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Thermodynamic properties of phagraphene

ABSTRACT The problem of calculating the thermodynamic properties of phagraphene (PG) was tackled within the quasi-harmonic approximation, and at the PBE level of density-functional theory. The Murnaghan isothermal equation of state was accordingly derived for the monolayer. The temperature dependence of internal and free energies, as well as the entropy were calculated and discussed in detail. The specific heat of the system also showed an asymptotic behaviour obeying the classical limit of Dulong and Petit at high temperatures for  K. For  K (the low-temperature limit), a -law was also derived being consistent with the two-dimensionality of PG. This is indeed a special case of a general law according to which the specific heat of an n-dimensional Debye system is proportional to assuming the excitations to be phonons. Thermal stability of PG was finally inferred to be high according to its estimated Debye temperature  K, which is also comparable to that of graphene (2100 K).