# Formula: Dispersion Relation for a Crystal with a Diatomic Basis Angular frequency    Angular wavenumber    Spring constant    Mass    Lattice constant

## Angular frequency

Unit
This dispersion relation $$\omega_{\pm}(k)$$ describes the relation between the frequency (energy) and the wavenumber (wavelength) of a diatomic chains of a crystal. The oscillation is purely longitudinal (or transversal) and only the interaction between the neighboring chains is considered here.

In a crystal with a diatomic basis there are two vibrational frequencies: $$\omega_{+}(k)$$ optical branch and $$\omega_{-}(k)$$ acoustic branch.

The angular frequency is related to the frequency $$f$$ via $$\omega = 2\pi \, f$$.

## Angular wavenumber

Unit
Wavenumber is related to wavelength $$\lambda$$ via $$k = 2\pi / \lambda$$.

## Spring constant

Unit
Spring constant (or coupling constant) comes from the Hooke spring law and describes how strongly a diatomic lattice plane is coupled to its neighboring lattice planes.

## Mass

Unit
The two masses of a diatomic basis.

## Lattice constant

Unit
Lattice constant is the distance between two adjacent lattice planes when they are in equilibrium (i.e. not deflected).

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