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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 11: Crystal Structure"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 1, Page number 299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "lattice constant is 4 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "n=4; #number of molecules per unit cell\n",
+ "M=60.2; #molecular weight\n",
+ "N=6.02*10**26; #avagadro number(kg mol-1)\n",
+ "rho=6250; #density(kg/m**3)\n",
+ "\n",
+ "#Calculations\n",
+ "a=(n*M/(rho*N))**(1/3); #lattice constant(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"lattice constant is\",int(a*10**10),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 2, Page number 299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "lattice constant is 2.867 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "n=2; #number of molecules per unit cell\n",
+ "M=55.8; #molecular weight\n",
+ "N=6.02*10**26; #avagadro number(kg mol-1)\n",
+ "rho=7870; #density(kg/m**3)\n",
+ "\n",
+ "#Calculations\n",
+ "a=(n*M/(rho*N))**(1/3); #lattice constant(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"lattice constant is\",round(a*10**10,3),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 3, Page number 299"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "distance between two nearest copper atoms is 2.55 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "n=4; #number of molecules per unit cell\n",
+ "M=63.5; #molecular weight\n",
+ "N=6.02*10**23; #avagadro number(kg mol-1)\n",
+ "rho=8.96; #density(gm/cm**3)\n",
+ "\n",
+ "#Calculations\n",
+ "a=(n*M/(rho*N))**(1/3); #lattice constant(m)\n",
+ "d=a/math.sqrt(2); #distance between two nearest copper atoms(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"distance between two nearest copper atoms is\",round(d*10**8,2),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 4, Page number 303"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "miller indices of plane are ( 3 2 1 )\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "a=1/2;\n",
+ "b=1/3;\n",
+ "c=1/6; #intercepts along the three axes\n",
+ "\n",
+ "#Calculations\n",
+ "def lcm(x, y):\n",
+ " if x > y:\n",
+ " greater = x\n",
+ " else:\n",
+ " greater = y\n",
+ " while(True):\n",
+ " if((greater % x == 0) and (greater % y == 0)):\n",
+ " lcm = greater\n",
+ " break\n",
+ " greater += 1\n",
+ " \n",
+ " return lcm\n",
+ "\n",
+ "z=lcm(1/a,1/b);\n",
+ "lcm=lcm(z,1/c);\n",
+ "h=a*lcm;\n",
+ "k=b*lcm;\n",
+ "l=c*lcm; #miller indices of plane\n",
+ "\n",
+ "#Result\n",
+ "print \"miller indices of plane are (\",int(h),int(k),int(l),\")\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 5, Page number 303"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "miller indices of plane are ( 3 4 0 )\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "a=1/4;\n",
+ "b=1/3;\n",
+ "x=float(\"inf\");\n",
+ "c=1/x; #intercepts along the three axes\n",
+ "\n",
+ "#Calculations\n",
+ "def lcm(x, y):\n",
+ " if x > y:\n",
+ " greater = x\n",
+ " else:\n",
+ " greater = y\n",
+ " while(True):\n",
+ " if((greater % x == 0) and (greater % y == 0)):\n",
+ " lcm = greater\n",
+ " break\n",
+ " greater += 1\n",
+ " \n",
+ " return lcm\n",
+ "\n",
+ "lcm=lcm(1/a,1/b);\n",
+ "h=a*lcm;\n",
+ "k=b*lcm;\n",
+ "l=c*lcm; #miller indices of plane\n",
+ "\n",
+ "#Result\n",
+ "print \"miller indices of plane are (\",int(h),int(k),int(l),\")\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 6, Page number 303"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "miller indices of plane are ( 6 -2 3 )\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "a=1/1;\n",
+ "b=-1/3;\n",
+ "c=1/2; #intercepts along the three axes\n",
+ "\n",
+ "#Calculations\n",
+ "def lcm(x, y):\n",
+ " if x > y:\n",
+ " greater = x\n",
+ " else:\n",
+ " greater = y\n",
+ " while(True):\n",
+ " if((greater % x == 0) and (greater % y == 0)):\n",
+ " lcm = greater\n",
+ " break\n",
+ " greater += 1\n",
+ " \n",
+ " return lcm\n",
+ "\n",
+ "z=lcm(1/a,1/b);\n",
+ "lcm=lcm(z,1/c);\n",
+ "h=a*lcm;\n",
+ "k=b*lcm;\n",
+ "l=c*lcm; #miller indices of plane\n",
+ "\n",
+ "#Result\n",
+ "print \"miller indices of plane are (\",int(h),int(k),int(l),\")\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 7, Page number 304"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "intercept on y-axis is 1.2 angstrom\n",
+ "intercept on z-axis is 4.0 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "p1=1.2; #x-primitive(angstrom)\n",
+ "p2=1.8; #y-primitive(angstrom)\n",
+ "p3=2.0; #z-primitive(angstrom)\n",
+ "x=2; #x-intercept\n",
+ "y=3; #y-intercept\n",
+ "z=1; #z-intercept\n",
+ "h=1.2; #intercept on x-axis(angstrom)\n",
+ "\n",
+ "#Calculations\n",
+ "h1=p1/x; \n",
+ "k1=p2/y;\n",
+ "l1=p3/z;\n",
+ "k=h*k1/h1; #intercept on y-axis(angstrom)\n",
+ "l=h*p3/h1; #intercept on z-axis(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"intercept on y-axis is\",k,\"angstrom\"\n",
+ "print \"intercept on z-axis is\",l,\"angstrom\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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