# Dispersion relation ~ modern phyics (solid state physics)

In summary: In two dimensional crystals, the chains can vibrate in two directions perpendicular to each other. In three dimensional crystals, the chains can vibrate in three directions perpendicular to each other.

## Homework Statement

Which cannot be the structure of two acoustic branches, nor three acoustic branches?
Simple cubic, FCC, BCC, diamond cubic, NaCl lattice

## Homework Equations

N/A
http://solid.fizica.unibuc.ro/cursuri/solid_en/curs_solid_EN.pdf#page=61
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/bravais.html
http://image.slidesharecdn.com/crys...-in-material-science-24-638.jpg?cb=1412805736

## The Attempt at a Solution

The dispersion relation only identifies acoustic branches which means there is only one atom in the basis of this crystal. But I don't know why.
Why is this true?
(And sorry I misspelt in the title.)

## Homework Statement

Which cannot be the structure of two acoustic branches, nor three acoustic branches?
Simple cubic, FCC, BCC, diamond cubic, NaCl lattice

## Homework Equations

N/A
http://solid.fizica.unibuc.ro/cursuri/solid_en/curs_solid_EN.pdf#page=61
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/bravais.html
http://image.slidesharecdn.com/crys...-in-material-science-24-638.jpg?cb=1412805736

## The Attempt at a Solution

The dispersion relation only identifies acoustic branches which means there is only one atom in the basis of this crystal. But I don't know why.
Why is this true?
(And sorry I misspelt in the title.)

I do not understand your question. The dispersion relations are relations between wavenumber vector and frequency of a wave. When the base of the crystal consists of a single atom, it can only vibrate with respect to the atoms in the other cells. At k=0, the frequency of the vibration is also 0. Such wave is called an acoustic wave. In a 3D crystal, there are three branches of acoustic waves, one branch for longitudinal and two branches for transverse waves. In highly symmetric crystals the two transverse branches coincide.
In case a base of more than one atom, the atoms of the base can vibrate with respect to each other giving rise to optical branches.
In the examples of your first reference, one-dimensional crystals (chains of atoms) are discussed. In one dimensional word, the atoms can only vibrate along the chain.

## 1. What is a dispersion relation in solid state physics?

A dispersion relation is a mathematical relationship that describes the energy and momentum of a particle or wave in a solid material. It shows how the energy of a particle changes as its momentum changes.

## 2. How is a dispersion relation related to the band structure of a solid material?

The dispersion relation is directly related to the band structure of a solid material. The band structure shows the allowed energy states of particles in the material, and the dispersion relation describes how the energy changes as the momentum of the particle changes.

## 3. Can a dispersion relation be experimentally measured?

Yes, a dispersion relation can be experimentally measured using various techniques such as angle-resolved photoemission spectroscopy (ARPES) or inelastic neutron scattering. These methods allow for the determination of the energy and momentum of particles in a solid material, which can then be used to calculate the dispersion relation.

## 4. What is the significance of the dispersion relation in modern physics?

The dispersion relation is a fundamental concept in modern physics, particularly in solid state physics. It helps us understand the behavior of particles and waves in materials, and plays a crucial role in many areas such as semiconductor devices, superconductivity, and magnetism.

## 5. How does the dispersion relation change in different types of materials?

The dispersion relation can vary significantly depending on the type of material. For example, in metals, the dispersion relation is typically linear, while in insulators it is non-linear. In addition, the presence of impurities, defects, or external fields can also affect the dispersion relation in a material.

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