{
"metadata": {
"name": "Chapter5"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": "Crystal Physics"
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 5.1, Page number 149"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the Miller indices\n\n#Calculation\n#The plane has intercepts a,2b,3c along 3 crystal axes\n#lattice points are r = pa+qb+sc\n#therefore p = 1 q = 2 s = 3\n#miller indices are [1/p,1/q,1/s]\n\n#Result\nprint \"lattice points are p = 1 q = 2 s = 3\"\nprint \"miller indices are [1/p,1/q,1/s] or [1,1/2,1/3] or [6,3,2]\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "lattice points are p = 1 q = 2 s = 3\nmiller indices are [1/p,1/q,1/s] or [1,1/2,1/3] or [6,3,2]\n"
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 5.2, Page number 150"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the density of Si\n\n#importing modules\nimport math\n\n#Variable declaration\nn = 8; #number of atoms per cell\na = 5.43*10**-8; #lattice constant(cm)\nw = 28.1; #atomic weight(gm)\nN = 6.02*10**23; #avagadro number\n\n#Calculation\nac = n/(a**3); #atomic concentration(atoms/cm**3)\nd = ac*w/N; #density of Si(g/cm**3)\nd=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"density of Si is\",d,\"g/cm**3\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "density of Si is 2.333 g/cm**3\n"
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 5.3, Page number 151"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the surface density of atoms\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\na = 5; #lattice constant(Angstrom)\n\n#Calculation\na = a*10**-10; #lattice constant(m)\n#to calculate the planar concentration, only equilateral triangular region is considered of length a*math.sqrt(2) and height a*math.sqrt(3/2)\nl = a*math.sqrt(2); #length of face diagonal(m)\nh = a*math.sqrt(3/2); #height of triangle(m)\nA = l*h/2; #area of shaded portion(m**2)\n#every atom at the corner contributes 1/6 to this area.\nn111 = (3/6)*(1/A); #planar concentration(atoms/m**2)\n\n#Result\nprint \"surface density of atoms is\",n111,\"atoms/m**2\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "surface density of atoms is 2.30940107676e+18 atoms/m**2\n"
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 5.4, Page number 152"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the spacing of planes\n\n#importing modules\nimport math\n\n#Variable declaration\na = 4.049; #lattice constant(Angstrom)\nh = 2;\nk = 2;\nl = 0; #miller indices of(2 2 0)\n\n#Calculation\nd = a/math.sqrt(h**2+k**2+l**2); #spacing of planes(Angstrom)\nd=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"spacing of planes is\",d,\"Angstrom\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "spacing of planes is 1.432 Angstrom\n"
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 5.5, Page number 152"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the size of unit cell\n\n#importing modules\nimport math\n\n#Variable declaration\nd110 = 2.03; #distance between planes(Angstrom)\nh = 1;\nk = 1;\nl = 0; #miller indices of(1 1 0)\n\n#Calculation\na = d110*math.sqrt(h**2+k**2+l**2); #size of unit cell(Angstrom)\na=math.ceil(a*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"size of unit cell is\",a,\"Angstrom\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "size of unit cell is 2.871 Angstrom\n"
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 5.6, Page number 152"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the spacing of planes\n\n#importing modules\nimport math\n\n#Variable declaration\na = 5.64; #lattice constant(Angstrom)\nh1 = 1;\nk1 = 0;\nl1 = 0; #miller indices of(1 0 0)\nh2 = 1;\nk2 = 1;\nl2 = 0; #miller indices of(1 1 0)\nh3 = 1;\nk3 = 1;\nl3 = 1; #miller indices of(1 1 1)\n\n#Calculation\nd100 = a/math.sqrt(h1**2+k1**2+l1**2); #spacing of planes[100](Angstrom)\nd110 = a/math.sqrt(h2**2+k2**2+l2**2); #spacing of planes[110](Angstrom)\nd111 = a/math.sqrt(h3**2+k3**2+l3**2); #spacing of planes[111](Angstrom)\nd111=math.ceil(d111*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"spacing of plane [100] is\",d100,\"Angstrom\"\nprint \"spacing of plane [110] is\",round(d110),\"Angstrom\"\nprint \"spacing of plane [111] is\",d111,\"Angstrom\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "spacing of plane [100] is 5.64 Angstrom\nspacing of plane [110] is 4.0 Angstrom\nspacing of plane [111] is 3.26 Angstrom\n"
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 5.7, Page number 153"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the volume of unit cell\n\n#importing modules\nimport math\n\n#Variable declaration\nr = 1.605; #radius of atom(Angstrom)\n\n\n#Calculation\nr = r*10**-10; #radius of atom(m)\na = 2*r; #size of unit cell(m)\nc = a*math.sqrt(8/3);\nV = 3*math.sqrt(3)*a**2*c/2; #volume of unit cell(m**3)\n\n#Result\nprint \"volume of unit cell is\",V,\"m**3\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "volume of unit cell is 1.40330266432e-28 m**3\n"
}
],
"prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": "",
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}