lattice vibrations part iv n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Lattice Vibrations Part IV PowerPoint Presentation
Download Presentation
Lattice Vibrations Part IV

Loading in 2 Seconds...

play fullscreen
1 / 26

Lattice Vibrations Part IV - PowerPoint PPT Presentation


  • 301 Views
  • Uploaded on

Lattice Vibrations Part IV. Solid State Physics 355. Thermal Expansion. Anharmonic effects can be important for physical properties. As you heat up the solid, internal energy of the lattice increases as k B T; and the lattice expands. Thermal Expansion.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

Lattice Vibrations Part IV


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
    Presentation Transcript
    1. Lattice VibrationsPart IV Solid State Physics 355

    2. Thermal Expansion • Anharmonic effects can be important for physical properties. • As you heat up the solid, internal energy of the lattice increases as kBT; and the lattice expands.

    3. Thermal Expansion The average displacement is determined from... After some manipulation... If A is zero, there is no thermal expansion.

    4. Thermal Expansion Dilatometer

    5. Thermal Expansion alumina (Al2O3)

    6. Thermal Expansion

    7. Negative Thermal Expansion Zirconium tungstate exhibits “negative thermal expansion” from 0.3 K up to at least 1400 K. The structure of ZrW2O8 consists of a framework of ZrO6 octahedra and WO4 tetrahedra linked at corners, but with one of the corners of the WO4 tetrahedra remaining unlinked.

    8. Negative Thermal Expansion Many tetrahedrally bonded materials show negative thermal expansion at low temperatures; for example, the thermal expansion of ice Ih becomes negative below 80 K. The dynamics of ice, even in its natural hexagonal form, are still a puzzle despite many decades of work. The combination of the rotational disorder and the complexity of the inter-molecular forces make modeling the system difficult. H2O, Si, Ge, ZnSe, GaP, GaAs

    9. Thermal Conductivity What is heat? Heat is the spontaneous flow of energy from an object at a higher temperature to an object at a lower temperature.

    10. Thermal Conductivity

    11. TH TC average particle velocity mean free path specific heat capacity per unit volume Thermal Conductivity • Thermal conduction is a diffusion process and proceeds via the random movement of electrons and phonons. • These particles carry energy from one part of the solid, where the internal energy is higher toward a region where the internal energy is lower. • From the kinetic theory of gases...

    12. Thermal Conductivity • As a phonon moves a distance d, it will reduce the temperature by T as it carries energy away. • This change in temperature is • The amount of energy carried by each phonon is then, • The number of phonons passing through a unit area per unit time is the

    13. Thermal Conductivity • The net flux of energy is then,

    14. Thermal Diffusivity

    15. Laser Flash Diffusivity ______ ___ __ _________

    16. Thermal Diffusivity

    17. Thermal Conductivity

    18. Thermal Conductivity

    19. Phonon Scattering

    20. Phonon Scattering • Phonon scattering with other phonons is the result of anharmonic effects. • If the forces between atoms were purely harmonic, there would be no mechanism for collisions between different phonons; and the mean free path would be limited solely by geometrical influences such as boundaries and imperfections.

    21. Phonon Scattering

    22. Phonon Scattering: N Processes

    23. Phonon Scattering: U Processes The physical result of all this is that a phonon comes along and “experiences” a different local “stiffness” due to the strain caused by another phonon.

    24. Phonon Scattering