{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 9: X Rays"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.1: highest_order_of_reflectio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_1,pg 237\n",
"\n",
"d=4.255*10^-10\n",
"\n",
"lam=1.549*10^-10//wavelength of K-copper line\n",
"\n",
"n=1//theta is smallest when n=1\n",
"\n",
"theta=asin(lam/(2*d))//glancing angle\n",
"\n",
"theta=theta*(180/%pi)\n",
"\n",
"//max value of sin(theta)=1\n",
"\n",
"//for highest order\n",
"\n",
"nmax=((2*d)/lam)//highest bragg's order\n",
"\n",
"printf('smallest glancing angle\n')\n",
"\n",
"printf('theta=%.2f deg.',theta)\n",
"\n",
"printf('\nmaximum order of reflection\n')\n",
"\n",
"printf('nmax=%.2f',nmax)\n",
"\n",
"printf('\nsince fraction is meaningless for order nmax=5')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.2: find_plancks_constant.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_2,pg 237\n",
"\n",
"V=60*10^3\n",
"\n",
"c=3*10^8\n",
"\n",
"e=1.6*10^-19\n",
"\n",
"lam=0.194*10^-10//min. wavelength of x-rays\n",
"\n",
"h=(lam*e*V)/c\n",
"\n",
"printf('plancks constant\n')\n",
"\n",
"disp(h)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.3: find_wavelength_and_maximum_order_of_reflection.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_3,pg 238\n",
"\n",
"//for 110 plane\n",
"\n",
"a=3*10^-10//lattice parameter\n",
"\n",
"d=(a/sqrt(2))//d110=(a/sqrt((1^2)+(1^2)+0))\n",
"\n",
"theta=12.5*(%pi/180)//glancing angle\n",
"\n",
"n=1\n",
"\n",
"lam=2*d*sin(theta)//wavelength of x-ray\n",
"\n",
"nmax=((2*d)/lam)//highest order\n",
"\n",
"printf('wavelength of x-ray beam\n')\n",
"\n",
"disp(lam)\n",
"\n",
"printf('\nhighest braggs order\n')\n",
"\n",
"printf('nmax=%.2f',nmax)\n",
"\n",
"printf('\nfraction is meaningless so nmax=4')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.4: find_plancks_constant.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_4,pg 238\n",
"\n",
"d=2.81*10^-10\n",
"\n",
"theta=14*(%pi/180)//glancing angle\n",
"\n",
"lam=2*d*sin(theta)//min. wavelength\n",
"\n",
"e=1.6*10^-19\n",
"\n",
"V=9100\n",
"\n",
"c=3*10^8\n",
"\n",
"h=(lam*e*V)/c\n",
"\n",
"printf('plancks constant\n')\n",
"\n",
"disp(h)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.5: find_wavelength_of_line_A.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_5,pg 238\n",
"\n",
"//for line A-> 2*d*sin(thetaA)=lamA(n=1)\n",
"\n",
"thetaA=30*(%pi/180)//glancing angle for line A\n",
"\n",
"//for line B-> 2*d*sin(thetaB)=3*lamB(n=3)\n",
"\n",
"thetaB=60*(%pi/180)\n",
"\n",
"lamB=0.97*10^-10\n",
"\n",
"d=(3*lamB)/(2*sin(thetaB))\n",
"\n",
"lamA=2*d*sin(thetaA)//wavelength of line A\n",
"\n",
"printf('wavelength of line A\n')\n",
"\n",
"disp(lamA)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.6: find_wavelength_of_x_rays.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_6,pg 239\n",
"\n",
"a=3.615*10^-10\n",
"\n",
"d111=a/sqrt(1+1+1)//for 111 plane \n",
"\n",
"theta=21.7*(%pi/180)//converting into radian\n",
"\n",
"lam=2*d111*sin(theta)\n",
"\n",
"printf('wavelength of X-rays\n')\n",
"\n",
"disp(lam)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.7: find_min_wavelength_and_glancing_angle.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_7,pg 239\n",
"\n",
"V=50*10^3\n",
"\n",
"lam=(12400/V)*10^-10\n",
"\n",
"n=4//FCC crystal\n",
"\n",
"m=74.6\n",
"\n",
"N=6.022*10^26\n",
"\n",
"rho=1.99*10^3\n",
"\n",
"a=(((n*m)/(N*rho))^(1/3))\n",
"\n",
"//for kcl ionic crystal\n",
"\n",
"d=a/2\n",
"\n",
"theta=asin(lam/(2*d))\n",
"\n",
"theta=theta*(180/%pi)\n",
"\n",
"printf('min. wavelength of spectrum from tube\n')\n",
"\n",
"disp(lam)\n",
"\n",
"printf('glancing angle for that wavelength\n')\n",
"\n",
"printf('theta=%.2f deg.',theta)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.8: identify_type_of_crystal.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_8,pg 239\n",
"\n",
"//from bragg's law\n",
"\n",
"//2*d*sin(theta)=n*lam\n",
"\n",
"n=1\n",
"\n",
"theta1=5.4*(%pi/180)\n",
"\n",
"theta2=7.6*(%pi/180)\n",
"\n",
"theta3=9.4*(%pi/180)\n",
"\n",
"d100=lam/2*sin(theta1)\n",
"\n",
"d110=lam/2*sin(theta2)\n",
"\n",
"d111=lam/2*sin(theta3)\n",
"\n",
"printf('ratio of interplannar spacing \n(1/d100):(1/d110):(1/d111)=')\n",
"\n",
"printf('%.2f:',sin(theta1));printf('%.2f:',sin(theta2));printf('%.2f',sin(theta3));\n",
"\n",
"printf('\nas ratio (1/d100):(1/d110):(1/d111)=1:sqrt(2):sqrt(3)this relation is valid for simple cubic crystal therefore, this is a SCC crystal')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 9.9: find_interplannar_spacing.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//chapter9,Example9_9,pg 240\n",
"\n",
"lam=0.58*10^-10\n",
"\n",
"theta1=6.5*(%pi/180)\n",
"\n",
"theta2=9.15*(%pi/180)\n",
"\n",
"theta3=13*(%pi/180)\n",
"\n",
"//from bragg's law\n",
"\n",
"d1=lam/(2*sin(theta1))*10^10\n",
"\n",
"d2=lam/(2*sin(theta2))*10^10\n",
"\n",
"d3=lam/(2*sin(theta3))*10^10\n",
"\n",
"printf('interplannar spacing of crystal\n')\n",
"\n",
"printf('%.2f:',d1);printf('%.2f:',d2);printf('%.2f',d3);"
   ]
   }
],
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		   "language": "scilab",
		   "name": "scilab"
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		   "file_extension": ".sce",
		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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