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{{for2|the physical processes that takes place at the melting point|[[Melting]], [[Freezing]] and [[Crystallization]]}}

The '''melting point''' (or, rarely, '''liquefaction point''') of a solid is the temperature at which it changes [[states of matter|state]] from [[solid]] to [[liquid]] at atmospheric pressure. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends (usually slightly) on pressure and is usually specified at [[Standard conditions for temperature and pressure|standard]] pressure. When considered as the temperature of the reverse change from liquid to solid, it is referred to as the '''freezing point''' or '''crystallization point'''. Because of the ability of some substances to [[supercool]], the freezing point is not considered as a characteristic property of a substance. When the "characteristic freezing point" of a substance is determined, in fact the actual methodology is almost always "the principle of observing the disappearance rather than the formation of ice", that is, the [[#Melting point measurements|melting point]].<ref>{{cite journal |url= http://jeb.biologists.org/cgi/reprint/26/1/57.pdf |title= A new method of freezing-point determination for small quantities |author= Ramsay, J. A. |journal= [[J. Exp. Biol.]] |year= 1949 |volume= 26 |issue= 1 |pages= 57–64 |pmid= 15406812}}</ref>

==Examples==
[[File:Carboxylic.Acids.Melting.&.Boiling.Points.jpg|thumb|right|Melting points (in blue) and boiling points (in pink) of the first eight [[carboxylic acids]] (°C)]]For most substances, [[melting]] and [[freezing]] points are approximately equal. For example, the melting point ''and'' freezing point of [[mercury (element)|mercury]] is 234.32 [[kelvin]] (−38.83&nbsp;[[Celsius|°C]] or −37.89&nbsp;[[Fahrenheit|°F]]).<ref>[[#Haynes|Haynes]], p. 4.122.</ref> However, certain substances possess differing solid-liquid transition temperatures. For example, [[agar]] melts at 85&nbsp;°C (185&nbsp;°F) and solidifies from 31&nbsp;°C to 40&nbsp;°C (89.6&nbsp;°F to 104&nbsp;°F); such direction dependence is known as [[hysteresis]].

The melting point of [[ice]] at 1 atmosphere of pressure is very close <ref>The melting point of purified water has been measured as 0.002519 ± 0.000002 °C, see {{cite journal|author = Feistel, R. and Wagner, W. |year = 2006
|title = A New Equation of State for H<sub>2</sub>O Ice Ih
|journal = J. Phys. Chem. Ref. Data|volume = 35|issue = 2
|pages = 1021–1047
|doi = 10.1063/1.2183324|bibcode = 2006JPCRD..35.1021F }}
</ref> to 0&nbsp;°C (32&nbsp;°F, 273.15&nbsp;K); this is also known as the '''ice point'''. In the presence of [[Nucleation|nucleating substances]] the freezing point of water is the same as the melting point, but in the absence of nucleators water can [[Supercooling|supercool]] to −42&nbsp;°C (−43.6&nbsp;°F, 231&nbsp;K) before freezing.

The [[chemical element]] with the highest melting point is [[tungsten]], at 3687 K (3414 °C, 6177 °F)<ref>[[#Haynes|Haynes]], p. 4.123.</ref> making it excellent for use as filaments in light bulbs. The often-cited [[carbon]] does not melt at ambient pressure but [[sublimation (physics)|sublimes]] at about 4000&nbsp;K; a liquid phase only exists above pressures of 10&nbsp;[[Pascal (unit)|MPa]] and estimated 4300–4700&nbsp;K (see [[:File:Carbon basic phase diagram.png|Carbon phase diagram]]). [[Tantalum hafnium carbide]] (Ta<sub>4</sub>HfC<sub>5</sub>) is a [[refractory]] compound with a very high melting point of 4488&nbsp;K (4215&nbsp;°C, 7619&nbsp;°F).<ref>{{cite journal|title=Researches on Systems with Carbides at High Melting Point and Contributions to the Problem of Carbon Fusion|journal=Z. Tech. Physik|author=Agte, C., and Alterthum, H.| volume= 11|year= 1930|pages=182–191}}</ref> At the other end of the scale, [[helium]] does not freeze at all at normal pressure, even at temperatures very close to [[absolute zero]]; pressures over 20 times normal atmospheric pressure are necessary.

==Melting point measurements==
{{main|Melting point apparatus}}
[[File:Koflerbank.jpg|thumb|Kofler bench with samples for calibration]]
Many [[laboratory techniques]] exist for the determination of melting points.
A [[Kofler bench]] is a metal strip with a temperature gradient (range from room temperature to 300 °C). Any substance can be placed on a section of the strip revealing its thermal behaviour at the temperature at that point. [[Differential scanning calorimetry]] gives information on melting point together with its [[enthalpy of fusion]].

[[File:KruessM5k.jpg|thumb|Automatic digital melting point meter]]
A basic melting point apparatus for the analysis of crystalline solids consists of an [[oil bath]] with a transparent window (most basic design: a [[Thiele tube]]) and a simple magnifier. The several grains of a solid are placed in a thin glass tube and partially immersed in the oil bath. The oil bath is heated (and stirred) and with the aid of the magnifier (and external light source) melting of the individual crystals at a certain temperature can be observed. In large/small devices, the sample is placed in a heating block, and optical detection is automated.

The measurement can also be made continuously with an operating process. For instance, oil refineries measure the freeze point of diesel fuel online, meaning that the sample is taken from the process and measured automatically. This allows for more frequent measurements as the sample does not have to be manually collected and taken to a remote laboratory.

==Thermodynamics==
[[File:Melting curve of water.jpg|thumb|right|Pressure dependence of water melting point]]Not only is heat required to raise the temperature of the solid to the melting point, but the melting itself requires heat called the [[heat of fusion]].

From a thermodynamics point of view, at the melting point the change in [[Gibbs free energy]] (ΔG) of the material is zero, but the [[enthalpy]] (''H'') and the [[entropy]] (''S'') of the material are increasing (ΔH, ΔS > 0). Melting phenomenon happens when the Gibbs free energy of the liquid becomes lower than the solid for that material. At various pressures this happens at a specific temperature. It can also be shown that:

: <math>\Delta S = \frac {\Delta H} {T}</math>

Here ''T'', ''ΔS'' and ''ΔH'' are respectively the [[temperature]] at the melting point, change of [[entropy]] of melting and the change of [[enthalpy]] of melting.

The melting point is sensitive to extremely large changes in [[pressure]], but generally this sensitivity is orders of magnitude less than that for the [[boiling point]], because the solid-liquid transition represents only a small change in volume.<ref>The exact relationship is expressed in the [[Clausius-Clapeyron relation]].</ref><ref>{{cite web |url= http://mpec.sc.mahidol.ac.th/RADOK/physmath/PHYSICS/j10.htm |title= J10 Heat: Change of aggregate state of substances through change of heat content: Change of aggregate state of substances and the equation of Clapeyron-Clausius |accessdate= 2008-02-19}}</ref> If, as observed in most cases, a substance is more dense in the solid than in the liquid state, the melting point will increase with increases in pressure. Otherwise the reverse behavior occurs. Notably, this is the case of water, as illustrated graphically to the right, but also of Si, Ge, Ga, Bi. With extremely large changes in pressure, substantial changes to the melting point are observed. For example, the melting point of silicon at ambient pressure (0.1 MPa) is 1415 °C, but at pressures in excess of 10 GPa it decreases to 1000 °C.<ref>Tonkov, E. Yu. and Ponyatovsky, E. G. (2005) ''Phase Transformations of Elements Under High Pressure'', CRC Press, Boca Raton, p. 98 ISBN 0-8493-3367-9</ref>
Melting points are often used to characterize organic and inorganic compounds and to ascertain their [[wiktionary:Purity|purity]]. The melting point of a pure substance is always higher and has a smaller range than the melting point of an impure substance or, more generally, of mixtures. The higher the quantity of other components, the lower the melting point and the broader will be the melting point range, often referred to as the pasty range. The temperature at which melting begins for a mixture is known as the solidus while the temperature where melting is complete is called the liquidus. Eutectics are special types of mixtures that behave like single phases. They melt sharply at a constant temperature to form a liquid of the same composition. Alternatively, on cooling a liquid with the eutectic composition will solidify as uniformly dispersed, small (fine-grained) mixed crystals with the same composition.

In contrast to crystalline solids, [[glass]]es do not possess a melting point;
on heating they undergo a smooth [[glass transition]] into a [[viscous liquid]].
Upon further heating, they gradually soften, which can be characterized by certain [[softening point]]s.

==Freezing-point depression==
{{main|Freezing-point depression}}

The freezing point of a [[solvent]] is depressed when another compound is added, meaning that a [[solution]] has a lower freezing point than a pure solvent. This phenomenon is used in technical applications to avoid freezing, for instance by adding salt or ethylene glycol to water.

==Carnelley's Rule==
In [[organic chemistry]] '''Carnelley's Rule''', established in 1882 by Thomas Carnelley, stated that ''high [[molecular symmetry]] is associated with high melting point''.<ref>{{cite journal |title= Melting Point and Molecular Symmetry |journal= [[Journal of Chemical Education]] |page= 724 |volume= 77 |issue= 6 |year= 2000 |doi= 10.1021/ed077p724 |author=Brown, R. J. C. & R. F. C.|bibcode = 2000JChEd..77..724B }}</ref> Carnelley based his rule on examination of 15,000 chemical compounds. For example for three [[structural isomer]]s with [[molecular formula]] C<sub>5</sub>H<sub>12</sub> the melting point increases in the series [[isopentane]] −160 °C (113 K) [[n-pentane]] −129.8 °C (143 K) and [[neopentane]] −16.4 °C (256.8 K).<ref>[[#Haynes|Haynes]], pp. 6.153–155.</ref> Likewise in [[xylene]]s and also [[dichlorobenzene]]s the melting point increases in the order [[arene substitution patterns|meta, ortho and then para]]. [[Pyridine]] has a lower symmetry than [[benzene]] hence its lower melting point but the melting point again increases with [[diazine]] and [[triazine]]s. Many cage-like compounds like [[adamantane]] and [[cubane]] with high symmetry have relatively high melting points.

A high melting point results from a high [[heat of fusion]], a low [[entropy of fusion]], or a combination of both. In highly symmetrical molecules the crystal phase is densely packed with many efficient intermolecular interactions resulting in a higher enthalpy change on melting.

==Predicting the melting point of substances (Lindemann's criterion)==
An attempt to predict the bulk melting point of crystalline materials was first made in 1910 by [[Frederick Lindemann]].<ref name="Lindemann1910">{{cite journal |author=Lindemann FA |title=The calculation of molecular vibration frequencies |journal=Physik. Z. |volume=11 |year=1910 |pages=609–612 |authorlink=Frederick Lindemann}}</ref> The idea behind the theory was the observation that the average amplitude of thermal vibrations increases with increasing temperature. Melting initiates when the amplitude of vibration becomes large enough for adjacent atoms to partly occupy the same space. The '''Lindemann criterion''' states that melting is expected when the root mean square vibration amplitude exceeds a threshold value.

Assuming that all atoms in a crystal vibrate with the same frequency ''ν'', the average thermal energy can be estimated using the [[equipartition theorem]] as<ref name=Sorkin>Sorkin, S., (2003), [http://phycomp.technion.ac.il/~phsorkin/thesis/thesis.html Point defects, lattice structure, and melting], Thesis, Technion, Israel.</ref>
:<math>
 E = 4\pi^2 m \nu^2~u^2 = k_B T
 </math>
where ''m'' is the [[atomic mass]], ''ν'' is the [[frequency]], ''u'' is the average vibration amplitude, k<sub>B</sub> is the [[Boltzmann constant]], and ''T'' is the [[Thermodynamic temperature|absolute temperature]]. If the threshold value of ''u<sup>2</sup>'' is ''c<sup>2</sup>a<sup>2</sup>'' where ''c'' is the [[Lindemann index|Lindemann constant]] and ''a'' is the [[atomic spacing]], then the melting point is estimated as
:<math>
 T_m = \cfrac{4\pi^2 m \nu^2 c^2 a^2}{k_B} .
 </math>
Several other expressions for the estimated melting temperature can be obtained depending on the estimate of the average thermal energy. Another commonly used expression for the Lindemann criterion is<ref name=Hofmann>{{cite book|author=Philip Hofmann|title=Solid state physics: an introduction|url=http://books.google.com/books?id=XfIpxi4kcM4C&pg=PA67|accessdate=13 March 2011|year=2008|publisher=Wiley-VCH|isbn=978-3-527-40861-0|page=67}}</ref>
:<math>
 T_m = \cfrac{m \nu^2 c^2 a^2}{k_B} .
 </math>
From the expression for the [[Debye frequency]] for ''ν'', we have
:<math>
 T_m = \cfrac{2\pi m c^2 a^2 \theta_D^2 k_B}{h^2}
 </math>
where θ<sub>D</sub> is the [[Debye temperature]] and ''h'' is the [[Planck constant]]. Values of ''c'' range from 0.15–0.3 for most materials.<ref name=Nelson>Nelson, D. R., (2002), [http://books.google.com/books?id=YtYFAqswRzUC&printsec=frontcover Defects and geometry in condensed matter physics], Cambridge University Press, ISBN 0-521-00400-4</ref>

==Open melting point data==
In February 2011<ref name=Bradley>Bradley, J-C., (2011), [http://usefulchem.blogspot.com/2011/02/alfa-aesar-melting-point-data-now.html Alfa Aesar melting point data now openly available]</ref> [[Alfa Aesar]] released over 10,000 melting points of compounds from their catalog as [[open data]]. These data have been curated and are freely available for download.<ref name=BradleyLang>[http://lxsrv7.oru.edu/~alang/meltingpoints/download.php Open Melting Point Datasets]. Lxsrv7.oru.edu. Retrieved on 2013-09-13.</ref> These data have been used to create a [[random forest]] model for melting point prediction<ref name=Lang>Bradley, J-C. and Lang A.S.I.D. (2011) [http://onschallenge.wikispaces.com/MeltingPointModel010 Random Forest model for melting point prediction]. onschallenge.wikispaces.com</ref> which is now available as a free-to-use webservice.<ref name=LangGuha>[http://www.qsardb.org/repository/predictor/10967/104?model=rf Predict melting point from SMILES]. Qsardb.org. Retrieved on 2013-09-13.</ref> Highly curated and open melting point data are also available from [[Nature Precedings]].<ref name=Williams>[http://precedings.nature.com/documents/6229/version/1 ONS Open Melting Point Collection]. Precedings.nature.com. Retrieved on 2013-09-13.</ref>

==See also==
* [[Liquidus temperature]]
* [[List of elements by melting point]]
* [[Melting points of the elements (data page)]]
* [[Phase (matter)|Phases of matter]]
* [[Triple point]]
* [[Slip melting point]]
* [[Solidus temperature]]

==References==
{{reflist|30em}}

==Bibliography==
*{{cite book|ref=Haynes|editor=Haynes, William M.|year=2011|title= CRC Handbook of Chemistry and Physics |edition=92nd ed.|publisher= CRC Press|isbn=1439855110}}

==External links==
* [http://www.archive.org/details/meltingboilingpo01carnuoft Melting and boiling point tables vol. 1] by Thomas Carnelley (Harrison, London, 1885–1887)
* [http://www.archive.org/details/meltingboilingpo02carnuoft Melting and boiling point tables vol. 2] by Thomas Carnelley (Harrison, London, 1885–1887)
* [http://lxsrv7.oru.edu/~alang/meltingpoints/ ONS melting point explorer] Over 10,000 [[Open Data]] melting points.

{{State of matter}}
{{Use dmy dates|date=June 2011}}

{{DEFAULTSORT:Melting Point}}
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