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

Explore the one-dimensional linear oscillations in monoatomic and diatomic crystal lattices with both equal and different particle masses. This simulation delves into the dynamics of chains and square lattices with varying masses, providing insightful equations and solutions.

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

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  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!

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