Dispersion relation of amorphous materials

[kulbir]

Hi,

I am trying to find dispersion relation of amorphous material (using data obtained by molecular dynamics simulation). As it is not periodic system one can not find it by standard method of diagonalizing the force constant matrix. I think one can do it by taking Fourier transform of displacements (like we do to find density of states, DOS, by taking Fourier transform of velocity auto correlation function, VACF). Is it correct ? If yes then how? what is the physical meaning ? and what is the exact relation?

Thanks.

 

[BigJDubs]

Amorphous materials are highly disordered and lack the periodicity of a crystalline lattice, so the standard method of finding the dispersion relation by diagonalizing the force constant matrix is not applicable. However, you can use Fourier transforms to find the dispersion relation in an amorphous material. The idea is to take the Fourier transform of the displacement data obtained from molecular dynamics simulations, and then use this to calculate the dispersion relation. The physical meaning of this is that the Fourier transform of the displacement data captures the correlation between the displacement of atoms over different distances, and thus provides information on how energy propagates through the material. The exact relation is given by: Dispersion relation = Fourier transform of displacement data.