Talk:Debye model

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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 [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)

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)

For upstairs

I'm not able to help you. But I know that Einstein's failure of solids' ${\displaystyle {\mathcal {C}}_{v}}$was he made the assumption of vibration by oscillators is constant. In some sense of physics,it may be yes but in modern common-sense may not. 'Cause as heat inputs into a flat metal(as for instance),energy is enough to thread everywhere on and in it but cannot have to stay the same area always(by macroscopic view). Thus easily gets ${\displaystyle {\mathcal {\frac {\partial {U}}{\partial {T}}}}=3R}$ which stands only at higher Temperatures but at lower T is in vain. Very simple: The more energy the more T(not absolute) and the fewer the fewer T. So Einstein didn't consider more about physical pictures of oscillators vibrating at lower T. We might image that this kind of a picture. As:
         Money is giving to some people. They are closed in a room.
When it were lower T so that everyone is lazy.
This time giving money to them,they just a little happy
feeling.
When it were higher T so that everyone is happy. Giving
money to them doesn't "obviously" make them happier.

So Petit's and Einstein's theory of capacity just can show the yes at higher T but cannot at lower T. Something's hide.--HydrogenSu 19:24, 3 February 2006 (UTC)

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)

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:

${\displaystyle {\mathcal {U}}=f\cdot {\frac {1}{2}}RT=6\cdot {\frac {1}{2}}RT=3RT}$
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 ${\displaystyle {\mathcal {,}}3RT,}$,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 ${\displaystyle 2\cdot 3=6}$ is as the show of that formula,respectively. --HydrogenSu 19:46, 3 February 2006 (UTC)

Actually one works with one effective sound velocity ${\displaystyle c_{s\,|\,{\rm {eff}}}}$, 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
${\displaystyle {\frac {1}{T_{D}^{3}}}}$${\displaystyle \propto {\frac {1}{(c_{s\,|\,{\rm {eff}}})^{3}}}}$${\displaystyle \,:={\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)

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 ${\displaystyle \nu _{n}=c_{s}/\lambda _{n}}$, 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 ${\displaystyle \nu \propto {\frac {1}{\lambda }}}$ between the frequency ${\displaystyle \nu }$ and the wavelength ${\displaystyle \lambda }$ of a wave. Actually this approximation applies only for long wavelengths, precisely for ${\displaystyle \lambda \gg a}$, where a is the lattice constant. This is in contrast to more complex behaviour, for example ${\displaystyle \nu \propto \sin({\vec {k}}\cdot {\vec {a}})\,,}$ for shorter wavelengths, e.g. comparable to a. For all wavelengths one has ${\displaystyle {\vec {k}}={\frac {2\pi }{\lambda }}{\vec {e}}\,,}$ where the vector ${\displaystyle {\vec {e}}}$ describes the direction of the wave-propagation. The second expression, with the ${\displaystyle \sin }$ 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 ${\displaystyle \lambda }$-range, up to the absolute high-frequency limit where ${\displaystyle \lambda }$ 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. ${\displaystyle \nu \propto {\frac {1}{\lambda ^{2}}}\,.}$   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 and 141.219.20.92 changed

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

into

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

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

The equation as it is currently in the article (${\displaystyle E_{n}^{2}=E_{nx}^{2}+E_{ny}^{2}+E_{nz}^{2}=\left({hc_{s} \over 2L}\right)^{2}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\right)\,}$) 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://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 ${\displaystyle E^{2}=p_{n}^{2}c_{s}^{2}}$ explicitly. It's clear that the equation ${\displaystyle E^{2}\propto n_{x}^{2}+n_{y}^{2}+n_{z}^{2}}$ 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.

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)

• ^ p. I–10 in C. Y. Ho, R. W. Powell, and P. E. Liley. "Thermal Conductivity of the Elements: A Comprehensive Review." Journal of Physical and Chemical Reference Data, volume 3, supplement 1, 1974, pp. I–1 to I–796.