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Unformatted text preview: Chapter 4. Phonons Lecture 5 1/18/10 XRay Tube Monochromator and/or Slits Sample Detector Stage/Goniometer ω 2θ From Tube To Detector Wide Slit Scenario Approx. 10mm x 10mm From Tube To Detector Narrow Slit Scenario Approx. 1mm x 10mm Detector Slits12000 100008000600040002000 10 10 1 10 2 10 3 10 4 10 5 10 6 Intensity (cps) ϖ2 θ (arcsec) Uses of XRay 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. Δ ω GaSb GaAs FWHM Last Lecture: TEM/XRD • TEM: • Resolution: 1 Å • Minimum spot size: 2000 Å • 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 Bragg’s Law: λ=2dhklsinθ θ hkl planes k0 kg In reciprocal space, only points intersecting Ewald sphere (r=k0) will satisfy the diffraction condition and k0=1/λ 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 ebeam200111 022 111 200 022111 111 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 • Hooke’s Law – force, displacement • Newton’s Law – force, mass, acceleration • Oscillation modes – longitudinal, transverse • Dispersion relation • Group velocity • Brillouin zone boundaries and limits • Monoatomic 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=π/a . • 4.5 For diatomic basis, find dispersion relationship at K=0 and K=π/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 S1 S S+1 S1 k k ∆X ∆y Longitudinal wave Transverse wave • Hooke’s 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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This note was uploaded on 02/20/2012 for the course EE 123B taught by Professor Dianahuffaker during the Winter '11 term at UCLA.
 Winter '11
 DianaHuffaker

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