upon recent studies of the Density of states and Specific heat capacities, ive found the Einstien and Debye Models to be very helpful, Debye being the more accurate of the two models at low temperatures as it takes into account the low frequency modes. However, the realistic density of states e.g for solid Argon, seems to not fit either the Debye or the Einstien model at moderate temperatures. The realistic density of states seems to increase faster than any other model as the temperature increases. Why is this? Are there additional modes we are not taking into account?
Do you have a reference for the density of modes in solid argon ? It's not clear (to me) what exactly you are comparing. Are you really looking at the temperature dependence or the frequency dependence ? And are you comparing each of the 3 modes (2 transverse and one longitudinal) separately ?
I think there needs to be a clearer distinction made here between the "regular" density of states, which is really the electronic density of states, versus the phonon density of states. The latter is what you are asking for. Zz.