The University of Michigan MSE 350-Fall 2007 Monday, October 8, 2007 ?Announcements ?Office Hours: today: after class (RG), 4-6 pm (LW: 2050 Dow); Tuesday: 10:30-11:30 am (RG) ?Suggested Reading: SOM 11.3 ?Homework #4: due Friday 10/12 ?Laue s Experiment ?Nanoworld Diffraction Slide ?Discovery Diffraction Slide ?Waves & Diffraction ?Bragg s Law The University of Michigan MSE 350-Fall 2007 Laue s Experiment (1912) If x-tals are composed of regularly spaced atoms which act as scattering centers for x-rays & if x-rays were EM waves w/ ~ interatomic spacing, then x-tals should diffract x-rays! 10 s keV anode cathode constructive interference transmission Laue diffraction pattern Proved that x-rays are waves!! e - The University of Michigan MSE 350-Fall 2007 Diffraction Experiment We will perform an analogous experiment using visible light and diffraction gratings: The University of Michigan MSE 350-Fall 2007 Nanoworld Diffraction Slide A B The University of Michigan MSE 350-Fall 2007 Diffraction Patterns with Red LED The University of Michigan MSE 350-Fall 2007 Comparison of Red & Blue LED: A The University of Michigan MSE 350-Fall 2007 Comparison of Red & Blue LED: B The University of Michigan MSE 350-Fall 2007 Discovery Diffraction Slide I The University of Michigan MSE 350-Fall 2007 Discovery Diffraction Slide II The University of Michigan MSE 350-Fall 2007 Investigation Questions ?What are the diffraction patterns of horizontal and vertical arrays of lines? ?What is the diffraction pattern of a square array of dots? ?How do the orientations of the diffraction patterns relate to the orientation of the array of dots? ?Find two similar arrays that differ only in size. Does an array with a smaller (larger) repeat distance give a diffraction pattern with a smaller (larger) repeat distance? The University of Michigan MSE 350-Fall 2007 Waves (reinforcement) (cancellation) phase = 180º phase = 0 or 360º The University of Michigan MSE 350-Fall 2007 What is Diffraction? Diffraction: Spatial redistribution of intensity of waves resulting from the presence of an object that causes variations of either the amplitude or phase of the waves ex.: diffraction of water waves in a ripple tank Interference pattern for water waves interfering circular waves incoming waves The University of Michigan MSE 350-Fall 2007 Single Particle vs. Crystal wave interacts with single particle wave interacts with crystal Particle scatters the incident beam uniformly in all directions! Scattered beams may add together in a few directions & reinforce each other to produce ?diffracted? beams The University of Michigan MSE 350-Fall 2007 Fraunhofer & Bragg Diffraction (parallel beams of light) for constructive interference: dsin =n for constructive interference: 2(dsin )=n The University of Michigan MSE 350-Fall 2007 Bragg s Law condition for constructive interference usually n=1 Why? Consider which planes are probed and what they are called! (Miller indices) The University of Michigan MSE 350-Fall 2007 Waves Out-of-Phase Bragg condition is NOT met!! (i.e. Bragg s Law is not satisfied) n integer The University of Michigan MSE 350-Fall 2007 Waves In-Phase Bragg condition is met!! (i.e. Bragg s Law is satisfied) n = 1 constructive interference Rachel S. Goldman MSE350-diffraction-8oct07b2.ppt