Disoersion relation and lattice constants

In summary, the conversation discusses the calculation of period or lattice constant for 1D and 2D crystals based on the energy wavevector relation. There is uncertainty about whether b represents the lattice constant or if the periodic boundary condition should be applied. There is also a desire to be able to calculate the lattice constant analytically rather than relying on a MATLAB plot.
  • #1
pazmush
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Dispersion relation and lattice constants

I need to be able to calculate the period (which I believe is the lattice constant) for a 1D crystal given the energy wavevector relation. Is this possible?

I also have to find the Bravais lattice of a 2D crystal give a similar relation.

What is it that I have to calculate.

1D
E = u[n+(1/3)(-1)^n cos(kb)]

2D
E = u[n+(1/3)(-1)^n cos(kx b)Xcos(ky b)]

What I thought was that either b just is the lattice constant, or that you should impose the periodic boundry condition and calculate it that way, allthoigh all that did was cancel down to nothing so I'm not sure. Do I have to change to real space?

Also I've been able to plot it in MATLAB and allthough that shows a sort of lattice I'm not 100% sure that this is correct, and i'd like to be able to do it analytically.

Thanks
 
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Anyone?
 

1. What is a dispersion relation?

A dispersion relation is an equation that describes the relationship between the frequency and wave vector of a wave in a material or medium. It shows how the energy and momentum of a particle or wave are related.

2. How is a dispersion relation related to lattice constants?

A dispersion relation is closely linked to the lattice constants of a material, as it describes the properties of a wave propagating through the crystal lattice. The lattice constants, such as the lattice spacing, determine the periodicity and symmetry of the crystal structure, which in turn affects the behavior of the waves within the material.

3. What is the importance of understanding dispersion relation and lattice constants?

Understanding the dispersion relation and lattice constants is crucial in many fields of science, such as materials science, solid state physics, and condensed matter physics. It allows us to predict the behavior of waves, such as electromagnetic or acoustic waves, in different materials and structures, and can help us design new materials with desired properties.

4. How are dispersion relation and lattice constants experimentally determined?

Dispersion relation and lattice constants can be determined experimentally using techniques such as X-ray diffraction, neutron scattering, or optical methods. These methods involve measuring the scattering of waves from a crystal and analyzing the resulting intensity patterns to determine the lattice constants and dispersion relation.

5. Can the dispersion relation and lattice constants change in a material?

Yes, the dispersion relation and lattice constants can change in a material under certain conditions, such as external stress, temperature, or doping with impurities. These changes can lead to altered wave properties and can be utilized to tune the properties of materials for specific applications.

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