  Different types of phase transition from hadron to quark at high density near
zero temperature may occur in the inner core of hybrid stars. We investigate
the impacts of phase transition types and quark models on properties of hybrid
star and quark cores. The quark-meson coupling (QMC) model is used to describe
hadronic matter, and the MIT bag model as well as the Nambu-Jona-Lasinio (NJL)
model are employed to describe quark matter for comparison. From the
mass-radius curves obtained by using equations of state (EOS), we find that
EOSs of hadron matter have a decisive influence on the maximum mass of a hybrid
star in the first-order phase transition case, while quark matter EOSs have
more impacts on results in the crossover transition case. It is also found in
the present work that the thermodynamic correction arising from an
interpolation scheme considerably stiffens the EOSs. Therefore the crossover
type phase transition generally leads to hybrid stars with higher masses. In
particular, by using the QMC model and the NJL model to construct crossover
EOSs with thermodynamic correction, we discover that the maximum masses of
hybrid stars can meet the recent observational constraint on mass from PSR
J0952-0607, i.e., $2.35\pm0.17M_\odot$.
