Phonon density of states of a bcc crystal

The form below plots the phonon density of states for a bcc crystal with one atom in the basis. It is assumed that the atoms of mass m are connected to their nearest neighbors by springs with spring constant C1 and they are connected to their second nearest neighbors by springs with a spring constant C2.

D(ω) [1015 s/(rad m³)] 

ω [1012 rad/s]

Mass: m =

[10-24 kg]

Lattice constant: a =


Spring constant: C1 =


C2/C1 =

A description of the calculation (in German) can be found here. The Matlab files used to calculate the plots can be found here.

The density of states data on the right can be used to calculate the temperature dependence of thermodynamic quantities. Copy the data on the right and paste it into the programs that calculate the thermodynamic properties found by following the links below.

 ω [rad/s]    D(ω) [J-1 m-1]