Talk:Debye model

Errors

There are some rather subtle errors on this page. I don't think the person responsible for the original lot of content really understands what the quantisation means. I'll put fixing this up on my holiday "to do" list. — Preceding unsigned comment added by 203.206.31.206 (talk) 04:16, 7 November 2011 (UTC)

Would somebody please remove Sapphire from the "table of Debye temperatures for several pure elements"? Maybe move it into a separate table for compounds? — Preceding unsigned comment added by 178.236.140.13 (talk) 11:47, 25 July 2013 (UTC)

Is there a typo in the Debye temperature for zinc? 237 K in and 234 K at http://www.infoplease.com/periodictable.php?id=30 — Preceding unsigned comment added by 131.188.6.12 (talk) 13:36, 8 August 2015 (UTC)

References

Untitled

• Does anybody have a good overlay of Debye, Einstein, and experimental data? This was originally in the article proper, but I figure here is a better place for it. Eldereft

I would like a figure showing: The Debye heat capacity, the low temperature limit, and the high temperature limit. Also a formula for the entropy according to Debye, and according to the limit formulae. Bo Jacoby 11:41, 19 October 2005 (UTC)

Hello Eric Kvaalen. You improved the accuracy of the article. I have a question. The factor 3 from polarization assumes that longitudinal and transversal waves move at the same speed. That is known not to be true. Can you please comment on that? Bo Jacoby 13:38, 21 October 2005 (UTC)

Hello again Eric Kvaalen. Your inclusion of the original Debye derivation is welcome, but the placement of it splits the debye formula from the asymptotic formulas, to make the latter unreadable. Find a better place to put it, please. Bo Jacoby 14:09, 31 October 2005 (UTC)

Intuitive idea of debye temperature

It seems to me that this article could be made slightly less technical (and more interesting for techies!), if the DeBye Temperature could be related to something intuitive. Somehow relating the heat capacity with other more tangible characteristics like hardness or whatever? Grj23 (talk) 15:08, 30 March 2009 (UTC)

it is the temperature which is required to excite all the phonon modes —Preceding unsigned comment added by 18.95.7.55 (talk) 15:00, 18 May 2009 (UTC)

Answering your question

Quote:

I have a question. The factor 3 from polarization assumes that longitudinal and transversal waves move at the same speed. That is known not to be true. Can you please comment on that? Bo Jacoby 13:38, 21 October 2005 (UTC)

Reply:

The 3 is from the freedom of in-x,y,z. That isn't from a polarization. It's said by my professor the day before yesterday. The main reason he talked in class is that phonon/sound is not like light wave which can have polarization. Just one mode only. Hmm...I might write math formula in physics:

${\mathcal {U}}=f\cdot {\frac {1}{2}}RT=6\cdot {\frac {1}{2}}RT=3RT$

Where f is as freedom,and U is as energy.

Hope I didn't make messy to your original question. However,even if the 3 in your question was supposed to mean 3 of ${\mathcal {,}}3RT,$,it might be still wrong. Because of "The factor 3 from polarization ". The reason was talked about in the early paragraph,you may be back to see. The other freedoms are from 2 of each direction's Kinetic and Potential energy. So $2\cdot 3=6$ is as the show of that formula,respectively. --HydrogenSu 19:46, 3 February 2006 (UTC)

Another reply:

Actually one works with one effective sound velocity $c_{s\,|\,{\rm {eff}}}$, which is a sum of contributions from the longitudinal and transverse sound velocities, respectively. Furthermore, the Debye temperature is proportional to this effective sound velocity, and thus measures the "hardness" of the crystal. More precisely one has

${\frac {1}{T_{D}^{3}}}$$\propto {\frac {1}{(c_{s\,|\,{\rm {eff}}})^{3}}}$$\,:={\frac {1}{c_{s\,|\,{\rm {long.}}}^{3}}}+{\frac {2}{c_{s\,|\,{\rm {trans.}}}^{3}}}$

87.160.85.141 (talk) 08:40, 16 August 2008 (UTC)

This article has many places that is not appropriate

As the title,in which Bose-Einstein's method of statics was put.....--HydrogenSu 15:18, 23 February 2006 (UTC)

Suggestion

[1]'s saying might be more complicated than that can be more easily done originally.

And we shall keep in mind that Debye's original derivation was easier and not yet involved something about Bose-Einstein's. --GyBlop 17:53, 26 February 2006 (UTC)

Beiser's and Blatt's saying might be easier than are here.--GyBlop 17:57, 26 February 2006 (UTC)

Clarification in Derivation section

Regarding the substitution $\nu _{n}=c_{s}/\lambda _{n}$, the article says,"We make the approximation that the frequency is inversely proportional to the wavelength..." Why is this necessarily an approximation? Leif (talk) 14:23, 12 June 2008 (UTC)

For phonons one has (at low frequencies) the approximate relation $\nu \propto {\frac {1}{\lambda }}$ between the frequency $\nu$ and the wavelength $\lambda$ of a wave. Actually this approximation applies only for long wavelengths, precisely for $\lambda \gg a$, where a is the lattice constant. This is in contrast to more complex behaviour, for example $\nu \propto \sin({\vec {k}}\cdot {\vec {a}})\,,$ for shorter wavelengths, e.g. comparable to a. For all wavelengths one has ${\vec {k}}={\frac {2\pi }{\lambda }}{\vec {e}}\,,$ where the vector ${\vec {e}}$ describes the direction of the wave-propagation. The second expression, with the $\sin$ function, corresponds at long wavelength to the expression given in the first-mentioned place.

The Debye model assumes(!), and this was actually at first glance a bold assumption, that the long-wavelength approximation is true (which actually is not the case) throughout the whole $\lambda$-range, up to the absolute high-frequency limit where $\lambda$ becomes as small as, e.g., 2a. Actually, it turned out that the assumption was not only bold, but also very clever; it just met the essential points both at low and at high temperatures. For other quasi-particles, e.g. magnons instead of the phonons, one has totally different relations, e.g. $\nu \propto {\frac {1}{\lambda ^{2}}}\,.$   But the essentials of the Debye model can be transferred even to this seemingly very different problem. - 87.160.123.57 (talk) 19:32, 15 August 2008 (UTC)

Dubious

In a few recent edits, 147.33.1.56 (talk · contribs · WHOIS) and 141.219.20.92 (talk · contribs · WHOIS) changed

$E_{n}^{2}=E_{nx}^{2}+E_{ny}^{2}+E_{nz}^{2}=\left({hc_{s} \over 2L}\right)^{2}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\right)\,.$

into

$E_{n}=E_{nx}+E_{ny}+E_{nz}=\left({hc_{s} \over 2L}\right)^{2}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\right)\,.$

It looks dubious to me! While I agree that energies are not added by Pythagoras' theorem, the right-hand side doesn't have any logic in it anymore. Knowers, please clarify! — Pt _(T) 12:26, 14 June 2009 (UTC)

One correct version is:  :$E_{n}^{2}=\left(E_{nx}+E_{ny}+E_{nz}\right)^{2}=\left({hc_{s} \over 2L}\right)^{2}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\right)\,.$ 141.211.99.69 (talk) 19:01, 21 October 2009 (UTC)

The equation as it is currently in the article ($E_{n}^{2}=E_{nx}^{2}+E_{ny}^{2}+E_{nz}^{2}=\left({hc_{s} \over 2L}\right)^{2}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\right)\,$) is --wrong--. Energy is a scalar; it doesn't add like a vector. The n^2 condition is due to imposing boundary conditions on a second order differential equation (schrodinger equation). See here--> http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html#c3 also. I'm changing it back to the correct formula.128.113.196.164 (talk) 23:15, 18 November 2009 (UTC)

This dispersion relation is linear in n . It would be the right one for photons but is wrong for phonons with wavelengths in the order of the lattice constant. For these the energy would be constant in a certain range of n corresponding to standing waves. Does Debye theorie take into account the dispersion relation for phonons as stated here: http://wiki.riteme.site/wiki/Phonon or does it simply ignore it? If it ignores it, the squares are ok. You measure the volume of your n space to compare it with the possible number of vibration modes. For that you need the Pythagoras. —Preceding unsigned comment added by 130.133.133.51 (talk) 16:42, 3 September 2010 (UTC)

Energy is not a vector quantity, and neither is wavelength, but the wave vector is... Obviously the confusion is caused by the use of the wavelength as the basic quantity in the derivation. It is much simpler to think about the wave vector (k) instead: The boundary conditions mean that k= pi/L n . Now, assuming linear dispersion, E=h/(2 pi) ck we get E^2= (hc/2L)^2 n ^2 . I'd write it down myself but as you can see I don't know how to properly create equations in wikipedia. Anyway, the linear dispersion is only an approximation, but it often works pretty well.

The entire derivation would be clearer had it been written in terms of the wave vector. I tried to motivate the final expression for the energy by adding in the dispersion relation $E^{2}=p_{n}^{2}c_{s}^{2}$ explicitly. It's clear that the equation $E^{2}\propto n_{x}^{2}+n_{y}^{2}+n_{z}^{2}$ is correct if you look at it as the dot product of the three-dimensional momentum vector with itself. Diracdeltas (talk) 00:32, 25 June 2011 (UTC)

Clarification

Check out this explanation. It's not supposed to make sense. As Richard Feynman once said, "I think I can safely say that nobody understands quantum mechanics." —Preceding unsigned comment added by 137.158.152.206 (talk) 11:30, 15 October 2009 (UTC)

When he said that I dont think he was talking about how to add energies. —Preceding unsigned comment added by 84.92.32.38 (talk) 19:30, 21 April 2011 (UTC)

Confusion Avogadro number/number of unit cells/total number of states

In this article, the letter capital N is used first as the number of unit cells, then 3N is said to equal the total number of states and last but not least, Cv/Nk ~ 3 which means N is the Avogadro number. I am not an expert on the subject, just a 6th semester physics student, but if anyone with suitable knowlegde about the topic could introduce a better notation (or at least clarify within the article), it would be great.

Added another Derivation

I added another derivation; if you find any errors or improvements, go ahead and edit it! Feedback is welcome as well. thedoctar (talk) 14:56, 9 June 2014 (UTC)

Btw, I added it because I thought the previous derivation was a bit confusing.

thedoctar (talk) 04:46, 10 June 2014 (UTC)

Merger proposal with Debye frequency article

I propose that Debye frequency be merged into this article, as the Debye frequency is a concept which doesn't exists outside this theory and the page for it is merely a stub.

--Pullus In Fabula (talk) 12:08, 26 November 2017 (UTC)

• Support! --Steve (talk) 15:50, 4 April 2018 (UTC)
• Comment surely Debye frequency is not a stub now. --MaoGo (talk) 10:29, 24 April 2018 (UTC)

It seems that User:Andeosr wasn't interested in the merge and so expanded the article greatly with this edit and subsequent ones (while removing a merge template). So, it was a stub when proposed, but is no longer. I also note that the concept of the Debye frequency doesn't seem to be used on the Debye model page. My physics is a bit rusty, but it may well be a concept that is independently notable. So, just as Mass in special relativity is a distinct page from Special relativity, so too it seems reasonable to keep Debye frequency separate from the Debye model page. Therefore, oppose. Klbrain (talk) 21:50, 22 January 2019 (UTC)

• Comment First of all I have to say that I’m a physics student and I made that article about Debye’s frequency as an assignment. There was a minimum amount of words I had to use, so some parts could be written much more briefly. Especially the paragraph “Allowing polarization to make a difference” is a lot of repition of the paragraph before that, and the last two paragraphs could probably be merged. If people think the three derivations for all three amounts of dimensions in the paragraph “Debye’s derivation” are also unnecessary, then the page could probably be merged with “The Debye Model” and be added as a chapter there, but I would recommend that at least the derivation for the one-dimensional system should be preserved (perhaps written more briefly as I said). I could do it if I have time, but I don’t mind if someone else would alter my work, as long as that person has at least as much understanding of theoretical physics as I do, and someone who has read Debye’s original texts more thoroughly. Andeosr (talk) 23:43, 22 January 2019 (UTC)
• Merge WP:NOTTEXTBOOK. Xxanthippe (talk) 10:19, 25 January 2019 (UTC).
• Merge as per Xxanthippe. --MaoGo (talk) 14:33, 25 January 2019 (UTC)

Moved all of the content over (consistent with WP:MERGETEXT); it can be refined in situ.   Y Merger complete. Klbrain (talk) 14:07, 23 June 2019 (UTC)

Structure, not lattice

All the occurrences of the term "lattice" in this article are used in an incorrect way. The article is about the vibrations of atoms, which build up a crystal structure, not of a "lattice" (the expression "lattice vibration" does not make any sense). I have corrected this once, but Xxanthippe reverted my changes. I contacted him on his talk page, but he seems to ignore my message. I post here to let know other contributors about this problem, before correcting again the mistakes in the article. --Mahlerite (talk) 22:13, 31 January 2019 (UTC)

So you require the 36 million references to "lattice dynamics" in Google [2] to be changed to "structure dynamics". I suggest you obtain consensus before making changes. Xxanthippe (talk) 02:15, 2 February 2019 (UTC).

Does an extensive use of a wrong expression make it less wrong? Do you know what a Bravais lattice is, and the difference between a lattice and a structure? --Mahlerite (talk) 17:58, 2 February 2019 (UTC)

Perhaps it would be best to obtain consensus for your views on the Wikipedia of your own native language before coming here. Xxanthippe (talk) 02:40, 3 February 2019 (UTC).

Could you give the definition of both words so we can be sure we are speaking in the same terms? --MaoGo (talk) 18:30, 2 February 2019 (UTC)

Cantab Physics and Materials 3rd Year Undergraduate, both times this has come up in courses it has been treated as lattice vibrations, again since the entire premise is based off the excitation of phonons in the lattice, which is how phonons have been defined, (example in Phonon) the term lattice should be retained. Tldr: Lattice vibration is the term used most in the literature. 131.111.5.184 (talk) 19:19, 2 February 2019 (UTC)

Terms like "lattice vibrations" are issued from a fundamental misunderstanding by people who do not know enough crystallography. I do not pretend to change a usage that, although incorrect, is by now rooted in the literature. But in the description of the phenomenon, one simply cannot confuse "lattice" with "structure". In the body of the article this mistake must be corrected. Many non-specialists come to WP to get a quick reference; it is therefore of paramount importance to avoid propagating such a fundamental mistake. --Mahlerite (talk) 10:05, 3 February 2019 (UTC)

@Mahlerite: could you elaborate on what is the difference between these terms? (according to you/your sources).--MaoGo (talk) 15:19, 5 February 2019 (UTC)

@Mahlerite: It would indeed be helpful, to demonstrate that your understanding of the subject is good enough for your views to be taken seriously here, if you would answer the question posed by MaoGo. Xxanthippe (talk) 21:32, 5 February 2019 (UTC).

Sorry for the late reply, I am not always on WP. A crystal is made up of atoms (ions, molecules...) which are distributed in a regular and periodic arrangement. In the description of its structure, we can neglect the presence of defects, at least in the first approximation, because the experimental investigation most commonly performed (diffraction, especially of X-rays) provides a space and time average where these defects are either "hidden" or treated as an average position (e.g. thermal vibrations about the equilibrium positions, sites partially occupied in case of disorder etc.). Time-resolved diffraction and other advanced techniques provide a more detailed picture, of course, but conventional experiments give indeed a time and space averaged picture. Therefore, we can describe a crystal structure with a model in which each atom occupies a precise point in space, about which it vibrates. The structure is periodic and can be obtained by pure translations applied to a smallest unit called the unit cell. This unit cell is a sort of "box" (container) where atoms are contained; the corners of the unit cell are called lattice nodes (better than "lattice points", also used often in the literature). In some very simple structures, the atoms are placed exactly on the lattice nodes, and this is probably the origin of the bad confusion between lattice nodes and atomic positions that we often see in the literature. However, in general, atomic positions are inside the unit cell, not on the lattice nodes. Take for example the hcp structure: atoms are in positions 1/3 2/3 1/4 and 2/3 1/3 3/4 in a hexagonal primitive unit cell, whereas lattice nodes are - obviously - in positions 0,0,0; 1,0,0; 0,1,0; 0,0,1; etc. Now, when you speak of the hcp structure (AB close packing of spheres) you address the atoms (content of the unit cell), not the lattice nodes that define the unit cell (container). These atoms vibrate (and not the lattice nodes) and the collective vibration produces phonons (although the hcp model is too simple to represent a real crystal). The lattice is just the collection of lattice nodes (imaginary points) the describe the periodicity of the structure. They do not exist other than in our minds: they are a very useful model, but what we are looking at are the atoms. Indeed, you have only 14 types of Bravais lattice (in 3D), but an infinite number of crystal structures. Too often people use the term "lattice" thinking about the distribution of atoms in space. But that is the structure (the "content"); the lattice is an infinite set of zero-dimensional points that we use to describe the periodicity of the structure through its unit cell (the "container"). I can provide more examples and details, as well as literature, if you find it useful. --Mahlerite (talk) 09:20, 6 February 2019 (UTC)

The statement above repeats textbook material, adding to it the fallacy that lattices are periodic. Most are not: in the last half-century there has been a vast number of theoretical and experimental studies of the vibrational spectra of amorphous condensed matter. But this is beside the point. Whether the editor’s idiosyncratic minority opinions are valid or not, and 30 million sources say that they are not, a Wikipedia talk page is not the appropriate forum in which to discuss them: Wikipedia:RIGHTGREATWRONGS. Wikipedia describes the world as it is, not as somebody thinks it should be. The editor should take his concerns to one of the many physics discussion forums that exist. Xxanthippe (talk) 00:18, 7 February 2019 (UTC).

Amorphous condensed matter are... amorphous (sic!), i.e. non-crystalline, and therefore possess no lattice! You do not understand the difference between a lattice and a structure but pretend to teach others about the subject. That's the limit of WP: when specialists in the field want to help and correct wrong statements, they have to convince non-specialists who are standing on their misunderstandings. Science is not the opinion of the largest number. But it seems I am wasting my time with you. --Mahlerite (talk) 06:31, 7 February 2019 (UTC)

FYI: the ridicoulous statement above is making scientists laugh --Mahlerite (talk) 13:15, 6 March 2019 (UTC)

Xxanthippe, I'm dismayed to find this - sorry I have to say this - not at all helpful statement of yours. Referring to Wikipedia:RIGHTGREATWRONGS is a smack in the face when all he asks for is to take a definition seriously. Your statement "the fallacy that lattices are periodic" is ridiculous, as lattices are periodic by their very definition (Check the Wikipedia articles, which refer back to the mathematical definition of lattices, if you don't believe it). It is the physical structure of materials that usually is not entirely (or not at all) periodic, but that is Mahlerite's point.WikiPidi (talk) 14:42, 5 March 2020 (UTC)

Another solid-state physicist here: Mahlerite is right in all but one factual point: In "For a two dimensional monatomic square lattice the Debye frequency is equal to" the term "lattice" is indeed correct, because if there is only a single atom per unit cell, the lattice is equivalent to the atomic positions. Yes, the lattice does not vibrate, and it is much more appropriate to call the structure vibrating. I admit that this field goes under lattice dynamics (and I find that heading appropriate, as the effect of translational symmetry is quite fundamental -- calling it structure dynamics would be much too general, as indeed the vibrational dynamics of amorphous solids have some similarities, but are fundamentally different), but the question here was not about renaming the whole field, but about what words to use in describing what happens. Does anybody want to argue that we should use the incorrect words? Seattle Jörg (talk) 21:40, 17 May 2020 (UTC)

Redundant section

The sections "Derivation with the actual dispersion relation" and "Alternative derivation" are virtually identical. Even the illustrating pictures are the same, the only difference being that one is animated, the other not. Comparing the sections, one appears to be written by a physicist, the other by a telecommunications engineer, each using corresponding language. But they are really talking the same thing. The Alternative claims to be about spatial frequencies as opposed to temporal (the other section), but with waves, this is not a proper distinction. I feel there is redundancy here, and propose to mention the terms Nyquist-Shannon and Aliasing in the section "Derivation with the actual dispersion relation", and delete the "Alternative derivation". WikiPidi (talk) 14:13, 5 March 2020 (UTC)

@WikiPidi: the sections that concern you came from a merge with a removed article (Debye frequency), please remove the additional content carefully.--MaoGo (talk) 15:12, 5 March 2020 (UTC)

I realised that when I looked up the history. But I also found out that BOTH sections came from the Debye frequency article. That article does not exist anymore as a separate entity, so I cannot investigate any further, hence some deliberation may be prudent.WikiPidi (talk) 15:46, 5 March 2020 (UTC)