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Negative thermal expansion (NTE) is an unusual
physicochemical Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mecha ...
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 0~4 °C. Water's NTE is the reason why ice floats, rather than sinks, in liquid water. Materials which undergo NTE have a range of potential engineering, photonic,
electronic Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor * ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of data using an electronic device *Electronic co ...
, and
structural A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...
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 what 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 Ice is water frozen into a solid state, typically forming at or below temperatures of 0 degrees Celsius or Depending on the presence of impurities such as particles of soil or bubbles of air, it can appear transparent or a more or less opaq ...
,
graphene Graphene () is an allotrope of carbon consisting of a single layer of atoms arranged in a hexagonal lattice nanostructure.
, 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 Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space.M. P. Allen and D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, Oxford, England, 1989 ...
, \Pi(x), at the equilibrium distance a : \Pi(a) > 0, where \Pi(a) is shorthand for the third derivative of the interatomic potential at the equilibrium point: \Pi(a) = \left.\frac\_ 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 \Pi(a)a > -(d-1)\Pi''(a), where d 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 Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space.M. P. Allen and D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, Oxford, England, 1989 ...
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 \Pi'' and \Pi 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 Zirconium tungstate () is the zirconium salt of tungstic acid and has unusual properties. The phase formed at ambient pressure by reaction of ZrO2 and WO3 is a metastable cubic phase, which has ''negative thermal expansion'' characteristics, n ...
(). 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 Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system w ...
materials like and also and are especially precious for applications in engineering because they exhibit
isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
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. Carbon fibers shows NTE between 20°C and 500°C. This property is utilized in tight-tolerance aerospace applications to tailor the CTE of carbon fiber reinforced plastic components for specific applications/conditions, by adjusting the ratio of carbon fiber to plastic and by adjusting the orientation of the carbon fibers within the part. Quartz () and a number of zeolites also show NTE over certain temperature ranges. Fairly pure silicon (Si) has a negative coefficient of thermal expansion for temperatures between about 18 K and 120 K. Cubic
Scandium trifluoride Scandium(III) fluoride, ScF3, is an ionic compound. This salt is slightly soluble in water but dissolves in the presence of excess fluoride to form the ScF63− anion. Production ScF3 can be produced by reacting scandium and fluorine.S.A.Cotton, ...
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. exhibits this property from 10 to 1100 K above which it shows the normal positive thermal expansion. Shape memory alloys such as NiTi are a nascent class of materials that exhibit zero and negative thermal expansion.


Applications

Forming a
composite Composite or compositing may refer to: Materials * Composite material, a material that is made from several different substances ** Metal matrix composite, composed of metal and other parts ** Cermet, a composite of ceramic and metallic materials ...
of a material with (ordinary) positive thermal expansion with a material with (anomalous) negative thermal expansion could allow for tailoring the thermal expansion of the composites or even having composites with a thermal expansion close to zero. Negative and positive thermal expansion hereby compensate each other to a certain amount if the temperature is changed. Tailoring the overall
thermal expansion coefficient Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic ...
(CTE) to a certain value can be achieved by varying the volume fractions of the different materials contributing to the thermal expansion of the composite. Especially in engineering there is a need for having materials with a CTE close to zero i.e. with constant performance over a large temperature range e.g. for application in precision instruments. But also in everyday life materials with a CTE close to zero are required.
Glass-ceramic Glass-ceramics are polycrystalline materials produced through controlled crystallization of base glass, producing a fine uniform dispersion of crystals throughout the bulk material. Crystallization is accomplished by subjecting suitable glasses t ...
cooktop A cooktop (American English), stovetop (American English) or hob (British English), is a device commonly used for cooking that is commonly found in kitchens and used to apply heat to the base of pans or pots. Cooktops are often found integrated ...
s like Ceran cooktops need to withstand large temperature gradients and rapid changes in temperature while
cooking Cooking, cookery, or culinary arts is the art, science and craft of using heat to prepare food for consumption. Cooking techniques and ingredients vary widely, from grilling food over an open fire to using electric stoves, to baking in vario ...
because only certain parts of the cooktops will be heated while other parts stay close to
ambient temperature Colloquially, "room temperature" is a range of air temperatures that most people prefer for indoor settings. It feels comfortable to a person when they are wearing typical indoor clothing. Human comfort can extend beyond this range depending on ...
. In general, due to its
brittleness A material is brittle if, when subjected to stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. Bre ...
temperature gradients in glass might cause cracks. However, the glass-ceramics used in cooktops consist of multiple different phases, some exhibiting positive and some others exhibiting negative thermal expansion. The expansion of the different phases compensate each other so that there is not much change in volume of the glass-ceramic with temperature and crack formation is avoided. An everyday life example for the need for materials with tailored thermal expansion are
dental fillings Dental restoration, dental fillings, or simply fillings are treatments used to restore the function, integrity, and morphology of missing tooth structure resulting from caries or external trauma as well as to the replacement of such structure su ...
. If the fillings tend to expand by an amount different from the
teeth A tooth ( : teeth) is a hard, calcified structure found in the jaws (or mouths) of many vertebrates and used to break down food. Some animals, particularly carnivores and omnivores, also use teeth to help with capturing or wounding prey, tea ...
, for example when drinking a hot or cold drink, it might cause a
toothache Toothache, also known as dental pain,Segen JC. (2002). ''McGraw-Hill Concise Dictionary of Modern Medicine''. The McGraw-Hill Companies. is pain in the teeth or their supporting structures, caused by dental diseases or pain referred to the te ...
. If dental fillings are, however, 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.


References


Further reading

* * * * * * * {{cite journal, doi=10.1016/j.scriptamat.2011.07.001, year=2011 , title=Origin of negative thermal expansion in solids, journal=Scripta Materialia , volume=65 , issue=8 , pages= 664–667 , last1=Liu, first1=Z.-K. , last2=Wang, first2=Yi , last3=Shang, first3=S.-L. Physical chemistry Thermodynamics Materials science