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The '''Curie–Weiss law''' describes the [[magnetic susceptibility]] {{math| <var>&chi;</var>}} of a [[ferromagnet]] in the [[paramagnetic]] region above the [[Curie point]]:
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:<math>
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\chi = \frac{C}{T - T_{c}}
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</math>
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where {{math| <var>C</var>}} is a material-specific [[Curie constant]], {{math| <var>T</var>}} is absolute temperature, measured in [[kelvin]], and {{math| <var>T<sub>c</sub></var>}} is the [[Curie temperature]], measured in kelvin. The law predicts a singularity in the susceptibility at {{math| <var>T {{=}} T<sub>c</sub></var>}}. Below this temperature the ferromagnet has a [[spontaneous magnetization]].
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In many materials the Curie–Weiss law fails to describe the susceptibility in the immediate vicinity of the Curie point, since it is based on a [[mean field theory|mean-field approximation]]. Instead, there is a [[critical behavior]] of the form
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


:<math>
<!--'''PNG'''  (currently default in production)
\chi \sim \frac{1}{(T - T_{c})^\gamma}
:<math forcemathmode="png">E=mc^2</math>
</math>


with the [[critical exponent]] {{math| <var>&gamma;</var>}}. However, at temperatures {{math| <var>T ≫ T<sub>c</sub></var>}} the expression of the Curie–Weiss law still holds, but with {{math| <var>T<sub>c</sub></var>}} replaced by a temperature {{math| <var>&Theta;</var>}} that is somewhat higher than the actual Curie temperature. Some authors call {{math| <var>&Theta;</var>}} the '''Weiss constant''' to distinguish it from the temperature of the actual Curie point.
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


==Curie-Weiss Derivation==
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


The Curie-Weiss Law is an adapted version of Curie's Law, which for a paramagnetic material is<ref name=Hall205>{{harvnb|Hall|1994|pp=205–206}}</ref>
==Demos==


:<math>\chi = \frac{M}{H} =\frac{M \mu_0}{B} =\frac{C}{T} .</math>
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


Here µ<sub>0</sub> is the [[permeability of free space]];  ''M'' the [[magnetization]] ([[magnetic moment]] per unit volume), {{math|''B''{{=}}''µ''<sub>0</sub>''H''}} two measures of the [[magnetic field]], and ''C'' the material-specific [[Curie constant]]:


:<math>C = \frac{\mu_B^2}{3 k_B}N g^2 J(J+1),</math>
* accessibility:
where {{math|''k''<sub>B</sub>}} is [[Boltzmann's constant]], {{math|''N''}} the number of magnetic atoms (or molecules) per unit volume, {{math|''g''}} the [[Landé g-factor]], {{math|''&mu;''<sub>B</sub>}} the [[Bohr magneton]], {{math|''J''}} the [[angular momentum]] quantum number.<ref name=Levy201>{{harvnb|Levy|1968|pp=201–202}}</ref>
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
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** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


For the Curie-Weiss Law the total magnetic field is {{math|''B+λM''}} where {{math|''λ''}} is the Weiss molecular field constant and then
==Test pages ==


:<math>\chi =\frac{M \mu_0}{B}</math> → <math>\frac{M \mu_0}{B+\lambda M} =\frac{C}{T}</math>
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
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which can be rearranged to get
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
:<math>\chi = \frac{C}{T \mu_0-C \lambda}</math>
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
which is the Curie-Weiss Law
 
:<math>
\chi = \frac{C}{T - T_{c}}
</math>
where the [[Curie Temperature]] {{math|''T''<sub>C</sub>}} is
 
:<math>T_C = \frac{C \lambda }{\mu_0}</math>
 
==See also==
*[[Curie's law]]
*[[Paramagnetism]]
*[[Pierre Curie]]
*[[Pierre-Ernest Weiss]]
 
== Notes ==
 
{{reflist}}
 
==References==
*{{cite book|last=Kittel|first=Charles|title=Introduction to solid state physics|year=1996|publisher=Wiley|location=New York [u.a.]|isbn=978-0471111818|edition=7th}}
*{{cite book|last=Hall|first=J.R. Hook, H.E.|title=Solid state physics|year=1994|publisher=Wiley|location=Chichester|isbn=0471928054|edition=2nd |ref=harv}}
*{{cite book|last=Levy|first=Robert A|title=Principles of Solid State Physics|year=1968|publisher=Academic Press |isbn=978-0124457508|ref=harv}}
 
==External links==
* [http://www.cond-mat.de/events/correl13/manuscripts/pavarini.pdf Magnetism: Models and Mechanisms] in E.  Pavarini, E. Koch, and U. Schollwöck: Emergent Phenomena in Correlated Matter, Jülich 2013, ISBN 978-3-89336-884-6
 
{{DEFAULTSORT:Curie-Weiss law}}
<!--Categories-->
[[Category:Magnetic ordering]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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