Density of States: Debye vs Einstein Models & Realistic Findings

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SUMMARY

The discussion focuses on the Density of States (DOS) in relation to the Debye and Einstein models, particularly in the context of solid Argon. The Debye model is identified as more accurate at low temperatures due to its consideration of low-frequency modes. However, at moderate temperatures, the realistic DOS for solid Argon diverges from both models, increasing more rapidly than predicted. This discrepancy raises questions about additional modes that may not be accounted for and emphasizes the need to distinguish between electronic and phonon density of states when analyzing specific heat capacity.

PREREQUISITES
  • Understanding of Density of States (DOS) in solid-state physics
  • Familiarity with Debye and Einstein models of specific heat capacity
  • Knowledge of phonon and electronic density of states
  • Basic concepts of temperature dependence in thermodynamic properties
NEXT STEPS
  • Research the differences between electronic and phonon density of states
  • Explore advanced models of DOS beyond Debye and Einstein, such as the Born-von Karman model
  • Investigate temperature dependence of specific heat capacity in various materials
  • Study the role of additional vibrational modes in solid-state systems
USEFUL FOR

Physicists, materials scientists, and researchers studying thermal properties of solids, particularly those interested in the limitations of traditional models like Debye and Einstein in explaining real-world phenomena.

drcrabs
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upon recent studies of the Density of states and Specific heat capacities, I've found the einstein 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 einstein 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?
 
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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 ?
 
Actuallty what I am looking at is the temperature dependacy of the specific heat capacity
 
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.
 

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