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author | root | 2014-07-14 15:31:28 +0530 |
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committer | root | 2014-07-14 15:31:28 +0530 |
commit | 5a3a66e158c99bbf7900278d8e7056136d628dbe (patch) | |
tree | 6d8c0f65acb3e9451d5092e8d718e7febcbd0d05 /Solid_state_physics | |
parent | 69aa63da6cb2bc3f5822533e3f97c46d7efbaafc (diff) | |
download | Python-Textbook-Companions-5a3a66e158c99bbf7900278d8e7056136d628dbe.tar.gz Python-Textbook-Companions-5a3a66e158c99bbf7900278d8e7056136d628dbe.tar.bz2 Python-Textbook-Companions-5a3a66e158c99bbf7900278d8e7056136d628dbe.zip |
adding books
Diffstat (limited to 'Solid_state_physics')
-rwxr-xr-x | Solid_state_physics/Chapter_1.ipynb | 200 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_10.ipynb | 181 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_11.ipynb | 102 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_12.ipynb | 252 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_2.ipynb | 331 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_3.ipynb | 459 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_4.ipynb | 189 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_5.ipynb | 498 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_6.ipynb | 386 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_7.ipynb | 330 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_8.ipynb | 436 | ||||
-rwxr-xr-x | Solid_state_physics/Chapter_9.ipynb | 845 | ||||
-rwxr-xr-x | Solid_state_physics/README.txt | 10 | ||||
-rwxr-xr-x | Solid_state_physics/screenshots/forbidden.png | bin | 0 -> 76264 bytes | |||
-rwxr-xr-x | Solid_state_physics/screenshots/interatomicspacing.png | bin | 0 -> 50245 bytes | |||
-rwxr-xr-x | Solid_state_physics/screenshots/magneticmoment.png | bin | 0 -> 63593 bytes |
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diff --git a/Solid_state_physics/Chapter_1.ipynb b/Solid_state_physics/Chapter_1.ipynb new file mode 100755 index 00000000..32644890 --- /dev/null +++ b/Solid_state_physics/Chapter_1.ipynb @@ -0,0 +1,200 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 1: Bonding in Solids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.1, Page number 1.4" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi\n", + "\n", + "#Variable declartion\n", + "E_a = 502 #first ionization energy of A(kJ/mol)\n", + "E_b = -335 #electron affinity for B atom(kJ/mol)\n", + "d = 3*10**-10 #inter-ionic seperation(m)\n", + "E = 8.85*10**-12 #permittivity of free space(C/N -m)\n", + "e = 1.602*10**-19#charge of an electron(C)\n", + "\n", + "#Calculations\n", + "C_e = (-e**2)/(4*pi*E*d) #Coulumbic attraction energy(J/ion pair)\n", + "C_e_kj = C_e *6.022*10**23*10**-3 #Converting C_e to KJ/mol\n", + "n_e = E_a + E_b + C_e_kj #Net change in energy per mole\n", + "\n", + "#Results\n", + "print \"Net change in energy is =\",round(n_e,3),\"kJ/mol\"\n", + "print \"As the net change in energy is negative, the molecule will be stable\"\n", + "print \"\\nThe solution differs because of rounding-off of the digits in the textbook\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Net change in energy is = -296.224 kJ/mol\n", + "As the net change in energy is negative, the molecule will be stable\n", + "\n", + "The solution differs because of rounding-off of the digits in the textbook\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.2, Page number 1.4" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi \n", + "\n", + "#Variable declaration\n", + "IP_K = 4.1 #ionization energy of K(eV)\n", + "EA_Cl = 3.6 #electron affinity of Cl(eV)\n", + "e = 1.602*10**-19 #charge of an electron(C)\n", + "Eo = 8.85*10**-12 #permittivity of free space(C/N -m)\n", + "\n", + "#Calcuations\n", + "del_E = IP_K - EA_Cl\n", + "#Ec = 0.5 = -e/4*pi*Eo*R\n", + "R = e/(4*pi*Eo*del_E)\n", + "\n", + "#Results\n", + "print \"(a) If their total energy is to be zero, then del_E = Ec\"\n", + "print \"(b) The seperation between the ion pair is\", round((R/1E-9),2), \"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(a) If their total energy is to be zero, then del_E = Ec\n", + "(b) The seperation between the ion pair is 2.88 nm\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.3, Page number 1.5" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi\n", + "\n", + "#Variable declaration\n", + "ro = 2.36*10**-10 #inter ionic equilibrium distance(m)\n", + "IP = 5.14 #ionization energy of Na(eV)\n", + "EA = 3.65 #electron affinity of Cl(eV)\n", + "e = 1.602*10**-19 #charge of an electron(C)\n", + "Eo = 8.85*10**-12 #permittivity of free space(C/N -m)\n", + "\n", + "#Calculations\n", + "Ue = (-e**2)/(4*pi*Eo*ro*e) #Potential energy in eV\n", + "Be = -Ue - IP + EA\n", + "\n", + "#Result\n", + "print \"Bond energy for NaCl molecule is\",round(Be,2),\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Bond energy for NaCl molecule is 4.61 eV\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 1.4, Page number 1.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi\n", + "\n", + "#Variable declaration\n", + "ro = 0.281*10**-9 #equilibrium seperation between the ion pair(m)\n", + "IP = 5.14 #ionization energy of Na(eV)\n", + "EA = 3.61 #electron affinity of Cl(eV)\n", + "A = 1.748 #Madelung constant\n", + "n = 9. #born replusive exponent\n", + "e = 1.602*10**-19 #charge of an electron(C)\n", + "Eo = 8.85*10**-12 #permittivity of free space(C/N -m)\n", + "\n", + "#Calculations\n", + "Ce = (A*(e**2)*(1-(1/n)))/(4*pi*Eo*ro) #joules\n", + "Ce_ev = Ce/e #Converting joules to eV\n", + "\n", + "#Result\n", + "print \"The cohesive energy of NaCl molecule is\",round(Ce_ev,2),\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The cohesive energy of NaCl molecule is 7.97 eV\n" + ] + } + ], + "prompt_number": 22 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_10.ipynb b/Solid_state_physics/Chapter_10.ipynb new file mode 100755 index 00000000..ac36fbe7 --- /dev/null +++ b/Solid_state_physics/Chapter_10.ipynb @@ -0,0 +1,181 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 10: Superconductivity" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.1, Page number 10.3" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "Tc = 3.7 #critical temperature(K)\n", + "Hc_o = 0.0306 #critical field(T)\n", + "T = 2 #temperature(K)\n", + "\n", + "#Calculation\n", + "Hc_2 = Hc_o*(1-((T/Tc)**2))\n", + "\n", + "#Result\n", + "print \"Critical field at 2K is\",round(Hc_2,5),\"T\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical field at 2K is 0.02166 T\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.2, Page number 10.5" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi\n", + "\n", + "#Variable declaration\n", + "T = 4.2 #temperature(K)\n", + "Tc = 7.18 #critical temperature(K)\n", + "Ho = 6.5*10**4 #A/m\n", + "d = 1*10**-3 #diameter(m)\n", + "\n", + "#Calculations\n", + "Hc = Ho*(1-((T/Tc)**2))\n", + "r = d/2\n", + "ic = 2*pi*r*Hc\n", + "\n", + "#Result\n", + "print \"Critical current =\",round(ic,2),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical current = 134.33 A\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.3, Page number 10.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#Variable declaration\n", + "T = 3.5 #temperature(K)\n", + "lamda_t = 750 #penetration depth at T(A)\n", + "Tc = 4.12 #K\n", + "\n", + "#Calculation\n", + "lamda_o = lamda_t*math.sqrt((1-((T/Tc)**4)))\n", + "\n", + "#Result\n", + "print \"Penetration depth at 4.12K is\",round(lamda_o,1),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Penetration depth at 4.12K is 519.2 A\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.4, Page number 10.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "T1 = 3 #temperature(K)\n", + "lamda_t1 = 396. #penetration depth at T1(A)\n", + "T2 = 7.1 #temperature(K)\n", + "lamda_t2 = 1730. #penetration depth at T2(A)\n", + "\n", + "#Calculations\n", + "x = lamda_t2**2/lamda_t1**2\n", + "Tc = math.sqrt(math.sqrt((-T1**4+(x*(T2**4)))/(x-1)))\n", + "\n", + "#Result\n", + "print \"Critical temperature =\",round(Tc,3),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical temperature = 7.193 K\n" + ] + } + ], + "prompt_number": 18 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_11.ipynb b/Solid_state_physics/Chapter_11.ipynb new file mode 100755 index 00000000..2ccb0979 --- /dev/null +++ b/Solid_state_physics/Chapter_11.ipynb @@ -0,0 +1,102 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 11:Lasers" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.1, Page number 11.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lamda = 6943.*10**-10 #wavelength(m)\n", + "T = 300. #temperature(K)\n", + "h = 6.626*10**-34 #Planck's constant\n", + "c = 3*10**8 #velocity of light(m/s)\n", + "K = 8.61*10**-5\n", + "\n", + "#Calculations\n", + "E2_E1 = (h*c)/(lamda*1.6*10**-19) #in eV\n", + "N2_N1 = math.exp(-E2_E1/(K*T))\n", + "\n", + "#Result\n", + "print \"The relative population of two states in a ruby laser is\",round((N2_N1/1E-31),2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The relative population of two states in a ruby laser is 8.2\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.2, Page number 11.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "a1 = 4. #diameter of laser beam for distance first(m)\n", + "a2 = 6. # diameter of laser beam from second distance(m)\n", + "d1 = 1. #First distance from laser to output beam spot(m)\n", + "d2 = 2. #Second distance from laser to output beam spot(m)\n", + "\n", + "#Calculation\n", + "D = (a2-a1)/(2*(d2-d1))\n", + "\n", + "#Result\n", + "print \"Divergence =\",D,\"milliradian\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Divergence = 1.0 milliradian\n" + ] + } + ], + "prompt_number": 14 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_12.ipynb b/Solid_state_physics/Chapter_12.ipynb new file mode 100755 index 00000000..2311a687 --- /dev/null +++ b/Solid_state_physics/Chapter_12.ipynb @@ -0,0 +1,252 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 12: Fiber Optics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.1, Page number 12.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "n1 = 1.55 #refractive inde of core\n", + "n2 = 1.50 #refractive index of cladding\n", + "\n", + "#Calculation\n", + "NA = math.sqrt(n1**2-n2**2)\n", + "\n", + "#Result\n", + "print \"Numerical Aperture =\",round(NA,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical Aperture = 0.391\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.2, Page number 12.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "n1 = 1.563 #refractive inde of core\n", + "n2 = 1.498 #refractive index of cladding\n", + "\n", + "#Calculation\n", + "NA = math.sqrt(n1**2-n2**2)\n", + "alpha_i = math.degrees(math.asin(NA))\n", + "\n", + "#Result\n", + "print \"Angle of acceptance =\",round(alpha_i,2),\"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angle of acceptance = 26.49 degrees\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.3, Page number 12.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "NA = 0.39 #numerical aperture\n", + "delta_n = 0.05 #differnce between refractive indices of core & cladding\n", + "\n", + "#Calculaations\n", + "n1 = NA/math.sqrt(2*delta_n)\n", + "\n", + "#Result\n", + "print \"Refractive index of core =\",round(n1,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index of core = 1.2333\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.4, Page number 12.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "n1 = 1.563 #refractive inde of core\n", + "n2 = 1.498 #refractive index of cladding\n", + "\n", + "#Calculation\n", + "delta = (n1-n2)/n1\n", + "\n", + "#Result\n", + "print \"Fractional index change for the given fiber is\",round(delta,4)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fractional index change for the given fiber is 0.0416\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.5, Page number 12.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "n1 = 1.48 #refractive inde of core\n", + "n2 = 1.45 #refractive index of cladding\n", + "\n", + "#Calculations\n", + "NA = math.sqrt(n1**2-n2**2)\n", + "alpha_i = math.degrees(math.asin(NA))\n", + "\n", + "#Result\n", + "print \"Numerical aperture =\",round(NA,4)\n", + "print \"Angle of acceptance =\",round(alpha_i,2),\"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.2965\n", + "Angle of acceptance = 17.25 degrees\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.6, Page number 12.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "Pout = 40. #output power(mW)\n", + "Pin = 100. #input power(mW)\n", + "\n", + "#Calculation\n", + "A = -10*math.log10(Pout/Pin) #Attenuation(dB)\n", + "\n", + "#Result \n", + "print \"Attenuation =\",round(A,2),\"dB\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Attenuation = 3.98 dB\n" + ] + } + ], + "prompt_number": 22 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_2.ipynb b/Solid_state_physics/Chapter_2.ipynb new file mode 100755 index 00000000..99284878 --- /dev/null +++ b/Solid_state_physics/Chapter_2.ipynb @@ -0,0 +1,331 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:64e1fbee0e1d9b8157cae12a98a7773b847a3c5e842a9d3f124a5485fe931875" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Crystal Structure" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1, Page number 2.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import sqrt \n", + "\n", + "#Variable declaration\n", + "#Assuming r=1 for simpliciy in calculations\n", + "r = 1\n", + "\n", + "#Calculations\n", + "a = (4*r)/sqrt(3)\n", + "#Let R be the radius of interstitial sphere that can fit into the void,therefore,\n", + "R = (a-2*r)/2 \n", + "\n", + "#Result\n", + "print \"The maximum radius of interstitial sphere is\",round(R,3),\"r\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum radius of interstitial sphere is 0.155 r\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2, Page number 2.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import sqrt\n", + "\n", + "#Variable declaration\n", + "r1 = 1.258*10**-10 #atomic radius(m)\n", + "r2 = 1.292*10**-10 #atomic radius(m)\n", + "\n", + "#Calculations\n", + "#In BCC\n", + "a_bcc = (4*r1)/sqrt(3)\n", + "v_bcc = a_bcc**3 #volume of unit cell(m^3)\n", + "n1 = ((1./8.)*8.)+1\n", + "V1 = v_bcc/n1 #volume occupied by 1 atom(m^3)\n", + "\n", + "#In FCC\n", + "a_fcc = 2*sqrt(2)*r2\n", + "v_fcc = a_fcc**3 #volume of unit cell(m^3)\n", + "n2 = ((1./2.)*6.)+((1./8.)*8.)\n", + "V2 = v_fcc/n2 #volume occupied by 1 atom(m^3)\n", + "\n", + "del_v = ((V1-V2)/V1)*100 #change in volume\n", + "\n", + "#Result\n", + "print \"During the conversion of iron from BCC to FCC, the decrease in volume is\",round(del_v,1),\"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "During the conversion of iron from BCC to FCC, the decrease in volume is 0.5 %\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3, Page number 2.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import sqrt\n", + "\n", + "#Variable declaration\n", + "a = 0.27*10**-9 #nearest neighbour distance(m)\n", + "c = 0.494*10**-9 #height of unit cell(m)\n", + "M = 65.37 #atomic weight of zinc\n", + "N = 6.023*10**26 #Avogadro's number(k/mol)\n", + "\n", + "#Calculations\n", + "V = (3*sqrt(3)*a**2*c)/2 #volume of unit cell\n", + "rho = (6*M)/(N*V) #density of crystal\n", + "\n", + "#Results\n", + "print \"Volume of unit cell =\",round((V/1E-29),2),\"*10^29 m^3\"\n", + "print \"Density of zinc =\",round(rho),\"kg/m^3\"\n", + "print \"\\nThe solution differs because of rounding-off of the digits in the textbook\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Volume of unit cell = 9.36 *10^29 m^3\n", + "Density of zinc = 6960.0 kg/m^3\n", + "\n", + "The solution differs because of rounding-off of the digits in the textbook\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4, Page number 2.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import sqrt\n", + "\n", + "#Varaible declaration\n", + "#Let r be the radius of atom and R be the radius of sphere\n", + "#For simplicity in calculations, let us assume r =1\n", + "r = 1\n", + "\n", + "#Calculations\n", + "#For FCC structure\n", + "a = (4*r)/sqrt(2)\n", + "R = (a/2)-r\n", + "\n", + "print \"Maximum radius of sphere =\",round(R,3),\"r\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum radius of sphere = 0.414 r\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5, Page number 2.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "a = 0.356*10**-9 #cube edge(m)\n", + "M = 12.01 #atomic weight of carbon\n", + "N = 6.023*10**26 #Avogadro's number(k/mol)\n", + "na = 1.77*10**29 #no. of atoms per meter cube\n", + "\n", + "#Calculations\n", + "#Diamond has 2 interpenetrating FCC lattices. Since each FCC unit cell has 4 atoms, the total no. of atoms per unit cell is 8\n", + "n = 8/a**3\n", + "m = M/N\n", + "rho = m*na\n", + "\n", + "#Result\n", + "print \"Number of atoms =\",round((n/1E+29),3),\"*10^29\"\n", + "print \"The density of diamond is\",round(rho,1),\"kg/m^3(Calculation mistake in the textbook)\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of atoms = 1.773 *10^29\n", + "The density of diamond is 3529.4 kg/m^3(Calculation mistake in the textbook)\n" + ] + } + ], + "prompt_number": 58 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6, Page number 2.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "rho = 2.18 #density of NaCl(gm/cm^3)\n", + "N = 6.023*10**23 #Avogadro's number(/mol)\n", + "\n", + "#Caculations\n", + "w = 23+35.5 #molecular weight of NaCl\n", + "m = w/N #mass of NaCl molecule\n", + "nm = rho/m #no. of molecules per unit volume(molecule/cm^3)\n", + "#Since NaCl is diatomic\n", + "n = 2*nm\n", + "#Let a be the distance between adjacent atoms in NaCl and\n", + "# n be the no. of atoms along the edge of the cube\n", + "#length of an edge = na\n", + "#volume of unit cube = n^3*a^3\n", + "a = (1/n)**(1./3.)\n", + "\n", + "#Result\n", + "print \"The distance between two adjacent atoms is\",round((a/1E-8),2),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The distance between two adjacent atoms is 2.81 A\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7, Page number 2.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import sqrt\n", + "\n", + "#Variable declaration\n", + "w = 63.5 #atomic weight of copper\n", + "r = 1.278*10**-8 #atomic rdius(m)\n", + "N = 6.023*10**23 #Avogadro's number(/mol)\n", + "\n", + "#Calculations\n", + "m = w/N #mass of each copper atom(gm)\n", + "#Since copper has FCC structure lattice constant\n", + "a = (4*r)/sqrt(2) \n", + "n = 4 #no. of atoms in unit cell of FCC structure\n", + "M = n*m #mass of unit cell\n", + "rho = M/a**3 #density\n", + "\n", + "#Result\n", + "print \"Density of copper =\",round(rho,2),\"gm/cm^3\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of copper = 8.93 gm/cm^3\n" + ] + } + ], + "prompt_number": 3 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_3.ipynb b/Solid_state_physics/Chapter_3.ipynb new file mode 100755 index 00000000..c7c45c55 --- /dev/null +++ b/Solid_state_physics/Chapter_3.ipynb @@ -0,0 +1,459 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:201c0242c8a2063b9a355e5a7deec7582a5a21b0e1187464be6b9fa32a384889" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3:Crystal planes and X-ray diffraction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.2, Page number 3.5" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "from sympy import *\n", + "\n", + "#Variable declaration\n", + "'''In a simple cubic structure, there are three types of atomic arrangement\n", + "(i)(100)\n", + "(ii)(110)\n", + "(iii)(111)'''\n", + "\n", + "#Calculations and results\n", + "\n", + "#Consider (100) plane\n", + "n = (1./4.)*4 #no. of atoms in this plane\n", + "#Let a be the lattice constant in mm\n", + "a = Symbol('a')\n", + "A1 = a**2\n", + "nm = n/A1 #no. of atoms per mm^2\n", + "print \"The number of atoms per square millimeter for (100) plane is\",nm\n", + "\n", + "#Consider (110) plane\n", + "n2 = 1 \n", + "A2 = math.sqrt(2)*a**2\n", + "nm2 = n2/A2\n", + "print \"The number of atoms per square millimeter for (110) plane is\",nm2\n", + "\n", + "#Consider (111) plane\n", + "n3 = (1./360.)*60*3\n", + "EO = a*math.sqrt(2)*math.cos(math.pi/6)\n", + "A3 = (a*math.sqrt(2)*EO)/2\n", + "nm3 = n3/A3\n", + "print \"The number of atoms per square millimeter for (111) plane is\",nm3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of atoms per square millimeter for (100) plane is 1.0/a**2\n", + "The number of atoms per square millimeter for (110) plane is 0.707106781186547/a**2\n", + "The number of atoms per square millimeter for (111) plane is 0.577350269189626/a**2\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.3, Page number 3.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import sqrt\n", + "\n", + "#Variable declartion\n", + "r = 0.1278*10**-9 #atomic radius(m)\n", + "\n", + "#Calculations\n", + "#For FCC structure,\n", + "a = (4*r)/sqrt(2)\n", + "\n", + "#For (110) plane,\n", + "h1 = 1\n", + "k1 = 1\n", + "l1 = 0\n", + "d1 = a/((h1**2+k1**2+l1**2)**0.5) \n", + "\n", + "#For (212) plane,\n", + "h2 = 2\n", + "k2 = 1\n", + "l2 = 2\n", + "d2 = a/((h2**2+k2**2+l2**2)**0.5)\n", + "\n", + "#Results\n", + "print \"Interplanar spacing for (110) plane =\",d1/1E-9,\"nm\"\n", + "print \"Interplanar spacing for (212) plane =\",round((d2/1E-9),4),\"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Interplanar spacing for (110) plane = 0.2556 nm\n", + "Interplanar spacing for (212) plane = 0.1205 nm\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.4, Page number 3.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from sympy import *\n", + "\n", + "#Variable declaration\n", + "#Let a be the lattice constant\n", + "#For calculations, let us assume a = 1\n", + "a = 1\n", + "\n", + "#Calculations\n", + "\n", + "#For (100) plane,\n", + "h1 = 1\n", + "k1 = 0\n", + "l1 = 0\n", + "d1 = 1/((h1**2+k1**2+l1**2)**0.5) \n", + "\n", + "#For (110) plane,\n", + "h2 = 1\n", + "k2 = 1\n", + "l2 = 0\n", + "d2 = 1/((h2**2+k2**2+l2**2)**0.5)\n", + "\n", + "#For (111) plane,\n", + "h3 = 1\n", + "k3 = 1\n", + "l3 = 1\n", + "d3 = 1/((h3**2+k3**2+l3**2)**0.5)\n", + "\n", + "#Result\n", + "print \"d100:d110:d111 =\",d1,\":\",d2,\":\",d3" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "d100:d110:d111 = 1.0 : 0.707106781187 : 0.57735026919\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.5, Page number 3.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "#Coefficients of intercepts along three axes\n", + "m = 1.\n", + "n = 1./2.\n", + "p = 3.\n", + "\n", + "#Calculations\n", + "m_inv = 1/m \n", + "n_inv = 1/n\n", + "p_inv = 1/p\n", + "\n", + "def gcd(a, b):\n", + " while b: \n", + " a, b = b, a % b\n", + " return a\n", + "\n", + "def lcm(a, b):\n", + " return (a * b)/ gcd(a, b)\n", + "\n", + "def lcmm(*args): \n", + " return reduce(lcm, args)\n", + "\n", + "mul_fact = lcmm(1,1,3)\n", + "m1 = m_inv*mul_fact #Clear the first fraction\n", + "m2 = n_inv*mul_fact #Clear the second fraction\n", + "m3 = p_inv*mul_fact #Clear the third fraction\n", + "print \"The required miller indices are\", m1,m2,m3\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required miller indices are 3.0 6.0 1.0\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.6, Page number 3.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "d = 0.282*10**-9 #lattice spacing(m)\n", + "n = 1 #first order\n", + "theta = 8.35 #glancing angle(degrees)\n", + "\n", + "#Calculations\n", + "lamda = (2*d*math.sin(math.radians(theta)))/n\n", + "\n", + "#For maximum value possible,\n", + "theta = 90\n", + "n = (2*d)/lamda\n", + "\n", + "#Results\n", + "print \"Wavelength of X-rays =\",round((lamda/1E-9),4),\"nm\"\n", + "print \"Maximum order of diffraction possible =\",round(n,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of X-rays = 0.0819 nm\n", + "Maximum order of diffraction possible = 6.89\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.8, Page number 3.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lamda = 1.5418*10**-10 #wavelength(m)\n", + "theta = 30 #angle(degrees)\n", + "n = 1 #first order\n", + "#For (111) plane\n", + "h = 1\n", + "k = 1\n", + "l = 1\n", + "\n", + "#Calculations\n", + "d = (n*lamda)/(2*math.sin(math.radians(theta)))\n", + "a = d*((h**2+k**2+l**2)**0.5)\n", + "\n", + "#Result\n", + "print \"Interatomic spacing =\",round((a/1E-10),3),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Interatomic spacing = 2.67 A\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.9, Page number 3.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import sqrt, pi \n", + "\n", + "#Variable declaration\n", + "d = 0.28 #lattice spacing\n", + "lamda = 0.074*10**-9 #Wavelength(m)\n", + "n = 2 #2nd order\n", + "\n", + "#Calculations\n", + "d110 = d/sqrt(2)\n", + "theta = math.asin((n*lamda)/(2*d110))*180/pi\n", + "\n", + "#Result\n", + "print \"Glancing angle =\",round(theta/1E-9),\"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Glancing angle = 21.0 degrees\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.10, Page number 3.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "a = 0.38*10**-9 #lattice constant\n", + "h = 1\n", + "k = 1\n", + "l = 0\n", + "\n", + "#Calculations\n", + "d = a/math.sqrt(h**2+k**2+l**2)\n", + "\n", + "#Result\n", + "print \"Distance =\",round((d/1E-9),2),\"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distance = 0.27 nm\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.11, Page number 3.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "from sympy import *\n", + "\n", + "#Variable declaration\n", + "a = Symbol('a')\n", + "\n", + "#Calculations\n", + "#For (110) plane\n", + "a1 = math.sqrt(2)*a**2 #area of plane\n", + "n1 = (1./4 )*4 #no. of atoms in this plane\n", + "rho1 = n1/a1\n", + "\n", + "#For (111) plane\n", + "EO = (a*math.sqrt(3))/math.sqrt(2)\n", + "a2 = (a*EO)/math.sqrt(2)\n", + "n2 = 3*(1./6.)\n", + "rho2 = n2/a2\n", + "\n", + "#Result\n", + "print \"Density of lattice points (111) plane:density of lattice points (110) plane =\",rho2,\":\",rho1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of lattice points (111) plane:density of lattice points (110) plane = 0.577350269189626/a**2 : 0.707106781186547/a**2\n" + ] + } + ], + "prompt_number": 12 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_4.ipynb b/Solid_state_physics/Chapter_4.ipynb new file mode 100755 index 00000000..019aaef9 --- /dev/null +++ b/Solid_state_physics/Chapter_4.ipynb @@ -0,0 +1,189 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:c896524cb6d8dfdd75df5649979d411984ee380fa5c3cbff49f27851e63b1fb4" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4:Defects in Solids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.1, Page number 4.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "k = 1.38*10**-23 #Boltzmann constant(eV/K)\n", + "e = 1.6*10**-19 #Electronic charge(C)\n", + "T1 = 500 #First temperature for metal(K)\n", + "T2 = 1000 #Second temperature for metal(K)\n", + "Ev = 1 #Average energy required to create a vacancy in metal(eV)\n", + "\n", + "#Calculations\n", + "x = k/e\n", + "#n_500 = N*exp(-Ev/T1*k) ---(1)\n", + "#n_1000 = N*exp(-Ev/T2*k) ---(2)\n", + "#Dividing (1) by (2), we get the following expression\n", + "n = math.exp(Ev/(T2*x))\n", + "\n", + "#Result\n", + "print \"Ratio of vacancies=\",round((n/1E+5),3),\"*10^5\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio of vacancies= 1.085 *10^5\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.2, Page number 4.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "n1_by_N = 1.*10**-10 #frequency of vacancy sites at 500 C\n", + "T1 = 500.+273. #K\n", + "T2 = 1000.+273. #K\n", + "\n", + "#Calculations\n", + "x = math.exp((T1/T2)*math.log(n1_by_N))\n", + "\n", + "#Result\n", + "print \"Frequency of vacancy sites at 1000 C =\",round((x/1E-7),4),\"*10^-7\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of vacancy sites at 1000 C = 8.467 *10^-7\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.3, Page number 4.9" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "r = 2.82*10**-10 #interionic distance(m)\n", + "n = 5*10**11 #density of Schottky defect(per m^3)\n", + "T = 25+273 #temperature(K)\n", + "k = 8.625*10**-5 #Boltzmann constant(/K)\n", + "\n", + "#Calculations\n", + "v = (2*r)**3 #volume of one unit cell(m^3)\n", + "N = 4/v #density of ion pairs\n", + "Es = 2*k*T*2.303*math.log10(N/n)\n", + "\n", + "#Result\n", + "print \"The average energy required for creation of one Schottky defect is\",round(Es,3),\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The average energy required for creation of one Schottky defect is 1.971 eV\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4, Page number 4.11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "T1 = 20+273 #K\n", + "T2 = 300+273 #K\n", + "Ef = 1.4 #average energy for creating a Freknel defect(eV)\n", + "k = 8.625*10**-5 #Boltzmann constant(J/K)\n", + "N = 1 #For simplicity assume total number of metal ions to be unity\n", + "Ni = 1 #For simplicity assume total number of metal ions to be unity\n", + "\n", + "#Calculations\n", + "n1 = (N*Ni)**0.5*math.exp(-Ef/(2*k*T1)) \n", + "n2 = (N*Ni)**0.5*math.exp(-Ef/(2*k*T2)) \n", + "x = n1/n2\n", + "\n", + "#Result\n", + "print \"The ratio of the number of Frenkel defects is\",round((x/1E-6),2),\"*10^-6 or\",round(((1/x)/1E+5),2),\"*10^5\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of the number of Frenkel defects is 1.32 *10^-6 or 7.56 *10^5\n" + ] + } + ], + "prompt_number": 27 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_5.ipynb b/Solid_state_physics/Chapter_5.ipynb new file mode 100755 index 00000000..42776694 --- /dev/null +++ b/Solid_state_physics/Chapter_5.ipynb @@ -0,0 +1,498 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:cd8528b1343f720ba16c3255f8c2f531a0d8db6500634023001bba60d12d390a" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 5:Principles of Quantum Mechanics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.1, Page number 5.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Varaible declaration\n", + "c = 3*10**8 #velocity of air(m/s)\n", + "m = 1.67*10**-27 #mass of proton(kg)\n", + "h = 6.626*10**-34 #Planck's constant(J x sec)\n", + "\n", + "#Calculation\n", + "v = c/10. #velocity of proton(m/s)\n", + "lamda = h/(m*v)\n", + "\n", + "#Result\n", + "print \"The de Brogile wavelength is\",round((lamda/1E-14),3),\"*10^-14 m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de Brogile wavelength is 1.323 *10^-14 m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.2, Page number 5.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Varaible declaration\n", + "V = 400 #potential(V)\n", + "\n", + "#Calculation\n", + "lamda = 12.26/math.sqrt(V)\n", + "\n", + "#Result\n", + "print \"The de Brogile wavelength is\",lamda,\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de Brogile wavelength is 0.613 A\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.3, Page number 5.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Varaible declaration\n", + "E = 0.025 #kinetic energy of neutron(eV)\n", + "m = 1.674*10**-27 #mass of neutron(kg)\n", + "h = 6.626*10**-34 #Planck's constant(J x sec)\n", + "\n", + "#Calculations\n", + "E_j = E*1.6*10**-19 #converting eV to joules\n", + "lamda = h/math.sqrt(2*m*E_j)\n", + "\n", + "#Result\n", + "print \"The de Brogile wavelength is\",round((lamda/1E-11),3),\"*10^-11 m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de Brogile wavelength is 18.106 *10^-11 m\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.4, Page number 5.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Varaible declaration\n", + "V = 1600 #potential(V)\n", + "\n", + "#Calculation\n", + "lamda = 12.26/math.sqrt(V)\n", + "\n", + "#Result\n", + "print \"The de Brogile wavelength is\",lamda,\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de Brogile wavelength is 0.3065 A\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5, Page number 5.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Varaible declaration\n", + "h = 6.626*10**-34 #Planck's constant(J x sec)\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "L = 0.1*10**-9 #length of each side of box(m)\n", + "#For lowest energy level,\n", + "nx = 1\n", + "ny = 1\n", + "nz = 1\n", + "\n", + "#Calculations\n", + "E1 = (((h**2)*(nx**2+ny**2+nz**2))/(8*m*L**2))/(1.6*10**-19)\n", + "\n", + "#Result\n", + "print \"The lowest energy of electron is\",round(E1,2),\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lowest energy of electron is 113.08 eV\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.6, Page number 5.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34 #Planck's constant(J x sec)\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "L = 0.1*10**-9 #length of each side of box(m)\n", + "#For level next to lowest energy level,\n", + "nx = 1\n", + "ny = 1\n", + "nz = 2\n", + "\n", + "#Calculations\n", + "E1 = (((h**2)*(nx**2+ny**2+nz**2))/(8*m*L**2))/(1.6*10**-19)\n", + "\n", + "#Result\n", + "print \"The lowest energy of electron is\",round(E1,2),\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lowest energy of electron is 226.15 eV\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.7, Page number 5.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34 #Planck's constant(J x sec)\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "E = 2000. #energy of electron(eV)\n", + "\n", + "#Calculations\n", + "Ej = E*1.6*10**-19 #converting eV to joules\n", + "lamda = h/math.sqrt(2*m*Ej)\n", + "\n", + "#Result\n", + "print \"The de Brogile wavelength is\",round((lamda/1E-9),4),\"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de Brogile wavelength is 0.0275 nm\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.8, Page number 5.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34 #Planck's constant(J x sec)\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "L = 4*10**-10 #length of each side of box(m)\n", + "#For minimum energy \n", + "n = 1\n", + "\n", + "#Calculations\n", + "E1 = ((h**2)*(n**2))/(8*m*L**2)\n", + "\n", + "#Result\n", + "print \"Minimum energy =\",round((E1/1E-18),3),\"*10^-18 J\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum energy = 0.377 *10^-18 J\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.9, Page number 5.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34 #Planck's constant(J x sec)\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "L = 1*10**-10 #length of each side of box(m)\n", + "n1 = 10 #For energy in ground state\n", + "n2 = 2 #For energy in first excited state\n", + "n3 = 3 #For energy in second excited state\n", + "\n", + "#Calculations\n", + "E1 = ((h**2)*(n1**2))/(8*m*L**2)\n", + "E2 = ((h**2)*(n2**2))/(8*m*L**2)\n", + "E3 = ((h**2)*(n3**2))/(8*m*L**2)\n", + "\n", + "#Results\n", + "print \"Energy in ground state =\",round((E1/1E-17),4),\"*10^17 J (Calculation mistake in textbook)\"\n", + "print \"Energy in first excited state =\",round((E2/1E-17),4),\"*10^17 J\"\n", + "print \"Energy in second excited state =\",round((E3/1E-17),4),\"*10^17 J\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy in ground state = 60.3075 *10^17 J (Calculation mistake in textbook)\n", + "Energy in first excited state = 2.4123 *10^17 J\n", + "Energy in second excited state = 5.4277 *10^17 J\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.10, Page number 5.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34 #Planck's constant(J x sec)\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "lamda = 1.66*10**-10 #wavelength(m)\n", + "\n", + "#Calculations\n", + "v = h/(m*lamda)\n", + "KE = (m*v**2)/(2*1.6*10**-19) #in joules\n", + "\n", + "#Result\n", + "print \"Velocity of electron =\",round((v/1E+7),4),\"*10^7 m\"\n", + "print \"Kinetic energy of electron =\",round(KE,2),\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Velocity of electron = 0.4386 *10^7 m\n", + "Kinetic energy of electron = 54.71 eV\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.11, Page number 5.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Varaible declaration\n", + "V = 15*10**3 #potential(V)\n", + "\n", + "#Calculation\n", + "lamda = 12.26/math.sqrt(V)\n", + "\n", + "#Result\n", + "print \"The de Brogile wavelength is\",round(lamda,2),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de Brogile wavelength is 0.1 A\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.12, Page number 5.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Varaible declaration\n", + "V = 344 #potential(V)\n", + "theta = 60 #glancing angle(degrees)\n", + "\n", + "#Calculation\n", + "lamda = 12.26/math.sqrt(V)\n", + "#For first reflection \n", + "n = 1\n", + "d = (n*lamda)/(2*math.sin(math.radians(theta)))\n", + "\n", + "#Result\n", + "print \"The interatomic spacing of the crystal is\",round(d,4),\"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The interatomic spacing of the crystal is 0.3816 A\n" + ] + } + ], + "prompt_number": 24 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_6.ipynb b/Solid_state_physics/Chapter_6.ipynb new file mode 100755 index 00000000..2b4f9a24 --- /dev/null +++ b/Solid_state_physics/Chapter_6.ipynb @@ -0,0 +1,386 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:425f92ebc94b7b662d737292c7c739a2d9f7bf01d4a0a5239c1380861a6af3a7" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 6: Electron theory of Metals" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.1, Page number 6.5" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "rho_s = 10.5*10**3 #density of silver(kg/m^3)\n", + "Na = 6.02*10**26 #Avogadro's number\n", + "Ma = 107.9 #atomic weight of silver\n", + "sigma = 6.8*10**7 #conductivity(/ohm-m)\n", + "e = 1.6*10**-19 #charge of an electron(C)\n", + "\n", + "#Calculations\n", + "n = (rho_s*Na)/Ma\n", + "u = sigma/(n*e)\n", + "\n", + "#Results\n", + "print \"Density of electrons =\",round((n/1E+28),2),\"*10^28\"\n", + "print \"Mobility of electrons =\",round((u/1E-2),3),\"*10^-2 m^2/V-s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density of electrons = 5.86 *10^28\n", + "Mobility of electrons = 0.725 *10^-2 m^2/V-s\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.2, Page number 6.6" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "den = 8.92*10**3 #density(kg/m^3)\n", + "rho = 1.73*10**-8 #resistivity of copper(ohm-m)\n", + "Ma = 63.5 #atomic weight\n", + "e = 1.6*10**-19 #charge of an electron(C)\n", + "Na = 6.02*10**26 #Avogadro's number\n", + "m = 9.1*10**-31 #mass of an electron(kg)\n", + "\n", + "#Calculations\n", + "n = (den*Na)/Ma\n", + "u = 1/(rho*n*e)\n", + "tou = m/(n*e**2*rho)\n", + "\n", + "#Results\n", + "print \"Mobility of electrons =\",round((u/1E-2),3),\"*10^-2 m/V-s\"\n", + "print \"Average time of collision of electrons =\",round((tou/1E-14),2),\"*10^-14 s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mobility of electrons = 0.427 *10^-2 m/V-s\n", + "Average time of collision of electrons = 2.43 *10^-14 s\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.3, Page number 6.7" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "P = 1.54*10**-8 #resistivity(ohm-m)\n", + "n = 5.8*10**28 #no. of electrons per m^3\n", + "m = 9.108*10**-31 #mass of an elecron(kg)\n", + "e = 1.602*10**-19 #charge of an electron(C)\n", + "\n", + "#Calculations\n", + "tou = m/(n*e**2*P)\n", + "\n", + "#Result\n", + "print \"The relaxation time of conducton of electrons is\",round((tou/1E-14),2),\"*10^-14 s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The relaxation time of conducton of electrons is 3.97 *10^-14 s\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.4, Page number 6.8" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Varaible declaration\n", + "R = 0.06 #resistance(ohms)\n", + "D = 5 #length of wire(m)\n", + "I = 15 #current(A)\n", + "p = 2.7*10**-8 #resistivity of aluminium(ohm-m)\n", + "Ma = 26.98 #atomic weight\n", + "Na = 6.025*10**26 #Avogadro's number\n", + "rho_s = 2.7*10**3 #sensity(kg/m^3)\n", + "\n", + "#Calculations\n", + "#Since each free atom atom contains 3 electrons, therefore,\n", + "n = (3*rho_s*Na)/Ma\n", + "\n", + "#For mobility\n", + "u = 1/(n*e*p)\n", + "\n", + "#For drift velocity\n", + "E = (I*R)/D\n", + "vd = u*E\n", + "\n", + "#Results\n", + "print \"Free electron concentration =\",round((n/1E+29),4),\"*10^29 electrons/m^2\"\n", + "print \"Mobility of electrons =\",round((u/1E-3),3),\"*10^-3 m/V-s\"\n", + "print \"Drift velocity of electrons =\",round((vd/1E-3),3),\"*10^-3 m/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Free electron concentration = 1.8088 *10^29 electrons/m^2\n", + "Mobility of electrons = 1.278 *10^-3 m/V-s\n", + "Drift velocity of electrons = 0.23 *10^-3 m/s\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.5, Page number 6.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "L = 0.1*10**-9 #length of each side of box(m)\n", + "h = 6.62*10**-34 #Planck's constant(J-s)\n", + "m = 9.1*10**-31 #mass of electron(kg)\n", + "#For lowest energy,\n", + "nx = 1\n", + "ny = 1\n", + "nz = 1\n", + "\n", + "#Calculations\n", + "E1 = (((h**2)*(nx**2+ny**2+nz**2))/(8*m*L**2))//(1.6*10**-19)\n", + "\n", + "#Result\n", + "print \"The lowest energy of electron is\",round(E1,2),\"eV\" " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lowest energy of electron is 112.0 eV\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Exmple 6.6, Page number 6.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "'''Fermi equation\n", + "F(E) = 1\n", + " ---------------\n", + " 1+exp((E-Ef)/kT)\n", + "Given, E-Ef = kT\n", + "therefore,\n", + "F(E) = 1\n", + " --------\n", + " 1+exp(1)\n", + "'''\n", + "\n", + "#Calculation\n", + "Fe = 1./(1.+math.exp(1.))\n", + "\n", + "#Result\n", + "print \"F(E) =\",round(Fe,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "F(E) = 0.269\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.7, Page number 6.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#Variable declaration\n", + "Fe = 10./100. #probability\n", + "Ef = 5.5 #Fermi energy(eV)\n", + "k = 1.38*10**-23\n", + " \n", + "#Calculations\n", + "'''Fermi equation\n", + "F(E) = 1\n", + " ---------------\n", + " 1+exp((E-Ef)/kT)\n", + "'''\n", + "E = Ef+(Ef/100)\n", + "E_Ef = (E - Ef)*1.6*10**-19 #(J)\n", + "\n", + "#Let x be E-Ef/k\n", + "x = E_Ef/k\n", + "T = x/math.log(-(1-(1/Fe)))\n", + "\n", + "#Result\n", + "print \"Temperature =\",round(T,2),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature = 290.22 K\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.8, Page number 6.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "#Variable declaration\n", + "Fe = 1./100. #probability\n", + "Ef = 0.5 #Fermi energy(eV)\n", + "k = 1.38*10**-23\n", + " \n", + "#Calculations\n", + "'''Fermi equation\n", + "F(E) = 1\n", + " ---------------\n", + " 1+exp((E-Ef)/kT)\n", + "'''\n", + "\n", + "E = Ef+0.5\n", + "E_Ef = (E - Ef)*1.6*10**-19 #(J)\n", + "\n", + "#Let x be E-Ef/k\n", + "x = E_Ef/k\n", + "T = x/math.log(-(1-(1/Fe)))\n", + "\n", + "#Result\n", + "print \"Temperature =\",round(T),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature = 1262.0 K\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_7.ipynb b/Solid_state_physics/Chapter_7.ipynb new file mode 100755 index 00000000..c3599dfb --- /dev/null +++ b/Solid_state_physics/Chapter_7.ipynb @@ -0,0 +1,330 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:9ccabd1c0a5d5861a1e63defe760a8b9caed49864d9aebb3ab3b0741ed755b61" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7: Dielectric Properties" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.1, Page number 7.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "C = 2*10**-6 #Capacitance(F)\n", + "V = 1000 #voltage(V)\n", + "Er = 100 #permittivity\n", + "\n", + "#Calculations\n", + "W = (C*V**2)/2\n", + "\n", + "Co = C/Er\n", + "Wo = (Co*V**2)/2\n", + "Wf = W-Wo\n", + "\n", + "#Result\n", + "print \"Energy stored in condenser =\",W,\"J\"\n", + "print \"Energy stored in polarizing the dilectric =\",Wf,\"J\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy stored in condenser = 1.0 J\n", + "Energy stored in polarizing the dilectric = 0.99 J\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.2, Page number 7.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaraion\n", + "Er = 4.94 #permittivity\n", + "n2 = 2.69 #index of refraction\n", + "\n", + "#Calculations\n", + "'''\n", + "Er - 1 N(ae+ai)\n", + "------ = ---------\n", + "Er + 2 3*Eo \n", + "Sunbstituting the values for Er, we get,\n", + "N(ae+ai) \n", + "-------- = 0.5677 ------------(1)\n", + " 3*ao\n", + "'''\n", + "x = 0.5677\n", + "\n", + "'''\n", + "Also, Er = n**2\n", + "Therefore, n**2-1 N*ae\n", + " ------- = -----\n", + " n**2+2 3*Eo\n", + "Substituting the values for n^2, we get,\n", + "N*ae\n", + "---- = 0.36034 ---------------(2)\n", + "3*Eo\n", + "'''\n", + "y = 0.36034\n", + "#Let z = ai/ae\n", + "#Dividing equation (1) by (2), we get,\n", + "\n", + "z = (x/y)-1\n", + "\n", + "#Result\n", + "print \"Ratio between electronic and ionic probabbility is\",round(z,3) ,\"or\",round((1/z),3)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio between electronic and ionic probabbility is 0.575 or 1.738\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.3, Page number 7.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "Er = 2.56 #permittivity\n", + "f = 1*10**6 #frequency(Hz)\n", + "A = 8*10**-4 #area(m^2)\n", + "d= 0.08*10**-3 #distance of seperation(m)\n", + "Eo = 8.85*10**-12\n", + "\n", + "#Calculations\n", + "Er_dash = Er*0.7*10**-4\n", + "w = 2*math.pi*f\n", + "Rp = d/(w*Eo*Er_dash*A)\n", + "\n", + "Cp = (A*Eo*Er)/d\n", + "\n", + "#Results\n", + "print \"Parallel loss resistance =\",round((Rp/1E+6),2),\"MOhms\"\n", + "print \"Capacitance =\",Cp,\"F(Calculation mistake in textbook)\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Parallel loss resistance = 10.04 MOhms\n", + "Capacitance = 2.2656e-10 F(Calculation mistake in textbook)\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.5, Page number 7.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Varaible declaration\n", + "N = 3.*10**28 #density(atoms/m^3)\n", + "ae = 10.**-40 #electronic polarizability(F m^2)\n", + "Eo = 8.854*10**-12 #permittivity of free space(F/m)\n", + "\n", + "#Calculaion\n", + "Er = 1+((N*ae)/Eo)\n", + "\n", + "#Result\n", + "print \"dielectric constant =\",round(Er,3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "dielectric constant = 1.339\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.5, Page number 7.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "Er = 1.0000684 #permittivity of dilectric\n", + "Eo = 8.854*10**-12 #permittivity of free space(F/m)\n", + "N = 2.7*10**25 #density(atoms/m^3)\n", + "\n", + "#Calculation\n", + "ae = (Eo*(Er-1))/N\n", + "\n", + "#Result\n", + "print \"Electronic polarizability =\",round((ae/1E-41),3),\"*10^-41 Fm^2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Electronic polarizability = 2.243 *10^-41 Fm^2\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.6, Page number 7.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "A = 100*10**-4 #area of parallel capacitor(m^2)\n", + "d = 1*10**-2 #separation between plates(m)\n", + "Eo = 8.854*10**-12 #permittivity of free space(F/m)\n", + "V = 100 #voltage(V)\n", + "\n", + "#Calculation\n", + "C = (Eo*A)/d\n", + "Q = C*V\n", + "\n", + "#Result\n", + "print \"Capacitance =\",round((C/1E-12),2),\"pF\"\n", + "print \"Charge =\",Q,\"C\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Capacitance = 8.85 pF\n", + "Charge = 8.854e-10 C\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.7, Page number 7.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "N = 6.02*10**26 #Avogadro's number\n", + "den = 2050 #density(kg/m^3)\n", + "Ma = 32 #atomic weight\n", + "Eo = 8.55*10**-12 #permittivity of free space(F/m)\n", + "v = 1/3 #internal field constant\n", + "Er = 3.75 #dielectric constant of sulphur\n", + "\n", + "#Calculations\n", + "n = (N*den)/Ma #no. of atoms per m^3\n", + "ae = ((Er-1)/(Er+2))*((3*Eo)/n)\n", + "\n", + "#Result\n", + "print \"Electronic polarizability =\",round((ae/1E-40),3),\"*10^-41 Fm^2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Electronic polarizability = 3.181 *10^-41 Fm^2\n" + ] + } + ], + "prompt_number": 11 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_8.ipynb b/Solid_state_physics/Chapter_8.ipynb new file mode 100755 index 00000000..161a8521 --- /dev/null +++ b/Solid_state_physics/Chapter_8.ipynb @@ -0,0 +1,436 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:fbb68fbb0713029438d419fcf28fa2bcf0bc60f8a093b90691d3e7397e7a942d" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 8:Magnetic Properties" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.1, Page number 8.3" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "M = 1.4 #value of magnetic field when filled with iron\n", + "H = 6.5*10**-4 #value of magnetic field in the interior\n", + "\n", + "#Calculations\n", + "x = M/H\n", + "ur = 1+x\n", + "\n", + "#Result\n", + "print \"Relative permeability of iron is\",round(ur,2),\"(Calculation mistake in textbook)\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Relative permeability of iron is 2154.85 (Calculation mistake in textbook)\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.2, Page number 8.3" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "M = 3300 #value of magnetic filed(amp/m) \n", + "H = 220 #strength of magnetic filed(amp/m)\n", + "\n", + "#Calculations\n", + "x = (M/H)+1\n", + "\n", + "#Result\n", + "print \"Relative permeability of iron is\",round(x,2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Relative permeability of iron is 16.0\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.3, Page number 8.4" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi\n", + "\n", + "#Variable declaration\n", + "H = 10**6 #magnetic field intensity(amp/m)\n", + "x = 1.5*10**-3 #susceptibility\n", + "Uo = 4*pi*10**-7 \n", + "\n", + "#Calculations\n", + "M = x*H #magnetization of material\n", + "B = Uo*(M+H) #flux density\n", + "\n", + "#Result\n", + "print \"Magnetization =\",round((M/1E+3),1),\"*10^3 A/m\"\n", + "print \"Flux density =\",round(B,3),\"T\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetization = 1.5 *10^3 A/m\n", + "Flux density = 1.259 T\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.4, Page number 8.4" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi\n", + "\n", + "#Variable declaration\n", + "H = 10**4 #magnetic field intensity(amp/m)\n", + "x = 3.7*10**-3 #susceptibility\n", + "Uo = 4*pi*10**-7 \n", + "\n", + "#Calculations\n", + "M = x*H #magnetization of material\n", + "B = Uo*(M+H) #flux density\n", + "\n", + "#Result\n", + "print \"Magnetization =\",M,\"A/m\"\n", + "print \"Flux density =\",round(B,4),\"wb/m^2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetization = 37.0 A/m\n", + "Flux density = 0.0126 wb/m^2\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.5, Page number 8.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi\n", + "\n", + "#Variable declaration\n", + "I = 500*10**-3 #current(A)\n", + "d = 10*10**-2 #diameter of loop(m)\n", + "\n", + "#Calculations\n", + "r = d/2 #radius(m)\n", + "A = 2*pi*r**2 #area(m^2)\n", + "Um = I*A\n", + "\n", + "#Result\n", + "print \"Magnetic moment =\",round((Um/1E-3),3),\"*10^-3 A-m^2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetic moment = 7.854 *10^-3 A-m^2\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.6, Page number 8.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "r = 5.29*10**-11 #radius of the orbit(m)\n", + "B = 2 #field strength(Tesla)\n", + "e = 1.602*10**-19 #charge of an electron(C)\n", + "m = 9.108*10**-31 #mass of an electron(kg)\n", + "\n", + "#Calculation\n", + "Uind = (e**2*r**2*B)/(4*m)\n", + "\n", + "#Result\n", + "print \"Change in magnetic moment =\",round((Uind/1E-29),3),\"*10^-29 A-m^2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Change in magnetic moment = 3.943 *10^-29 A-m^2\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.7, Page number 8.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Varaible declaration\n", + "T1 = 350 #temperature(K)\n", + "x1 = 2.8*10**-4 #susceptibility at T1\n", + "T2 = 300 #temperature(K)\n", + "\n", + "#Calculation\n", + "x2 = (x1*T1)/T2\n", + "\n", + "#Result\n", + "print \"Susceptibility at 300k is\",round((x2/1E-4),3),\"*10^-4\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Susceptibility at 300k is 3.267 *10^-4\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8, Page number 8.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi \n", + "\n", + "#Variable declaration\n", + "den = 8906 #density of nickel(kg/m^3)\n", + "N = 6.025*10**26 #Avogadro's number\n", + "Ma = 58.7 #atomic weight\n", + "Bs = 0.65 #magnetic induction(wb/m^2)\n", + "Uo = 4*pi*10**-7\n", + "\n", + "#Calculations\n", + "n = (den*N)/Ma #no. of nickel atoms per m^3\n", + "\n", + "#Since x is very large, B = n*Uo*Um\n", + "Um = Bs/(n*Uo))\n", + "\n", + "#Result\n", + "print \"Magnetic moment =\",Um,\"A-m^2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetic moment = 5.65850692635e-24 A-m^2\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.9, Page number 8.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "H = 2 #magnetic filed intensity(wb/m^2)\n", + "U = 9.4*10**-24\n", + "k = 1.38*10**-23\n", + "\n", + "#Calculations\n", + "'''\n", + "n = c*no*exp(-Eg/kT) #no. of electrons\n", + "where Eg = -U*H\n", + "For parallel orientation,Eg = -U*H\n", + "For antiparallel orientation, Eg = U*H\n", + "therefore,\n", + "np = c*no*exp(U*H/kT) ---(1)\n", + "na = c*no*exp(-U*H/kT) ---(2)\n", + "Dividing (1) by (2), we get,'''\n", + "\n", + "T = (2*U*H)/(math.log(2)*k)\n", + "\n", + "#Result\n", + "print \"T=\",round(T,1),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "T= 3.9 K\n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.10, Page number 8.29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi\n", + "\n", + "#Variable declaration\n", + "Uo = 4*pi*10**-7\n", + "Ma = 157.26 #atomic weight og gadolinium\n", + "den = 7.8*10**3 #density(kg/m^3)\n", + "N = 6.025*10**26 #Avogadro's number\n", + "x = 7.1 #Bohr magnetron per atom\n", + "Um = 9.27*10**-24\n", + "\n", + "#Calculations\n", + "n = (den*N)/Ma #no. of atoms in 1 kg\n", + "n1 = n*10**-3 #no. of atoms in 1 gm\n", + "M = n1*x*Um #magnetic moment per gram(a-m^2)\n", + "\n", + "Bs = n*Uo*Um #saturization magnetization\n", + "\n", + "#Result\n", + "print \"Magnetic moment per gram =\",round(M,3),\"Am^2\"\n", + "print \"Saturization magnetization =\",round(Bs,3),\"Wb/m^2(Calculation mistake in textbok)\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetic moment per gram = 1966.851 Am^2\n", + "Saturization magnetization = 0.348 Wb/m^2(Calculation mistake in textbok)\n" + ] + } + ], + "prompt_number": 41 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/Chapter_9.ipynb b/Solid_state_physics/Chapter_9.ipynb new file mode 100755 index 00000000..70a3843c --- /dev/null +++ b/Solid_state_physics/Chapter_9.ipynb @@ -0,0 +1,845 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:b86f6f4d444d5177f7a40efe10b2b4ac505571f2f5cf98eeaa6619afa2ee7d22" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 9: Semiconductors" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.1, Page number 9.11" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "ni = 2.37*10**19 #intrinsic carrier density(m^-3)\n", + "ue = 0.38 #electron mobility(m^2/V-s)\n", + "uh = 0.18 #hole mobility(m^2/V-s)\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "\n", + "#Calculations\n", + "sigma_i = ni*e*(ue+uh) #(1/ohm-m)\n", + "p = 1/sigma_i\n", + "\n", + "#Result\n", + "print \"Resistivity =\",round(p,3),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity = 0.471 m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.2, Page number 9.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "Eg = 1.12 #bandgap(eV)\n", + "k = 1.38*10**-23 #Boltzman constant(J/K)\n", + "T = 300 #Temperature(K)\n", + "mh = 0.28 #Effective Mass of the hole(kg)\n", + "me = 0.12 #Effective Mass of the hole(kg)\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "\n", + "#Calculation\n", + "Ef = (Eg/2)+3/4*k*T*(math.log(mh/me))/e\n", + "\n", + "#Result \n", + "print \"The position of the Fermi level is at\",round(Ef,2),\"from the top of valence band\" " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The position of the Fermi level is at 0.56 from the top of valence band\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.3, Page number 9.12" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi, exp\n", + "\n", + "#Variable declaration\n", + "m = 9.109*10**-31 #mass of an electron(kg)\n", + "k = 1.38*10**-23 #Boltzman constant(J/K)\n", + "T = 300 #Temperature(K)\n", + "h = 6.626*10**-34 #Planck's constant\n", + "Eg = 0.7 #bandgap(eV)\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "\n", + "#Calculation\n", + "C = (((2*pi*m*k)/h**2)**(3./2.)) \n", + "T1 = T**(3./2.)\n", + "E = exp((-Eg*e)/(2*k*T))\n", + "ni = 2*C*T1*E\n", + "\n", + "#Result\n", + "print \"Concentration of intrinsic charge carriers =\",round((ni/1E+18),2),\"*10**18/m^3\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Concentration of intrinsic charge carriers = 33.48 *10**18/m^3\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.4, Page number " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "ni = 2.4*10**19 #intrinsic carrier density(m^-3)\n", + "ue = 0.39 #electron mobility(m^2/V-s)\n", + "uh = 0.19 #hole mobility(m^2/V-s)\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "\n", + "#Calculations\n", + "sigma_i = ni*e*(ue+uh) #(1/ohm-m)\n", + "p = 1/sigma_i\n", + "\n", + "#Result\n", + "print \"Resistivity =\",round(p,3),\"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity = 0.449 m\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.5, Page number 9.13" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "ni = 2.5*10**19 #intrinsic carrier density(m^-3)\n", + "ue = 0.39 #electron mobility(m^2/V-s)\n", + "uh = 0.19 #hole mobility(m^2/V-s)\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "l = 1*10**-2 #length of rod(m)\n", + "A = 10**-3*10**-3 #area(m^2)\n", + "\n", + "#Calculations\n", + "sigma = ni*e*(ue+uh) #(1/ohm-m)\n", + "R = 1/(sigma*A)\n", + "\n", + "#Result\n", + "print \"Resistivity =\",round(R,3),\"Ohms\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity = 431034.483 Ohms\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.6, Page number 9.14" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi, exp\n", + "\n", + "#Variable declaration\n", + "ue = 0.48 #electron mobility(m^2/V-s)\n", + "uh = 0.013 #hole mobility(m^2/V-s)\n", + "Eg = 1.1 #bandgap(eV)\n", + "T = 300 #assumption - Temperature(K)\n", + "h = 6.626*10**-34 #Planck's constant\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "k = 1.38*10**-23 #Boltzman constant(J/K)\n", + "m = 9.1*10**-31 #mass of an electron(kg)\n", + "\n", + "#Calculation\n", + "C = 2*(((2*pi*m*k)/h**2))**(3./2.)\n", + "ni = C*T**(3./2.)*exp((-Eg*e)/(2*k*T))\n", + "sigma_i = ni*e*(ue+uh)\n", + "\n", + "#Result\n", + "print \"Conductivity=\",round((sigma_i/1E-3),3),\"*10^-3/ohm-m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Conductivity= 1.159 *10^-3/ohm-m\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.7, Page number 9.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import pi, exp\n", + "\n", + "#Variable declaration\n", + "ue = 0.4 #electron mobility(m^2/V-s)\n", + "uh = 0.2 #hole mobility(m^2/V-s)\n", + "Eg = 0.7 #bandgap(eV)\n", + "T = 300 #assumption - Temperature(K)\n", + "h = 6.626*10**-34 #Planck's constant\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "k = 1.38*10**-23 #Boltzman constant(J/K)\n", + "m = 9.1*10**-31 #mass of an electron(kg)\n", + "\n", + "#Calculation\n", + "C = 2*(((2*pi*m*k)/h**2))**(3./2.)\n", + "ni = C*T**(3./2.)*exp((-Eg*e)/(2*k*T))\n", + "sigma_i = ni*e*(ue+uh)\n", + "\n", + "#Result\n", + "print \"Intrinsic carrier density =\",round((ni/1E+19),2),\"*10^19 per m^3\"\n", + "print \"Conductivity=\",round(sigma_i,2),\"/ohm-m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Intrinsic carrier density = 3.34 *10^19 per m^3\n", + "Conductivity= 3.21 /ohm-m\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.8, Page number 9.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "ue = 0.36 #electron mobility(m^2/V-s)\n", + "uh = 0.17 #hole mobility(m^2/V-s)\n", + "P = 2.12 #resistivity(ohm-m)\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "k = 1.38*10**-23 #Boltzman constant(J/K)\n", + "m = 9.1*10**-31 #mass of an electron(kg)\n", + "h = 6.626*10**-34 #Planck's constant\n", + "T = 300 #assumption - Temperature(K)\n", + "\n", + "#Calculations\n", + "sigma = 1/P\n", + "ni = sigma/(e*(ue+uh))\n", + "C = 2*(((2*pi*m*k)/h**2))**(3./2.)\n", + "Eg = ((2*k*T)/e)*math.log(C*(T**(3./2.))/ni)\n", + "\n", + "#Result\n", + "print \"Forbidden energy gap =\",round(Eg,3),\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Forbidden energy gap = 0.793 eV\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.9, Page number 9.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import log10\n", + "\n", + "#Variable declaration\n", + "p1 = 2 #resistivity(ohm-m)\n", + "p2 = 4.5 #resistivity(ohm-m)\n", + "T1 = 20.+273 #Temperature(K)\n", + "T2 = 32.+273 #temperature(K)\n", + "k = 1.38*10**-23 #Boltzman constant(J/K)\n", + "\n", + "#Calculations\n", + "dy = log10(p2)-log10(p1)\n", + "dx = (1/T1)-(1/T2)\n", + "dy_by_dx = dy/dx\n", + "Eg = (2*k*dy_by_dx)/e\n", + "\n", + "#Result\n", + "print \"Energy band gap =\",round(Eg,3),\"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy band gap = 0.452 eV\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.10, Page number 9.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import log\n", + "\n", + "#Variable declaration\n", + "e = 1.602*10**-19 #charge on electron(C)\n", + "k = 1.38*10**-23 #Boltzman constant(J/K)\n", + "Eg = 1*e #bandgap(J)\n", + "\n", + "#Calculations\n", + "'''At T = 0K\n", + "(Ev+0.5)=(Ec+Ev)/2 -----(1)\n", + "\n", + "Let at temperature T, fermi level be shited by 10%\n", + "(Ev+06) = (Ec+Ev)/2 +(3kT*ln(4))/4 ----(2)\n", + "\n", + "Subtracting (1) from (2), we get the following expression'''\n", + "\n", + "T = (4*e/10)/(3*k*log(4))\n", + "\n", + "#Result\n", + "print \"Temperature =\",round(T,2),\"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature = 1116.52 K\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.11, Page number 9.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "Na = 5*10**23 #no. of atoms of boron\n", + "Nd = 3*10**23 #no. of atoms of arsenic\n", + "ni = 2*10**16 #intrinsic charge carriers(/m^3)\n", + "\n", + "#Calculations\n", + "p = (2*(Na-Nd))/2 #hole concentration(/m^3)\n", + "n = ni**2/p #electron concentration(/m^3)\n", + "\n", + "#Result\n", + "print \"Hole concentration =\",round((p/1E+23),2),\"*10^23 per m^3\"\n", + "print \"Electron concentration =\",round((n/1E+9),2),\"*10^9 per m^3\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hole concentration = 2.0 *10^23 per m^3\n", + "Electron concentration = 2.0 *10^9 per m^3\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.12, Page number 9.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "ue = 0.13 #electron mobility(m^2/V-s)\n", + "uh = 0.05 #hole mobility(m^2/V-s)\n", + "e = 1.602*10**-19 #charge on electron(C)\n", + "ni = 1.5*10**16 #intrinsic charge carriers(/m^3) \n", + "\n", + "\n", + "#Calculations\n", + "#Part a\n", + "sigma = ni*e*(ue+uh) #conductivity(1/ohm-m)\n", + "\n", + "#Part b\n", + "w = 28.1 #atomic weight of Si\n", + "den = 2.33*10**3 #density of Si(kg/m^3)\n", + "n = (den*6.02*10**26)/w #no. of atoms of silicon\n", + "#Since one donor type impurity atom is added in 10^8 Si atoms, \n", + "Nd = n/10**8\n", + "p = ni**2/Nd\n", + "sigma_ex = Nd*e*ue #(per ohm-m)\n", + "\n", + "#Part c\n", + "Na = Nd #Since one acceptor type impurity atom is added in 10^8 Si atoms\n", + "n2 = ni**2/Na\n", + "sigma_ax = Na*e*uh #(per ohm-m)\n", + "\n", + "#Results\n", + "print \"a)Conductivity =\",round((sigma/1E-3),3),\"*10^-3 per ohm-m\"\n", + "print \"b)Conductivity if donor type impurity is added =\",round(sigma_ex,2),\"per ohm-m\"\n", + "print \"c)Conductivity if acceptor type impurity is added =\",round(sigma_ax,2),\"per ohm-m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a)Conductivity = 0.433 *10^-3 per ohm-m\n", + "b)Conductivity if donor type impurity is added = 10.4 per ohm-m\n", + "c)Conductivity if acceptor type impurity is added = 4.0 per ohm-m\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.13, Page number 9.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "from math import log\n", + "\n", + "#Variable declaration\n", + "ue = 0.135 #electron mobility(m^2/V-s)\n", + "uh = 0.048 #hole mobility(m^2/V-s)\n", + "e = 1.602*10**-19 #charge on electron(C)\n", + "ni = 1.5*10**16 #intrinsic charge carriers(atoms/m^3)\n", + "k = 1.38*10**-23 #Boltzman constant(J/K)\n", + "T = 300 #assumption - Temperature(K)\n", + "Nd = 10**23 #doping concentration(atoms/m^3)\n", + "\n", + "#Calculations\n", + "sigma = ni*e*(ue+uh) #conductivity of intrinsic Si\n", + "\n", + "p = ni**2/Nd #hole concentration\n", + "\n", + "sigma_ex = Nd*e*ue #conductivity at equilibrium\n", + "F = (3*k*T)/(4*e)*log(ue/uh) #position of Fermi level\n", + "\n", + "#Results\n", + "print \"Conductivity of intrinsic Si is\",round((sigma/1E-3),4),\"*10^-3 per ohm-m\"\n", + "print \"Hole concentration at equilibrium is\",round((Nd/1E+23)),\"*10^23 per m^3\"\n", + "print \"Conductivity at equilibrium is\",round((sigma_ex/1E+3),2),\"*10^3 per m^3\"\n", + "print \"Fermi level will be\",round(F,2),\"eV above intrinsic level\" " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Conductivity of intrinsic Si is 0.4397 *10^-3 per ohm-m\n", + "Hole concentration at equilibrium is 1.0 *10^23 per m^3\n", + "Conductivity at equilibrium is 2.16 *10^3 per m^3\n", + "Fermi level will be 0.02 eV above intrinsic level\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.14, Page number 9.35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "ue = 0.19 #electron mobility(m^2/V-s)\n", + "e = 1.602*10**-19 #charge on electron(C)\n", + "T = 300 #Temperature(K)\n", + "\n", + "#Calculation\n", + "Dn = (ue*k*T)/e\n", + "\n", + "#Result\n", + "print \"Diffusion co-efficient =\",round((Dn/1E-4),2),\"*10^-4 m^2/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diffusion co-efficient = 49.1 *10^-4 m^2/s\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.15, Page number 9.45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "Rh = 3.66*10**-4 #Hall coefficient\n", + "I = 10**-2 #current(A)\n", + "B = 0.5 #magnetic field intensity(wb/m^2)\n", + "t = 1.*10**-3 #thickness of plate(m)\n", + "\n", + "#Calculations\n", + "Vh = (Rh*I*B)/t\n", + "\n", + "#Result\n", + "print \"Hall coefficient =\",(Vh/1E-3),\"mV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall coefficient = 1.83 mV\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.16, Page number 9.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "Vy = 37*10**-6 #voltage(V)\n", + "t = 10**-3 #thickness of crystal(m)\n", + "Bz = 0.5 #magnetic field intensity(Wb/m^2)\n", + "Ix = 20*10**-3 #current(A)\n", + "\n", + "#Calculations\n", + "Vh = (Vy*t)/(Ix*Bz)\n", + "\n", + "#Result\n", + "print \"Hall coefficient =\",(Vh/1E-6),\"*10^-6 m^3/C\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall coefficient = 3.7 *10^-6 m^3/C\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.17, Page number 9.46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "Rh = 7.35*10**-5 #Hall coefficient(m^3/C)\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "sigma = 200 #conductivity(/ohm-m)\n", + "n = 8.023*10**22 #Avogadro's number\n", + "\n", + "#Calculations\n", + "n = 1/(Rh*e)\n", + "\n", + "u = sigma/(n*e)\n", + "\n", + "#Results\n", + "print \"Density =\",round((n/1E+22),3),\"*10^22 m^3\"\n", + "print \"Conductivity =\",round((u/1E-3),2),\"*10^-3 m^2/V-s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Density = 8.503 *10^22 m^3\n", + "Conductivity = 14.7 *10^-3 m^2/V-s\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.18, Page number 9.47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "I = 50 #current(A)\n", + "B = 1.5 #magnetic field intensity(T)\n", + "n = 8.4*10**28 #free electron concentration in copper(electron/m^3)\n", + "t = 0.5*10**-2 #thickness of slab(m)\n", + "\n", + "#Calculation\n", + "Vh = (I*B)/(n*e*t)\n", + "\n", + "#Result\n", + "print \"The magnitude of Hall voltage is\",round((Vh/1E-6),3),\"*10^-6 V\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The magnitude of Hall voltage is 1.116 *10^-6 V\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 9.19, Page number 9.48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Variable declaration\n", + "Rh = 3.66*10**-4 #Hall coefficient(m^3/C)\n", + "e = 1.6*10**-19 #charge on electron(C)\n", + "Pn = 8.93*10**-3 #resistivity(ohm-m)\n", + "\n", + "#Calculation\n", + "n = 1/(Rh*e)\n", + "\n", + "ue = Rh/Pn\n", + "\n", + "#Result\n", + "print \"n =\",round((n/1E+22),3),\"*10^22/m^3\"\n", + "print \"u =\",round(ue,3),\"m^2/V-s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "n = 1.708 *10^22/m^3\n", + "u = 0.041 m^2/V-s\n" + ] + } + ], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Solid_state_physics/README.txt b/Solid_state_physics/README.txt new file mode 100755 index 00000000..604bb793 --- /dev/null +++ b/Solid_state_physics/README.txt @@ -0,0 +1,10 @@ +Contributed By: Muktesh Chaudhary +Course: be +College/Institute/Organization: Anglo Eastern ship management india Pvt. Ltd +Department/Designation: Electrical & Electronics Officer +Book Title: Solid state physics +Author: P. K. Palanisamy +Publisher: Scitech Publication (India) Pvt. Ltd., Chennai +Year of publication: 2011 +Isbn: 9788188429279 +Edition: 1st
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