{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 1 CRYSTAL STRUCTURES"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1_4 pgno:10"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a= 1.0\n",
"r=a/2 = 0.5\n",
"Volume of one atom ,v=((4∗%pi∗(rˆ3))/3)= 0.523598775598\n",
"Total Volume of the cube ,V=aˆ3 = 1.0\n",
"Fp(S.C)=(v∗100/V)= 52.3598775598\n"
]
}
],
"source": [
"#exa 1.4\n",
"from math import pi\n",
"a=1.\n",
"print \"a= \",a # initializing value of lattice constant(a)=1.\n",
"r=a/2.\n",
"print \"r=a/2 = \",r # initializing value of radius of atom for simple cubic .\n",
"v=((4*pi*(r**3))/3)\n",
"print \"Volume of one atom ,v=((4∗%pi∗(rˆ3))/3)= \",v # calcuation . \n",
"V=a**3\n",
"print \"Total Volume of the cube ,V=aˆ3 = \",V # calcuation .\n",
"Fp=(v*100/V)\n",
"print \"Fp(S.C)=(v∗100/V)= \",Fp,# calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 1_5 pgno:11"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a= 1.0\n",
"Radius of the atoms,r=(sqrt(3)∗(aˆ2/4)) = 0.433012701892\n",
"Volume of two atom,v=((4∗pi∗(rˆ3))/3)∗2 = 0.680174761588\n",
"Total Volume of the cube ,V=aˆ3 = 1.0\n",
"Fp(B.C.C)=(v∗100/V)= 68.0174761588 %\n"
]
}
],
"source": [
"#exa 1.5\n",
"from math import sqrt\n",
"a=1.\n",
"print \"a= \",a # initializing value of lattice constant(a)=1.\n",
"r=(sqrt(3)*(a**2/4))\n",
"print \"Radius of the atoms,r=(sqrt(3)∗(aˆ2/4)) = \",r # initializing value of radius of atom for BCC.\n",
"v=((4*pi*(r**3))/3)*2\n",
"print \"Volume of two atom,v=((4∗pi∗(rˆ3))/3)∗2 = \",v # calcuation \n",
"V=a**3\n",
"print \"Total Volume of the cube ,V=aˆ3 = \",V # calcuation .\n",
"Fp=(v*100/V)\n",
"print \"Fp(B.C.C)=(v∗100/V)= \",Fp,\"%\" # calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_6 pgno:12"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a= 1\n",
"Radius of the atom,r=(a/(2∗sqrt(2)))= 0.353553390593\n",
"Volume of the four atom,v=(((4∗pi∗(rˆ3))/3)∗4)= 0.740480489693\n",
"Total volume of the cube ,V=aˆ3= 2\n",
"Fp(F.C.C)=(v∗100/V)= 37.0240244847 %\n"
]
}
],
"source": [
"#exa 1.6\n",
"a=1\n",
"print \"a= \",a # initializing value of lattice constant(a)=1.\n",
"r=(a/(2*sqrt(2)))\n",
"print \"Radius of the atom,r=(a/(2∗sqrt(2)))= \",r # initializing value of radius of atom for FCC .\n",
"v=(((4*pi*(r**3))/3)*4)\n",
"print \"Volume of the four atom,v=(((4∗pi∗(rˆ3))/3)∗4)= \",v # calcuation \n",
"V=a^3\n",
"print \"Total volume of the cube ,V=aˆ3= \",V # calcuation .\n",
"Fp=(v*100/V)\n",
"print \"Fp(F.C.C)=(v∗100/V)= \",Fp,\"%\" # calculation\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_8 pgno:14"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a= 1\n",
"Radius of the atom , r=(sqrt (3)∗a/8))= 0.216506350946\n",
"v=(((4∗pi∗(rˆ3))/3)∗8) = 0.340087380794\n",
"V=aˆ3= 2\n",
"Fp(Diamond)=(v∗100/V) = 17.0043690397 %\n"
]
}
],
"source": [
"#Exa 1.8 \n",
"a=1\n",
"print \"a= \",a # initializing value of lattice constant(a)=1.\n",
"r=((sqrt(3)*a/8))\n",
"print \"Radius of the atom , r=(sqrt (3)∗a/8))= \",r # initializing value of radius of atom for diamond .\n",
"v=(((4*pi*(r**3))/3)*8)\n",
"print \"v=(((4∗pi∗(rˆ3))/3)∗8) = \",v # calcuation .\n",
"V=a^3\n",
"print \"V=aˆ3= \",V # calcuation .\n",
"Fp=(v*100/V)\n",
"print \"Fp(Diamond)=(v∗100/V) = \",Fp,\"%\" # calculation\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_9 pgno:14"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a = 5e-08 cm\n",
"Radius of the atom,r=(sqrt(3)∗(a/4))= 2.16506350946e-08\n",
"Volume of the two atoms ,v=((4∗pi∗(rˆ3))/3)∗2= 8.50218451985e-23\n",
"Total Volume of the cube ,V=aˆ3 = 1.25e-22\n",
"Fp(B.C.C)=(v∗100/V) = 68.0174761588 %\n"
]
}
],
"source": [
"#exa 1.9\n",
"a=5*10**-8\n",
"print \"a = \",a,\" cm\" # initializing value of lattice constant .\n",
"r=(sqrt(3)*(a/4))\n",
"print \"Radius of the atom,r=(sqrt(3)∗(a/4))= \",r # initializing value of radius of atom for BCC.\n",
"v=((4*pi*(r**3))/3)*2\n",
"print \"Volume of the two atoms ,v=((4∗pi∗(rˆ3))/3)∗2= \",v # calcuation .\n",
"V=a**3\n",
"print \"Total Volume of the cube ,V=aˆ3 = \",V # calcuation .\n",
"Fp=(v*100/V)\n",
"print \"Fp(B.C.C)=(v∗100/V) = \",Fp,\"%\" # calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_10 pgno:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x intercept = 1\n",
"y intercept = inf\n",
"z intercept = inf\n",
"miller indices ,h=(1/x )= [1]\n",
"k=(1/y)= [0.0]\n",
"l=(1/z) = [0.0]\n"
]
}
],
"source": [
"#exa 1.10\n",
"x=1\n",
"print \"x intercept = \",x # initializing value of x intercept .\n",
"y=float('inf')\n",
"print \"y intercept = \",y # initializing value of y intercept .\n",
"z=float('inf')\n",
"print \"z intercept = \",z # initializing value of z intercept .\n",
"h=[1/x]\n",
"print \"miller indices ,h=(1/x )= \",h # calculation\n",
"k=[1/y]\n",
"print \"k=(1/y)= \",k # calculation\n",
"l=[1/z]\n",
"print \"l=(1/z) = \",l # calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_11 pgno:15"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x intercept = inf\n",
"y intercept = inf\n",
"z intercept = 1\n",
"miller indices ,h=[1/x] = [0.0]\n",
"k=[1/y] = [0.0]\n",
"l=[1/z] = [1]\n"
]
}
],
"source": [
"#exa 1.11\n",
"x=float('inf')\n",
"print \"x intercept = \",x # initializing of x intercept .\n",
"y=float('inf') \n",
"print\"y intercept = \",y # initializing of Y intercept .\n",
"z=1\n",
"print \"z intercept = \",z # initializing of Z intercept .\n",
"h=[1/x]\n",
"print \"miller indices ,h=[1/x] = \",h # calculation\n",
"k=[1/y]\n",
"print \"k=[1/y] = \",k # calculation \n",
"l=[1/z]\n",
"print \"l=[1/z] = \",l # calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_12 pgno: 16"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x intercept = inf\n",
"y intercept = 1\n",
"z intercept = inf\n",
"miller indices ,h=[1/x] = [0.0]\n",
"k=[1/y] = [1]\n",
"l=[1/z] = [0.0]\n"
]
}
],
"source": [
"#exa 1.12\n",
"x=float('inf') \n",
"print \"x intercept = \",x # initializing of X intercept .\n",
"y=1\n",
"print \"y intercept = \",y # initializing of X intercept .\n",
"z=float('inf') \n",
"print \"z intercept = \",z # initializing of X intercept .\n",
"h=[1/x]\n",
"print \"miller indices ,h=[1/x] = \",h # calculation\n",
"k=[1/y]\n",
"print \"k=[1/y] = \",k # calculation \n",
"l=[1/z]\n",
"print \"l=[1/z] = \",l #calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_13 pgno:16"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x intercept = 1\n",
"y intercept = 1\n",
"z intercept = inf\n",
"miller indices ,h=[1/x] = [1]\n",
"k=[1/y] = [1]\n",
"l=[1/z] = [0.0]\n"
]
}
],
"source": [
"#exa 1.13\n",
"x=1\n",
"print \"x intercept = \",x # initializing of X intercept .\n",
"y=1\n",
"print \"y intercept = \",y # initializing of X intercept .\n",
"z=float('inf') \n",
"print \"z intercept = \",z # initializing of X intercept .\n",
"h=[1/x]\n",
"print \"miller indices ,h=[1/x] = \",h # calculation\n",
"k=[1/y]\n",
"print \"k=[1/y] = \",k # calculation \n",
"l=[1/z]\n",
"print \"l=[1/z] = \",l #calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_14 pgno:17"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x intercept = inf\n",
"y intercept = 1\n",
"z intercept = 1\n",
"miller indices ,h=[1/x] = [0.0]\n",
"k=[1/y] = [1]\n",
"l=[1/z] = [1]\n"
]
}
],
"source": [
"#exa 1.14\n",
"x=float('inf') \n",
"print \"x intercept = \",x # initializing of X intercept .\n",
"y=1\n",
"print \"y intercept = \",y # initializing of X intercept .\n",
"z=1\n",
"print \"z intercept = \",z # initializing of X intercept .\n",
"h=[1/x]\n",
"print \"miller indices ,h=[1/x] = \",h # calculation\n",
"k=[1/y]\n",
"print \"k=[1/y] = \",k # calculation \n",
"l=[1/z]\n",
"print \"l=[1/z] = \",l #calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_15 pgno:18"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x intercept = 2\n",
"y intercept = 2\n",
"z intercept = 2\n",
"common factor of all the intercept= 2\n",
"miller indices ,h=[c/x] = [1]\n",
"k=[c/y] = [1]\n",
"l=[c/z] = [1]\n"
]
}
],
"source": [
"x=2\n",
"print \"x intercept = \",x # initializing of X intercept .\n",
"y=2\n",
"print \"y intercept = \",y # initializing of X intercept .\n",
"z=2\n",
"print \"z intercept = \",z # initializing of X intercept .\n",
"c=2\n",
"print \"common factor of all the intercept= \",c # initializing value of common factor of all the intercepts .\n",
"h=[c/x]\n",
"print \"miller indices ,h=[c/x] = \",h # calculation\n",
"k=[c/y]\n",
"print \"k=[c/y] = \",k # calculation \n",
"l=[c/z]\n",
"print \"l=[c/z] = \",l #calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_16 pgno: 18"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wa = 28.1\n",
"D = 2.33 ram/cmˆ3\n",
"Na = 6.02e+23 atoms/mole\n",
"na =(Na∗D)/(Wa)= 4.99167259786e+22 atoms/cmˆ3\n"
]
}
],
"source": [
"#exa 1.16\n",
"Wa =28.1\n",
"print \"Wa = \",Wa # initializing value of atomic weight .\n",
"D=2.33\n",
"print \"D = \",D,\"ram/cmˆ3\" # initializing value of density .\n",
"Na=6.02*10**23\n",
"print \"Na = \",Na,\"atoms/mole\" # initializing value of avagadro number .\n",
"na =(Na*D)/(Wa)\n",
"print \"na =(Na∗D)/(Wa)= \",na,\" atoms/cmˆ3\" # calculation\n",
"# the value of na (number of atoms in 1 cmˆ3 of silicon ) , provided after calculation in the book is wrong."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_17 pgno: 18"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a= 5e-08 cm\n",
"N= 2\n",
"V=aˆ3 = 1.25e-22 cmˆ3\n",
"na=(no.of atoms in unit cell/Volume of theunit cell) =(N/(V))= 1.6e+22\n"
]
}
],
"source": [
"#exa 1.17\n",
"a=5*10**-8\n",
"print \"a= \",a,\"cm\" # initializing value of lattice constant .\n",
"N=2\n",
"print \"N= \",N # initializing value of no. of atoms in unit cell .\n",
"V=a**3\n",
"print \"V=aˆ3 = \",V,\"cmˆ3\" # initializing value of total Volume of the unit cell.\n",
"na =(N/(V))\n",
"print \"na=(no.of atoms in unit cell/Volume of theunit cell) =(N/(V))= \",na # calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_18 pgno: 18"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a = 5.43e-08 cm\n",
"N = 8\n",
"Number of atom in the cmˆ3,ns =(N/(aˆ3))= 4.99678310227e+22\n"
]
}
],
"source": [
"#exa 1.18\n",
"a=5.43*10**-8\n",
"print \"a = \",a,\"cm\" # initializing value of lattice constant .\n",
"N=8\n",
"print \"N = \",N # initializing value of no. of atoms in a unit cell .\n",
"ns =(N/(a**3))\n",
"print \"Number of atom in the cmˆ3,ns =(N/(aˆ3))= \",ns # calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_19 pgno: 18"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a = 5.43e-08 cm\n",
"Wa = 28.1\n",
"Na = 6.02e+23\n",
"ns = 50000000000000000000000 atoms/cmˆ3\n",
"Density of silicon ,D =(ns∗Wa)/(Na)= 2.33388704319 gm/cmˆ2\n"
]
}
],
"source": [
"#exa 1.19\n",
"a=5.43*10**-8\n",
"print \"a = \",a,\"cm\" # initializing value of lattice constant .\n",
"Wa =28.1\n",
"print \"Wa = \",Wa # initializing value of atomic weight .\n",
"Na=6.02*10**23\n",
"print \"Na = \",Na # initializing value of avagdro number .\n",
"ns =5*10**22\n",
"print \"ns = \",ns,\"atoms/cmˆ3\" # initializing value of atoms/cmˆ3.\n",
"D =(ns*Wa)/(Na)\n",
"print \"Density of silicon ,D =(ns∗Wa)/(Na)= \",D,\" gm/cmˆ2\" # calculation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## example 1_20 pgno: 19"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a = 4.75e-08 cm\n",
"N = 4\n",
"na =(N/(aˆ3))= 3.73232249599e+22\n"
]
}
],
"source": [
"#exa 1.20\n",
"a=4.75*10**-8\n",
"print \"a = \",a,\"cm\" # initializing value of lattice constant .\n",
"N=4\n",
"print \"N = \",N # initializing value of number of atoms in the unit cell .\n",
"na =(N/(a**3))\n",
"print \"na =(N/(aˆ3))=\",na # calculation"
]
}
],
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"file_extension": ".py",
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