Editing Debye model (section)

== Debye temperature table ==
Even though the Debye model is not completely correct, it gives a good approximation for the low temperature heat capacity of insulating, crystalline solids where other contributions (such as highly mobile conduction electrons) are negligible. For metals, the electron contribution to the heat is proportional to <math>T</math>, which at low temperatures dominates the Debye <math>T^3</math> result for lattice vibrations. In this case, the Debye model can only be said to approximate the lattice contribution to the specific heat. The following table lists Debye temperatures for several pure elements<ref name=Kittel/> and sapphire:

{|
|
{| class="wikitable"
| [[Aluminium]]
| {{0}}428 K
|-
| [[Beryllium]]
| 1440 K
|-
| [[Cadmium]]
| {{0}}209 K
|-
| [[Caesium]]
| {{0}}{{0}}38 K
|-
| [[Carbon]] ([[diamond]])
| 2230 K
|-
| [[Chromium]]
| {{0}}630 K
|-
|}
||
{| class="wikitable"
| [[Copper]]
| {{0}}343 K
|-
| [[Germanium]]
| {{0}}374 K
|-
| [[Gold]]
| {{0}}170 K
|-
| [[Iron]]
| {{0}}470 K
|-
| [[Lead]]
| {{0}}105 K
|-
| [[Manganese]]
| {{0}}410 K
|-
|}
||
{| class="wikitable"
| [[Nickel]]
| {{0}}450 K
|-
| [[Platinum]]
| {{0}}240 K
|-
| [[Rubidium]]
| {{0}}{{0}}56 K
|-
| [[Sapphire]]
| 1047 K
|-
| [[Selenium]]
| {{0}}{{0}}90 K
|-
| [[Silicon]]
| {{0}}645 K
|}
||
{| class="wikitable"
| [[Silver]]
| {{0}}215 K
|-
| [[Tantalum]]
| {{0}}240 K
|-
| [[Tin]] (white)
| {{0}}200 K
|-
| [[Titanium]]
| {{0}}420 K
|-
| [[Tungsten]]
| {{0}}400 K
|-
| [[Zinc]]
| {{0}}327 K
|}
|
|}
The Debye model's fit to experimental data is often phenomenologically improved by allowing the Debye temperature to become temperature dependent;<ref>{{cite book |title=Solid-State Physics: Introduction to the Theory |first1=James D |last1=Patterson |first2=Bernard C. |last2=Bailey |publisher=Springer |isbn=978-3-540-34933-4 |year=2007 |pages=96–97}}</ref> for example, the value for ice increases from about 222 K<ref>{{Cite journal | last1 = Shulman | first1 = L. M. | doi = 10.1051/0004-6361:20031746 | title = The heat capacity of water ice in interstellar or interplanetary conditions | journal = Astronomy and Astrophysics | volume = 416 | pages = 187–190| year = 2004 |bibcode = 2004A&A...416..187S | doi-access = free }}</ref> to 300 K<ref>{{Cite journal | last1 = Flubacher | first1 = P. | last2 = Leadbetter | first2 = A. J. | last3 = Morrison | first3 = J. A. | doi = 10.1063/1.1731497 | title = Heat Capacity of Ice at Low Temperatures | journal = The Journal of Chemical Physics | volume = 33 | issue = 6 | pages = 1751 | year = 1960 |bibcode = 1960JChPh..33.1751F }}</ref> as the temperature goes from [[absolute zero]] to about 100 K.