1 / 7

Simulation of the linear oscillations in the monoatomic and diatomic crystal lattices

Simulation of the linear oscillations in the monoatomic and diatomic crystal lattices. Osokina Alena, St.Petersburg State Polytechnic al University. One-dimensional case. Chain with equal masses of particles.

leyva
Télécharger la présentation

Simulation of the linear oscillations in the monoatomic and diatomic crystal lattices

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Simulation of the linear oscillations in the monoatomic and diatomic crystal lattices Osokina Alena, St.Petersburg State Polytechnical University.

  2. One-dimensional case. Chain with equal masses of particles. • Chain consists of N atoms with masses M. Let the displacement of each particle be ui. • For the chain with equal masses of particles the equationis: • The solution:

  3. One-dimensional case. Chain with different masses of particles • Let the displacements be ui and vi for particles witn masses m1 and m2 respectively. • Then the chain: System of equations in this case:

  4. One-dimensional case. Chain with different masses of particles • The solution in this case:

  5. Square Lattice Withequal masses of particles.

  6. Square Lattice Withequal masses of particles. • Considering the stiffness tensor componentwise: • We get the system of equations for the square crystal lattice:

  7. Thank you for your attention!

More Related