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diff --git a/Engineering_Physics_by_A_Marikani/6-Crystallography.ipynb b/Engineering_Physics_by_A_Marikani/6-Crystallography.ipynb new file mode 100644 index 0000000..5a729e8 --- /dev/null +++ b/Engineering_Physics_by_A_Marikani/6-Crystallography.ipynb @@ -0,0 +1,609 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Crystallography" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.10: Ratio_of_cubic_system.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"// Example No.6.10.\n", +"// Page No.189.\n", +"clc;clear;\n", +"h=1;k=0;l=0;\n", +"d100=1/sqrt(h^2+k^2+l^2);\n", +"disp('Interplanar spacing for d100 plane = a');\n", +"h=1;k=1;l=0;\n", +"d110=1/sqrt(h^2+k^2+l^2);\n", +"disp('Interplanar spacing for d110 plane = a/1.414');\n", +"h=1;k=1;l=1;\n", +"d111=1/sqrt(h^2+k^2+l^2);\n", +"disp('Interplanar spacing for d111 plane = a/1.732');\n", +"x = sqrt(6);\n", +"y = sqrt(3);\n", +"z = sqrt(2);\n", +"printf('\nx = %.3f',x);\n", +"printf('\ny = %.3f',y);\n", +"printf('\nz = %.3f',z);\n", +"printf('\nd100:d110:d111 = %.3f:%.3f:%.3f',x,y,z);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.11: Ratio_of_intercepts.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// Example No.6.11.\n", +"// Page No.190.\n", +"clc;clear;\n", +"l1 = 6*(1/2);\n", +"l2 = 6*(1/3);\n", +"l3 = (6*1/6);\n", +"disp('For the plane (231) the intercepts are (a/2),(b/3),(c/1)');\n", +"disp('Ratio of the intercepts made by (231) plane in simple cubic crystal is as follows :');\n", +"disp('l1:l2:l3 = 3:2:6');\n", +"\n", +"//As there are no numerical steps and hence the display statement has been typed directly." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.12: Length_of_the_intercepts.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"// Example No.6.12.\n", +"// Page No.190.\n", +"//To find the lengths of the intercepts.\n", +"clc;clear;\n", +"a = 0.8;\n", +"b = 1.2;\n", +"c = 1.5;\n", +"disp('Ratio of the intercepts are as follows : ');\n", +"disp('I1:I2:I3 = a:b/2:c/3');\n", +"I1 = 0.8;\n", +"disp('0.8:I2:I3 = a:b/2:c/3');\n", +"disp('By substituting values');\n", +"I2=(1.2/2);\n", +"printf('\nI2 = %.1f A',I2);\n", +"I3=(1.5/3);\n", +"printf('\nI3 = %.1f A',I3);\n", +"\n", +"\n", +"\n", +"//As there are no numerical steps and hence the display statement has been typed directly." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.13: Nearest_neighbour_distance.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// Example No.6.13.\n", +"// Page No.191.\n", +"//To find the nearest neighbour distance.\n", +"clc;clear;\n", +"disp('i)Simple cubic unit cell');\n", +"disp('The nearest neighbour distance is a');//nearest neighbour distance.\n", +"disp('ii)Body-centered cubic unit cell');\n", +"disp('2r = (0.866)a');\n", +"disp('iii)Face-centered cubic unit cell');\n", +"disp('2r = (0.7071)a');\n", +"\n", +"//As there are no numerical steps and hence the display statement has been typed directly." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.14: Interplanar_distance.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.14.\n", +"//Page No.191.\n", +"//To find interplanar distance.\n", +"clc;clear;\n", +"// (h,k,l) are the miller indices of the given lattice plane (212).\n", +"h = 2;\n", +"k = 1;\n", +"l = 2;\n", +"a = 2.04;//Lattice constant -[A].\n", +"d = (a/sqrt(h^2+k^2+l^2));\n", +"printf('\nThe interplanar distance is %.2f A',d);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.15: Number_of_atoms_per_unit_cell.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"//Example No.6.15.\n", +"//Page No.191.\n", +"clc;clear;\n", +"r = 1.278*10^(-10),'m';\n", +"M = 63.54;//Atomic weight of copper.\n", +"Na = 6.022*10^(26);\n", +"d = 8980;//density\n", +"a = r*sqrt(8);//Interatomic distance.\n", +"printf('\n The interatomic distance is %3.3e m',a);\n", +"n = ((d*a^(3)*Na)/(M));//The number of atoms per unit cell.\n", +"printf('\n Number of atoms per Cu unit cell is %.f',n);\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.16: Miller_indices_of_the_faces.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// Example No.6.16.\n", +"// Page No.192.\n", +"//To find the miller indices.\n", +"clc;clear;\n", +"disp('i)Ratio of the intercepts are 0.214 : 1 : 0.188');\n", +"disp('Miller indices for the given plane is (212)');\n", +"disp('ii)Ratio of the intercepts are 0.858 : 1 : 0.754');\n", +"disp('Miller indices for the given plane is (121)');\n", +"disp('iii)Ratio of the intercepts are 0.429 : infinity : 0.126');\n", +"disp('Miller indices for the given plane is (103)');\n", +"\n", +"//There are no numerical computations involved in this example and hence the display statement has been typed directly." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.17: Number_of_atoms_present.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// Example No.6.13.\n", +"// Page No.191.\n", +"//To find the number neighbour distance.\n", +"clc;clear;\n", +"disp('i)For (100) plane');\n", +"disp('Number of atoms per m^2 = 1/4r^2');\n", +"disp('i)For (110) plane');\n", +"c1 = 1/(8*sqrt(2));\n", +"printf('\nc1= %.4f',c1);\n", +"disp('Number of atoms per m^2 = (0.084/r^2)');\n", +"disp('i)For (111) plane');\n", +"c2 = 1/(2*sqrt(3));\n", +"printf('\nc2= %.4f',c2);\n", +"disp('Number of atoms per m^2 = (0.2887/r^2)');\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.18: Ionic_packing_factor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.18\n", +"//Page No.194.\n", +"clc;clear;\n", +"r = 0.97*10^(-10);\n", +"R = 1.81*10^(-10);\n", +"Pd = ((%pi)/(3*sqrt(2)));\n", +"printf('\nThe packing density is %.2f',Pd);\n", +"//Ionic factor of NaCl//\n", +"IPF = (4*(4/3)*%pi*(r^(3)+R^(3)))/((2*(r+R))^(3));//Ionic packing factor of NaCl crystal.\n", +"printf('\nThe ionic packing factor of NaCl crystal is %.3f',IPF);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: Density_of_diamond.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.1\n", +"//Page No.185.\n", +"clc;clear;\n", +"Mc = 12;// Mc is the mass of one carbon atom.\n", +"r = 0.071*10^(-9);//radius -[m].\n", +"D = ((8*Mc)/(6.022*10^(26)*((8*r)/(sqrt(3)))^(3)));//density of the diamond.\n", +"printf('\nThe density of diamond is %.1f kg/m^3',D);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2: percentage_volume.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.2.\n", +"//Page No.185.\n", +"clc;clear;\n", +"a1 = 0.332*10^(-9);//Lattice parameter for BCC structure -[m].\n", +"a2 = 0.296*10^(-9);//Lattice parameter for HCP structure -[m].\n", +"c = 0.468*10^(-9);// -[m]\n", +"disp('BCCv is the volume of BCC unit cell');\n", +"BCCv = a1^(3);//Volume of BCC unit cell.\n", +"printf('\nThe volume of BCC unit cell is %3.3e m^-3',BCCv);\n", +"disp('HCPv is the volume of HCP unit cell');\n", +"HCPv = (6*(sqrt(3)/4)*a2^(2)*c);//Volume of HCP unit cell.\n", +"printf('\nThe volume of HCP unit cell is %3.3e m^3',HCPv);\n", +"Cv = (HCPv-BCCv);\n", +"printf('\nThe change in volume is %3.3e',Cv);\n", +"Vp = (Cv/BCCv)*100;\n", +"printf('\nThe volume change in percentage is %.1f percent',Vp);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3: Atomic_structure_and_density.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.3\n", +"//Page No.186.\n", +"clc;clear;\n", +"r = 1.278*10^(-10);//Atomic radius of copper -[m].\n", +"A = 63.54;//Atomic weight of copper.\n", +"n = 4;\n", +"Na = 6.022*10^(26);\n", +"a = (2*sqrt(2)*r);\n", +"printf('\nThe lattice constant for FCC is %3.3e',a); \n", +"d = ((n*A)/(Na*a^(3)));//for FCCn=4.\n", +"d = ((n*A)/(Na*(3.61*10^(-10))^(3)));\n", +"printf('\nThe density of copper is %.0f kg/m^3',d);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4: Interatomic_distance_of_NACL.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.4.\n", +"//Page No.186.\n", +"clc;clear;\n", +"Na = 23;//Atomic weight of Na\n", +"Cl = 35.5;//Atomic weight of Cl\n", +"d = 2180;//Density of Nacl -[kg/m^3].\n", +"nA = 6.022*10^(26);\n", +"NaCl = (Na+Cl)//Molecular weight of NaCl.\n", +"printf('\n1) Molecular weigth of NaCl is %.1f',NaCl);\n", +"n = 4;\n", +"A = 58.5;\n", +"a = (((n*A)/(nA*d))^(1/3));\n", +"printf('\n2) The interatomic distance of NaCl crystal is %3.3e m',a); " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5: Relation_between_interatomic_and_interplanar.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.5.\n", +"//Page No.187.\n", +"clc;clear;\n", +"a = 0.42;//Lattice constant -[nm].\n", +"//(h1,k1,l1) are the miller indices of the plane (101).\n", +"h1 = 1;\n", +"k1 = 0;\n", +"l1 = 1;\n", +"d1 = (a/sqrt(h1^(2)+k1^(2)+l1^(2)));//interplanar and interatomic distance of plane (101)\n", +"printf('\nFor (101) plane, the interplanar and interatomic distance is %.4f nm',d1);\n", +"// (h2,k2,l2) are the miller indices of the plane (221).\n", +"h2 = 2;\n", +"k2 = 2;\n", +"l2 = 1;\n", +"d2 = (a/sqrt(h2^(2)+k2^(2)+l2^(2)));//interplanar and interatomic distance of plane (221)\n", +"printf('\nFor (221) plane, the interplanar and interatomic distance is %.2f nm',d2);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: Axial_intercepts.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// Example No.6.6.\n", +"// Page No.187.\n", +"clc;clear;\n", +"disp('For the plane (102),the intercepts are (a/1) = a,(b/0) = infinity ,c/2');\n", +"disp('For the plane (231),the intercepts are a/2 , b/3 and (c/1) = c');\n", +"disp('For the plane (312),the intercepts are a/3 ,(b/-1) = -b ,c/2');\n", +"\n", +"//As there are no numerical steps available and hence the display statement has been typed directly.\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7: Angle_between_the_planes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.7\n", +"//Page No.188.\n", +"//Find the angle between two planes (111) and (212) in a cubic lattice.\n", +"clc;clear;\n", +"// (u1,v1,w1) are the miller indices of the plane (111).\n", +"u1 = 1;\n", +"v1 = 1;\n", +"w1 = 1;\n", +"// (u2,v2,w2) are the miller indices of the plane (212).\n", +"u2 = 2;\n", +"v2 = 1;\n", +"w2 = 2;\n", +"u = acosd(((u1*u2)+(v1*v2)+(w1*w2))/((sqrt((u1^2)+(v1^2)+(w1^2))*sqrt((u2^2)+(v2^2)+(w2^2)))));//u is the angle between two planes.\n", +"printf('\n The angle between the planes (111) and (212) is %.3f degree',u);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.8: Crystallographic_planes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// Example No.6.8.\n", +"// Page No.188.\n", +"clc;clear;\n", +"disp('The intercepts of the plane(100) are a ,infinity ,infinity.');\n", +"disp('The intercepts of the cubic plane(110) are a ,a ,infinity.');\n", +"disp('The intercepts of the plane(111) are a ,a ,a.');\n", +"disp('The intercepts of the plane(200) are a/2 ,infinity ,infinity.');\n", +"disp('The intercepts of the plane(120) are a ,a/2 ,infinity.');\n", +"disp('The intercepts of the plane(211) are a/2 ,a ,a.');\n", +"\n", +"//As there are no numerical steps and hence the display statement has been typed directly.\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.9: Lattice_constant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//Example No.6.9.\n", +"//Page No.189.\n", +"clc;clear;\n", +"d = 0.2338;//'d' is the interplanar distance -[nm].\n", +"// (h,k,l) are the miller indices of the given plane.\n", +"h = (-1);\n", +"k = 1;\n", +"l = 1;\n", +"a = (d*sqrt(h^2+k^2+l^2));//'a' is the lattice constant\n", +"printf('\nThe lattice constant is %.4f nm',a); " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |