1. Phonons in Crystal Structures
Jorge Valdez - PHYS 3305

2. Contents Crystal Structures Lattices The Atom Phonons in One Dimension
Atomic Vibrations
Three Dimensional Structures
Phonons Revisited
Sound Velocities
Conclusion
Works Cited

3. Crystal Structures Matter Types of structures
Groups of atoms make structures
Solids are condensed atoms
Super condensed solids form crystals
Types of structures
Single crystalline Structures
Polycrystalline Structures

4. Lattices Periodically repeating patterns of atoms that form structures
Form Unit Cells, or offset lattices
There are 14 different lattice structures
Transformations form different combinations

5. Lattices Cont.

6. The Atom Bonds form from interactions between valence electrons
Different types of bonds are formed
Classical atomic model
Orbitals
Radius
Ionization Energy
Electronegativity
Electron affinity

7. Phonons Collective movement/excitations of atoms in a crystal
Deviations from equilibrium states
Do not move in clouds, but occupy bands in space
Still bound by uncertainty principle
Classical model similar to quantum model

8. Atomic Vibrations
Potential energy model is similar to the spring potential model
Harmonic crystals
One-Dimensional model can then be translated to three dimensions

9. Atomic Vibrations Cont.
One-Dimensional Monatomic Harmonic Crystal
Fundamentals of Solid State Engineering

10. Atomic Vibrations Cont.
Two-Dimensional Monatomic Harmonic Crystal
Fundamentals of Solid State Engineering

11. Three Dimensional Structures
Are an addition to the original model
Fundamentals of Solid State Engineering

12. Phonons Revisited Lattice waves are regarded as phonons
Group velocity is the speed of the corresponding traveling wave of a phonon

13. Sound Velocity
Speed at which sound propagates and is related to velocity of a traveling wave
Phase Velocity
The velocity of the phase of the wave or, in other words, the speed at which the peak of the wave travels in space
Never reaches zero

14. Sound Velocity
Fundamentals of Solid State Engineering

15. Conclusion
Crystal structures are formed from lattice structures of atoms
Phonons exist as excitations of atoms in a crystal structure
Excitations cause vibrations as waves in the structures, which can produce sound or heat depending on wavelength

16. Works Cited
Razeghi, M. Fundamentals of Solid State Engineering. 3rd ed. New York:
Springer, Print.
Baroni, Stefano, Stefano De Gironcoli, Andrea Dal Corso, and Paolo
Giannozzi. "Phonons and Related Crystal Properties from Density-functional Perturbation Theory." Reviews of Modern Physics 73.2 (2001): Web.
Fujimoto, Minoru. Thermodynamics of Crystalline States. New York: Springer, Print.

17. Phonons in Crystal Structures
Jorge Valdez - PHYS 3305