Negative thermal expansion
Negative thermal expansion (NTE) is a physicochemical process in which some materials contract upon heating rather than expanding as most materials do. Materials which undergo this unusual process have a range of potential engineering, photonic, electronic, and structural applications. For example, if one were to mix a negative thermal expansion material with a "normal" material which expands on heating, it could be possible to make a zero expansion composite material, such as Invar.
Origin of negative thermal expansion
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.
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.
Glass-ceramic is used for cooktops.
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.
Rubber elasticity shows NTE at normal temperatures, but the reason for the effect is rather different to that in most other materials. Put simply, as the long polymer chains absorb energy, they adopt a more contorted configuration, reducing the volume of the material.
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.
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