It is the degree of energy that excites all the vibrational models included by the BZ.

the case is also applicable for nanoscale solids including Nano crystals

Values for Debye temperature are well known and it has been measured and calculated for most elements and compounds in their bulk states

for nanoscale range materials it can be calculated from its bulk value through out certain mathematical relations

for more details try to see the following references

1-Size effects on cohesive energy, Debye temperature and lattice heat capacity from first-principles calculations of Sn nanoparticles

BJ Abdullah, MS Omar, Q Jiang

Proceedings of the National Academy of Sciences, India Section A: Physical …, 2018

2-Debye–Einstein approximation approach to calculate the lattice specific heat and related parameters for a Si nanowire

A KH. Alassafee, MS Omar

Journal of Taibah University for Science 11 (6), 1226-1231, 2017

3-Structural and Thermal Properties of Elementary and Binary Tetrahedral Semiconductor Nanoparticles

MS Omar

International Journal of Thermophysics 37 (1), 11, 2016

4-Temperature-dependence calculation of lattice thermal conductivity and related parameters for the zinc blende and wurtzite structures of InAs nanowires

HH Karim, MS Omar

Bulletin materials Science 43, 2020

1-Solid Surface and Nanoscale materials Structure

• July 2016
• DOI:
• 10.13140/RG.2.2.31947.59684
• Conference: Charmo
• At: University of Charmo
• Affiliation: University of Salahaddin
• 📷Omar M S

Dear D.S. Kumar,

the Debye temperature is a rough approximation to describe the phonon spectrum and the specific (phononic portion) heat of materials (Debye model). It is a very good approximation for low temperatures:

-The phonon dispersion of the acoustic phonons is assumed to be linearly, e.g. you have a constant velocity of sound vS up to a certain cut of frequency omega:

vS = d omega /dk (k - wave vector). The velocity of sound is an average value with 2 transversale and one longitudinale value: 1/vS³ = 0,333*(2/vt³ + 1/vl³). It is clear, that for reduced dimensions another value follows.

For high frequencies, vs reduces and the spectrum exhibits undulations (nonlinearities).

- The Debye temperature is important to describe the specific heat for low temperatures (T