Talk:Electronic specific heat

Cleaning up

Hi, I am adding this page to my todo list. I am not sure if I count as an "expert" in physics, but I am a physicists and will do my best. I want to say off the top, though, that the Aschroft and Mermin textbook does not make a single reference to heat capacity at all. It does discuss similar concepts for specific heat, which is, naively, heat capacity per unit mass. So none of the math transfers and I am not sure sure why it would be referenced. It also never explicitly uses the term electron or electronic specific heat, though it does discuss acoustic phonon contributions to the heat capacity, which is a main point of this article (though this article never mentions acoustic phonons). I'm assuming none of the original editors are still around, due to the maintenance templates, but if you are, I would love to discuss how we can improve the article and add in some inline citations. Thanks! Footlessmouse (talk) 04:38, 15 August 2020 (UTC)

Kittel table

@Solfra: I saw your edit [1], could you please indicate where in Kittel book the table appears so we can remove the clean up template? Thanks.--ReyHahn (talk) 18:41, 20 November 2020 (UTC)

@ReyHahn: The table can be found (set up like the periodic table) on page 146 of Kittel (2005), Introduction to Solid State Physics (8th ed.) ISBN 0-471-41526-X. I figured I would go ahead and answer since I have been working on the article and have the textbook readily available. Footlessmouse (talk) 20:07, 20 November 2020 (UTC)

It might be easier to cite Chapter 6 "Free Electron Fermi Gas" as pages 133 through 157 for that part. Chapter 5 (p. 105) on "Thermal Properties" also contains extensive discussions of the phonon heat capacity and thermal conductivity. Those two chapters make excellent sources for this article. Footlessmouse (talk) 20:15, 20 November 2020 (UTC)

It also seems to me that large portions of this article are directly taken from chapter 6 of Aschroft and Mermin (1976) on "The Sommerfeld Theory of Metals". For instance, however, the whole of the "Final Expression" section is contained on page 47 of the book. I will begin adding references in the next couple of hours if no one else beats me to the punch. It seems that pretty much everything can be covered between those two texts, but we'll have a better idea once we get started. Footlessmouse (talk) 20:43, 20 November 2020 (UTC)

@Footlessmouse: I think the most important question to ask here is if the table has exactly the same values as Kittel's book. If yes, we can add the reference and clear up the template. If no, then it has to be cleaned up.--ReyHahn (talk) 21:36, 20 November 2020 (UTC)

@ReyHahn: All but Mn, Fe, and Co are correct. Those three metals only have observed values in the table and do not offer the calculations supplied in the table here. They could have been included in a previous edition, but that would be strange and begs the question on why they would be left out of a modern update. We should delete those rows and source the table, IMO. Footlessmouse (talk) 22:30, 20 November 2020 (UTC)

@ReyHahn: Yes, I indicate the page. I have the book of Kittel (2005), Introduction to Solid State Physics (8th ed.) ISBN 0-471-41526-X and it's page 146. I check all the value and make "?" where we don't have value. I think we can remove this ligne in the table.

Incorrect use of terminology

To be clear, according to Aschroft and Mermin, the electronic specific heat is specifically the specific heat of an electron gas. Though it may contribute (a very timy amount) to the specific heat of a metal, it is not defined as a component of the overall specific heat. I think it would be less confusing to rewrite this article. Footlessmouse (talk) 21:00, 20 November 2020 (UTC)

Agreed, it is misleading.--ReyHahn (talk) 21:37, 20 November 2020 (UTC)

@ReyHahn: with my talk of incorrect use of terminology, I missed one of the most glaring problem in the article: Specific heat and heat capacity are not the same thing. Do you know if electronic specific heat is more common than electron heat capacity? If so, we should move the page. Kittel doesn't significantly discuss either, but Ashcroft and Mermin spend a lot of time on electronic specific heat. Either way, I'm going to start working on a new lead to replace what's there and will ask for your comment when I am done. Thanks! Footlessmouse (talk) 19:22, 21 November 2020 (UTC)

Move to Electronic specific heat

@ReyHahn: if you do not object, I am going to move this page to electronic specific heat in the next couple of days without waiting on a formal discussion. All of the books use different terms, electronic specific heat is present in two of them, and all of the textbooks refer to specific heat even when they use the term "heat capacity" the specific part is implied. It honestly doesn't make a whole lot of sense to talk about the general heat capacity of electrons anyways. I do not own the book by Rosenberg, but have all the others and am trying to piece together a new lead and sources to fill out the page. But it needs to be moved to its proper name. If it weren't for conciseness, I would propose to move it to Specific heat of an electron gas, which is explicitly used in multiple sources. Footlessmouse (talk) 21:36, 21 November 2020 (UTC)

Sure go on with [[electronic specific heat, although Specific heat of an electron gas is not bad either.--ReyHahn (talk) 23:10, 21 November 2020 (UTC)

Derivation free electron model

The derivation has to be rewritten, there is an $\epsilon _{f}$ that is badly defined. I cannot tell if it is the Fermi energy of something else, and I do not understand why the ground state is important here. Fermi-Dirac distribution is weirdly defined. Phrases like This implies that the ground state is the only occupied state for electrons in the limit $T\rightarrow 0$ are worrysome for fermions. Also I am unsure that you can pass from writing a sum over the energies to an integral over k in the way is done here. The article first transforms the sum into an integral and later introduces the integrals with the density of states, this is confusing.--ReyHahn (talk) 12:13, 22 November 2020 (UTC)

ReyHahn, I think the whole page needs to be rewritten following sources. I'm confused about several parts of the article. It doesn't look like anyone is objecting to our edits, so we can go through and rewrite anything that misses the mark. I think it would be best to more or less rewrite the page section by section to bring it up to standards with verifiability and such. Footlessmouse (talk) 09:06, 27 November 2020 (UTC)