Negative thermal expansion

Negative thermal expansion (NTE) is an unusual physicochemical process in which some materials contract upon heating, rather than expand as most other materials do. 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 make a zero expansion composite material. Negative thermal expansion (NTE) is an unusual physicochemical process in which some materials contract upon heating, rather than expand as most other materials do. 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 make a zero expansion composite material. There are a number of physical processes which may cause contraction with increasing temperature, including transverse vibrational modes, Rigid Unit Modes and phase transitions. Recently, 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 Fe3Pt) Negative thermal expansion is usually observed in non-close-packed systems with directional interactions (e.g. ice, graphene, etc.) and complex compounds (e.g. Cu2O, ZrW2O8, 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, Π ( x ) {displaystyle Pi (x)} , at the equilibrium distance a {displaystyle a} : Π ‴ ( a ) > 0 , {displaystyle Pi '''(a)>0,} Where Π ‴ ( a ) {displaystyle Pi '''(a)} is shorthand for the third derivative of the interatomic potential at the equilibrium point: Π ‴ ( a ) = d 3 Π ( x ) d x 3 | x = a {displaystyle Pi '''(a)=left.{frac {d^{3}Pi (x)}{dx^{3}}} ight|_{x=a}} 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 Π ‴ ( a ) a > − ( d − 1 ) Π ″ ( a ) , {displaystyle Pi '''(a)a>-(d-1)Pi ''(a),}