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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 [1] 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
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)
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)
Quote:
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:
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 ,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 is as the show of that formula,respectively. -- HydrogenSu 19:46, 3 February 2006 (UTC)
Another reply:
As the title,in which Bose-Einstein's method of statics was put.....-- HydrogenSu 15:18, 23 February 2006 (UTC)
[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)
Regarding the substitution , 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)
In a few recent edits, 147.33.1.56 ( talk · contribs · WHOIS) and 141.219.20.92 ( talk · contribs · WHOIS) changed
into
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: : 141.211.99.69 ( talk) 19:01, 21 October 2009 (UTC)
The equation as it is currently in the article () 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://en.wikipedia.org/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 explicitly. It's clear that the equation 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)
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)
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.
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)
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)
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)
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)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
![]() | The contents of the Debye frequency page were merged into Debye model on 23 June 2019. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
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 [1] 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
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)
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)
Quote:
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:
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 ,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 is as the show of that formula,respectively. -- HydrogenSu 19:46, 3 February 2006 (UTC)
Another reply:
As the title,in which Bose-Einstein's method of statics was put.....-- HydrogenSu 15:18, 23 February 2006 (UTC)
[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)
Regarding the substitution , 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)
In a few recent edits, 147.33.1.56 ( talk · contribs · WHOIS) and 141.219.20.92 ( talk · contribs · WHOIS) changed
into
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: : 141.211.99.69 ( talk) 19:01, 21 October 2009 (UTC)
The equation as it is currently in the article () 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://en.wikipedia.org/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 explicitly. It's clear that the equation 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)
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)
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.
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)
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)
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)
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)