What are the components in flux equations?

  • Context: Graduate 
  • Thread starter Thread starter nabla_foo
  • Start date Start date
  • Tags Tags
    Flux
Click For Summary

Discussion Overview

The discussion revolves around the concept of "components" in flux equations related to electromigration, specifically in the context of equations presented in a paper by P. S. Ho and T. Kwok. Participants explore the meaning of components in relation to the phenomenological coefficients and the electrochemical potential within the framework of electromigration.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on what constitutes a "component" in the context of electromigration, suggesting that it could refer to atoms of the lattice, electrons, or impurities, but questions how these relate to the varying electrochemical potential.
  • Another participant notes that coefficients can encapsulate multiple variables and emphasizes the importance of understanding which terms are coupled, indicating that the interpretation of "component" can vary between mathematical and physical perspectives.
  • A later reply expresses confusion about the term "component" despite understanding the coefficients and their simplifications, indicating a need for further clarification.
  • One participant acknowledges a mix-up between the terms "coefficient" and "component," suggesting a misunderstanding in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definition of "component," and multiple interpretations remain unresolved. There is a shared recognition of the complexity of the topic, but clarity on the term itself is lacking.

Contextual Notes

The discussion highlights the potential ambiguity in terminology and the need for precise definitions in the context of flux equations and electromigration. There are indications of varying interpretations of the term "component," which may depend on the specific physical context or mathematical formulation being considered.

nabla_foo
Messages
2
Reaction score
0
Dear all,

this is my first post in PF, and I really don't know if the level of my question is below, above or just right for this place, so bear with me.I'm writing a paper on electromigration, and I am the kind of person that wants to understand well every aspect of the subject he is working on. One of the articles I use is Electromigration in metals" by P. S. Ho and T. Kwok. The first equation is:

[tex]Ji = \sum^{n}_{j=1} {Lij Xj}[/tex]

And equation 2:

Ji = T[tex]^{-1}[/tex] [tex]\sum[/tex][tex]^{n}_{j=1}[/tex] Lij [tex]\nabla[/tex] ([tex]\mu[/tex]j + qj[tex]\phi[/tex])

where Lij are phenomenological coefficients correlating the flux of the ith component, to the driving force Xj of the jth component. ([tex]\mu[/tex]j + qj[tex]\phi[/tex]) is the electrochemical potential of the jth component.My pressing and (to me at least) not-so-trivial question is: what exactly are these components? I can understand that in case of electromigration, the atoms of the lattice could be one, the electrons could be another, and the impurities could be yet more components. That would be fine, if not for the fact that the electrochemical potential of the atoms (of the lattice, for instance) is not the same everywhere along the conductor.
But then again, this equation surely wasn't written so that one would sum across all atoms in the system.Could someone explain the meaning of "component" in this context?
 
Last edited:
Physics news on Phys.org
It is not uncommon to heap a bunch of variables into a single coefficient (or matrix of coefficients) - this is frequently done in optics as well. The important detail is often which terms are coupled to one another, the actual strength of the coupling is usually incidental. Often too, such coefficients are more easily measured than calculated from first principles.

The term "component" can therefore be read two ways - either from a purely mathematical standpoint, or as a label that umbrellas all the various physical factors that determine the value of the coefficient.

Claude.
 
Claude Bile said:
It is not uncommon to heap a bunch of variables into a single coefficient (or matrix of coefficients) - this is frequently done in optics as well. The important detail is often which terms are coupled to one another, the actual strength of the coupling is usually incidental. Often too, such coefficients are more easily measured than calculated from first principles.

The term "component" can therefore be read two ways - either from a purely mathematical standpoint, or as a label that umbrellas all the various physical factors that determine the value of the coefficient.

Claude.

I actually understand the coefficients, and even - believe it or not - understand the conditions under which they can be simplified using Onsager's relations. I still don't understand what a component is, though. I must admit your answer left me as puzzled as before.
 
My apologies, I mentally exchanged the terms coefficient and component, whoops.

Claude.
 

Similar threads

Graduate What Are the Fundamental Principles of Maxwell's Equations?
  • · Replies 0 ·
Replies
0
Views
3K