From c7fe425ef3c5e8804f2f5de3d8fffedf5e2f1131 Mon Sep 17 00:00:00 2001 From: hardythe1 Date: Tue, 7 Apr 2015 15:58:05 +0530 Subject: added books --- Material_Science/material_science_ch_8.ipynb | 853 +++++++++++++++++++++++++++ 1 file changed, 853 insertions(+) create mode 100755 Material_Science/material_science_ch_8.ipynb (limited to 'Material_Science/material_science_ch_8.ipynb') diff --git a/Material_Science/material_science_ch_8.ipynb b/Material_Science/material_science_ch_8.ipynb new file mode 100755 index 00000000..400defda --- /dev/null +++ b/Material_Science/material_science_ch_8.ipynb @@ -0,0 +1,853 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 8.: Statics and Band theory of Solids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.1, page no-208" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Fermi Energy of metals\n", + "\n", + "import math\n", + "# variable declaration\n", + "d_cu=8.96*10**3 # density of cu\n", + "a_cu=63.55 # Atomic weight of cu\n", + "d_z=7.14*10**3 # density of Zn \n", + "a_z=65.38 # Atomic weight of Zn\n", + "d_al=2700 # density of Al\n", + "a_al=27 # Atomic weight of Al \n", + "avg=6.022*10**26 # Avogadro's number \n", + "h=6.626*10**-34 # Planck's constant\n", + "m=9.1*10**-31 # mass of an electrons\n", + "e=1.6*10**-19 # charge of an electron\n", + "\n", + "\n", + "\n", + "#(i)\n", + "\n", + "# Calculations\n", + "n_cu=d_cu*avg/a_cu\n", + "e_cu=(h**2/(8*m))*(3*n_cu/math.pi)**(2.0/3.0)\n", + "e_cu=e_cu/e\n", + "\n", + "#Result\n", + "print(\"\\n(i)For Cu\\nThe electron concentration in Cu is %.4f*10^28 per m^3\\nFermi energy at 0 k =%.4f eV \"%(n_cu*10**-28,e_cu))\n", + "\n", + "#(ii)\n", + "\n", + "# calculations\n", + "n_z=d_z*avg*2/a_z\n", + "e_z=(h**2/(8*m))*(3*n_z/math.pi)**(2.0/3.0)\n", + "e_z=e_z/e\n", + "\n", + "# Result\n", + "print(\"\\n(ii)For Zn\\nThe electron concentration in Zn is %.5f*10^28 per m^3\\nFermi energy at 0 k =%.2f eV \"%(n_z*10**-28,e_z))\n", + "\n", + "#(iii)\n", + "\n", + "# Calculations\n", + "n_al=d_al*avg*3/a_al\n", + "e_al=(h**2/(8*m))*(3*n_al/math.pi)**(2.0/3.0)\n", + "e_al=e_al/e\n", + "\n", + "#Result\n", + "print(\"\\n(iii)For Al\\nThe electron concentration in Al is %.3f*10^28 per m^3\\nFermi energy at 0 k =%.2f eV \"%(n_al*10**-28,e_al))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "(i)For Cu\n", + "The electron concentration in Cu is 8.4905*10^28 per m^3\n", + "Fermi energy at 0 k =7.0608 eV \n", + "\n", + "(ii)For Zn\n", + "The electron concentration in Zn is 13.15298*10^28 per m^3\n", + "Fermi energy at 0 k =9.45 eV \n", + "\n", + "(iii)For Al\n", + "The electron concentration in Al is 18.066*10^28 per m^3\n", + "Fermi energy at 0 k =11.68 eV \n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.2, page no-210" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Density of states for Cu\n", + "\n", + "import math\n", + "# variable declaration\n", + "avg=6.023*10**26 # avogadro's number\n", + "h=6.626*10**-34 # Planck's constant \n", + "m=9.1*10**-31 # mass of an electron\n", + "e=1.6*10**-19 # charge of an electron\n", + "n=8.4905*10**28 # sphere of radius\n", + "gam=6.82*10**27 # gamma\n", + "\n", + "# Calculations\n", + "ef=(h**2/(8*m))*(3*n/math.pi)**(2.0/3.0)\n", + "ef=ef/e\n", + "x=(gam*math.sqrt(ef))/2\n", + "\n", + "#Result\n", + "print(\"The density of states for Cu at the Fermi level for T = 0 K is %.0f*10^27 m^-3\"%(x*10**-27))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The density of states for Cu at the Fermi level for T = 0 K is 9*10^27 m^-3\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.3, page no-210" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Nordheims coeeficient\n", + "\n", + "import math\n", + "#Variable declaration\n", + "rni=63 # Resistivity of Ni\n", + "rcr=129 # Resistivity of Cr\n", + "k=1120 # Resistivity of 80% Ni + 20% Cr\n", + "\n", + "#Calculations\n", + "c=(k*10**-9)/(0.8*(1-0.8))\n", + "\n", + "#Result\n", + "print(\"The Nordheims coeeficient is %.0f *10^-6 Ohm-m\"%(c*10**6))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Nordheims coeeficient is 7 *10^-6 Ohm-m\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.4, page no-211" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Conductivity of Al\n", + "\n", + "import math\n", + "#Variable declaaration\n", + "d=2700 # Density of Al\n", + "awt=27 # Atomic weight\n", + "t=10**-14 # Relaxation time\n", + "e=1.6*10**-19 # charge of an electron\n", + "m=9.1*10**-31 # mass of an electron\n", + "avg=6.022*10**26 # Avogadros number\n", + "\n", + "# calculation\n", + "n=avg*d*3/awt\n", + "sig=(n*t*e**2)/m\n", + "\n", + "#Result\n", + "print(\"The conductivity of Al is %.4f*10^7 ohm-m.\"%(sig*10**-7))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The conductivity of Al is 5.0823*10^7 ohm-m.\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.5, page no-211" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Fermi distribution function\n", + "\n", + "import math\n", + "#variable declaration\n", + "e1=0.01 # difference between energy level to fermi level in eV\n", + "e=1.6*10**-19 # charge of an electron\n", + "ed=e*e1 # difference between energy level to fermi level in J\n", + "T=200 # Temperature\n", + "k=1.38*10**-23 # Boltzmann's constant\n", + "\n", + "# Calculations\n", + "E=1/(1+math.e**(ed/(T*k)))\n", + "print(\"The Fermi distribution function for energy E is %.4f\"%E)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Fermi distribution function for energy E is 0.3590\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.6, page no-212" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Fermi energy and fermi temperature\n", + "\n", + "import math\n", + "#variable declaration\n", + "v=0.86*10**6 # velocity of electron\n", + "m=9.11*10**-31 # mass of electron\n", + "e=1.6*10**-19 # electronic charge \n", + "k=1.38*10**-23 # Boltzmann's constant \n", + "\n", + "#calculations\n", + "E=(m*v**2)/2\n", + "E= math.floor(E*10**22)/10**22\n", + "T=E/k\n", + "\n", + "#Result\n", + "print(\"\\nThe fermi energy is %.3f*10^-19 J\\nThe Fermi Temperature Tf is %.2f*10^4 K\"%(E*10**19,T*10**-4))\n", + "# answer in the book for Temperature id 2.43 x 10^4" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "The fermi energy is 3.368*10^-19 J\n", + "The Fermi Temperature Tf is 2.44*10^4 K\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.7, page no-212" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# No of states lying between energy levels\n", + "\n", + "import math\n", + "# variable declaration\n", + "m=9.1*10**-31 # mass of electron\n", + "dE=0.01 # energy interval\n", + "h=6.63*10**-34 # planck's constant\n", + "eF=3.0 # Fermi energy\n", + "e=1.6*10**-19 # electronic charge\n", + "\n", + "#Calculations\n", + "E1=eF*e\n", + "E2=E1+e*dE\n", + "n=(4*math.pi*(2*m)**(1.5))/h**3\n", + "k=((2*0.3523/3)*((E2**(1.5)-(E1**(1.5)))))\n", + "n=n*k\n", + "\n", + "#Result\n", + "print(\"The number of states lying between the energy level is %.2f*10^25\"%(n*10**-25))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of states lying between the energy level is 4.14*10^25\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.8, page no-214" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Fermi Velocity\n", + "\n", + "import math\n", + "#Variable declaration\n", + "Tf=24600 # Fermi temperature of the metal\n", + "m=9.11*10**-31 # mass of electron\n", + "k=1.38*10**-23 # Boltzmann's constant\n", + "\n", + "#Calculations\n", + "vf=math.sqrt(2*k*Tf/m)\n", + "\n", + "#Result\n", + "print(\"The Fermi Velocity is %.4f *10^6 m/s\"%(vf*10**-6))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Fermi Velocity is 0.8633 *10^6 m/s\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.9, page no-214" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Fermi energy\n", + "\n", + "import math\n", + "#variable declaration\n", + "n=18.1*10**28 # elecron density of electron\n", + "h=6.62*10**-34 # Planck's constant\n", + "m=9.1*10**-31 # mass of an electron\n", + "e=1.6*10**-19 # electronic charge\n", + "\n", + "#calculations\n", + "ef=((3*n/(8*math.pi))**(2.0/3.0))*((h**2)/(2*m))\n", + "ef=ef/e\n", + "ef=math.ceil(ef*100)/100\n", + "\n", + "#Result\n", + "print(\"The Fermi energy at 0 K is %.2f eV \"%(ef))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Fermi energy at 0 K is 11.68 eV \n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.10, page no-215" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Fermi energy \n", + "\n", + "import math\n", + "#variable declaration\n", + "n=18.1*10**28 # elecron density of electron\n", + "h=6.62*10**-34 # Planck's constant\n", + "m=9.1*10**-31 # mass of an electron\n", + "e=1.6*10**-19 # electronic charge\n", + "\n", + "#calculations\n", + "ef=((3*n/(8*math.pi))**(2.0/3.0))*((h**2)/(2*m))\n", + "ef=ef/e\n", + "ef=math.ceil(ef*100)/100\n", + "\n", + "#result\n", + "print(\"The Fermi energy at 0 K is %.2f eV \"%ef)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Fermi energy at 0 K is 11.68 eV \n" + ] + } + ], + "prompt_number": 45 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.11, page no-215" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Temperature calculation\n", + "\n", + "import math\n", + "#variable declaration\n", + "e=1.6*10**-19 # electronic charge\n", + "Ed=0.5*e # difference between energy level to fermi level\n", + "k=1.38*10**-23 # Boltzmann's constant\n", + "x=0.01 # probability\n", + "\n", + "#Calculaations\n", + "T=Ed/(k*math.log((1/x)-1))\n", + "\n", + "#Result\n", + "print(\"Temperature at which there is 1%% probability that a state with 0.5 eV energy occupied above the Fermi energy level is %.1f K\"%T)\n", + "#answer is not matching with the answer given in the book" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temperature at which there is 1% probability that a state with 0.5 eV energy occupied above the Fermi energy level is 1261.6 K\n" + ] + } + ], + "prompt_number": 49 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.14, page no-218" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#energies for the occupying of electrons\n", + "import math\n", + "\n", + "#variable declaration\n", + "ef=2.1 # Fermi energy\n", + "k=1.38*10**-23 # Boltzmann's constant\n", + "T=300 # Temperature\n", + "e=1.6*10**-19 # Electronic charge\n", + "\n", + "#calculations\n", + "\n", + "#(i)\n", + "p1=0.99 # probability\n", + "E1=ef+(k*T*math.log(-1+1/p1))/e\n", + "\n", + "#(ii)\n", + "p2=0.01 # probability\n", + "E2=ef+(k*T*math.log(-1+1/p2))/e\n", + "\n", + "#(iii)\n", + "p3=0.5 # probability\n", + "E3=ef+(k*T*math.log(-1+1/p3))/e\n", + "\n", + "#Result\n", + "\n", + "print(\"\\nThe energies for the occupying of electrons at %d K for the probability of %.2f are %.2f eV\"%(T,p1,E1))\n", + "\n", + "print(\"\\nThe energies for the occupying of electrons at %d K for the probability of %.2f are %.2f eV\"%(T,p2,E2))\n", + "\n", + "print(\"\\nThe energies for the occupying of electrons at %d K for the probability of %.2f are %.2f eV\"%(T,p3,E3))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "The energies for the occupying of electrons at 300 K for the probability of 0.99 are 1.98 eV\n", + "\n", + "The energies for the occupying of electrons at 300 K for the probability of 0.01 are 2.22 eV\n", + "\n", + "The energies for the occupying of electrons at 300 K for the probability of 0.50 are 2.10 eV\n" + ] + } + ], + "prompt_number": 53 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.15, page no-219" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Fermi distribution function\n", + "\n", + "import math\n", + "# Variable declarations\n", + "e=1.6*10**-19 # Electronic charge\n", + "ed=0.02*e # difference between energy level to fermi level\n", + "T1=200 # Temperature 1\n", + "T2=400 # Temperature 2\n", + "k=1.38*10**-23 # Boltzmann's constant\n", + "\n", + "#Calculations\n", + "fe1=1/(1+math.e**(ed/(k*T1)))\n", + "fe2=1/(1+math.e**(ed/(k*T2)))\n", + "\n", + "#Result\n", + "print(\"\\nThe Fermi distribution function for the given energy at %d K is %.5f\"%(T1,fe1))\n", + "print(\"\\nThe Fermi distribution function for the given energy at %d K is %.4f\"%(T2,fe2))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "The Fermi distribution function for the given energy at 200 K is 0.23877\n", + "\n", + "The Fermi distribution function for the given energy at 400 K is 0.3590\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.16, page no-220" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Fermi energy for given metal\n", + "\n", + "import math\n", + "#Variaable declaration\n", + "d=10500 # Density of the metal\n", + "avg=6.022*10**26 # Avogadro's number\n", + "awt=107.9 # Atomic weight of metal\n", + "h=6.62*10**-34 # Planck's constant\n", + "m=9.1*10**-31 # mass of an electron\n", + "e=1.6*10**-19 # electronic charge\n", + "\n", + "#Calculattions\n", + "n=d*avg/awt\n", + "ef=((3*n/(8*math.pi))**(2.0/3.0))*((h**2)/(2*m))\n", + "ef=ef/e\n", + "\n", + "#Result\n", + "print(\"The Fermi energy for given metal is %.1f eV \"%ef)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Fermi energy for given metal is 5.5 eV \n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.17, page no-221" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Fermi distribution function \n", + "\n", + "import math\n", + "#Variable declaration\n", + "e=1.6*10**-19 # electronic charge\n", + "ed=0.2*e # difference between energy level to Fermi level\n", + "T1=300 # Temperature 1\n", + "T2=1000 # Temperature 2\n", + "k=1.38*10**-23 # Boltzmann's constant\n", + "\n", + "#Calculations\n", + "fe1=1/(1+math.e**(ed/(k*T1)))\n", + "fe2=1/(1+math.e**(ed/(k*T2)))\n", + "\n", + "#Result\n", + "print(\"\\nThe Fermi distribution function for the given energy at %d K is %.7f\"%(T1,fe1))\n", + "print(\"\\nThe Fermi distribution function for the given energy at %d K is %.4f\"%(T2,fe2))\n", + "# Answer for 300 K is wrong in the book" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "The Fermi distribution function for the given energy at 300 K is 0.0004395\n", + "\n", + "The Fermi distribution function for the given energy at 1000 K is 0.0896\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.18, page no-221" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Free electrons concentration\n", + "\n", + "import math\n", + "#Variable declarations\n", + "h=6.62*10**-34 # Planck's constant\n", + "m=9.1*10**-31 # Mass of electron\n", + "e=1.6*10**-19 # Charge of an electron\n", + "ef=3*e # Fermi Energy\n", + "\n", + "#Calculations\n", + "k=((3/(8*math.pi))**(2.0/3.0))*((h**2)/(2*m))\n", + "k=ef/k\n", + "n=k**(1.5)\n", + "\n", + "#Result\n", + "print(\"The number of free electrons concentration in metal is %.2f *10^28 per cubic meter \"%(n*10**-28))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of free electrons concentration in metal is 2.36 *10^28 per cubic meter \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.19, page no-221" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Free electrons concentration in metal \n", + "\n", + "import math\n", + "#Variable declaration\n", + "h=6.626*10**-34 # Planck's constant\n", + "m=9.1*10**-31 # Mass of electron\n", + "e=1.6*10**-19 # Charge of electron\n", + "ef=5.5*e # Fermi energy\n", + "\n", + "# Calculation\n", + "k=((3/(8*math.pi))**(2.0/3.0))*((h**2)/(2*m))\n", + "k=ef/k\n", + "n=k**(1.5)\n", + "\n", + "#Result\n", + "print(\"The number of free electrons concentration in metal is %.3f * 10^28 per cubic meter \"%(n*10**-28))\n", + "#Answer is matching with the answer given in the book" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of free electrons concentration in metal is 5.837 * 10^28 per cubic meter \n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 8.20, page no-221" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# electrons concentration and termal velocity of electrons\n", + "\n", + "import math\n", + "#variable declaration\n", + "h=6.626*10**-34 # Planck's constant\n", + "m=9.1*10**-31 # mass of electron\n", + "e=1.6*10**-19 # charge of electron\n", + "ef=7*e # Fermi energy\n", + "\n", + "#calculations\n", + "k=((3/(8*math.pi))**(2.0/3.0))*((h**2)/(2*m))\n", + "k=ef/k\n", + "n=k**(1.5)\n", + "vth=math.sqrt(2*ef/m)\n", + "\n", + "#Result\n", + "print(\"The number of free electrons concentration in metal is %.2f *10^28 per cubic meter \"%(math.ceil(n*10**-28*10**2)/10**2))\n", + "print(\"\\nThe termal velocity of electrons in copper is %.3f *10^6 m/s\"%(math.floor(vth*10**-6*10**3)/10**3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number of free electrons concentration in metal is 8.39 *10^28 per cubic meter \n", + "\n", + "The termal velocity of electrons in copper is 1.568 *10^6 m/s\n" + ] + } + ], + "prompt_number": 41 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit