Phonons in Crystal Structures Jorge Valdez - PHYS 3305

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

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

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

Lattices Cont. http://home.iitk.ac.in/~sangals/crystosim/crystaltut.html

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

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

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

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

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

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

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

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

Sound Velocity Fundamentals of Solid State Engineering

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

Works Cited Razeghi, M. Fundamentals of Solid State Engineering. 3rd ed. New York: Springer, 2009. 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): 515-62. Web. Fujimoto, Minoru. Thermodynamics of Crystalline States. New York: Springer, 2010. Print.

Phonons in Crystal Structures Jorge Valdez - PHYS 3305