Bragg Diffraction

• Purpose
• Introduction
• Methods
• Results
• Discussion

Purpose:  The purpose of this lab in physics was to:

• detect and to understand the Bragg diffraction of x-rays
• to measure the wavelength of the x-rays (electrons) using a NaCl crystal
• to be able to predict the diffraction for other crystals

Introduction:
    X-rays were first discovered by Wilhelm Konrad Rontgen, who was awarded the first Nobel Prize in 1901 for his discovery.  The production of x-rays involve electrons bombarding a metal target anode at high energy, where the target anode is oriented at a position of 45^o to the electron beam and the x-rays are emitted at 90^o to the electron beam.  Keep in mind, these angles are approximate and the x-rays are actually being emitted at many angles in a broad path.  X-rays, despite being a possible hazard to health, are quite useful for studying crystal structure, the periodic table of elements, and for diagnosing medical conditions.
    The Telexometer apparatus we used in this lab has been designed with safety in mind, and is approved for use in colleges.  The x-ray tube has a safety leaded-shield to absorb all x-rays that are not in the experimental port, and the apparatus has a cover, which absorbs scattered rays and consists of interlocks, which prevent the x-rays from being generated when the cover is open.  Above all, the intensity of the x-rays is kept low and the rays would not be sufficient enough for anything other than analyzing crystal structure.  Due to the understanding that x-rays are electromagnetic radiation, we know that x-rays have a wavelength and can be quantified as photons according to the Planck’s radiation law, which we studied in the another laboratory exercise concerning the photoelectric effect.
     X-rays can be detected using a Geiger-Mueller tube, which is a transducer that gives a pulse output voltage for each radiation “particle” that is detected.  The pulse is then counted by a computer using a specialized program.  The display for the computer shows counts vs. the detector angle.  The Telexometer apparatus consists of a x-ray tube, a crystal holder, collimators at the source and the detector, and a G-M tube mounted on a moveable arm.  The computer is then used as a counting device, which gives us a graph of counts vs. detector angle (2q).  This program can then control the angle of the G-M tube, the number of counts, and can display the x-rays.  Bragg diffraction differs from that of optical diffraction due to a grating.  This is because the crystal (which serves as a grating) is three-dimensional, and consists of successive layers of crystal planes separated by the inter-atomic spacing (d).  The released x-rays penetrate the atomic layers of the crystal and are specularly scattered from each layer.  It is then at certain angles where the path-difference is a multiple of the wavelength and constructive interference results.  We can then calculate the Bragg condition using the equation 2dSin(q)=n*(wavelength).  This condition is shown in the below diagram of the NaCl crystal structure:

    The graph for the counts shows the K-alpha radiation, the K-beta radiation, and the Bremstrahlung radiation.  The K-alpha radiation is the radiation (photons released) that results from an electron in the K-level being replaced by a falling electron from the L-level.  K-beta radiation is the radiation that results from an electron in the K-level being replaced by a falling electron from the M-level.  K-beta radiation has a higher energy than K-alpha radiation, as well as a shorter wavelength.  The Bremstrahlung radiation is German for "breaking radiation".  It is the radiation that results from electrons coming to a stop and crashing into the anode.  This abrubt stop causes kinks in the field line, resulting in this radiation "noise" that we see in the background of our graphs.  The below Calvin and Hobbes comic shows a simulation of the breaking radiation and the "kinks" that result (Calvin represents the electron and Hobbes represents the opposing anode).  The only alteration is that the electrons don't even "try" to slow down as Calvin is attempting in this comic:

Methods:
    In order to detect Bragg diffraction from crystals, the surface of the crystal must be rotated with respect to the x-ray beam (q).  The detector arm must be rotated at twice the angle theta, in order to fulfill the Bragg condition.  We started the lab by mounting a NaCl crystal (with the dull surface being the reflecting surface of the x-rays) and activating the x-rays.  We programmed the computer so that it would gather data from a detector angle of 20^o up to 115^o.  The computer then automatically displays a graph of the counting rate vs. detector angle, which was then converted to a Graphical Analysis file.  We then measured the angles for the K-alpha and K-beta peaks at the 1st, 2nd, and 3rd order wavelengths.  We used these diffraction angle values to calculate the wavelengths and determine which was the K-alpha and which was the K-beta wavelength.
    We repeated the above procedure with two more crystals, one being lithium flouride and the second being rhubium chloride.
 
 

Results:
    We determined that the K-alpha is the larger wavelength and the k-beta is the smaller wavelength.  The wavelengths and angles are shown in the below table:

    The wavelengths were determined using the Bragg equation and the calculated bond length (found to be 2.81 * 10-8 cm) which involves a literature value for the density of NaCl and Avogadro’s Number.  The calculated wavelengths and diffraction angles for lithium flouride (LiF) are in the below Table Two, and the calculated values for rubidium chloride (RbCl) are in the below Table Three.

Discussion:
    It can be observed from this data that the wavelengths for K-alpha are the same for the 1st, 2nd, 3rd and so forth order.  The same phenomenon can be seen with K-beta.  We can determine that the larger peaks on the three graphs seem to signify the K-alpha peaks, and the 1st smaller peak signifies the K-beta peak.  This bright peak can be understood as K-alpha radiation.  Even though these two emissions are repeated at larger diffraction angles for the 2nd and 3rd order, we can understand that the emissions are wavelengths that are characteristic of the anode material, and the wavelengths are the same for each order.
 

The line used in this webpage was a free gif animation obtained from the website:
http://www.world-of-animated-gifs.com