D(ω) [10^{15} s/rad m^{-3}] | |
ω [10^{12} 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 × 10^{28}. Multipying this by 3 to get the number of degrees of freedom yields 1.498 × 10^{29} 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}] |