Lecture_27

Lecture_27 - PHYS 342 Fall 2011 Lecture 27: The Structure...

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PHYS 342 Fall 2011 Lecture 27: The Structure of Crystalline Solids Ron Reifenberger Birck Nanotechnology Center urdue University Purdue University Lecture 27 1
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Different Phases of Matter Gaseous Phase High T Liquid Phase Slow Cool Rapid Cool Lower T Solid Phase 2 Crystalline Amorphous ordered disordered
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highly crystalline solids found everywhere ruby amethyst calcite rock diamond sodium chloride 3
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Highly crystalline solids are comprised of highly ordered arrays of atoms 4
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X-ray diffraction from solid materials (circa 1912) X-rays reflected from crystalline solid move in well-defined irections similar to interference effects in two slit experiment directions, similar to interference effects in two slit experiment. Expected result, since an X-ray is an EM wave? 5
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What’s the physics? m X-ray ~0.3n 6
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D R Working it out: Parallel nes A  lines C d sin d () Path Difference t AR RD AB BC C  B , cos 2 si s n in but Path Difference dd A BC d R D R AB d      2 1 cos 22 sin 2 sin sin sin 2 d path difference phase change    Two click 2 2 sin 2 1, 2,3. ...for constructive interference const dn n     ructive interference when 2 sin nd  Bragg condition 7
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Key idea: One single crystal presents many sets of parallel planes to the incident X-ray beam incident X-ray eam incident X-ray beam beam incident X-ray eam beam 8 There will be many values of Θ that satisfy Bragg’s condition
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Lecture_27 - PHYS 342 Fall 2011 Lecture 27: The Structure...

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