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Negative Thermal Expansion (NTE, also known as thermomiotic behavior) is a physicochemical process in which a material contracts upon heating, rather than undergoing thermal expansion as most materials do. The potential of thermomiotic materials to compensate for positive thermal expansion has generated much interest in the fields of engineering, photonic, electronic, and structural applications. In principle a composite or solid solution of two materials with varying coefficients of thermal expansion (CTE) could be used to make a material with near-zero expansion, such as Invar.

Origin of Negative Thermal Expansion
While the most interesting materials exhibit thermomiotic behavior in all three crystallographic directions there are cases where NTE is only present along certain directions. In other materials an effective NTE is achieved via a solid-solid phase transition from one unit cell volume to another.

In order to develop a complete understanding of the mechanisms involved in negative thermal expansion, it may be useful to first review the general mechanisms related to positive thermal expansion materials. While negative thermal expansion is counterintuitive and driven by mechanisms that compete with positive thermal expansion a number of mechanism have been elucidated to explain the phenomena. To date a number of review articles have been published concerning the origins of negative thermal expansion and the history of the science exploring this phenomenon. There are a number of physical processes which, while not in themselves indicative of thermomiotic behavior, can lead to NTE.

Lattice Vibrations


Phonons, which are quantized units of lattice vibrations can either exist along the propogation direction (logitudinal waves) or perpendicular to it (transverse waves). These vibrations are excited with thermal energy and in some specialized cases can lead to a decrease along one or more crystallographic directions or even the overall volume of a material, giving rise to negative thermal expansion. If a simple metal oxide linkage is concidered where two metal centers are bridged by a connecting oxigen, M-O-M, then it can easily be visualized how the longitudinal stetching of the anharmonic M-O bond can lead to positive thermal expansion. However, the transverse vibrations can lead to an apparent decrease of the mean bondlength as shown in figure 1.

Rigid Unit Modes (RUMs) and quasi Rigid Unit Modes (qRUMs)
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Macroscopic Negative Thermal Expansion
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Other Mechanisms
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\\Recently, Liu et al. showed that the NTE phenomenon originates from the existence of high pressure, small volume phases with higher entropy, with their configurations present in the stable phase matrix through thermal fluctuations.\\

Applications
There are many potential applications for materials with controlled thermal expansion properties, as thermal expansion causes many problems in engineering, and indeed in everyday life. One simple example of a thermal expansion problem is the tendency of dental fillings to expand by an amount different from the teeth, for example when drinking a hot drink, causing toothache. If dental fillings were made of a composite material containing a mixture of materials with positive and negative thermal expansion then the overall expansion could be precisely tailored to that of tooth enamel.

Current Applications
Glass-ceramic is used for cooktops.

Materials
Perhaps one of the most studied materials to exhibit negative thermal expansion is Cubic Zirconium Tungstate (ZrW2O8). This compound contracts continuously over a temperature range of 0.3 to 1050 K (at higher temperatures the material decomposes). Other materials that exhibit this behaviour include: other members of the AM2O8 family of materials (where A = Zr or Hf, M = Mo or W) and ZrV2O7. A2(MO4)3 also is an example of controllable negative thermal expansion.

Ordinary ice shows NTE in its hexagonal and cubic phases at very low temperatures (below -200 °C). In its liquid form, water also displays negative thermal expansivity below 3.984°C.

Quartz and a number of zeolites also show NTE over certain temperature ranges. Fairly pure silicon has a negative coefficient of thermal expansion for temperatures between about 18 K and 120 K. Cubic Scandium trifluoride has this property which is explained by the quartic oscillation of the fluoride ions. The energy stored in the bending strain of the fluoride ion is proportional to the fourth power of the displacement angle, unlike most other materials where it is proportional to the square of the displacement. A fluorine atom is bound to two scandium atoms, and as temperature increases the fluorine oscillates more perpendicularly to its bonds. This draws the scandium atoms together throughout the material and it contracts. ScF3 exhibits this property from 10K to 1100K above which it shows the normal positive thermal expansion.