drive and discuss dispersion relation of the one dimensional monoatomic vibration
Answers
Answer: The wave number, k, is a measure of the spatial periodicity of a wave, i.e. the number of oscillations per length unit. It is therefore measured in m−1. Since a wave may travel in different directions, the wave number is the magnitude of the wave vector, k⃗ . In spectroscopy, where the oscillating medium is electromagnetic radiation, the wave number is usually denoted as ν~, and there is a fixed relationship between the wave number (m−1) and the frequency (s−1):
ν=cν~
where the speed of light acts as the constant of proportionality.
The "beads" of an electromagnetic wave have no rest mass, so they will be propagating at the speed of light. However, atoms in a crystal have a finite mass; therefore they travel at a lower speed, and the frequency of oscillation will become dependent on the wave number (and also on the direction of the wave vector). The relationship between frequency (usually expressed as an angular frequency, ω) and wave number is known as a dispersion relation.
Just as the concept of photons is used to express the particle-like aspects of electromagnetic waves, the term phonon is used to refer to lattice vibrations where they behave in a particle-like manner. For example, when two oscillations along different lattice vectors meet and interact in a crystal, their interaction can be interpreted as two pseudo-particles, phonons, scattering off one another.
Answer:
The monatomic chain model represents a crystal in one dimension where all atoms ... At the same time, we can also represent the oscillation of all the atoms in the ... and finally for ω to produce the dispersion relation for the monatomic chain.
Explanation:
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