Editing Melting (section)

==Criteria==
{{See also|Melting point#Predicting the melting point of substances (Lindemann's criterion)|Lindemann index}}
Among the theoretical criteria for melting, the [[Frederick Lindemann, 1st Viscount Cherwell|Lindemann]]<ref>{{cite journal|first=F.A.|last=Lindemann|author-link=Frederick Lindemann, 1st Viscount Cherwell|journal=Physikalische Zeitschrift|volume=11|issue=14|year=1910|pages=609–614|title=Über die Berechnung molekularer Eigenfrequenzen|url=https://babel.hathitrust.org/cgi/pt?id=njp.32101054770845&view=1up&seq=147|language=de}}</ref> and [[Max Born|Born]]<ref>{{cite journal | last=Born | first=Max |author-link=Max Born | title=Thermodynamics of Crystals and Melting | journal=The Journal of Chemical Physics | publisher=AIP Publishing | volume=7 | issue=8 | year=1939 | issn=0021-9606 | doi=10.1063/1.1750497 | pages=591–603 | bibcode=1939JChPh...7..591B }}</ref> criteria are those most frequently used as a basis to analyse the melting conditions.

The Lindemann criterion states that melting occurs because of "vibrational instability", e.g. [[crystal]]s melt; when the average amplitude of thermal vibrations of atoms is relatively high compared with interatomic distances, e.g. <''δu<sup>2</sup>''><sup>1/2</sup> > ''δ<sub>L</sub>R<sub>s</sub>'', where ''δu'' is the atomic displacement, the Lindemann parameter ''δ<sub>L</sub>'' ≈ 0.20...0.25 and ''R<sub>s</sub>'' is one-half of the inter-atomic distance.<ref name="Rice2008">{{cite book|author=Stuart A. Rice|title=Advances in Chemical Physics|date=15 February 2008|publisher=John Wiley & Sons|isbn=978-0-470-23807-3}}</ref>{{rp|177}} The "Lindemann melting criterion" is supported by experimental data both for [[crystal]]line materials and for [[glass-liquid transition]]s in amorphous materials.

The Born criterion is based on a rigidity catastrophe caused by the vanishing elastic shear modulus, i.e. when the crystal no longer has sufficient rigidity to mechanically withstand the load, it becomes liquid.<ref>[[Robert W. Cahn]] (2001) [http://www.nature.com/nature/journal/v413/n6856/full/413582a0.html Materials science: Melting from Within], [[Nature (journal)|Nature]] 413 (#6856)</ref>