Title 



Theory of thermal expansion in 2D crystals


Author 





Abstract 



The thermal expansion alpha(T) in layered crystals is of fundamental and technological interest. As suggested by I. M. Lifshitz in 1952, in thin solid films (crystalline membranes) a negative contribution to alpha(T) is due to anharmonic couplings between inplane stretching modes and outofplane bending (flexural modes). Genuine inplane anharmonicities give a positive contribution to alpha(T). The competition between these two effects can lead to a change of sign (crossover) from a negative value of alpha(T) in a temperature (T) range T <= Talpha to a positive value of alpha(T) for T > Talpha in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a twodimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The inplane and outofplane contributions to the thermal expansion are studied as functions of T for crystals of different sizes. Besides, renormalization of the flexural mode frequencies plays a crucial role in determining the crossover temperature Talpha. Numerical examples are given for graphene where the anharmonic couplings are determined from experiments. The theory is applicable to other layer crystals wherever the anharmonic couplings are known. (C) 2015 WILEYVCH Verlag GmbH & Co. KGaA, Weinheim  

Language 



English


Source (journal) 



Physica status solidi: B: basic research.  Berlin 

Publication 



Berlin : 2015


ISSN 



03701972


Volume/pages 



252:11(2015), p. 24332437


ISI 



000364690400014


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