microwavediffraction_2010.pdfxraydiffraction_2010.pdfMicrowave Diffraction Introduction Microwaves have wavelengths of the order of centimeters, and thus will interfere with objects which are of a similar size, thus creating "macroscopic diffraction". This is interesting because one can readily see the crystal structure which is diffracting the microwaves, in contrast to the atomic structure which diffraction x-rays. The diffraction theory is the same as the Bragg theory which applies to electron and X-ray diffraction. Useful Topics you should know: Bragg Diffraction: http://www.doitpoms.ac.uk/tlplib/xray-diffraction/index.php Miller Indices: http://www.doitpoms.ac.uk/tlplib/miller_indices/lattice_index.php In this lab you will perform experiments typically done with visible light (reflection, refraction, interference) with microwaves instead to see that the physics remains the same independent of wavelength. In particular, you will have the opportunity to explore diffracting from multiple planes in a crystal, which you can see, to gain a better understanding of how crystal diffraction works. Equipment Pasco WA-9314B Microwave Optics set Procedure 1. Familiarize yourself with the use and detection of microwaves using the Transmitter and receiver (Expt 1) 2. Determine the wavelength of the microwaves (Expt 8), compare it with direct measurement of (Expt 3) 3. Perform the double-slit interference experiment as a pre-cursor to the crystal diffraction (Expt 6) 4. Perform the crystal diffraction experiment (Expt 12) including the investigation of the (110) and (210) planes References David J. Griffiths, Introduction to Electrodynamics, Prentice Hall, Englewood Cliffs, New Jersey (1989). D. W. Preston and E. R. Dietz, The Art of Experimental Physics, Wiley, New York(1991). C. H. Townes and A. L. Schawlow, Microwave Spectroscopy, Dover, New York (1975). H. C. Torrey and C. A. Whitmer, Crystal Rectifiers, MIT Radiation Lab, McGraw Hill, New York (1948).X-Ray Diffraction Introduction (From University of Florida Advanced Physics Laboratory Manual) When an electron beam of energy around 20 keV strikes a metal target, two different processes produce x-rays. In one process, the deceleration of beam electrons from collisions with the target produces a broad continuum of radiation called bremsstrahlung having a short wavelength limit that arises because the energy of the photon hc/ ¸can be no larger than the kinetic energy of the electron. In the other process, beam electrons knock atomic electrons in the target out of inner shells. When electrons from higher shells fall into the vacant inner shells, a series of discrete xrays lines characteristic of the target material are emitted. In our machine, which has a copper target,only two emission lines are of appreciable intensity. Copper K x-rays ( = 0:1542 nm) are produced when an n = 2 electron makes a transition to a vacancy in the n = 1 shell. A weaker K xray with a shorter wavelength ( = 0:1392 nm) occurs when the vacancy is filled by an n = 3 electron. Thus, the spectrum of x-rays from an x-ray tube consists of the discrete lines superimposed on the Bremsstrahlung continuum. This spectrum can be analyzed in much the same way that a visible spectrum is analyzed using a grating. Because x-rays have much smaller wavelengths than visible light, the grating spacing must be much smaller. A single crystal with its regularly spaced, parallel planes of atoms is often used as a grating for x-ray spectroscopy. The incident x-ray wave is reflected specularly as it leaves the crystal planes, but most of the wave energy continues through to subsequent planes where additional reflected waves are produced. The path length difference for waves reflected from successive planes is 2d sin where d is the distance between atomic planes. Note that the scattering angle (the angle between the original and outgoing rays) is 2. Constructive interference of the reflected waves occurs when 2d sin  is equal to an integer number of wavelengths n For more detail about the theory, the Tel-X-Ometer manual has a lengthy explanation, as does the Art of Experimental Physics (excerpt from the textbook is linked here), which is available in hardcopy in the classroom. The first two chapters of C. Kittel, Introduction to Solid State Physics, or an equivalent text such as Fundamentals of Modern Physics by Eisberg also have good background on diffraction. In the Tel-X-Ometer, the x-rays from the tube are collimated to a thick line and reflected from the crystal placed on the sample table. The detector, a Geiger-Muller (GM) tube, is placed behind collimating slits on the detector arm which can be placed at various scattering angles 2. In order to obey the Bragg condition, the crystal must rotate to an angle  when the detector is at an angle 2. This  : 2 relationship is maintained by gears under the sample table. Equipment- X-ray diffraction system (Tel-X-Ometer) experiment manual and its setup manual - Geiger-Müller tube and stepping motor - Computer and interface ( Labview software) - Alkali halide large single crystals - Counter and ratemeter - Radiation safety guide (just in case you want to know more) Theory Questions: What does the x-ray spectrum look like that is emitted from the x-ray tube? How does the Geiger-Müller tube work? Procedure 1. Please read the Tel-X-Ometer setup manual (particularly sections 10.1-12.5), and any sections regarding safety features. Realize, you are working with a radioactive source, and thus should be aware of any possible hazards. 2. To operate the Tel-X-Ometer: a. To open or close the scatter shield (the main cover), the whole shield must be displaced to the right or the left of center, depending on the position of the detector. b. To turn on the power to the unit, turn POWER ON key on the control panel; the unit will only function when the TIME SWITCH is rotated away from zero, and when the key is turned ON. This is to ensure that the x-rays only turn on when enclosed within the leaded glass. The filament of the x-ray tube should then be illuminated. Wait 5 minutes, then depress the X-RAYS ON switch (the red light will turn on). c. Use the radiation test kit (Geiger-Mueller counter at the gamma ray experiment) to measure radiation levels outside the unit when x-rays are on (in fact, this does not accurately detect x-rays. Why?). d. The Ratemeter