{ "metadata": { "name": "", "signature": "sha256:296c4bd8d9302a92dd3772adca6817eea05f8e0c9e58e45daf4ced8630943a9e" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter03:Crystal Structure" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.1:pg-50" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.1: miller indices\n", "import math \n", "#given data \n", "x1=1.0;#\n", "x2=1.0;#\n", "x3=2.0;#\n", "h1=1/x1;#\n", "h2=1/x2;#\n", "h3=1/x3;#\n", "print \"Miller indices of the plane (112) are: \",h1,\",\",h2,\",\",h3\n", "x11=0.0;#\n", "x21=0.0;#\n", "x31=1.0;#\n", "h11=inf;#\n", "h21=inf;#\n", "h31=1/x31;#\n", "print \"Miller indices of the plane (001) are : \",h11,\",\",h21,\",\",h31\n", "x111=1.0;#\n", "x211=0.0;#\n", "x311=1.0;#\n", "h111=1/x111;#\n", "h211=inf;#\n", "h311=1/x311;#\n", "print \"Miller indices of the plane (101) are : \",h111,\",\",h211,\",\",h311\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Miller indices of the plane (112) are: 1.0 , 1.0 , 0.5\n", "Miller indices of the plane (001) are : inf , inf , 1.0\n", "Miller indices of the plane (101) are : 1.0 , inf , 1.0\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.2:pg-51" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.2: miller indices\n", " \n", "#given data \n", "x1=0.0;#\n", "x2=2.0;#\n", "x3=0.0;#\n", "h1=inf;#\n", "h2=1/x2;#\n", "h3=inf;#\n", "print\"Miller indices of the plane (020) are: \",h1,\",\",h2,\",\",h3\n", "x11=1.0;#\n", "x21=2.0;#\n", "x31=0;#\n", "h11=1/x11;#\n", "h21=1/x21;#\n", "h31=inf;#\n", "print\"Miller indices of the plane (120) are : \",h11,\",\",h21,\",\",h31\n", "x111=2.0;#\n", "x211=2.0;#\n", "x311=0.0;#\n", "h111=1/x111;#\n", "h211=1/x211;#\n", "h311=inf;#\n", "print\"Miller indices of the plane (220) are : \",h111,\",\",h211,\",\",h311\n", "#miller indices for plane (120) is calculated wrong in the book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Miller indices of the plane (020) are: inf , 0.5 , inf\n", "Miller indices of the plane (120) are : 1.0 , 0.5 , inf\n", "Miller indices of the plane (220) are : 0.5 , 0.5 , inf\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.3:pg-52" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.3: miller indices\n", " \n", "x=1/2.0;#\n", "x1=1/x;#\n", "r2=0;#\n", "r3=0;#\n", "x10=-1;#\n", "x2=1.0/x10;#\n", "r4=0;#\n", "r5=0;#\n", "print\"miller indices (Case 1) of the given plane are \",x1,\" : \",r2,\" : \",r3\n", "print\"miller indices (Case 2) of the given plane are \",x2,\" : \",r3,\" : \",r4 \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "miller indices (Case 1) of the given plane are 2.0 : 0 : 0\n", "miller indices (Case 2) of the given plane are -1.0 : 0 : 0\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.4:pg-52" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.4: miller indices\n", " \n", "a=0.529;#\n", "b=1;#\n", "c=0.477;#\n", "a1=0.264;#\n", "b1=1;#\n", "c1=0.238;#\n", "r1=round(a/a1);#\n", "r2=b/b1;#\n", "r3=round(c/c1);#\n", "print\"miller indices of the given plane are \",r1,\" : \",r2,\" : \",r3\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "miller indices of the given plane are 2.0 : 1 : 2.0\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.5:pg-53" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.5: miller indices\n", " \n", "#given data \n", "x1=1;#\n", "x2=1;#\n", "x3=0;#\n", "h1=1/x1#\n", "h2=1/x2;#\n", "h3=inf;#\n", "print\"Miller indices of the plane (110) are: \",h1,\",\",h2,\",\",h3\n", "x11=1;#\n", "x21=1;#\n", "x31=1;#\n", "h11=1/x11;#\n", "h21=1/x21;#\n", "h31=1/x31;#\n", "print\"Miller indices of the plane (111) are : \",h11,\",\",h21,\",\",h31\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Miller indices of the plane (110) are: 1 , 1 , inf\n", "Miller indices of the plane (111) are : 1 , 1 , 1\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.9:pg-58" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.9: atoms per unit cell\n", " \n", "c=8;#corners\n", "f=6;#faces\n", "nf=(1/2.0)*f;#no. of atoms in all six faces\n", "nc=(1/8.0)*c;#no. of atoms in all corners\n", "ta=nf+nc;#\n", "print ta,\"are total number of atoms \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "4.0 are total number of atoms \n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.10:pg-61" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.10 : largest diameter\n", "import math \n", "#given data :\n", "\n", "a=3.61; # edge length in angstrum\n", "r=(a*math.sqrt(2))/4;\n", "d=2*r;\n", "print round(d,4),\"= largest diameter,d(angstrom) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.5527 = largest diameter,d(angstrom) \n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.11:pg-62" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.11 : volume change in percentage\n", "import math\n", "#given data :\n", "r_bcc=0.1258; # in nm\n", "r_fcc=0.1292;# in nm\n", "a_bcc=(r_bcc*4)/math.sqrt(3);\n", "a_fcc=(r_fcc*4)/math.sqrt(2);\n", "v_fcc=(a_fcc)**3;# in nmn**3\n", "v_bcc=(a_bcc)**3; # in nm**3\n", "V=((v_fcc-v_bcc)/v_bcc)*100;\n", "print round(V,2),\"=volume change in percentage,V(%) \"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "99.01 =volume change in percentage,V(%) \n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.12:pg-64" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Example 3.12 : number of atom/mm**2\n", " \n", "\n", "#given data :\n", "a=3.03*10**-7; # lattice constant in mm\n", "A=1/a**2;# for 100 planes \n", "B=0.707/a**2;#for(110) planes\n", "C=0.58/a**2;# for(111) planes\n", "print round(A,-11),\"=number of atoms for (100) plane \"\n", "print round(B,-10),\"=number of atoms for (110) plane \"\n", "print round(C,-11),\"=number of atoms for (111) plane \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.09e+13 =number of atoms for (100) plane \n", "7.7e+12 =number of atoms for (110) plane \n", "6.3e+12 =number of atoms for (111) plane \n" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.13:pg-66" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Example 3.13 : number of atom/mm**2 of planes\n", " \n", "#given data :\n", "\n", "a=2.87*10**-7; # lattice constant in mm\n", "A=1/a**2;# for 100 planes \n", "B=1.414/a**2;#for(110) planes\n", "C=1.732/a**2;# for(111) planes\n", "print round(A,-11),\"=number of atoms for (100) plane \"\n", "print round(B,-11),\"=number of atoms for (110) plane \"\n", "print round(C,-11),\"=number of atoms for (111) plane \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.21e+13 =number of atoms for (100) plane \n", "1.72e+13 =number of atoms for (110) plane \n", "2.1e+13 =number of atoms for (111) plane \n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.14:pg-69" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Example 3.14 : number of atom/mm**2 surface area\n", " \n", "#given data :\n", "a=4.93*10**-7; # lattice constant in mm\n", "A=2/a**2;# for 100 planes \n", "B=1.414/a**2;#for(110) planes\n", "C=2.31/a**2;# for(111) planes\n", "print round(A,-11),\"=number of atoms for (100) plane \"\n", "print round(B,-11),\"=number of atoms for (110) plane \"\n", "print round(C,-11),\"=number of atoms for (111) plane \"\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "8.2e+12 =number of atoms for (100) plane \n", "5.8e+12 =number of atoms for (110) plane \n", "9.5e+12 =number of atoms for (111) plane \n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.15:pg-69" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.15 : planar density\n", " \n", "#given data :\n", "\n", "a=0.143*10**-6; # atomic radius in mm\n", "A=2.31/(a**2);# for(111) planes\n", "print round(A,-10),\"= atom,A(atoms/mm**2) \"\n", "# answer is wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.1296e+14 = atom,A(atoms/mm**2) \n" ] } ], "prompt_number": 48 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.16:pg-71" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.16 : volume\n", " \n", "import math\n", "#given data :\n", "a=0.2665; # in mm\n", "c=0.4947;# in mm\n", "V=(3*math.sqrt(3)*a**2*c)/2.0;\n", "print round(V,4),\"=volume,V(mm**3) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.0913 =volume,V(mm**3) \n" ] } ], "prompt_number": 51 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.17:pg-72" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Example 3.17 : find the packing efficiency and lattice parameter\n", " \n", "\n", "#given data :\n", "r=1.22# in angstrum\n", "a=(4*r)/math.sqrt(3);\n", "efficiency=(math.pi*math.sqrt(3))/8;\n", "print round(efficiency,2),\"=efficiency \"\n", "print round(a,2),\"= lattice parameter,a(angstrom) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.68 =efficiency \n", "2.82 = lattice parameter,a(angstrom) \n" ] } ], "prompt_number": 53 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.18:pg-73" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.18 : interplanar distance\n", "import math \n", "#given data :\n", "h=1;\n", "k=1;\n", "l=1;\n", "#d=a/math.sqrt(h**2+k**2+l**2)\n", "dBYa=1/math.sqrt(h**2+k**2+l**2);\n", "print \"Interplanor distance in (Angstrom) is a*\",round(dBYa,3)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Interplanor distance in (Angstrom) is a* 0.577\n" ] } ], "prompt_number": 55 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.19:pg-74" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.19 : spacing\n", "import math\n", "#given data :\n", "h1=2;\n", "k1=0;\n", "l1=0;\n", "h2=2;\n", "k2=2;\n", "l2=0;\n", "h3=1;\n", "k3=1;\n", "l3=1;\n", "r=1.246;\n", "a=(4*r)/math.sqrt(2);# in angstrum\n", "#d=a/math.sqrt(h**2+k**2+l**2)\n", "d1=a/math.sqrt(h1**2+k1**2+l1**2);\n", "d2=a/math.sqrt(h2**2+k2**2+l2**2);\n", "d3=a/math.sqrt(h3**2+k3**2+l3**2);\n", "print round(d1,2),\"=d_200 spacind,d1(angstrom) \"\n", "print round(d2,2),\"=d_220 spacind,d2(angstrom) \"\n", "print round(d3,2),\"=d_111 spacind,d3(angstrom) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.76 =d_200 spacind,d1(angstrom) \n", "1.25 =d_220 spacind,d2(angstrom) \n", "2.03 =d_111 spacind,d3(angstrom) \n" ] } ], "prompt_number": 57 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.20:pg-74" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.20 : interplaner spacing d_220\n", "import math \n", "\n", "#given data :\n", "a=0.316;# in nm\n", "h=2;\n", "k=2;\n", "l=0;\n", "d=a/math.sqrt(h**2+k**2+l**2);\n", "print round(d,3),\"= inter planer spacing d_220,d(nm) \"\n", "# answer is wrong in book\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.112 = inter planer spacing d_220,d(nm) \n" ] } ], "prompt_number": 59 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.21:pg-74" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.21: interplanar spacing d220\n", " \n", "import math\n", "a=1;#constant assume\n", "a1=[1,0,0];#lattice planes\n", "a2=[1,1,0];#lattice planes\n", "a3=[1,1,1];#lattice planes\n", "d100=a/(math.sqrt(a1[0]+a1[1]**2+a1[2]**2));#interplanar distance between (100)planes\n", "d110=a/(math.sqrt(a2[0]**2+a2[1]**2+a2[2]**2));#interplanar distance between (110)planes\n", "d111=a/(math.sqrt(a3[0]**2+a3[1]**2+a3[2]**2));#interplanar distance between (111)planes\n", "print \"ratio of interplanar distances is \",d100,\":\",round(d110,2),\":\",round(d111,2)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "ratio of interplanar distances is 1.0 : 0.71 : 0.58\n" ] } ], "prompt_number": 63 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.22:pg-75" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.22: perpendicular distance\n", "import math \n", "a=1;#constant assume\n", "a1=[1,1,1];#lattice planes\n", "a2=[2,2,2];#lattice planes\n", "d1=a/(math.sqrt(a1[0]**2+a1[1]**2+a1[2]**2));#perpendicular distance between origin and (111)planes\n", "d2=a/(math.sqrt(a2[0]**2+a2[1]**2+a2[2]**2));#perpendicular distance between origin and (222)planes\n", "d22 = d1-d2;#perpendicular distance between the planes (111) and (222)\n", "print round(d22,2),\"= perpendicular distance between the planes (111) and (222)\"\n", "\n", "# a is assumed to be 1\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.29 = perpendicular distance between the planes (111) and (222)\n" ] } ], "prompt_number": 65 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.23:pg-76" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.23: angle between planes (122) and (111)\n", "import math\n", "a=1;# assume\n", "a1=[1,2,2];#lattice planes\n", "a2=[1,1,1];#lattice planes\n", "d1=a/(math.sqrt(a1[0]**2+a1[1]**2+a1[2]**2));#perpendicular distance between origin and (111)planes\n", "d2=a/(math.sqrt(a2[0]**2+a2[1]**2+a2[2]**2));#perpendicular distance between origin and (222)planes\n", "cphi= ((a1[0]*a2[0])+(a1[1]*a2[1])+(a1[2]*a2[2]))*(d1*d2);#\n", "d=math.degrees(math.acos((cphi)));# in degree\n", "d1=math.floor(d);#\n", "d2=d-d1;#\n", "print\"angle between planes (122) and (111) is \",d1,\" degree \",round(60*d2),\" minutes\"\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "angle between planes (122) and (111) is 15.0 degree 48.0 minutes\n" ] } ], "prompt_number": 72 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.24:pg-77" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.24 : concentration of iron\n", " \n", "\n", "#given data :\n", "d=7.87;\n", "N=6.023*10**23; # avogadro's number\n", "A=55.85;# atomic weight\n", "I=A/N;# mass of iron atom\n", "atom=d/I;\n", "print round(atom,-20),\"= number of atoms(atoms/cm**3) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "8.49e+22 = number of atoms(atoms/cm**3) \n" ] } ], "prompt_number": 83 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.25:pg-77" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.25 : lattice constant\n", " \n", "#given data :\n", "\n", "n=2;\n", "A=55.8;\n", "N=6.023*10**26; # avogadro's number in /kg-mole\n", "b=7.87*10**3;# in kg/m**3\n", "a=((A*n)/(N*b))**(1/3.0);\n", "print round(a*10**10,3),\"= lattice constant,a(angstrom)\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.866 = lattice constant,a(angstrom)\n" ] } ], "prompt_number": 85 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.26:pg-77" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.26 : density\n", "import math\n", "#given data :\n", "\n", "n=4;\n", "N=6.023*10**23; # avogadro's number\n", "r=1.278*10**-8;# in cm\n", "A=63.5;\n", "a=(r*4)/math.sqrt(2);# in cm\n", "b=(A*n)/(a**3*N);\n", "print round(b,2),\"= density of copper,b(g/cc) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "8.93 = density of copper,b(g/cc) \n" ] } ], "prompt_number": 87 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.27:pg-77" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.27 : number of atoms\n", " \n", "#given data :\n", "n=4;\n", "N=6.023*10**23; # avogadro's number\n", "A=55.85;\n", "a=2.9*10**-8;\n", "b=7.87;#density in g/cc\n", "#a**3=(A*n)/(N*b)\n", "n=round((a**3*N*b)/A);\n", "print n,\"= number of atoms,n \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.0 = number of atoms,n \n" ] } ], "prompt_number": 88 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.28:pg-78" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.28 : lattice constant\n", " \n", "#given data :\n", "d=6250;#density\n", "N=6.02*10**23;#avogadro's number\n", "n=4;\n", "m=60.2*10**-3;# atomic mass\n", "M=(n*m)/N;\n", "V=M/d;\n", "a=V**(1/3.0)*10**9;\n", "print a,\"= the lattice constant,a(nm) \"\n", "#ANSWER IS WRONG IN THE TEXT BOOK\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.4 = the lattice constant,a(nm) \n" ] } ], "prompt_number": 89 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.29:pg-78" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.29 : the number of atoms\n", " \n", "#given data :\n", "d=7.87;#in g/cm**3\n", "A=55.85;\n", "a=2.9*10**-8;# in cm\n", "N=6.02*10**23;#avogadro's number\n", "n=(d*a**3*N)/A;\n", "print round(n),\"= the number of atom,n \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.0 = the number of atom,n \n" ] } ], "prompt_number": 90 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.30:pg-83" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.30: calculate the number of vacancies in the copper\n", "import math \n", "B=1.38*10**-23;#boltzman constant in J/atom-K\n", "B1=8.62*10**-5;# bolzman constant in ev/atom-K\n", "Qv=0.9;# eV/atom\n", "t=27;# room temperatyre in degree celsius\n", "pcu=8.4;#in g/cm**3\n", "Acv=63.5;# in g/mol\n", "T=t+273;#temperture in kelvin\n", "Nv=6.023*10**23;#\n", "P=8.4;#\n", "Ns=(Nv*P)/Acv;# number of regular lattice sites\n", "Nv1=Ns*math.exp(-Qv/(B1*T));#\n", "print Nv1,\"is number of vacancies in copper in vacancies/cm**3\"\n", "#answer is wrong in the textbook\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "61187298.8086 is number of vacancies in copper in vacancies/cm**3\n" ] } ], "prompt_number": 91 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.31:pg-86" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.31 : interplanar spacing\n", "import math \n", "#given data :\n", "\n", "theta=20.3;#in degree\n", "lamda=1.54;# in angstrum\n", "n=1.0;\n", "a=math.sin(math.radians(theta))\n", "d=lamda/(2*a);\n", "print round(d,2),\"= interplanar spacing,d(angstrom) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.22 = interplanar spacing,d(angstrom) \n" ] } ], "prompt_number": 101 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.32:pg-86" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.32 : interatomic spacing\n", "import math \n", "#given data :\n", "\n", "theta=30;#in degree\n", "lamda=1.54;# in angstrum\n", "n=1;\n", "a=math.sin(math.radians(theta))\n", "d=lamda/(2*a);\n", "print d,\"=interatomic spacing,d(angstrom) \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.54 =interatomic spacing,d(angstrom) \n" ] } ], "prompt_number": 102 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.33:pg-87" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Example 3.33 : number of per order\n", "import math \n", "#given data :\n", "\n", "theta=90;#in degree\n", "lamda=1.54;# in angstrum\n", "a=math.sin(math.radians(theta))\n", "d=1.181;\n", "n=(2*d*a)/lamda;\n", "print round(n,2),\"= number of order,n \"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1.53 = number of order,n \n" ] } ], "prompt_number": 106 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.34:pg-87" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.34: size of unit cell\n", "import math \n", "n=1.0;#\n", "a=1.0;#assume\n", "h=0.58;#wavelnegth in armstrong\n", "th=9.5;#reflection angle in degree\n", "a1=[2.0,0,0];#miller indices\n", "d200=a/(math.sqrt(a1[0]**2+a1[1]**2+a1[2]**2));#interplanar distance between (200)planes\n", "a=((n*h)/(2*d200*math.sin(math.radians(th))));#zsize of unit cell\n", "print round(a,3),\"= size of unit cell in \u00c4\"\n", "#amswer is wrong in the textbook\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "3.514 = size of unit cell in \u00c4\n" ] } ], "prompt_number": 111 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.35:pg-87" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.35: bragg angle\n", "import math\n", "n=1;#\n", "a=3.57;#in \u00c4\n", "h=0.54;#wavelnegth in \u00c4 \n", "a1=[1,1,1];#miller indices\n", "d111=a/(math.sqrt(a1[0]**2+a1[1]**2+a1[2]**2));#interplanar distance between (111)planes\n", "snd=((n*h)/(2*d111));#\n", "th=math.degrees(math.asin(snd));# bragg angle in degree\n", "d1=math.floor(th);#\n", "d2=th-math.floor(d1);#\n", "print\"angle between planes (122) and (111) is \",d1,\" degree \",round(60*d2),\" minutes\"\n", "#wavelength is given wrong in example it is 0.54\u00c4 and it is taken as 1.54\u00c4\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "angle between planes (122) and (111) is 7.0 degree 32.0 minutes\n" ] } ], "prompt_number": 113 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.36:pg-88" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.36: interplanner spacing and miller indices\n", " \n", "a=3.16;# in \u00c4\n", "h=1.54;# in \u00c4\n", "n=1;#\n", "th=20.3;# in degree\n", "d=((n*h)/(2*math.sin(math.radians(th))));# interplanner spacing in \u00c4\n", "x=a/d;#\n", "y=x**2;#\n", "print round(d,2),\"= interplanner spacing in \u00c4 \"\n", "print \"miller indices are (110) , (011) or (101)\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "2.22 = interplanner spacing in \u00c4 \n", "miller indices are (110) , (011) or (101)\n" ] } ], "prompt_number": 115 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex3.37:pg-88" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Example 3.36: interplanner spacing and diffraction angle\n", "import math \n", "a=.2866;# in \u00c4\n", "h=0.1542;# in nm\n", "n=1.0;#\n", "a1=[2.0,1.0,1.0];#miller indices\n", "d211=a/(math.sqrt(a1[0]**2+a1[1]**2+a1[2]**2));#interplanar distance between (211)planes\n", "snd=((n*h)/(2*d211));#\n", "th=math.degrees(math.asin(snd));# bragg angle in degree\n", "d1=math.floor(th);#\n", "d2=th-math.floor(d1);#\n", "print\"angle between planes (122) and (111) is \",d1,\" degree \",round(60*d2),\" minutes\"\n", "print round(d211,2),\"=interplanner spacing in \u00c4 \"\n", "#answer is wrong in the textbook\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "angle between planes (122) and (111) is 41.0 degree 13.0 minutes\n", "0.12 =interplanner spacing in \u00c4 \n" ] } ], "prompt_number": 121 } ], "metadata": {} } ] }