# Melting point

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The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at a standard pressure such as 1 atmosphere or 100 kPa.

## Contents

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. [1]

## Examples

For most substances, melting and freezing points are approximately equal. For example, the melting point and freezing point of mercury is 234.32 Kelvin (−38.83  °C or −37.89  °F). [2] However, certain substances possess differing solid-liquid transition temperatures. For example, agar melts at 85 °C (185 °F) and solidifies from 31 °C (88 °F; 304 K); such direction dependence is known as hysteresis. The melting point of ice at 1 atmosphere of pressure is very close [3] to 0 °C (32 °F; 273 K); this is also known as the ice point. In the presence of nucleating substances, the freezing point of water is not always the same as the melting point. In the absence of nucleators water can exist as a supercooled liquid down to −48.3 °C (−55 °F, 224.8 K) before freezing.

The chemical element with the highest melting point is tungsten, at 3,414 °C (6,177 °F; 3,687 K); [4] this property makes tungsten excellent for use as filaments in light bulbs. The often-cited carbon does not melt at ambient pressure but sublimes at about 3,726.85 °C (6,740.33 °F; 4,000.00 K); a liquid phase only exists above pressures of 10 MPa (99 atm) and estimated 4,030–4,430 °C (7,290–8,010 °F; 4,300–4,700 K) (see carbon phase diagram). Tantalum hafnium carbide (Ta4HfC5) is a refractory compound with a very high melting point of 4215 K (3942 °C, 7128 °F). [5] Quantum mechanical computer simulations have predicted that the alloy HfN0.38C0.51 has an even higher melting point (about 4400 K), making it the substance with the highest known melting point at ambient pressure. [6] At the other end of the scale, helium does not freeze at all at normal pressure even at temperatures arbitrarily close to absolute zero; a pressure of more than twenty times normal atmospheric pressure is necessary.

List of common chemicals
Chemical [upper-roman 1] Density (/)Melt () [7] Boil (K)
Water @STP1273373
Solder (Pb60Sn40)456
Cocoa butter 307.2-
Paraffin wax 0.9310643
Hydrogen 0.0000898814.0120.28
Helium 0.0001785 [upper-roman 2] 4.22
Beryllium 1.8515602742
Carbon 2.26738004300
Nitrogen 0.001250663.1577.36
Oxygen 0.00142954.3690.20
Sodium 0.971370.871156
Magnesium 1.7389231363
Aluminium 2.698933.472792
Sulfur 2.067388.36717.87
Chlorine 0.003214171.6239.11
Potassium 0.862336.531032
Titanium 4.5419413560
Iron 7.87418113134
Nickel 8.91217283186
Copper 8.961357.772835
Zinc 7.134692.881180
Gallium 5.907302.91462673
Silver 10.5011234.932435
Indium 7.31429.752345
Iodine 4.93386.85457.4
Tantalum 16.65432905731
Tungsten 19.2536955828
Platinum 21.462041.44098
Gold 19.2821337.333129
Mercury 13.5336234.43629.88
Bismuth 9.807544.71837

Notes

1. Z is the standard symbol for atomic number; C is the standard symbol for heat capacity; and χ is the standard symbol for electronegativity on the Pauling scale.
2. Helium does not solidify at a pressure of one atmosphere. Helium can only solidify at pressures above 25 atmospheres, which corresponds to a melting point of absolute zero.

## Melting point measurements

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.

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.

### Techniques for refractory materials

For refractory materials (e.g. platinum, tungsten, tantalum, some carbides and nitrides, etc.) the extremely high melting point (typically considered to be above, say, 1800 °C) may be determined by heating the material in a black body furnace and measuring the black-body temperature with an optical pyrometer. For the highest melting materials, this may require extrapolation by several hundred degrees. The spectral radiance from an incandescent body is known to be a function of its temperature. An optical pyrometer matches the radiance of a body under study to the radiance of a source that has been previously calibrated as a function of temperature. In this way, the measurement of the absolute magnitude of the intensity of radiation is unnecessary. However, known temperatures must be used to determine the calibration of the pyrometer. For temperatures above the calibration range of the source, an extrapolation technique must be employed. This extrapolation is accomplished by using Planck's law of radiation. The constants in this equation are not known with sufficient accuracy, causing errors in the extrapolation to become larger at higher temperatures. However, standard techniques have been developed to perform this extrapolation.

Consider the case of using gold as the source (mp = 1063 °C). In this technique, the current through the filament of the pyrometer is adjusted until the light intensity of the filament matches that of a black-body at the melting point of gold. This establishes the primary calibration temperature and can be expressed in terms of current through the pyrometer lamp. With the same current setting, the pyrometer is sighted on another black-body at a higher temperature. An absorbing medium of known transmission is inserted between the pyrometer and this black-body. The temperature of the black-body is then adjusted until a match exists between its intensity and that of the pyrometer filament. The true higher temperature of the black-body is then determined from Planck's Law. The absorbing medium is then removed and the current through the filament is adjusted to match the filament intensity to that of the black-body. This establishes a second calibration point for the pyrometer. This step is repeated to carry the calibration to higher temperatures. Now, temperatures and their corresponding pyrometer filament currents are known and a curve of temperature versus current can be drawn. This curve can then be extrapolated to very high temperatures.

In determining melting points of a refractory substance by this method, it is necessary to either have black body conditions or to know the emissivity of the material being measured. The containment of the high melting material in the liquid state may introduce experimental difficulties. Melting temperatures of some refractory metals have thus been measured by observing the radiation from a black body cavity in solid metal specimens that were much longer than they were wide. To form such a cavity, a hole is drilled perpendicular to the long axis at the center of a rod of the material. These rods are then heated by passing a very large current through them, and the radiation emitted from the hole is observed with an optical pyrometer. The point of melting is indicated by the darkening of the hole when the liquid phase appears, destroying the black body conditions. Today, containerless laser heating techniques, combined with fast pyrometers and spectro-pyrometers, are employed to allow for precise control of the time for which the sample is kept at extreme temperatures. Such experiments of sub-second duration address several of the challenges associated with more traditional melting point measurements made at very high temperatures, such as sample vaporization and reaction with the container.

## Thermodynamics

For a solid to melt, heat is required to raise its temperature to the melting point. However, further heat needs to be supplied for the melting to take place: this is called the heat of fusion, and is an example of latent heat.

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:

${\displaystyle \Delta S={\frac {\Delta H}{T}}}$

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. [8] [9] 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. [10]

Melting points are often used to characterize organic and inorganic compounds and to ascertain their 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, glasses 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 points.

## 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, states that high molecular symmetry is associated with high melting point. [11] Carnelley based his rule on examination of 15,000 chemical compounds. For example, for three structural isomers with molecular formula C5H12 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). [12] Likewise in xylenes and also dichlorobenzenes the melting point increases in the order 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 triazines. 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. [14] 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 vibration root mean square 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 [15]

${\displaystyle E=4\pi ^{2}m\nu ^{2}~u^{2}=k_{\rm {B}}T}$

where m is the atomic mass, ν is the frequency, u is the average vibration amplitude, kB is the Boltzmann constant, and T is the absolute temperature. If the threshold value of u2 is c2a2 where c is the Lindemann constant and a is the atomic spacing, then the melting point is estimated as

${\displaystyle T_{\rm {m}}={\cfrac {4\pi ^{2}m\nu ^{2}c^{2}a^{2}}{k_{\rm {B}}}}.}$

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 [16]

${\displaystyle T_{\rm {m}}={\cfrac {4\pi ^{2}m\nu ^{2}c^{2}a^{2}}{2k_{\rm {B}}}}.}$

From the expression for the Debye frequency for ν, we have

${\displaystyle T_{\rm {m}}={\cfrac {2\pi mc^{2}a^{2}\theta _{\rm {D}}^{2}k_{\rm {B}}}{h^{2}}}}$

where θD is the Debye temperature and h is the Planck constant. Values of c range from 0.15–0.3 for most materials. [17]

## Melting point prediction

In February 2011, Alfa Aesar released over 10,000 melting points of compounds from their catalog as open data. This dataset has been used to create a random forest model for melting point prediction which is now freely available. [18] Open melting point data are also available from Nature Precedings . [19] High quality data mined from patents and also models [20] developed with these data were published by Tetko et al. [21]

## Related Research Articles

The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which increases the substance's temperature to the melting point. At the melting point, the ordering of ions or molecules in the solid breaks down to a less ordered state, and the solid melts to become a liquid.

In the physical sciences, a phase is a region of space, throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase.

In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases of that substance coexist in thermodynamic equilibrium. It is that temperature and pressure at which the sublimation curve, fusion curve and the vaporisation curve meet. For example, the triple point of mercury occurs at a temperature of −38.83440 °C and a pressure of 0.2 mPa.

The enthalpy of vaporization, also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance, to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

Vapor pressure or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of particles to escape from the liquid. A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The pressure exhibited by vapor present above a liquid surface is known as vapor pressure. As the temperature of a liquid increases, the kinetic energy of its molecules also increases. As the kinetic energy of the molecules increases, the number of molecules transitioning into a vapor also increases, thereby increasing the vapor pressure.

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

The term phase transition is most commonly used to describe transitions between solid, liquid, and gaseous states of matter, as well as plasma in rare cases. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of external conditions, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions commonly occur in nature and are used today in many technologies.

A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases occur and coexist at equilibrium.

In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI derived unit of m²/s. Thermal diffusivity is usually denoted α but a,h,κ, K, and D are also used. The formula is:

Latent heat is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition.

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

Freezing is a phase transition where a liquid turns into a solid when its temperature is lowered below its freezing point. In accordance with the internationally established definition, freezing means the solidification phase change of a liquid or the liquid content of a substance, usually due to cooling.

Sublimation is the transition of a substance directly from the solid to the gas phase, without passing through the intermediate liquid phase. Sublimation is an endothermic process that occurs at temperatures and pressures below a substance's triple point in its phase diagram, which corresponds to the lowest pressure at which the substance can exist as a liquid. The reverse process of sublimation is deposition or desublimation, in which a substance passes directly from a gas to a solid phase. Sublimation has also been used as a generic term to describe a solid-to-gas transition (sublimation) followed by a gas-to-solid transition (deposition). While a transition from liquid to gas is described as evaporation if it occurs below the boiling point of the liquid, and as boiling if it occurs at the boiling point, there is no such distinction within the solid-to-gas transition, which is always described as sublimation.

Freezing-point depression is the decrease of the freezing point of a solvent on the addition of a non-volatile solute. Examples include salt in water, alcohol in water, or the mixing of two solids such as impurities into a finely powdered drug. In all cases, the substance added/present in smaller amounts is considered the solute, while the original substance present in larger quantity is thought of as the solvent. The resulting liquid solution or solid-solid mixture has a lower freezing point than the pure solvent or solid because the chemical potential of the solvent in the mixture is lower than that of the pure solvent, the difference between the two being proportional to the natural logarithm of the mole fraction. In a similar manner, the chemical potential of the vapor above the solution is lower than that above a pure solvent, which results in boiling-point elevation. Freezing-point depression is what causes sea water, to remain liquid at temperatures below 0 °C (32 °F), the freezing point of pure water.

Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the standard pressure of 101.325 kPa, or 100 kPa. Unfortunately, both of these definitions for the standard condition for pressure are in use.

Melting-point depression is the phenomenon of reduction of the melting point of a material with reduction of its size. This phenomenon is very prominent in nanoscale materials, which melt at temperatures hundreds of degrees lower than bulk materials.

In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit of mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.

The enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid, at constant pressure. For example, when melting 1 kg of ice, 333.55 kJ of energy is absorbed with no temperature change. The heat of solidification is equal and opposite.

Thermoporometry and cryoporometry are methods for measuring porosity and pore-size distributions. A small region of solid melts at a lower temperature than the bulk solid, as given by the Gibbs–Thomson equation. Thus, if a liquid is imbibed into a porous material, and then frozen, the melting temperature will provide information on the pore-size distribution. The detection of the melting can be done by sensing the transient heat flows during phase transitions using differential scanning calorimetry – DSC thermoporometry, measuring the quantity of mobile liquid using nuclear magnetic resonance – NMR cryoporometry (NMRC) or measuring the amplitude of neutron scattering from the imbibed crystalline or liquid phases – ND cryoporometry (NDC).

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8. The exact relationship is expressed in the Clausius–Clapeyron relation.
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• Haynes, William M., ed. (2011). CRC Handbook of Chemistry and Physics (92nd ed.). CRC Press. ISBN   1439855110.