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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3: Metallic Crystal Structure"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.1 Page No: 44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determination of FCC Unit Cell Volume\n",
"\n",
"#Given\n",
"#For FCC a=2*R*math.sqrt(2)\n",
"from sympy import Symbol\n",
"\n",
"#Calculation \n",
"R=Symbol('R') \n",
"#Edge Length\n",
"a=2*R*round(math.sqrt(2),2)\n",
"#Volume determination\n",
"V=a**3\n",
"\n",
"#result\n",
"print\"Volume is\",V,\" m**3\"\n",
"print\"which is also equal to 16*sqrt(2)*R**3\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Volume is 22.425768*R**3 m**3\n",
"which is also equal to 16*sqrt(2)*R**3\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.2 Page No: 44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Computation of the Atomic Packing Factor for FCC\n",
"\n",
"#Given\n",
"#for FCC no. of atoms are 4\n",
"n=4\n",
"#For FCC a=2*R*math.sqrt(2)\n",
"R=1 #say\n",
"\n",
"#Calculation\n",
"#Edge Length\n",
"a=2*R*math.sqrt(2)\n",
"#Volume determination of cube\n",
"Vc=a**3\n",
"#Volume of sphere\n",
"Vs=n*4*math.pi*R**3/3.0\n",
"#Atomic packing Fraction\n",
"APF=Vs/Vc\n",
"\n",
"#Result\n",
"print\"Atomic packing fraction is\",round(APF,2)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Atomic packing fraction is 0.74\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.3 Page No: 45"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Theoretical Density Computation for Copper\n",
"\n",
"#Given\n",
"R=1.28*10**-8 #Atomic radius in cm\n",
"A_Cu=63.5 #Atomic wt of copper\n",
"n=4 #For FCC\n",
"Na=6.023*10**23 #Avogadro no.\n",
"\n",
"#Calculation\n",
"a=2*R*math.sqrt(2)\n",
"Vc=a**3\n",
"den=n*A_Cu/(Vc*Na)\n",
"\n",
"#result\n",
"print\"Density is \",round(den,2),\"g/cm**3\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Density is 8.89 g/cm**3\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.6 Page No: 52"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determination of Directional Indices\n",
"\n",
"#Given\n",
"#Projection of given vector\n",
"a=1/2.0\n",
"b=1\n",
"c=0\n",
"\n",
"x=[2*a,2*b,2*c]\n",
"\n",
"#Result\n",
"print\"The intercept for the given plane is\",x\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The intercept for the given plane is [1.0, 2, 0]\n"
]
}
],
"prompt_number": 44
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.8 Page No: 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determination of Directional Indices for a Hexagonal Unit Cell\n",
"\n",
"#Given\n",
"#Projection in terms of unit cell parameter\n",
"du=1\n",
"dv=1\n",
"dw=1\n",
"\n",
"#Calculation\n",
"#For hexagonal system\n",
"u=(2*du-dv)/3.0\n",
"v=(2*dv-du)/3.0\n",
"t=-(u+v)\n",
"w=dw\n",
"\n",
"x=[3*u,3*v,3*t,3*w]\n",
"print\"The indices for the given directions are\",x\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The indices for the given directions are [1.0, 1.0, -2.0, 3]\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.9 Page No: 56"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determination of Planar (Miller) Indices\n",
"\n",
"#Given\n",
"a=-1\n",
"b=1/2.0\n",
"\n",
"\n",
"#Calculation\n",
"#Reciprocal\n",
"l=0 #Reciprocal of infinity\n",
"m=1/a\n",
"n=1/b\n",
"x=[l,m,n]\n",
"\n",
"#Result\n",
"print\"The intercept for the given plane is\",x\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The intercept for the given plane is [0, -1, 2.0]\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.11 Page No: 59"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determination of Miller\u2013Bravais Indices for a Plane Within a Hexagonal Unit Cell\n",
"\n",
"#Intersection in terms of lattics Parameters\n",
"h=1 #Reciprocal of intersection point\n",
"k=-1\n",
"l=1\n",
"i=-(h+k)\n",
"\n",
"#Calculation\n",
"x=[h,k,i,l]\n",
"\n",
"#Result\n",
"print\"The indices of plane are\",x\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The indices of plane are [1, -1, 0, 1]\n"
]
}
],
"prompt_number": 31
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.12 Page No: 70"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Interplanar Spacing\n",
"\n",
"#Given\n",
"a=0.2866 #Lattice parameter in nm\n",
"h=2\n",
"k=2\n",
"l=0\n",
"\n",
"#Calculation\n",
"import math\n",
"#(a)\n",
"d_hkl=a/(math.sqrt(h**2+k**2+l**2))\n",
"\n",
"#(b)Diffraction Angle Computations\n",
"lam=0.1790 #Wavelength in nm\n",
"n=1\n",
"theta=math.asin(n*lam/(2*d_hkl))\n",
"\n",
"#Result\n",
"print\"(a)Interplanar spacing is \",round(d_hkl,4),\"nm\"\n",
"print\"(b)Diffraction angle is \",round(2*theta*(180/math.pi),1),\"degree\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Interplanar spacing is 0.1013 nm\n",
"(b)Diffraction angle is 124.1 degree\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
