ME 697R Lecture 2.4: Lattice Dynamics - Dynamical Matrix and Phonon Dispersion

By Xiulin Ruan

Mechanical Engineering, Purdue University, West Lafayette, IN

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Researchers should cite this work as follows:

  • Xiulin Ruan (2019), "ME 697R Lecture 2.4: Lattice Dynamics - Dynamical Matrix and Phonon Dispersion," https://nanohub.org/resources/31118.

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2004 Mechanical Engineering, Purdue University, West Lafayette, IN

ME 697R Lecture 2.4: Lattice Dynamics - Dynamical Matrix and Phonon Dispersion
  • Lecture 2.4: Dynamical Matrix and Phonon Dispersion 1. Lecture 2.4: Dynamical Matrix … 0
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  • Harmonic Approximation 2. Harmonic Approximation 72.372372372372382
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  • Crystal Vibration for Monatomic Chain 3. Crystal Vibration for Monatomi… 371.93860527193863
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  • Solution of the Wave Equation 4. Solution of the Wave Equation 631.96529863196531
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  • Solution of the Wave Equation 5. Solution of the Wave Equation 786.48648648648657
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  • Phonon Dispersion Relation 6. Phonon Dispersion Relation 891.79179179179187
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  • Polarization and Group Velocity 7. Polarization and Group Velocit… 1133.9673006339674
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  • Longitudinal Acoustic Phonons 8. Longitudinal Acoustic Phonons 1393.2932932932934
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  • Two-Atom Chain 9. Two-Atom Chain 1576.6766766766768
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  • Solution of the Wave Equation 10. Solution of the Wave Equation 1707.5075075075076
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  • Dynamical Matrix Approach 11. Dynamical Matrix Approach 1899.0657323990658
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  • Dispersion Relation 12. Dispersion Relation 2073.1064397731066
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  • Dispersion Relation Profiles 13. Dispersion Relation Profiles 2196.2629295962629
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  • Acoustic and Optical Phonons 14. Acoustic and Optical Phonons 2320.3536870203538
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  • Atomic Position Nomenclature in 3D 15. Atomic Position Nomenclature i… 2429.6963630296964
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  • Force Constant Matrix 16. Force Constant Matrix 2860.5271938605274
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  • Equations of Motion 17. Equations of Motion 3042.475809142476
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  • Dynamical Matrix and Dispersion Relation 18. Dynamical Matrix and Dispersio… 3365.5321988655323
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  • Phonon Dispersion of Silicon 19. Phonon Dispersion of Silicon 3519.1524858191528
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