Role of acoustic phonons in the negative thermal expansion of layered structures and nanotubes based on them

Abstract

Calculations on a microscopic level are used to explain the experimentally observed negative linear thermal expansion along some directions in a number of crystalline compounds with complicated lattices and anisotropic interactions between atoms. Anomalies in the temperature dependence of the coefficient of linear thermal expansion are analyzed in layered crystals made up of monatomic layers (graphite and graphene nanofilms) and multilayer “sandwiches” (transition metal dichalcogenides), in multilayered crystal structures such as high-temperature superconductors where the anisotropy of the interatomic interactions is not conserved in the long-range order, and in graphene nanotubes. The theoretical calculations are compared with data from x-ray, neutron diffraction, and dilatometric measurements.

Uniaxial Heat Balance Model of the Solar Collector

“…3). To analyze the configuration of the reduced areas, we apply the law of heat balance of a unit area [12,13] (steady-state energy balance of an element) and obtain the following equation:…”

Negative thermal expansion of group III-Nitride monolayers

“…Among the acoustical branches, especially the out-of-plane acoustic (ZA) branches give the dominant contribution to the thermal expansion coefficient of the materials. This phenomenon is well known and extensively studied for various 2D materials [57][58][59][65][66][67]. As can be easily seen from the equations ( 6)-( 8) that the α(T) is directly proportional to the thermal (β T ) tension and the β T is related to the Grüneisen parameters.…”

“…More details related with the calculation of LTEC can be find in the literature [57][58][59]. The thermal properties of a material are correlated with phonon modes and electronic excitations.…”