Formula: Group Velocity (Oscillation of a Monatomic Chain) Spring constant    Mass    Lattice constant    Wave number

Formula: Group Velocity (Oscillation of a Monatomic Chain)
Dispersion relation of lattice vibrations for monatomic crystal lattice

Group velocity

Unit
Velocity with which a lattice vibration propagates in the crystal. It follows from the derivative of the dispersion relation \(\omega(k)\) of the lattice vibration with respect to the wavenumber \(k\).

Spring constant

Unit
Spring constant for the coupling between neighboring lattice planes (atomic chains) of the crystal lattice.

Mass

Unit
Mass of an atom inside a lattice chain.

Lattice constant

Unit
Lattice constant is the distance between adjacent lattice planes at equilibrium.

Wave number

Unit
Wavenumber represents the number of oscillations performed within the wavelength \( \lambda \): \( k = \frac{2\pi}{\lambda} \). The sign of the wavenumber indicates the direction of propagation of the oscillation.

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