The** key difference** between Debye and Einstein model is that the **Debye model treats vibrations of the atomic lattice as phonons in a box whereas Einstein model treats solids as many individual, non-interacting quantum harmonic oscillators. **

The terms Debye model and Einstein model are used mainly in physical chemistry, regarding the thermodynamic properties of solids. The Debye model was named as such after the scientist Peter Debye in 1912. The Einstein model was named after Einstein who proposed the original theory in 1907.

### CONTENTS

1. Overview and Key Difference

2. What is Debye Model

3. What is Einstein Model

4. Side by Side Comparison – Debye vs Einstein Model in Tabular Form

5. Summary

## What is Debye Model?

Debye model is a method developed by the scientist Peter Debye to estimate phonon contribution to the specific heat in a solid. This term comes under thermodynamics in solid state physical chemistry. A phonon can be defined as a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter (specifically solid and liquid states). The term specific heat, on the other hand, refers to the heat capacity of a substance divided by the mass of the substance (or, it is the amount of energy that must be added as heat to one unit of the mass of the substance to increase one unit of temperature).

The Debye model, unlike the Einstein model, treats the vibrations of the atomic lattice of solid as phonons in a box. The model can accurately predict the low-temperature dependence of the heat capacity that is proportional to T^{3} (the Debye T^{3} law).

We can describe the Debye model as a solid-state equivalent to the Planck’s law of black body radiation. Planck’s law of black body radiation treats electromagnetic radiation as a photon gas, but the Debye model treats atomic vibrations as phonons in a box.

## What is Einstein Model?

Einstein model is a method developed by Einstein in 1907 based on two assumptions: each atom in the solid lattice acts as an independent 3D quantum harmonic oscillator and all atoms oscillate with the same frequency. Therefore, Einstein model is a solid-based method which is opposite to the Debye model. The assumption that a solid has independent oscillations is very accurate. These oscillations are sound waves or phonons that are collective modes involving many atoms. However, according to the Einstein model, each atom oscillates independently.

According to the Einstein model, we can observe that the specific heat of a solid approaches the zero exponentially fast at low temperatures. This happens because all oscillations have one common frequency. The correct behaviour was described later in Debye model as a modification of the Einstein model.

## What is the Difference Between Debye and Einstein Model?

Debye and Einstein’s models are thermodynamic concepts in physical chemistry. The key difference between Debye and Einstein model is that the Debye model treats the vibrations of the atomic lattice as phonons in a box whereas the Einstein model treats the solids as many individual, non-interacting quantum harmonic oscillators.

Below infographic summarizes the difference between Debye and Einstein model.

## Summary – Debye vs Einstein Model

Debye and Einstein’s models are thermodynamic concepts in physical chemistry. The key difference between Debye and Einstein model is that the Debye model teats the vibrations of the atomic lattice as phonons in a box whereas the Einstein model treats the solids as many individual, non-interacting quantum harmonic oscillators.

##### Reference:

1. “Einstein’s Model.” Einstein’s Model – an Overview | ScienceDirect Topics, Available here.

##### Image Courtesy:

1. “DebyeVSEinstein” (Public Domain) via Commons Wikimedia

2. “Escv” (Public Domain) via Commons Wikimedia

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