-We extend the unsymmetrized self-consistent-field method (USF) for anharmonic crystals to layered non-Bravais crystals to investigate structural, dynamical and thermodynamic properties of a free-standing graphene monolayer. In this theory, the main anharmonicity of the crystal lattice has been included and the quantum corrections are taken into account in an h-expansion for the one-particle density matrix. The obtained result for the thermal expansion coefficient (TEC) of graphene shows a strong temperature dependence and agrees with experimental results by Bao et al. (Nat. Nanotechnol., 4 (2009) 562). The obtained value of TEC at room temperature (300 K) is −6.4 × 10 −6 K −1 and it becomes positive for T > Tα = 358 K. We find that quantum effects are significant for T < 1000 K. The interatomic distance, effective amplitudes of the graphene lattice vibrations, adiabatic and isothermal bulk moduli, isobaric and isochoric heat capacities are also calculated and their temperature dependences are determined.

PACS 68.35.Ja, 68.35.Md We describe self-consistently the effects of non-nearest neighbor interactions and anharmonicity on the atomic properties of a crystal surface. An approach is developed based on the unsymmetrized selfconsistent field approximation (USF). The structural, dynamical and thermodynamic properties of a semiinfinite linear chain are studied in the classical limit. Expressions for the lattice relaxation in the vicinity of the surface, the mean-squared atomic displacements and for the surface energy and free energy are obtained. Quantitative estimates were made using the Lennard-Jones 6-12 interatomic potential.Ñàìîñîãëàñîâàííûì îáðàçîì îïèñûâàåòñÿ âëèÿíèå âçàèìîäåéñòâèÿ ìåaeäó íåáëèaeàéøèìè ñîñåäÿìè è àíãàðìîíèçìà íà àòîìíûå ñâîéñòâà ïîâåðõíîñòåé êðèñòàëëîâ. Ïîäõîä îñíîâàí íà íåñèììåòðèçîâàííîì ïðèáëèaeåíèè ñàìîñîãëàñîâàííîãî ïîëÿ.  êëàññè÷åñêîì ïðåäåëå èçó-÷àþòñÿ ñòðóêòóðíûå, äèíàìè÷åñêèå è òåðìîäèíàìè÷åñêèå ñâîéñòâà ïîëóáåñêîíå÷íîé ëèíåéíîé öåïî÷êè. Ïîëó÷åíû âûðàaeåíèÿ äëÿ ðåëàêñàöèè ðåøåòêè âáëèçè ïîâåðõíîñòè, ñðåäíåê-âàäðàòè÷íûõ ñìåùåíèé, ïîâåðõíîñòíîé ýíåðãèè è ñâîáîäíîé ýíåðãèè. Êîëè÷åñòâåííûå îöåíêè ñäåëàíû äëÿ ïîòåíöèàëà âçàèìîäåéñòâèÿ Ëåííàðä-Äaeîíñà.