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Diffstat (limited to 'Engineering_Physics/Chapter2_1.ipynb')
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1 files changed, 431 insertions, 0 deletions
diff --git a/Engineering_Physics/Chapter2_1.ipynb b/Engineering_Physics/Chapter2_1.ipynb new file mode 100755 index 00000000..b527497e --- /dev/null +++ b/Engineering_Physics/Chapter2_1.ipynb @@ -0,0 +1,431 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:ad2a8335720a8ceacd5db30334fb790c6a4c8fa5b69e23fcad6e232d80ed69c2"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "2: Crystal Structure"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.1, Page number 29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "d=6.5*10**3; #density of silver bromide(Kg/m**3)\n",
+ "m=187.8; #molecular weight of silver bromide\n",
+ "\n",
+ "#Calculation\n",
+ "M=(4*m)/(6.022*10**26); #mass of ion in unit cell(kg)\n",
+ "#d=mass of ions in unit cell/volume of unit cell\n",
+ "a=((M/d)**(1/3))*10**10; #lattice parameter(Angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lattice parameter is\",round(a,2),\"Angstrom\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The lattice parameter is 5.77 Angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.2, Page number 29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r=2.3; #atomic radius(Angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(4*r)/math.sqrt(3); \n",
+ "fv=((a)**3-(2*(4/3)*math.pi*r**3))*10**-30; #free volume(m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The free volume per unit cell is\",round(fv*10**30,1),\"*10**-30 m**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The free volume per unit cell is 47.9 *10**-30 m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.3, Page number 29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "k=8.625*10**-5; #Boltzmann constant(eV/K)\n",
+ "#n1000/n500=ln[n1000/n500]=Ev/1000k\n",
+ "Ev=1.08; #average energy required to create a vacancy(eV)\n",
+ "\n",
+ "#Calculation\n",
+ "N=math.exp(Ev/(1000*k)); #ratio of vacancies\n",
+ "\n",
+ "#Result\n",
+ "print \"The ratio of vacancies is\",round(N/10**5,1),\"*10**5\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The ratio of vacancies is 2.7 *10**5\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.4, Page number 29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "#n500=N*exp(-Ev/500k)\n",
+ "k=8.625*10**-5; #Boltzmann constant(eV/K)\n",
+ "Ev=0.95; #average energy required to create a vacancy\n",
+ "\n",
+ "#Calculation\n",
+ "n=math.exp(-Ev/(500*k)); #n500/N\n",
+ "\n",
+ "#Result\n",
+ "print \"The ratio of number of vacancies to the number of atoms is\",round(n*10**10,1),\"*10**-10\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The ratio of number of vacancies to the number of atoms is 2.7 *10**-10\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.5, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=1;\n",
+ "k=1;\n",
+ "l=1;\n",
+ "#d(hkl)=a/sqrt(h^2+k^2+l^2) where \"a\" is the lattice parameter\n",
+ "r=0.18; #atomic radius(nm)\n",
+ "\n",
+ "#Calculation\n",
+ "d111=(2*math.sqrt(2)*r)/math.sqrt((h**2)+(k**2)+(l**2)); #spacing(nm)\n",
+ "\n",
+ "#Result\n",
+ "print \"The spacing of (111) planes in a monoatomic structure is\",round(d111,2),\"nm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The spacing of (111) planes in a monoatomic structure is 0.29 nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.6, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "M=200; #atomic weight \n",
+ "a=5; #lattice parameter(angstrom)\n",
+ "Na=6.022*(10**26);\n",
+ "\n",
+ "#Calculation\n",
+ "rho=(2*M)/(Na*(a*10**-10)**3); #density of the structure(kg/m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The density of the bcc structure is\",round(rho/10**3,2),\"*10**3 kg/m**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The density of the bcc structure is 5.31 *10**3 kg/m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.7, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "#Free volume=a^3-[(4/3)*pi*r^3];for sc,a=2r\n",
+ "#Therefore free volume =(2r)^3-[(4/3)*pi*r^3]\n",
+ "fv=30.48*10**-30; #free volume per unit cell(m**3)\n",
+ "\n",
+ "#Calculation\n",
+ "r=(fv/(8-(4/3)*math.pi))**(1/3)*(10**10); #atomic radius(angstrom) \n",
+ "\n",
+ "#Result\n",
+ "print \"The atomic radius is\",round(r),\"Angstrom\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The atomic radius is 2.0 Angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.8, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "#free volume=a^3-[2*(4/3)*pi*r^3]\n",
+ "#for bcc a=4r/3^(1/3)\n",
+ "fv=61.72*(10**-30); #free volume(m**3)\n",
+ "\n",
+ "#Calculation\n",
+ "a=-(fv/(1-math.pi*math.sqrt(3))/8)**1/3*10**31; #lattice parameter(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lattice parameter is\",round(a,2),\"Angstrom\"\n",
+ "print \"answer in the book varies due to rounding off errors\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The lattice parameter is 5.79 Angstrom\n",
+ "answer in the book varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.9, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "rho=9000; #density(kg/m**3)\n",
+ "w=65; #atomic weight\n",
+ "v=1; #volume(m**3)\n",
+ "a=1.4; #average number of free electrons per atom\n",
+ "\n",
+ "#Calculation\n",
+ "n=(rho*v)/(w/(6.022*10**26)); #number of atoms\n",
+ "rhoe=n*a; #density of free electrons per atom(electrons/m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The density of free electrons is\",round(rhoe/10**29,3),\"*10**29 electrons/m**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The density of free electrons is 1.167 *10**29 electrons/m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 2.10, Page number 31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=1;\n",
+ "k=0;\n",
+ "l=1;\n",
+ "d101=0.5; #spacing of (101) plane\n",
+ "\n",
+ "#Calculation\n",
+ "#d101=a/sqrt((h^2)+(k^2)+(l^2))\n",
+ "a=d101*math.sqrt(2) #lattice parameter(Angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lattice parameter is\",round(a,1),\"Angstrom\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The lattice parameter is 0.7 Angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |