# What is the Difference Between Debye and Einstein Model

The main difference between Debye and Einstein model is that the Debye model is based on the assumption that lattice vibrations in a solid can be treated as a continuous spectrum of oscillators, whereas the Einstein model is built on the basis that each atom vibrates independently of the others.

Debye’s and Einstein’s models are theoretical models describing the vibrational motion of atoms in a solid. But they have some differences among them.

### Key Areas Covered

1. What is Debye Model
– Definition, Assumptions, Properties
2. What is Einstein Model
– Definition, Assumptions, Properties
3. Similarities Between Debye and Einstein Model
– Outline of Common Features
4. Difference Between Debye and Einstein Model
– Comparison of Key Differences

### Key Terms

Einstein Model, Debye Model

## What is Debye Model

Debye model is a theoretical model in solid-state physics that describes the behavior of solids at low temperatures. This model is based on the assumption that atoms or molecules in a solid vibrate around their equilibrium positions in a harmonic manner, similar to springs.

Debye’s model starts by assuming that a solid material is made up of a lattice of atoms that are held together by interatomic forces. Moreover, these atoms are assumed to be vibrating in a regular pattern around their equilibrium positions. The energy associated with these vibrations is called the thermal energy of the solid. Furthermore, the Debye model assumes that this energy is distributed among a set of harmonic oscillators that represent the individual atoms in the lattice.

Debye’s model also makes some simplifying assumptions about the behaviour of the atoms in the lattice. One of these assumptions is that the atoms are arranged in a regular pattern and that this pattern is repeated throughout the entire material. Another assumption is that the interatomic forces between the atoms can be represented by a simple potential function such as a harmonic oscillator. Thus, using these assumptions, the Debye model is able to calculate the total amount of thermal energy in a solid material as a function of temperature.

There are many applications of the Debye model. It helps to predict the specific heat of solids as a function of temperature. It can also help to calculate the dispersion relations of phonons in crystals which are the curves that describe the dependence of the phonon frequency on the wave vector. In the field of thermal conductivity, this model can be used to estimate the thermal conductivity of the materials. Debye model also helps to calculate the vibrational spectra of solids.

## What is Einstein Model

Einstein model assumes that the atoms in a solid vibrate independently and are not influenced by neighboring atoms. Albert Einstein developed this model. This model is based on the assumption that each atom in a solid is attached to the spring that is responsible for the atom’s vibration. The frequency of vibration is determined by the atom’s mass and the spring’s stiffness. In the Einstein model, one assumes that all atoms in a solid state have the same mass and connect to springs with the same stiffness.

The main assumption of the Einstein model is that the vibrations of the atoms in a solid are not uncorrelated, meaning that each atom vibrates independently and is not influenced by neighboring atoms. This assumption also allows for the calculation of the vibrational energy of the solid as a sum of the energies of the individual atoms. In addition, this model predicts that the vibrational energy of the solid is quantized, meaning that the energy can only take on certain discrete values.

Einstein’s model has many applications. It is useful in the prediction of specific heat of solids at low temperatures. As the model assumes that all atoms in a solid vibrate at the same frequency, one can calculate the specific heat by summing up the energies of all the oscillators. It also helps to calculate the phonon contribution to thermal conductivity and helps in the study of the elastic properties of solids. Another use is interpreting the vibrational spectroscopy data. In addition, Einstein’s model is useful in the study of vibrational modes of nanoparticles. It also helps in determining their specific heat and thermal conductivity,

## Similarities Between Debye and Einstein Model

• Both are theoretical models that describe the vibrational motion of atoms in a solid.
• Moreover, both are based on several assumptions.

## Difference Between Debye and Einstein Model

### Definition

Debye model, created by Peter Debye, is a theoretical model that describes the vibrational motion of atoms in a solid as a series of oscillating waves, while the Einstein model, developed by Albert Einstein, is a theoretical model that describes the vibrational motion of atoms in a solid as if they are attached to springs with the same stiffness and vibrating at the same frequency.

### Main Assumption

Debye’s model assumes that a continuous spectrum of oscillators can treat lattice vibrations in a solid. Meanwhile, the Einstein model assumes that each atom vibrates independently of the others.

### Energy Distribution

In the Debye model, all phonons have the same energy and are distributed according to a Debye frequency, whereas in the Einstein model, all phonons have the same frequency, but their energy is distributed according to the Boltzmann distribution.

### Elastic Properties

Moreover, the Debye model assumes that the atoms in a solid are connected by springs, and the elastic properties of the solid are determined by the spring constant, while in the Einstein model, the atoms in a solid are connected by more complex interatomic forces, and these forces determine the elastic properties of the solid.

### Conclusion

In brief, Debye and Einstein’s models are both theoretical models that describe the vibrational motion of atoms in a solid. The main difference between Debye and Einstein models is that the Debye model assumes that a continuous spectrum of oscillators can treat lattice vibrations in a solid, while the Einstein model assumes that each atom vibrates independently of the others.

##### Reference:

1. “Debye’s Contribution to Specific Heat Theory.” Hyper Physics.
2. “Einstein Model of a Solid.” Hyper Physics.

##### Image Courtesy:

1. “Debye limit” By Daniel M. Short –(CC BY-SA 3.0) via Commons Wikimedia
2. “Einstein solids 1” By Daniel M. Short – (CC BY-SA 3.0) via Commons Wikimedia