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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 4: Crystal Physics"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.10: example_10.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"//let three intercepts are I1,I2,I3\n",
+"I1=0.96;\n",
+"I2=0.64;\n",
+"I3=0.48;\n",
+"//as they are ratios we will multiply by some some constants so that it will become integers\n",
+"I1=6;\n",
+"I2=4;\n",
+"I3=3 ;\n",
+"//let their reciprocals are I1_1,I2_1,I3_1\n",
+"I1_1=1/I1;\n",
+"I2_1=1/I2;\n",
+"I3_1=1/I3;\n",
+"//LCM of I1_1,I2_1,I3_1 are 12. \n",
+"//By multiply LCM with I1_!,I2_1,I3_1 we will get miller indices\n",
+"LCM=12;\n",
+"M_1=LCM*I1_1;\n",
+"M_2=LCM*I2_1 ;\n",
+"M_3=LCM*I3_1;\n",
+"disp(M_1,'Miller indices of plane =');\n",
+"disp(M_2);\n",
+"disp(M_3);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.1: example_1.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"clear all;\n",
+"r=1.278*1e-8 ;//atomic radius in cm\n",
+"M=63.5; //atomic weight\n",
+"N=6.023*1e23; //avogadro number\n",
+"n=4//for fcc n=4\n",
+"a=4*r/(sqrt(2));\n",
+"density=n*M/(N*a^3);//Density of copper\n",
+"disp(+'g/cc',density,'Density of copper =')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.2: example_2.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"M=58.45;//atomic mass\n",
+"N=6.02*1e23;//avogadro number\n",
+"density=2.17*1e3 ; //in kg/m^3\n",
+"n=4 //Nacl is FCC\n",
+"a=(n*M/(N*density))^(1/3);//lattice constant\n",
+"disp(+'m',a,'lattice constant = ');\n",
+"//slight variation in ans than book.. checked in calculator also"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.3: example_3.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"//let three intercepts are I1,I2,I3\n",
+"I1=3;\n",
+"I2=-2;\n",
+"I3=3/2;\n",
+"//let their reciprocals are I1_1,I2_1,I3_1\n",
+"I1_1=1/I1;\n",
+"I2_1=1/I2;\n",
+"I3_1=1/I3;\n",
+"//LCM of I1_1,I2_1,I3_1 are 6 . \n",
+"//By multiply LCM with I1_!,I2_1,I3_1 we will get miller indices\n",
+"LCM=6;\n",
+"M_1=LCM*I1_1;\n",
+"M_2=LCM*I2_1 ;\n",
+"M_3=LCM*I3_1;\n",
+"disp(M_1,'Miller indices of plane =');\n",
+"disp(M_2);\n",
+"disp(M_3);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.4: example_4.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"r=1.246 //in A\n",
+"a=4*r/sqrt(2)\n",
+"d_200=3.52/sqrt(4+0+0)\n",
+"disp(+'m',d_200*1e-10,'d200 = ')\n",
+"d_220=3.52/sqrt(4+4)\n",
+"disp(+'m',d_220*1e-10,'d220 = ')\n",
+"d_111=3.52/sqrt(1+1+1)\n",
+"disp(+'m',d_111*1e-10,'d111 = ')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.5: example_5.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"h=1\n",
+"k=1\n",
+"l=1\n",
+"h1=1\n",
+"k1=1\n",
+"l1=1\n",
+"a=((h*h1)-(k*k1)+(l*l1))/(sqrt((h*h)+(k*k)+(l*l))*sqrt((h1*h1)+(k1*k1)+(l1*l1)));\n",
+"//cosine angle=a so angle=cosine inverse of a\n",
+"thita=acosd(a);//angle between two planes\n",
+"disp(+'degree',thita,'angle between two planes =')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.6: example_6.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"a=2.9*1e-8; //in cm\n",
+"M=55.85;//atomic mass\n",
+"density=7.87 //in g/cc\n",
+"N=6.023*1e23;\n",
+"n=(a^3*N*density)/M;//Number of atoms per unit cell\n",
+"disp(n,'Number of atoms per unit cell =');\n",
+"//slight variation in ans than book.. checked in calculator also"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.7: example_7.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"M=55.85;//atomic mass\n",
+"d=7.86 //density of iron in g/cc\n",
+"N=6.023*1e23\n",
+"n=2//BCC structure\n",
+"a=((n*M)/(N*d))^(1/3);\n",
+"r=(sqrt(3)*a)/4;//radius of iron atom \n",
+"disp(+'cm',r,'radius of iron atom =')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.8: example_8.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"M=207.21;//atomic mass\n",
+"d=11.34*1e3 //in kg/m^3\n",
+"N=6.023*1e26 //in kg/m^3\n",
+"n=4;//for FCC\n",
+"a=((n*M)/(N*d))^(1/3);//lattice constant\n",
+"r=(sqrt(2)*a)/4;//Atomic radius\n",
+"disp(+'m',a,'lattice constant =');\n",
+"disp(+'m',r,'Atomic radius =');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 4.9: example_9.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc;\n",
+"n=1;\n",
+"thita=30;//angle in degree\n",
+"lamda=1.75; //in A\n",
+"h=1;\n",
+"k=1;\n",
+"l=1;\n",
+"//d111=a/sqrt((h*h)+(k*k)+(l*l))\n",
+"//2dsin(thita)=n*lamda\n",
+"d=n*lamda/(2*sind(thita));\n",
+"a=sqrt(3)*d;//lattice constant \n",
+"disp(+'meters',a*1e-10,'lattice constant =')"
+ ]
+ }
+],
+"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
+}
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