L= 2.26*10^-8 //Lorentz number (in W*m /K^2)\n",
+"T=27+273 //temperature (in K) (converting celsius into kelvin)\n",
+"rho=1.72*10^-8 //electrical resistivity (in ohm *m)\n",
+"\n",
+"//according to Wiedemann-Franz law\n",
+"K=(L*T)/rho //thermal conductivity\n",
+"printf('Thermal conductivity =')\n",
+"printf('K=%.0f W/(m*K)',K)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.8: calculate_Lorentz_number.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 8 , pg 174\n",
+"sigma=5.87*10^7 // electrical conductivity (in /(ohm m))\n",
+"K=390 //thermal conductivity (in W/(m K))\n",
+"T=293 //temperature (in K)\n",
+"L=K/(sigma*T) //Lorentz number by wiedemann-Franz law\n",
+"printf('Lorentz number (in W*ohm /K^2)')\n",
+"disp(L)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.9: find_F_E.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// chapter 6 , Example6 9 , pg 174\n",
+"del_E=0.01*1.6*10^-19 // del_E = E-Ef (in J) (converting eV into J)\n",
+"T=200 //temperature (in K)\n",
+"k=1.38*10^-23 //boltzmanns constant (in J/K)\n",
+"F_E=1/(1+exp(del_E/(k*T))) //Fermi Dirac distribution function\n",
+"printf('F_E=%.2f',F_E)"
+ ]
+ }
+],
+"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 2025-01-09 02:44:11 +0000