# Dispersion relation of amorphous materials

• kulbir
In summary, a dispersion relation in amorphous materials is a mathematical equation that describes the relationship between the frequency and wavevector of a wave. It is different from that of crystalline materials due to the random arrangement of atoms, and it is influenced by various factors such as material type, density, temperature, and bonding strength. The dispersion relation has a significant impact on the mechanical, thermal, and optical properties of amorphous materials and can be modified through various processes for specific applications.
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.

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.

## 1. What is a dispersion relation in amorphous materials?

A dispersion relation is a mathematical equation that describes the relationship between the frequency and wavevector of a wave in an amorphous material. It shows how the energy of the wave is distributed in the material.

## 2. How is the dispersion relation different in amorphous materials compared to crystalline materials?

In amorphous materials, the atoms are arranged randomly, leading to a more complex and continuous distribution of energy levels. In contrast, crystalline materials have a periodic arrangement of atoms, resulting in a more discrete and predictable dispersion relation.

## 3. What factors affect the dispersion relation in amorphous materials?

The dispersion relation in amorphous materials is influenced by various factors such as the type of material, its density, temperature, and presence of impurities. The bonding strength between atoms and the arrangement of atomic bonds also play a role in determining the dispersion relation.

## 4. How does the dispersion relation impact the properties of amorphous materials?

The dispersion relation affects the mechanical, thermal, and optical properties of amorphous materials. It determines the speed of sound and light propagation, thermal conductivity, and energy absorption. Understanding the dispersion relation is crucial for designing amorphous materials with desired properties.

## 5. Can the dispersion relation in amorphous materials be controlled or modified?

Yes, it is possible to alter the dispersion relation in amorphous materials by changing the structure or composition of the material. This can be achieved through processes such as doping, annealing, and alloying. Researchers are also exploring new techniques to manipulate the dispersion relation in amorphous materials for various applications.

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