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UMass Amherst CHEM 242 - Experiment 2b X-Ray Diffraction

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Experiment 2b X-Ray Diffraction* * Adapted from “Teaching General Chemistry: A Materials Science Companion” by A. B. Ellis et al.: ACS, Washington, DC (1993). Introduction Inorganic chemists, physicists, geologists, and materials scientists use X-ray diffraction to determine molecular structures in the solid state. Depending on the type of sample and the information desired, a number of diffraction techniques are available: however, they all depend on the same principles of diffraction. In this laboratory experience, you will learn how diffraction works using optical diffraction, and identify an unknown mineral from its powder x-ray diffraction pattern. You will work with a partner for the optical diffraction experiments, but everyone must turn in their own report. The lab report will consist of a separate sheet of paper with your typed answers to the questions from the various sections, a data table, and sample calculations. Optical Diffraction Experiments Purpose To discover how a diffraction pattern is related to a repeating dot array; to use the diffraction pattern to measure the dimensions of the repeating dot array. Introduction Diffraction of a wave by a periodic array is due to phase differences that result in constructive and destructive interference (illustrated in Figure 1). Diffraction can occur when waves pass through a periodic array if the repeat distance of the array is similar to the wavelength of the waves. Observation of diffraction patterns when beams of electrons, neutrons, or X-rays pass through crystalline solids thus serves as evidence both for the wave nature of those beams and for the periodic nature of the crystalline solids. However, X-rays are hazardous and they require special detectors.Figure 1. When waves line up (the oscillations are in phase), they add to give a bigger wave. When the peak of one wave is aligned with the trough of another, the waves annihilate each other. Atoms, with spacings of about 10–10 m, require X-rays to create diffraction patterns. In this experiment, you make a change of scale. By using dots with spacings of about 10–4 m, visible light can be used instead of X-rays to create diffraction patterns. You will shine red laser light (633 nm wavelength) through a slide containing repeating arrays of dots, and observe Fraunhofer diffraction (see Figure 2). Projection ScreenVisible Light Laser35mm slideLXφ Figure 2. The Fraunhofer diffraction experiment. Mathematically, the equations for Fraunhofer and Bragg diffraction (the basis of X-ray diffraction) are similar and embody the same functional dependence on the dot spacing (d), wavelength (λ), and scattering angle (φ or θ), (see Figure 3). In this experiment, you will first check how the size and orientation of the diffraction pattern is related to the periodic array that produced it, and then you will measure distances in diffraction pattern spacings in order to calculate the repeat distance for the array in the slide. By measuring the distances between the diffraction peaks (X) and the distance between the slide and the wall (L), shown in Figure 2, you can solve for φ by using the trigonometry definition that tan φ = X/L. Use of the Fraunhofer equation (below) then gives the lattice spacing (d) when the radiation wavelength (λ) is known. d sin φ = nλ Procedure Obtain slides containing greatly reduced versions of arrays like those in the bottom half of Figure 4. Each photographic slide contains eight patches with a different periodic array. Question 1. Look through a slide at a point source of white light. What do you see? Is the slide a diffraction grating? Why? Shine a He-Ne laser (633-nm wavelength), or a diode laser pointer (approximately 650 nm) at a white piece of paper several meters away. Fasten the laser in place. CAUTION: The laser ispotentially dangerous. Do not look directly into a laser beam or shine a laser toward other people, as damage to the eye can occur. Question 2. Look through a slide at the laser dot on the paper. What do you see? Why? Question 3. Put the slide in the laser beam and watch the paper. What happens? Light travels from the laser to the paper and then to your eye. Are the same results obtained if the beam goes through the slide before it hits the paper as after it hits the paper? Fraunhofer diffraction Bragg diffractionFor constructive interference, d sin φ = n λ For constructive interference, 2(d sin θ) = n λ }dθθθdd sin θd sin θ}}φdd sin φ}}dφ Figure 3. A comparison of Fraunhofer diffraction with Bragg diffraction. When waves are scattered by a periodic array, the path difference between any two waves must be a whole number of wavelengths, n, if the waves are to remain in phase and give constructive interference. Question 4. Pretend that you want to sketch the shape of the diffraction pattern from an array. Why should you use the laser light source? Should you shine the beam through the slide or look at the spot through the slide? Pretend that you want to measure the spacing between the spots. What method is easiest? Use a hand lens to examine the arrays on the slide. For ease of interpretation, you may prefer to keep a consistent orientation for the slide. Devise and conduct experiments to answer the following questions. You may need to sketch an array and the resulting diffraction pattern to answer some of the questions, and should include any measurements of distances.ABCDEGHF aceghfdb Figure 4. Arrays of dots that can be used to generate diffraction patterns with a laser. The actual patterns on the slide are those shown on the lower-half of the figure, and are much smaller.Question 5. This question regards how the orientations of the diffraction patterns relate to the orientation of the array of dots. Be sure to indicate which array leads to a particular diffraction pattern. For example, array e is a rectangular dot-array that leads to a rectangular diffraction pattern. The ‘long axis’ of the array exhibits shorter diffraction spacings due to the inverse relationship between lattice spacing and diffraction angle. What is the diffraction pattern of: A square array of dots? A rectangular array of dots? A parallelogram array of dots where the angle is not 90°? A hexagonal array of dots? Question 6. Find two similar arrays that differ only in size. How does the repeat distance of the array relate to the repeat distance of the


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