| D(ω) [1015 s/rad m-3] | |
ω [1012 rad/s] |
The integral of the density of states should be the number of degrees of freedom in a cubic meter of Si. The integral of the data below is 1.498e+29. The density of silicon is 2.33 g/cm³ = 2330 kg/m³. The mass of a silicon atom is 4.664 × 10-26 kg. The number of silicon atoms in a cubic meter is 4.99 × 1028. Multipying this by 3 to get the number of degrees of freedom yields 1.498 × 1029 so this density of states is consistent with the known number of vibrational modes in silicon.
| ω [rad/s] D(ω) [s/rad m-3] |