Application of zone‐folding approach to the first‐principles estimation of thermodynamic properties of carbon and ZrS2‐based nanotubes

A zone‐folding (ZF) approach is applied for the estimation of the phonon contributions to thermodynamic properties of carbon‐and ZrS₂‐based nanotubes (NTs) of hexagonal morphology with different chiralities. The results obtained are compared with those from the direct calculation of the thermodynamic properties of NTs using PBE0 hybrid exchange‐correlation functional. The phonon contribution to the stability of NTs proved to be negligible for the internal energy and small for the Helmholtz free energy. It is found that the ZF approach allows us an accurate estimation of phonon contributions to internal energy, but slightly overestimates the phonon contributions to entropy. © 2015 Wiley Periodicals, Inc.