{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#2: Crystal Structures"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.1, Page number 2.23"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"lattice constant is 4.0 *10**-10 m\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"M=60.2; #molecular weight\n",
"Na=6.023*10**26; #avagadro number(kg/mole)\n",
"n=4; \n",
"rho=6250; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"a=(n*M/(rho*Na))**(1/3); #lattice constant(m)\n",
"\n",
"#Result\n",
"print \"lattice constant is\",round(a*10**10),\"*10**-10 m\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.2, Page number 2.23"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"density is 8.93 gm/cm**3\n",
"answer 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",
"M=63.5; #molecular weight\n",
"Na=6.023*10**26; #avagadro number(kg/mole)\n",
"n=4; \n",
"r=1.278*10**-8; #atomic radius(cm)\n",
"\n",
"#Calculation\n",
"a=2*math.sqrt(2)*r; #lattice constant(m)\n",
"rho=n*M/(a**3*Na); #density(kg/cm**3)\n",
"\n",
"#Result\n",
"print \"density is\",round(rho*10**3,2),\"gm/cm**3\"\n",
"print \"answer in the book varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.3, Page number 2.24"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ratio of densities is 0.92\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"pf_BCC=math.pi*math.sqrt(3)/8; #packing factor for BCC\n",
"pf_FCC=math.pi/(3*math.sqrt(2)); #packing factor of FCC\n",
"\n",
"#Calculation\n",
"r=pf_BCC/pf_FCC; #ratio of densities\n",
"\n",
"#Result\n",
"print \"ratio of densities is\",round(r,2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.4, Page number 2.24"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"lattice constant is 2.8687 angstrom\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"M=55.85; #molecular weight\n",
"Na=6.02*10**26; #avagadro number(kg/mole)\n",
"n=2; \n",
"rho=7860; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"a=(n*M/(rho*Na))**(1/3); #lattice constant(m)\n",
"\n",
"#Result\n",
"print \"lattice constant is\",round(a*10**10,4),\"angstrom\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.5, Page number 2.24"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"lattice constant is 5.6 angstrom\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"M=58.5; #molecular weight\n",
"Na=6.02*10**26; #avagadro number(kg/mole)\n",
"n=4; \n",
"rho=2189; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"a=(n*M/(rho*Na))**(1/3); #lattice constant(m)\n",
"\n",
"#Result\n",
"print \"lattice constant is\",round(a*10**10,1),\"angstrom\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.6, Page number 2.25"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"lattice constant is 3.517 angstrom\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"M=6.94; #molecular weight\n",
"Na=6.02*10**26; #avagadro number(kg/mole)\n",
"n=2; \n",
"rho=530; #density(kg/m**3)\n",
"\n",
"#Calculation\n",
"a=(n*M/(rho*Na))**(1/3); #lattice constant(m)\n",
"\n",
"#Result\n",
"print \"lattice constant is\",round(a*10**10,3),\"angstrom\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.7, Page number 2.25"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"percent volume change is 0.493 %\n",
"answer 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",
"r1=1.258*10**-10; #radius(m)\n",
"r2=1.292*10**-10; #radius(m)\n",
"\n",
"#Calculation\n",
"a_bcc=4*r1/math.sqrt(3);\n",
"v=a_bcc**3;\n",
"V1=v/2;\n",
"a_fcc=2*math.sqrt(2)*r2;\n",
"V2=a_fcc**3/4;\n",
"V=(V1-V2)*100/V1; #percent volume change is\",V,\"%\"\n",
"\n",
"#Result\n",
"print \"percent volume change is\",round(V,3),\"%\"\n",
"print \"answer in the book varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.8, Page number 2.26"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of atoms/m**3 is 1.77 *10**29\n",
"density of diamond is 3534.47 kg/m**3\n",
"answer in the book is wrong\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.356*10**-9; #cube edge(m)\n",
"w=12; #atomic weight\n",
"Na=6.02*10**26; #avagadro number(kg/mole)\n",
"\n",
"#Calculation\n",
"n=8/(a**3); #number of atoms/m**3\n",
"m=w/Na; #mass(kg)\n",
"rho=m*n; #density of diamond(kg/m**3)\n",
"\n",
"#Result\n",
"print \"number of atoms/m**3 is\",round(n/10**29,2),\"*10**29\"\n",
"print \"density of diamond is\",round(rho,2),\"kg/m**3\"\n",
"print \"answer in the book is wrong\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.9, Page number 2.26"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"maximum radius of sphere is 0.414 r\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"from sympy import *\n",
"\n",
"#Variable declaration\n",
"r=Symbol('r')\n",
"\n",
"#Calculation\n",
"a=4*r/math.sqrt(2);\n",
"R=(4*r/(2*math.sqrt(2)))-r; #maximum radius of sphere\n",
"\n",
"#Result\n",
"print \"maximum radius of sphere is\",round(R/r,3),\"r\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 2.10, Page number 2.26"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"radius of largest sphere is 0.155 r\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"from sympy import *\n",
"\n",
"#Variable declaration\n",
"r=Symbol('r')\n",
"\n",
"#Calculation\n",
"a=4*r/math.sqrt(3);\n",
"R=(a/2)-r; #radius of largest sphere\n",
"\n",
"#Result\n",
"print \"radius of largest sphere is\",round(R/r,3),\"r\""
]
}
],
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"file_extension": ".py",
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