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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 16: Crystal Physics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.1, Page 820"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"p = 1; q = 2; r = 3; # Coefficients of intercepts along three axes\n",
"\n",
"#Calculations\n",
"p_inv = 1./p; # Reciprocate the first coefficient\n",
"q_inv = 1./q; # Reciprocate the second coefficient\n",
"r_inv = 1./r; # Reciprocate the third coefficient\n",
"mul_fact = p*q*r; # Find l.c.m. of m,n and p\n",
"m1 = p_inv*mul_fact; # Clear the first fraction\n",
"m2 = q_inv*mul_fact; # Clear the second fraction\n",
"m3 = r_inv*mul_fact; # Clear the third fraction\n",
"\n",
"#Result\n",
"print \"The required miller indices are : (%d %d %d) \"%(m1,m2,m3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The required miller indices are : (6 3 2) \n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.2, Page 820"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"p = 2; q = 3; r = -4; # Coefficients of intercepts along three axes\n",
"\n",
"#Calculations\n",
"p_inv = 1./p; # Reciprocate the first coefficient\n",
"q_inv = 1./q; # Reciprocate the second coefficient\n",
"r_inv = 1./r; # Reciprocate the third coefficient\n",
"mul_fact = p*q*abs(r); # Find l.c.m. of m,n and p\n",
"m1 = p_inv*mul_fact; # Clear the first fraction\n",
"m2 = q_inv*mul_fact; # Clear the second fraction\n",
"m3 = r_inv*mul_fact; # Clear the third fraction\n",
"\n",
"#Result\n",
"print \"The miller indices of laticce plane are : (%d %d %d) \"%(m1,m2,m3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The miller indices of laticce plane are : (12 8 -6) \n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.3, Page 821"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy\n",
"\n",
"#Variable declaration\n",
"p = 3; q = 4; r = numpy.inf; # Coefficients of intercepts along three axes\n",
"\n",
"#Calculations\n",
"p_inv = 1./p; # Reciprocate the first coefficient\n",
"q_inv = 1./q; # Reciprocate the second coefficient\n",
"r_inv = 1./r; # Reciprocate the third coefficient\n",
"mul_fact = p*q; # Find l.c.m. of m,n and p\n",
"m1 = p_inv*mul_fact; # Clear the first fraction\n",
"m2 = q_inv*mul_fact; # Clear the second fraction\n",
"m3 = r_inv*mul_fact; # Clear the third fraction\n",
"\n",
"#Result\n",
"print \"The miller indices of the given planes are : (%d %d %d) \"%(m1,m2,m3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The miller indices of the given planes are : (4 3 0) \n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.4, Page 822 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"p = 1.2; # First coefficient of intercept along X-axis, angstrom\n",
"a = 1.2\n",
"b = 1.8\n",
"c = 2.0; # Lattice parameters along three axes, angstrom\n",
"h = 2.\n",
"k = 3.\n",
"l = 1.; # Miller indices of lattice plane\n",
"\n",
"#Calculations\n",
"# As p:q:r = a/h:b/k:c/l, solving for q and r\n",
"q = p*(b/k)/(a/h); # Second coefficient of intercept along X-axis, angstrom \n",
"r = p*(c/l)/(a/h); # Third coefficient of intercept along X-axis, angstrom \n",
"\n",
"#Result\n",
"print \"The lengths of the intercepts on Y and Z axes are %3.1f angstrom and %3.1f angstrom respectively\"%(q, r)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The lengths of the intercepts on Y and Z axes are 1.2 angstrom and 4.0 angstrom respectively\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.5, Page 822"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"M = 58.5; # Molecular weight of NaCl, g-mole\n",
"rho = 2.198e+03; # Density of Nacl, kg per metre cube\n",
"n = 4; # No. of atoms per unit cell for an fcc lattice of NaCl crystal\n",
"NA = 6.023e+26; # Avogadro's No., atoms/k-mol\n",
"\n",
"#Calculations\n",
"# Volume of the unit cell is given by\n",
"# a^3 = M*n/(N*d)\n",
"# Solving for a\n",
"a = (n*M/(rho*NA))**(1./3); # Lattice constant of unit cell of NaCl\n",
"\n",
"#Result\n",
"print \"Lattice constant for the NaCl crystal = %4.2f angstrom\"%(a/1e-010)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Lattice constant for the NaCl crystal = 5.61 angstrom\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.6, Page 823"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"M = 119; # Molecular weight of KBr, g-mole\n",
"rho = 2.7; # Density of KBr, g per cm-cube\n",
"n = 4; # No. of atoms per unit cell for an fcc lattice of KBr crystal\n",
"NA = 6.023e+23; # Avogadro's No., atoms/mol\n",
"\n",
"#Calculations\n",
"# Volume of the unit cell is given by\n",
"# a^3 = M*n/(N*d)\n",
"# Solving for a\n",
"a = (n*M/(rho*NA))**(1./3); # Lattice constant of unit cell of KBr\n",
"\n",
"#Result\n",
"print \"Lattice constant for the KBr crystal = %4.2f angstrom\"%(a/1e-008)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Lattice constant for the KBr crystal = 6.64 angstrom\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.7, Page 823"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"M = 63.5; # Molecular weight of Cu, g-mole\n",
"rho = 8.96; # Density of Cu, g per cm-cube\n",
"n = 4; # No. of atoms per unit cell for an fcc lattice of Cu \n",
"NA = 6.023e+23; # Avogadro's No., atoms/mol\n",
"\n",
"#Calculations\n",
"# Volume of the unit cell is given by\n",
"# a^3 = M*n/(N*d)\n",
"# Solving for a\n",
"a = (n*M/(rho*NA))**(1./3); # Lattice constant of unit cell of Cu\n",
"d = a/sqrt(2); # Distance between the two nearest Cu atoms, angstrom \n",
"\n",
"#Results\n",
"print \"Lattice constant for the Cu crystal = %4.2f angstrom\"%(a/1e-008)\n",
"print \"The distance between the two nearest Cu atoms = %4.2f angstrom\"%(d/1e-008)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Lattice constant for the Cu crystal = 3.61 angstrom\n",
"The distance between the two nearest Cu atoms = 2.55 angstrom\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.8, Page 824"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"a = 1; # For simplicity assume lattice parameter of cubic crystal to be unity, unit\n",
"# For (011) planes\n",
"h = 0; k = 1; l = 1; # Miller Indices for planes in a cubic crystal\n",
"d_011 = a/(h**2+k**2+l**2)**(1./2); # The interplanar spacing for cubic crystals, m\n",
"print \"The interplanar spacing between consecutive (011) planes = a/sqrt(%d)\"%(1/d_011**2)\n",
"\n",
"# For (101) planes\n",
"h = 1; k = 0; l = 1; # Miller Indices for planes in a cubic crystal\n",
"d_101 = a/(h**2+k**2+l**2)**(1./2); # The interplanar spacing for cubic crystals, m\n",
"print \"The interplanar spacing between consecutive (101) planes = a/sqrt(%d)\"%(1/d_101**2)\n",
"\n",
"# For (112) planes\n",
"h = 1; k = 1; l = 2; # Miller Indices for planes in a cubic crystal\n",
"d_112 = a/(h**2+k**2+l**2)**(1./2); # The interplanar spacing for cubic crystals, m\n",
"print \"The interplanar spacing between consecutive (112) planes = a/sqrt(%d)\"%(1/d_112**2) #incorrect answer in textbook\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The interplanar spacing between consecutive (011) planes = a/sqrt(2)\n",
"The interplanar spacing between consecutive (101) planes = a/sqrt(2)\n",
"The interplanar spacing between consecutive (112) planes = a/sqrt(5)\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.9, Page 824"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"a = 4.2e-010; # Lattice parameter of cubic crystal, m\n",
"h = 3; k = 2; l = 1; # Miller Indices for planes in a cubic crystal\n",
"\n",
"#Calculations\n",
"d_321 = a/(h**2+k**2+l**2)**(1./2); # The interplanar spacing for cubic crystals, m\n",
"\n",
"#Result\n",
"print \"The interplanar spacing between consecutive (321) planes = %4.2f angstrom\"%(d_321/1e-010)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The interplanar spacing between consecutive (321) planes = 1.12 angstrom\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.10, Page 825"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"a = 2.5\n",
"b = 2.5\n",
"c = 1.8; # Lattice parameter of tetragonal crystal, angstrom\n",
"h = 1\n",
"k = 1\n",
"l = 1; # Miller Indices for planes in a tetragonal crystal\n",
"\n",
"#Calculations\n",
"d_hkl = 1/sqrt((h/a)**2+(k/b)**2+(l/c)**2); # The interplanar spacing for tetragonal crystals, m\n",
"\n",
"#Result\n",
"print \"The interplanar spacing between consecutive (111) planes = %4.2f angstrom\"%d_hkl\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The interplanar spacing between consecutive (111) planes = 1.26 angstrom\n"
]
}
],
"prompt_number": 27
}
],
"metadata": {}
}
]
}