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Author |
Michel, K.H.; Costamagna; Peeters, F.M. |
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Title |
Theory of thermal expansion in 2D crystals |
Type |
A1 Journal article |
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Year  |
2015 |
Publication |
Physica status solidi: B: basic research |
Abbreviated Journal |
Phys Status Solidi B |
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Volume |
252 |
Issue |
252 |
Pages |
2433-2437 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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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 in-plane stretching modes and out-of-plane bending (flexural modes). Genuine in-plane 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 <= T-alpha to a positive value of alpha(T) for T > T-alpha in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a two-dimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The in-plane and out-of-plane 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 T-alpha. 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 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim |
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Publisher |
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Place of Publication |
Berlin |
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Wos |
000364690400014 |
Publication Date |
2015-08-06 |
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Series Issue |
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Edition |
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ISSN |
0370-1972 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
1.674 |
Times cited |
21 |
Open Access |
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Notes |
; We thank B. Verberck, D. Lamoen, and A. Dobry for useful comments. We acknowledge funding from the FWO (Belgium)-MINCyT (Argentina) collaborative research project. This work is supported by the Euro GRAPHENE project CONGRAN. ; |
Approved |
Most recent IF: 1.674; 2015 IF: 1.489 |
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Call Number |
UA @ lucian @ c:irua:130281 |
Serial |
4264 |
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Author |
Michel, K.H.; Costamagna; Peeters, F.M. |
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Title |
Theory of anharmonic phonons in two-dimensional crystals |
Type |
A1 Journal article |
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Year |
2015 |
Publication |
Physical review : B : condensed matter and materials physics |
Abbreviated Journal |
Phys Rev B |
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Volume |
91 |
Issue |
91 |
Pages |
134302 |
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Keywords |
A1 Journal article; Condensed Matter Theory (CMT) |
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Abstract |
Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semiempirical model for anharmonic couplings of third and fourth orders, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Gruneisen parameters, the thermal tension and the thermal expansion coefficients as a function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions, we obtain the renormalization and decay rate of in-plane and flexural phonons as a function of temperature, wave vector, and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There, we find that the transition temperature T-alpha from negative to positive thermal expansion is lowered with smaller system size. Renormalization of the flexural mode has the opposite effect and leads to values of T-alpha approximate to 300 K for systems of macroscopic size. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of normal and umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals. |
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Corporate Author |
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Publisher |
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Place of Publication |
Lancaster, Pa |
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Wos |
000353031000001 |
Publication Date |
2015-04-17 |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1098-0121; 1550-235x |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
3.836 |
Times cited |
38 |
Open Access |
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Notes |
; We thank B. Verberck, D. Lamoen, and A. Dobry for useful comments. We acknowledge funding from the FWO (Belgium)-MINCyT (Argentina) collaborative research project. This work is supported by the EuroGRAPHENE project CONGRAN. ; |
Approved |
Most recent IF: 3.836; 2015 IF: 3.736 |
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Call Number |
UA @ lucian @ c:irua:132512 |
Serial |
4263 |
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