Debye model

The Debye model replaces the crystal's vibrational spectrum by a continuum of phonon modes up to a cutoff chosen to preserve the total number of vibrational degrees of freedom.

Table of contents
- Debye frequency Debye model
  - Debye temperature Debye frequency
- Two-dimensional power-law Debye model Debye model

Debye frequency ( $ω_{D}$ )

The Debye frequency is the upper frequency cutoff fixed by equating the continuum mode count to the crystal's number of vibrational degrees of freedom.

Debye temperature ( $T_{D}$ )

The Debye temperature is

T_{D} = ℏ ω_{D} / k_{B}

.

Two-dimensional power-law Debye model

For two polarizations,

n

A

, and

ω = C ∣ k ∣^{α}

, mode counting gives

ω_{D} = C (\frac{4 πn}{A})^{α /2} .

At low temperature its energy scales as

T^{1 + 2/ α}

and its constant-volume heat capacity as

T^{2/ α}

.

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 35A / b / ii / Solution

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Wikipedia Bot  1

The Debye model is a theoretical framework used to describe the specific heat capacity of solids, particularly at low temperatures. Developed by physicist Peter Debye in 1912, it extends the classical Einstein model of specific heat by considering acoustic phonons, or quantized lattice vibrations, in a more comprehensive manner.

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Ciro Santilli  40 Updated 2025-07-16

Wikipedia mentions that it is completely analogous to Planck's law.

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