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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# 2: Crystallography and Crystal Structures"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 2, Page number 2.21"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "spacing between (100) plane is 5.64 angstrom\n",
- "spacing between (110) plane is 3.99 angstrom\n",
- "answer for spacing between (110) plane given in the book is wrong\n",
- "spacing between (111) plane is 3.26 angstrom\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "a=5.64; #lattice constant(angstrom)\n",
- "h1=1;\n",
- "k1=0;\n",
- "l1=0;\n",
- "h2=1;\n",
- "k2=1;\n",
- "l2=0;\n",
- "h3=1;\n",
- "k3=1;\n",
- "l3=1;\n",
- "\n",
- "#Calculation\n",
- "d100=a/math.sqrt(h1**2+k1**2+l1**2); #spacing between (100) plane\n",
- "d110=a/math.sqrt(h2**2+k2**2+l2**2); #spacing between (110) plane\n",
- "d111=a/math.sqrt(h3**2+k3**2+l3**2); #spacing between (111) plane\n",
- "\n",
- "#Result\n",
- "print \"spacing between (100) plane is\",d100,\"angstrom\"\n",
- "print \"spacing between (110) plane is\",round(d110,2),\"angstrom\"\n",
- "print \"answer for spacing between (110) plane given in the book is wrong\"\n",
- "print \"spacing between (111) plane is\",round(d111,2),\"angstrom\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 3, Page number 2.22"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "number of atoms in (100) is 1.535 *10**13 atoms/mm**2\n",
- "number of atoms in (110) is 1.085 *10**13 atoms/mm**2\n",
- "number of atoms in (111) is 1.772 *10**13 atoms/mm**2\n",
- "answers given in the book vary due to rounding off errors\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "a=3.61*10**-7; #lattice constant(mm)\n",
- "\n",
- "#Calculation\n",
- "A100=a**2; #surface area(mm**2)\n",
- "n=1+(4*(1/4));\n",
- "N1=n/A100; #number of atoms in (100)(per mm**2)\n",
- "A110=math.sqrt(2)*a**2; #surface area(mm**2)\n",
- "N2=n/A110; #number of atoms in (110)(per mm**2)\n",
- "A111=math.sqrt(3)*a**2/2; #surface area(mm**2)\n",
- "N3=n/A111; #number of atoms in (110)(per mm**2)\n",
- "\n",
- "#Result\n",
- "print \"number of atoms in (100) is\",round(N1/10**13,3),\"*10**13 atoms/mm**2\"\n",
- "print \"number of atoms in (110) is\",round(N2/10**13,3),\"*10**13 atoms/mm**2\"\n",
- "print \"number of atoms in (111) is\",round(N3/10**13,3),\"*10**13 atoms/mm**2\"\n",
- "print \"answers given in the book vary due to rounding off errors\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 4, Page number 2.23"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "wavelength of x rays is 1.552 angstrom\n",
- "answer varies due to rounding off errors\n",
- "energy of x rays is 8 *10**3 eV\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "n=4; \n",
- "A=107.87; #atomic weight\n",
- "rho=10500; #density(kg/m**3)\n",
- "N=6.02*10**26; #number of molecules\n",
- "theta=19+(12/60); #angle(degrees)\n",
- "h=1;\n",
- "k=1;\n",
- "l=1;\n",
- "h0=6.625*10**-34; #planck constant\n",
- "c=3*10**8; #velocity of light(m/s)\n",
- "e=1.6*10**-19; #charge(coulomb)\n",
- "\n",
- "#Calculation\n",
- "theta=theta*math.pi/180; #angle(radian)\n",
- "a=(n*A/(N*rho))**(1/3);\n",
- "d=a*10**10/math.sqrt(h**2+k**2+l**2); \n",
- "lamda=2*d*math.sin(theta); #wavelength of x rays(angstrom)\n",
- "E=h0*c/(lamda*10**-10*e); #energy of x rays(eV)\n",
- "\n",
- "#Result\n",
- "print \"wavelength of x rays is\",round(lamda,3),\"angstrom\"\n",
- "print \"answer varies due to rounding off errors\"\n",
- "print \"energy of x rays is\",int(E/10**3),\"*10**3 eV\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 5, Page number 2.23"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "density is 2332 kg/m**3\n",
- "answer varies due to rounding off errors\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "n=8; #number of atoms\n",
- "r=2.351*10**-10; #bond length(angstrom)\n",
- "A=28.09; #Atomic wt. of NaCl\n",
- "N=6.02*10**26 #Avagadro number\n",
- "\n",
- "#Calculation\n",
- "a=4*r/math.sqrt(3); \n",
- "rho=n*A/(N*a**3); #density(kg/m**3)\n",
- "\n",
- "#Result\n",
- "print \"density is\",int(rho),\"kg/m**3\"\n",
- "print \"answer varies due to rounding off errors\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 6, Page number 2.24"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "radius of largest sphere is 0.1547 r\n",
- "maximum radius of sphere is 0.414 r\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "from sympy import Symbol\n",
- "\n",
- "#Variable declaration\n",
- "r=Symbol('r')\n",
- "\n",
- "#Calculation\n",
- "a1=4*r/math.sqrt(3);\n",
- "R1=(a1/2)-r; #radius of largest sphere\n",
- "a2=4*r/math.sqrt(2);\n",
- "R2=(a2/2)-r; #maximum radius of sphere\n",
- "\n",
- "#Result\n",
- "print \"radius of largest sphere is\",round(R1/r,4),\"r\"\n",
- "print \"maximum radius of sphere is\",round(R2/r,3),\"r\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 7, Page number 2.25"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "percent volume change is 0.5 %\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "r1=1.258*10**-10; #radius(m)\n",
- "r2=1.292*10**-10; #radius(m)\n",
- "\n",
- "#Calculation\n",
- "a_bcc=4*r1/math.sqrt(3);\n",
- "v=a_bcc**3;\n",
- "V1=v/2;\n",
- "a_fcc=2*math.sqrt(2)*r2;\n",
- "V2=a_fcc**3/4;\n",
- "V=(V1-V2)*100/V1; #percent volume change is\",V,\"%\"\n",
- "\n",
- "#Result\n",
- "print \"percent volume change is\",round(V,1),\"%\""
- ]
- }
- ],
- "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
-}
generated by cgit (git 2.34.1) at 2025-01-06 22:38:09 +0000