Negative thermal expansion (NTE) is an unusual physicochemical process in which some materials contract upon heating, rather than expand as most other materials do. The most well-known material with NTE is water at 0 to 3.98 °C. Also, the density of water ice is smaller than the density of liquid water. Water's NTE is the reason why water ice floats, rather than sinks, in liquid water. Materials which undergo NTE 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 use it as a thermal expansion compensator that might allow for forming composites with tailored or even close to zero thermal expansion.
Origin of negative thermal expansion
There are a number of physical processes which may cause contraction with increasing temperature, including transverse vibrational modes, rigid unit modes and phase transitions.
In 2011, Liu et al. showed that the NTE phenomenon originates from the existence of high pressure, small volume configurations with higher entropy, with their configurations present in the stable phase matrix through thermal fluctuations. They were able to predict both the colossal positive thermal expansion (In cerium) and zero and infinite negative thermal expansion (in ). Alternatively, large negative and positive thermal expansion may result from the design of internal microstructure.
Negative thermal expansion in close-packed systems
Negative thermal expansion is usually observed in non-close-packed systems with directional interactions (e.g. ice, graphene, etc.) and complex compounds (e.g. , , beta-quartz, some zeolites, etc.). However, in a paper, it was shown that negative thermal expansion (NTE) is also realized in single-component close-packed lattices with pair central force interactions. The following sufficient condition for potential giving rise to NTE behavior is proposed for the interatomic potential, , at the equilibrium distance :
where is shorthand for the third derivative of the interatomic potential at the equilibrium point:
This condition is (i) necessary and sufficient in 1D and (ii) sufficient, but not necessary in 2D and 3D. An approximate necessary and sufficient condition is derived in a paper
where is the space dimensionality. Thus in 2D and 3D negative thermal expansion in close-packed systems with pair interactions is realized even when the third derivative of the potential is zero or even negative. Note that one-dimensional and multidimensional cases are qualitatively different. In 1D thermal expansion is caused by anharmonicity of interatomic potential only. Therefore, the sign of thermal expansion coefficient is determined by the sign of the third derivative of the potential. In multidimensional case the geometrical nonlinearity is also present, i.e. lattice vibrations are nonlinear even in the case of harmonic interatomic potential. This nonlinearity contributes to thermal expansion. Therefore, in multidimensional case both and are present in the condition for negative thermal expansion.
Materials
Perhaps one of the most studied materials to exhibit negative thermal expansion is zirconium tungstate (). This compound contracts continuously over a temperature range of 0.3 to 1050 K (at higher temperatures the material decomposes). Other materials that exhibit NTE behaviour include other members of the family of materials (where A = or , M = or ) and and , though and only in their high temperature phase starting at 350 to 400 K. also is an example of controllable negative thermal expansion. Cubic materials like and also and are especially precious for applications in engineering because they exhibit isotropic NTE i.e. the NTE is the same in all three dimensions making it easier to apply them as thermal expansion compensators.
Ordinary ice shows NTE in its hexagonal and cubic phases at very low temperatures (below –200 °C). In its liquid form, pure water also displays negative thermal expansivity below 3.984 °C.
ALLVAR Alloy 30, a titanium-based alloy, shows NTE over a wide temperature range, with a -30 ppm/°C instantaneous coefficient of thermal expansion at 20 °C. ALLVAR Alloy 30's negative thermal expansion is anisotropic. This commercially available material is used in the optics, aerospace, and cryogenics industries in the form of optical spacers that prevent thermal defocus, ultra-stable struts, and washers for thermally-stable bolted joints.