# Melting

Ice melting

Melting is a physical process that results in the phase transition of a substance from a solid to a liquid. The internal energy of a substance is increased, typically by the application of heat or pressure, resulting in a rise of its temperature to the melting point, at which the ordering of ionic or molecular entities in the solid breaks down to a less ordered state and the solid liquefies. An object that has melted completely is molten. Substances in the molten state generally have reduced viscosity with elevated temperature; an exception to this maxim is the element sulfur, whose viscosity increases to a point due to polymerization and then decreases with higher temperatures in its molten state.[1]

Some organic compounds melt through mesophases, states of partial order between solid and liquid.

## Thermodynamics of melting

When a substance melts and the solid and liquid phases are in an equilibrium, it maintains a constant temperature, the melting point. The energy used for melting is a latent heat. This characterizes the process of melting as a first-order phase transition.

From a thermodynamics point of view, at the melting point the change in Gibbs free energy ∆G of the material is zero, but the enthalpy (H) and the entropy (S) of the material are increasing (∆H, ∆S > 0). Melting occurs when the Gibbs free energy of the liquid becomes lower than the solid for that material. The temperature at which this occurs is dependent on the ambient pressure.

Low-temperature helium is the only known exception to the general rule.[2] Helium-3 has a negative enthalpy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative enthalpy of fusion below 0.8 K. This means that, at appropriate constant pressures, heat must be removed from these substances in order to melt them.[3]

## Melting criteria

Among the theoretical criteria for melting, the Lindemann [4] and Born [5] 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. crystals melt when the average amplitude of thermal vibrations of atoms is relatively high compared with interatomic distances, e.g. <δu2>1/2 > δLRs, where δu is the atomic displacement, the Lindemann parameter δL ≈ 0.20...0.25 and Rs is a half of the inter-atomic distance.[6]:177 The Lindemann melting criterion is supported by experimental data both for crystalline materials and for glass-liquid transitions in amorphous materials. The Born criterion is based on rigidity catastrophe caused by the vanishing elastic shear modulus, e.g. when the crystal no longer has sufficient rigidity to mechanically withstand load.

## Supercooling

Under a standard set of conditions, the melting point of a substance is a characteristic property. The melting point is often equal to the freezing point. However, under carefully created conditions, supercooling or superheating past the melting or freezing point can occur. Water on a very clean glass surface will often supercool several degrees below the freezing point without freezing. Fine emulsions of pure water have been cooled to −38 degrees Celsius without nucleation to form ice.[citation needed]. Nucleation occurs due to fluctuations in the properties of the material. If the material is kept still there is often nothing (such a physical vibration) to trigger this change, and supercooling (or superheating) may occur. Thermodynamically, the supercooled liquid is in the metastable state with respect to the crystalline phase, and it is likely to crystallize suddenly.

## Melting of amorphous solids (glasses)

Glasses are amorphous solids (e.g. amorphous materials that are at temperatures below the glass transition temperature) which are usually fabricated when the viscous molten material cools very rapidly to below its glass transition temperature, without sufficient time for a regular crystal lattice to form. Whether a material is liquid or solid depends primarily on the connectivity between its elementary building blocks so that solids are characterised by a high degree of connectivity where as fluids occur at lower connectivity of the structural blocks. Melting of a solid material can also be considered as a percolation via broken connections between particles e.g. connecting bonds.[7] In this approach melting of an amorphous material occurs when the broken bonds form a percolation cluster with Tg dependent on quasi-equilibrium thermodynamic parameters of bonds e.g. on enthalpy (Hd) and entropy (Sd) of formation of bonds in a given system at given conditions:[8]

$T_g = \frac{H_d}{S_d+ R \ln(\frac{1-f_c}{f_c})},$

where fc is the percolation threshold and R is the universal gas constant. Although Hd and Sd are not true equilibrium thermodynamic parameters and can depend on the cooling rate of a melt they can be found from available experimental data on viscosity of amorphous materials.

## Premelting (surface melting)

Premelting (also: Surface melting) describes the fact that, even below its melting point $T_s$, quasi-liquid films can be observed on crystalline surfaces. The thickness of the film is temperature dependent. This effect is common for all crystalline materials. Premelting shows its effects in e.g. frost heave, the growth of snowflakes and, taking grain boundary interfaces into account, maybe even in the movement of glaciers.

## Related concepts

In genetics, melting DNA means to separate the double-stranded DNA into two single strands by heating or the use of chemical agents, cf. Polymerase chain reaction.

## References

1. ^ C.Michael Hogan (2011) Sulfur, Encyclopedia of Earth, eds. A.Jorgensen and C.J.Cleveland, National Council for Science and the environment, Washington DC
2. ^ Atkins, Peter; Jones, Loretta (2008), Chemical Principles: The Quest for Insight (4th ed.), W. H. Freeman and Company, p. 236, ISBN 0-7167-7355-4
3. ^ Ott, J. Bevan; Boerio-Goates, Juliana (2000), Chemical Thermodynamics: Advanced Applications, Academic Press, pp. 92–93, ISBN 0-12-530985-6
4. ^ F.A. Lindemann, Z. Phys. 11 (1910) 609–615.
5. ^ M. Born, J. Chem. Phys. 7 (1939) 591–601.
6. ^ Stuart A. Rice (15 February 2008). Advances in Chemical Physics. John Wiley & Sons. ISBN 978-0-470-23807-3.
7. ^ S.Y. Park and D. Stroud, Phys. Rev. B 67, 212202 (2003).
8. ^ M.I. Ojovan, W.E. Lee. J. Non-Cryst. Solids, 356, 2534–2540 (2010).