How could one theoretically predict a material's permittivity?

  • Context: Graduate 
  • Thread starter Thread starter VortexLattice
  • Start date Start date
  • Tags Tags
    Permittivity
Click For Summary

Discussion Overview

The discussion revolves around the theoretical prediction of a material's permittivity, focusing on the complexities involved in relating it to the material's atomic structure and electronic properties. Participants explore various methods and approaches, including experimental and computational techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that permittivity is defined through the relationship ##\vec D = \epsilon \vec E## and suggests that determining it theoretically would involve analyzing how atoms in a unit cell respond to an applied electric field, which could be complex due to multiple atoms and electrons.
  • Another participant mentions that permittivity can be calculated using band structure programs, referencing an article by Adler as a source for this method.
  • A subsequent reply expresses confusion about how to derive permittivity from band structure, indicating a need for clarification on the process.
  • Another participant explains that linear response theory or perturbation theory can be used to calculate changes in charge density due to an applied field, emphasizing the necessity of knowing the band structure and Bloch states of the material.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the methods for calculating permittivity, with some proposing computational approaches while others seek clarification on the relationship between band structure and permittivity. The discussion remains unresolved regarding the best theoretical approach.

Contextual Notes

Participants highlight the complexity of predicting permittivity theoretically, noting dependencies on atomic structure, electronic properties, and the need for advanced computational methods. Specific assumptions about the applicability of linear response theory and the role of band structure are not fully explored.

Who May Find This Useful

This discussion may be of interest to researchers and students in materials science, condensed matter physics, and electrical engineering, particularly those focused on the theoretical aspects of material properties and computational modeling.

VortexLattice
Messages
140
Reaction score
0
I know experimentally, the permittivity of a material is ##\vec D = \epsilon \vec E##, and you can also relate the Polarization to it. So it's basically a response of the material to an applied E field.

But that seems like it would be a fairly complex thing to figure out theoretically. I guess one way would be to, for a given E field applied to a unit cell of the material, see how each atom gets polarized. But that seems like it would be incredibly complicated for unit cells with several atoms and a basis, and each atom having multiple electrons.

So I'm wondering how you could figure out the permittivity of a general crystal, like if you were told its interatomic distances, lattice constants, band structure, etc. Is there a better way than what I described above?

Thanks!
 
Physics news on Phys.org
Permittivity can be calculated routinely with programs to calculate band structure. The basic approach is described in the article by Adler:

http://prola.aps.org/abstract/PR/v126/i2/p413_1
 
DrDu said:
Permittivity can be calculated routinely with programs to calculate band structure. The basic approach is described in the article by Adler:

http://prola.aps.org/abstract/PR/v126/i2/p413_1

Hi, thank you very much for the reply! However, after a quick glance at this I don't see how to get the permittivity assuming you already know the band structure... I'm sorry if I'm misunderstanding this, but is this what you meant?
 
Basically you use linear response (i.e. perturbation theory) to calculate the change in charge density due to an applied field. This requires you to know the band structure and Bloch states of the material being studied.
 

Similar threads

Undergrad How Does Each Element in the Permittivity Tensor Matrix Represent an Anisotropic Material?
  • · Replies 9 ·
Replies
9
Views
6K
Undergrad How does permittivity in Coulomb's law work?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Time rondeau crystals, experimental observations
  • · Replies 1 ·
Replies
1
Views
3K
Graduate How are the thermal expansion of a solid and the stress tensor related?
  • · Replies 3 ·
Replies
3
Views
3K
How charge density of plate is changed by permittivity
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How to practically perform first-principles calculations on Li-ion batteries?
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Photons through transparent materials, what's going on?
  • · Replies 22 ·
Replies
22
Views
8K
Capacitance with dielectric permittivity that depends on r
  • · Replies 1 ·
Replies
1
Views
2K
Graduate About band structure calculation
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Interpreting the Permittivity of Metals
  • · Replies 4 ·
Replies
4
Views
2K