123B_1_EE 123B W 11 Chapter 4 slides for posting

123B_1_EE 123B W 11 Chapter 4 slides for posting - Chapter...

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Unformatted text preview: Chapter 4. Phonons Lecture 5 1/18/10 X-Ray Tube Monochromator and/or Slits Sample Detector Stage/Goniometer 2 From Tube To Detector Wide Slit Scenario Approx. 10mm x 10mm From Tube To Detector Narrow Slit Scenario Approx. 1mm x 10mm Detector Slits-12000 -10000-8000-6000-4000-2000 10 10 1 10 2 10 3 10 4 10 5 10 6 Intensity (cps) -2 (arcsec) Uses of X-Ray Diffraction XRD can be used to: Determine the crystal structure of an unknown material. Calculate the lattice constant of a crystal. Calculate strain in a crystal layer. Calculate thickness of a layer. GaSb GaAs FWHM Last Lecture: TEM/XRD TEM: Resolution: 1 Minimum spot size: 2000 Use: Visual image of sample Reciprocal space Lattice constant Lattice mismatch Crystal quality Electron sample interaction TEM utilizes the transmitted electrons Requiring thin sample (<100nm for 100kV electron beam) Diffraction condition Braggs Law: =2dhklsin hkl planes k0 kg In reciprocal space, only points intersecting Ewald sphere (r=k0) will satisfy the diffraction condition and |k0|=1/ http://www.physics.byu.edu/faculty/campbell/images/ewald.jpg k0 Diffraction pattern in TEM Crystallographic information Lattice planes Materials quality Specimen orientation with respect to the e-beam-200-11-1 02-2 1-11 200 0-22-1-11 11-1 GaAs GaSb Materials properties Lattice constants Materials identification Strain analysis GaAs (fcc) DP Z=[011] GaAs and GaSb (fcc) DP Z=[011] This Lecture: Chapter 4 Phonons Hookes Law force, displacement Newtons Law force, mass, acceleration Oscillation modes longitudinal, transverse Dispersion relation Group velocity Brillouin zone boundaries and limits Mono-atomic and diatomic chains Homework #3 due Feb. 2 Tuesday 4.1: For a monatomic chain, detemine total energy in an elastic wave. 4.3 For a diatomic basis, calculate wave amplitude ratio , u/v at K=/a . 4.5 For diatomic basis, find dispersion relationship at K=0 and K=/a. Excitations in Solids Phonon What are they? Propagation lattice vibrations that carry energy through a crystal Crystal can be considered an array of mass centers connected by springs Phonons Phonons exist as both longitudinal and transverse excitations. S S+1 S-1 S S+1 S-1 k k X y Longitudinal wave Transverse wave Hookes law describes this picture Phonon contd. Why do we care? Phonons (lattice vibration) are energy propagation We will study them further in Chapter 5 for heat transfer Heat capacity Thermal expansion Heat transport etc. How do phonons transfer energy?...
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123B_1_EE 123B W 11 Chapter 4 slides for posting - Chapter...

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