Geometrical Origin and Theory of Negative Thermal Expansion in Framework Structures

Abstract

By framework structures are meant materials consisting of relatively stiff units such as octahedra or tetrahedra, joined by shared oxygen (or other) atoms at the corners. Examples are ZrW 2 O 8 and many aluminosilicates. Rigid rotation of the units often gives a reduction of the volume or of some lattice constant as a purely geometrical effect. The theory of this effect is developed and shown to give a negative contribution to the thermal expansion coefficient. This is in addition to the usual positive contribution from anharmonicity of the interatomic forces. The negative effect varies through the phonon spectrum, being strongest for low frequencies, but the sign of the temperature coefficient may be reversed above a soft mode phase transition.

Framework flexibility and the negative thermal expansion mechanism of copper(I) oxideCu2O

“…This is a type of tension effect known as a rigid unit mode 23 (RUM), an established NTE mechanism in some silicate minerals. 24,25 The same mechanism has also been proposed as a result of evidence from neutron powder diffraction 9 where anisotropy of Cu thermal displacement parameters points to significant Cu motion transverse to the 111 directions.…”

Simulation study of pressure and temperature dependence of the negative thermal expansion in Zn(CN)2

“…18, the average Zn-C/N-N/C angle starts to possess an almost linear pressure dependence at medium temperature and contributes to the pressure-induced volume change of the material. According to a simple geometrical relation 45 , the relative decrease in cell is roughly proportional to the Zn-C/N-N/C angle squared, hence to the pressure squared, resulting in negative B 0 . However, this contribution from the pressure-induced change in the Zn-C/N-N/C angle to the volume contraction will be hindered at high temperature due to the anharmonic stiffening of the corresponding modes ( Fig.…”

Origin of the colossal positive and negative thermal expansion in Ag3[Co(CN)6]: anab initiodensity functional theory study

“…This imbalance gives rise to rotational motions of stiff CoC 6 , CN and AgN 2 units that will cause a shortening of the Co...Co chain. These motions correspond to the Rigid Unit Modes that are known to give negative contributions to the overall Gruneisen parameter [6,28,29,30].…”