{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 6: Crystallography" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 1, Page number 207" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "density is 5.38 *10**4 kg/m**3\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "n=8; #number of atoms per unit cell\n", "a=5.6*10**-10; #lattice constant(m)\n", "M=710.59; #atomic weight(amu)\n", "N=6.02*10**26; #avagadro number(kg/mol)\n", "\n", "#Calculation\n", "rho=n*M/(a**3*N); #density(kg/m**3) \n", "\n", "#Result\n", "print \"density is\",round(rho/10**4,2),\"*10**4 kg/m**3\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 2, Page number 207" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lattice constant is 0.29 angstrom\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "n=2; #number of atoms per unit cell\n", "M=55.85; #atomic weight(amu)\n", "N=6.02*10**23; #avagadro number(kg/m**3)\n", "rho=7860; #density(kg/m**3) \n", "\n", "#Calculation \n", "a=(n*M/(rho*N))**(1/3); #lattice constant(m) \n", "\n", "#Result\n", "print \"lattice constant is\",round(a*10**8,2),\"angstrom\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 3, Page number 208" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lattice constant is 3.52 angstrom\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "n=2; #number of atoms per unit cell\n", "M=6.94; #atomic weight(amu)\n", "N=6.02*10**26; #avagadro number(kg/mol)\n", "rho=530; #density(kg/m**3) \n", "\n", "#Calculation \n", "a=(n*M/(rho*N))**(1/3); #lattice constant(m) \n", "\n", "#Result\n", "print \"lattice constant is\",round(a*10**10,2),\"angstrom\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 4, Page number 208" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of atoms per unit cell is 2\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "M=55.85; #atomic weight(amu)\n", "N=6.02*10**26; #avagadro number(kg/mol)\n", "rho=7870; #density(kg/m**3) \n", "a=2.9*10**-10; #lattice constant(m) \n", "\n", "#Calculation \n", "n=a**3*rho*N/M; #number of atoms per unit cell\n", "\n", "#Result\n", "print \"number of atoms per unit cell is\",int(n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 5, Page number 208" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "density is 53771 kg/m**3\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "n=8; #number of atoms per unit cell\n", "a=5.6*10**-10; #lattice constant(m)\n", "M=710.59; #atomic weight(amu)\n", "N=6.02*10**26; #avagadro number(kg/mol)\n", "\n", "#Calculation\n", "rho=n*M/(a**3*N); #density(kg/m**3) \n", "\n", "#Result\n", "print \"density is\",int(rho),\"kg/m**3\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 6, Page number 209" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lattice constant is 0.2869 angstrom\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "n=2; #number of atoms per unit cell\n", "M=55.85; #atomic weight(amu)\n", "N=6.02*10**23; #avagadro number(kg/m**3)\n", "rho=7860; #density(kg/m**3) \n", "\n", "#Calculation \n", "a=(n*M/(rho*N))**(1/3); #lattice constant(m) \n", "\n", "#Result\n", "print \"lattice constant is\",round(a*10**8,4),\"angstrom\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 7, Page number 209" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lattice constant is 3.517 angstrom\n", "answer given in the book varies due to rounding off errors\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "n=2; #number of atoms per unit cell\n", "M=6.94; #atomic weight(amu)\n", "N=6.02*10**26; #avagadro number(kg/mol)\n", "rho=530; #density(kg/m**3) \n", "\n", "#Calculation \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\"\n", "print \"answer given in the book varies due to rounding off errors\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 8, Page number 209" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of atoms per unit cell is 2\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "M=55.85; #atomic weight(amu)\n", "N=6.02*10**26; #avagadro number(kg/mol)\n", "rho=7870; #density(kg/m**3) \n", "a=2.9*10**-10; #lattice constant(m) \n", "\n", "#Calculation \n", "n=a**3*rho*N/M; #number of atoms per unit cell\n", "\n", "#Result\n", "print \"number of atoms per unit cell is\",int(n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 9, Page number 210" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "density is 8933.25 kg/m**3\n", "answer given in the book is wrong\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "r=0.1278*10**-9; #atomic radius(m)\n", "n=4; #number of atoms per unit cell\n", "M=63.5; #atomic weight(amu)\n", "N=6.02*10**26; #avagadro number(kg/mol)\n", "\n", "#Calculation\n", "a=math.sqrt(8)*r; #lattice constant(m)\n", "rho=n*M/(a**3*N); #density(kg/m**3) \n", "\n", "#Result\n", "print \"density is\",round(rho,2),\"kg/m**3\"\n", "print \"answer given in the book is wrong\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 10, Page number 210" ] }, { "cell_type": "code", "execution_count": 45, "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", "n1=2; #number of atoms per unit cell\n", "n2=4; #number of atoms per unit cell\n", "\n", "#Calculation\n", "a_bcc=4*r1/math.sqrt(3);\n", "v=a_bcc**3;\n", "V1=v/n1;\n", "a_fcc=2*math.sqrt(2)*r2;\n", "V2=a_fcc**3/n2;\n", "V=(V1-V2)*100/V2; #percent volume change is\",V,\"%\"\n", "\n", "#Result\n", "print \"percent volume change is\",round(V,1),\"%\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 12, Page number 211" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of atoms per unit volume is 4.49 *10**22 atoms/cm**3\n", "distance between adjacent atoms is 2.81 angstrom\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "w=23+35.5; #molecular weight of NaCl(gm/mole)\n", "N=6.023*10**23; #avagadro number(gm/mol)\n", "rho=2.18; #density of NaCl(gm/cm**3)\n", "n=2; #number of atoms\n", "\n", "#Calculation\n", "m=w/N; #mass of NaCl(gm)\n", "nm=rho/m; #number of molecules(mole/cm**3)\n", "N_NaCl=n*nm; #number of atoms per unit volume(atoms/cm**3) \n", "a=(1/N_NaCl)**(1/3); #distance between adjacent atoms(cm)\n", "\n", "\n", "#Result\n", "print \"number of atoms per unit volume is\",round(N_NaCl/10**22,2),\"*10**22 atoms/cm**3\"\n", "print \"distance between adjacent atoms is\",round(a*10**8,2),\"angstrom\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 13, Page number 212" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "glancing angle is 21.01 degrees\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "lamda=0.071*10**-9; #wavelength(m)\n", "h=1;\n", "k=1;\n", "l=0; #miller indices\n", "a=0.28*10**-9; #lattice constant(m)\n", "n=2; #order\n", "\n", "#Calculation\n", "d=a/math.sqrt(h**2+k**2+l**2); \n", "theta=math.asin(n*lamda/(2*d))*180/math.pi; #glancing angle(degrees)\n", "\n", "#Result\n", "print \"glancing angle is\",round(theta,2),\"degrees\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 14, Page number 213" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "space of reflecting plane is 2.3336 angstrom\n", "volume of unit cell is 1.27 *10**-29 m**3\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "lamda=3*10**-10; #wavelength(m)\n", "h=1;\n", "k=0;\n", "l=0; #miller indices\n", "theta=40*math.pi/180; #glancing angle(radian)\n", "n=1; #order\n", "\n", "#Calculation\n", "d=n*lamda/(2*math.sin(theta)); #space of reflecting plane(m)\n", "a=d*math.sqrt(h**2+k**2+l**2); \n", "V=a**3; #volume of unit cell(m**3)\n", "\n", "#Result\n", "print \"space of reflecting plane is\",round(d*10**10,4),\"angstrom\"\n", "print \"volume of unit cell is\",round(V*10**29,2),\"*10**-29 m**3\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 15, Page number 213" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "space of reflecting plane is 0.42 angstrom\n", "answer given in the book is wrong\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "lamda=0.82; #wavelength(m)\n", "theta=75.86*math.pi/180; #glancing angle(radian)\n", "n=1; #order\n", "a=3; #lattice constant(angstrom)\n", "\n", "#Calculation\n", "d=n*lamda/(2*math.sin(theta)); #space of reflecting plane(angstrom)\n", "#here the value of d comes to 0.422 angstrom which is not equal to the value of a. hence the problem cannot be solved further \n", "\n", "#Result\n", "print \"space of reflecting plane is\",round(d,2),\"angstrom\"\n", "print \"answer given in the book is wrong\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 16, Page number 214" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "wavelength of X-ray beam is 3 angstrom\n", "energy of X-ray beam is 4.14 *10**5 eV\n", "answer for energy given in the book is wrong\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "a=5.63*10**-10; #lattice constant(m)\n", "h=1;\n", "k=1;\n", "l=1; #miller indices\n", "theta=27.5*math.pi/180; #glancing angle(radian)\n", "n=1; #order\n", "h=6.625*10**-34; #planck's constant\n", "c=3*10**10; #velocity of light(m/sec)\n", "e=1.6*10**-19; #charge of electron(c)\n", "\n", "#Calculation\n", "d111=a/math.sqrt(h**2+k**2+l**2); \n", "lamda=2*d111*math.sin(theta)/n; #wavelength of X-ray beam(m) \n", "lamda=int(lamda*10**10); #wavelength of X-ray beam(angstrom) \n", "E=h*c/(lamda*10**-10*e); #energy of X-ray beam(eV) \n", "\n", "#Result\n", "print \"wavelength of X-ray beam is\",lamda,\"angstrom\"\n", "print \"energy of X-ray beam is\",round(E/10**5,2),\"*10**5 eV\"\n", "print \"answer for energy given in the book is wrong\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 17, Page number 215" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lattice constant is 3.7935 angstrom\n", "answer given in the book varies due to rounding off errors\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=2;\n", "k=0;\n", "l=2; #miller indices\n", "theta=34*math.pi/180; #glancing angle(radian)\n", "n=1; #order\n", "lamda=1.5*10**-10; #wavelength of X-ray beam(m) \n", "\n", "#Calculation\n", "d=n*lamda/(2*math.sin(theta)); \n", "a=d*math.sqrt(h**2+k**2+l**2); #lattice constant(m)\n", "\n", "#Result\n", "print \"lattice constant is\",round(a*10**10,4),\"angstrom\"\n", "print \"answer given in the book varies due to rounding off errors\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 19, Page number 216" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ratio of d100:d110:d111 is math.sqrt( 6 ) : math.sqrt( 3 ) : math.sqrt( 2 )\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h1=1;\n", "k1=0;\n", "l1=0; #miller indices\n", "h2=1;\n", "k2=1;\n", "l2=0; #miller indices\n", "h3=1;\n", "k3=1;\n", "l3=1; #miller indices\n", "a=1; #assume\n", "\n", "#Calculation\n", "Dr1=(h1**2+k1**2+l1**2);\n", "Dr2=(h2**2+k2**2+l2**2);\n", "Dr3=(h3**2+k3**2+l3**2);\n", "d100=a/math.sqrt(Dr1);\n", "d110=a/math.sqrt(Dr2);\n", "d111=a/math.sqrt(Dr3);\n", "def lcm(x, y): \n", " if x > y: \n", " z = x \n", " else: \n", " z = y \n", " \n", " while(True): \n", " if((z % x == 0) and (z % y == 0)): \n", " lcm = z \n", " break \n", " z += 1 \n", " \n", " return lcm\n", "lcm=lcm(Dr2,Dr3);\n", "r=math.sqrt(lcm);\n", "r_d100=d100*r;\n", "r_d110=d110*r;\n", "r_d111=d111*r;\n", "\n", "#Result\n", "print \"ratio of d100:d110:d111 is math.sqrt(\",int(round(r_d100**2)),\") : math.sqrt(\",int(round(r_d110**2)),\") : math.sqrt(\",int(round(r_d111**2)),\")\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 20, Page number 217" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "interplanar spacing is 159.1 nm\n", "answer given in the book is wrong\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=2;\n", "k=2;\n", "l=0; #miller indices\n", "a=450; #length(nm) \n", "\n", "#Calculation\n", "d220=a/math.sqrt(h**2+k**2+l**2); #interplanar spacing(nm)\n", "\n", "#Result\n", "print \"interplanar spacing is\",round(d220,1),\"nm\"\n", "print \"answer given in the book is wrong\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 21, Page number 217" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "interplanar spacing is 2.09 *10**-10 m\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=1;\n", "k=1;\n", "l=1; #miller indices\n", "r=1.278*10**-10; #radius(m)\n", "\n", "#Calculation\n", "a=4*r/math.sqrt(2); \n", "d111=a/math.sqrt(h**2+k**2+l**2); #interplanar spacing(m)\n", "\n", "#Result\n", "print \"interplanar spacing is\",round(d111*10**10,2),\"*10**-10 m\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 22, Page number 217" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "wavelength of X-rays is 1.549 angstrom\n", "answer in the book 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", "h=1;\n", "k=1;\n", "l=1; #miller indices\n", "n=4;\n", "A=107.87; #atomic weight(amu)\n", "N=10500*6.052*10**26; #density(kg/m**3)\n", "theta=(19+(12/60))*math.pi/180; #angle(radian)\n", "r=1.278*10**-10; #radius(m)\n", "hp=6.625*10**-34; #plancks constant(Js)\n", "c=3*10**8; #velocity of light(m/sec)\n", "e=1.6*10**-19; #charge of electron(coulomb)\n", "\n", "#Calculation\n", "a=(n*A/N)**(1/3); #lattice constant(m)\n", "d=a/math.sqrt(h**2+k**2+l**2); #interplanar spacing(m)\n", "lamda=2*d*math.sin(theta); #wavelength of X-rays(m)\n", "E=hp*c/(e*lamda); #energy of X-rays(eV) \n", "\n", "#Result\n", "print \"wavelength of X-rays is\",round(lamda*10**10,3),\"angstrom\"\n", "print \"answer in the book 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 23, Page number 217" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "glancing angle is 21 degrees\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=1;\n", "k=1;\n", "l=0; #miller indices\n", "d100=0.28; #lattice constant(nm)\n", "n=2;\n", "lamda=0.071; #wavelength(nm)\n", "\n", "#Calculation\n", "d110=d100/math.sqrt(h**2+k**2+l**2); #interplanar spacing(m)\n", "theta=math.asin(n*lamda/(2*d110))*180/math.pi; #glancing angle(degrees)\n", "\n", "#Result\n", "print \"glancing angle is\",int(theta),\"degrees\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 24, Page number 218" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "distance between the planes is 0.27 nm\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=1;\n", "k=1;\n", "l=0; #miller indices\n", "a=0.38; #lattice constant(nm)\n", "\n", "#Calculation\n", "d=a/math.sqrt(h**2+k**2+l**2); #distance between the planes(nm)\n", "\n", "#Result\n", "print \"distance between the planes is\",round(d,2),\"nm\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 26, Page number 219" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "intercept along y axis is 0.123 nm\n", "intercept along y axis is 0.394 nm\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=2;\n", "k=3;\n", "l=1; #miller indices\n", "a=0.121; \n", "b=0.184;\n", "c=0.197; #parameters(nm)\n", "\n", "#Calculation\n", "OB=2*b/3; #intercept along y axis(nm)\n", "OC=2*c; #intercept along z axis(nm) \n", "\n", "#Result\n", "print \"intercept along y axis is\",round(OB,3),\"nm\"\n", "print \"intercept along y axis is\",OC,\"nm\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 27, Page number 219" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "interplanar distance between (123) planes is 0.213 nm\n", "interplanar distance between (246) planes is 0.1066 nm\n", "answers given in the book are wrong\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h1=1;\n", "k1=2;\n", "l1=3; #miller indices\n", "h2=2;\n", "k2=4;\n", "l2=6; #miller indices\n", "a=0.82; \n", "b=0.94;\n", "c=0.75; #parameters(nm)\n", "\n", "#Calculation\n", "d123=(((h1/a)**2)+((k1/b)**2)+((l1/c)**2))**(-1/2); #interplanar distance between (123) planes\n", "d246=d123/2; #interplanar distance between (246) planes\n", "\n", "#Result\n", "print \"interplanar distance between (123) planes is\",round(d123,3),\"nm\"\n", "print \"interplanar distance between (246) planes is\",round(d246,4),\"nm\"\n", "print \"answers given in the book are wrong\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 28, Page number 219" ] }, { "cell_type": "code", "execution_count": 109, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "wavelength of Xrays is 0.159 nm\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=1;\n", "k=1;\n", "l=1; #miller indices\n", "a=0.2; #lattice parameter(nm)\n", "theta=(87/2)*math.pi/180; #angle(radian)\n", "\n", "#Calculation\n", "d=a/math.sqrt(h**2+k**2+l**2);\n", "lamda=2*d*math.sin(theta); #wavelength of Xrays(nm)\n", "\n", "#Result\n", "print \"wavelength of Xrays is\",round(lamda,3),\"nm\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 29, Page number 219" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "effective temperature of neutrons is 169 K\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=1;\n", "k=1;\n", "l=1; #miller indices\n", "a=0.352; #lattice parameter(nm)\n", "theta=(28+(30/60))*math.pi/180; #angle(radian)\n", "hp=6.626*10**-34; #plancks constant(Js)\n", "m=1.67*10**-27; #mass of proton(kg)\n", "kB=1.38*10**-23; #boltzmann constant\n", "\n", "#Calculation\n", "d=a/math.sqrt(h**2+k**2+l**2);\n", "lamda=2*d*math.sin(theta); #wavelength(nm)\n", "T=(hp**2)/(3*m*kB*(lamda*10**-9)**2); #effective temperature of neutrons(K)\n", "\n", "#Result\n", "print \"effective temperature of neutrons is\",int(round(T)),\"K\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 30, Page number 220" ] }, { "cell_type": "code", "execution_count": 125, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lattice parameter for regular crystal is 0.3609 nm\n", "lattice parameter for sample A is 0.3673 nm\n", "lattice parameter for sample B is 0.361 nm\n", "lattice parameter of sample A is 1.75% greater than that of pure copper\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=1;\n", "k=1;\n", "l=1; #miller indices\n", "lamda=0.152; #wavelength(nm)\n", "D=0.2552; #diameter(nm)\n", "theta1=21*math.pi/180; #angle(radian)\n", "theta2=(21+(23/60))*math.pi/180; #angle(radian)\n", "\n", "#Calculation\n", "a=D*math.sqrt(2); #lattice parameter for regular crystal(nm)\n", "d111_1=lamda/(2*math.sin(theta1));\n", "alpha1=d111_1*math.sqrt(h**2+k**2+l**2); #lattice parameter for sample A(nm)\n", "d111_2=lamda/(2*math.sin(theta2));\n", "alpha2=d111_2*math.sqrt(h**2+k**2+l**2); #lattice parameter for sample B(nm)\n", "\n", "#Result\n", "print \"lattice parameter for regular crystal is\",round(a,4),\"nm\"\n", "print \"lattice parameter for sample A is\",round(alpha1,4),\"nm\"\n", "print \"lattice parameter for sample B is\",round(alpha2,3),\"nm\"\n", "print \"lattice parameter of sample A is 1.75% greater than that of pure copper\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example number 31, Page number 220" ] }, { "cell_type": "code", "execution_count": 131, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the value of h**2+k**2+l**2 is 11.69\n", "answer given in the book is wrong\n", "highest possible values of (hkl) are (222)\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "h=1;\n", "k=1;\n", "l=1; #miller indices\n", "lamda=0.154; #wavelength of X-rays(nm)\n", "D=0.228; #diameter(nm)\n", "\n", "#Calculation\n", "x=lamda/2;\n", "y=2*D/(x*math.sqrt(h**2+k**2+l**2));\n", "z=y**2;\n", "\n", "#Result\n", "print \"the value of h**2+k**2+l**2 is\",round(z,2)\n", "print \"answer given in the book is wrong\"\n", "print \"highest possible values of (hkl) are (222)\"" ] } ], "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 }