  Understanding the thermodynamic phase transition of black holes can provide a
deep insight into the fundamental properties of black hole gravity to establish
the theory of quantum gravity. We investigate the condition and latent heat of
phase transition for non-linear charged AdS black holes using the Maxwell's
equal-area law, and analysis the boundary and curve of the two-phase
coexistence area in the expanded phase space. We suggest that the phase
transition of the non-linear charged AdS black hole with the fixed temperature
($T<T_c$) is related to the electric potential at the horizon, not only to the
location of horizon. Recently, the molecular number density was introduced to
study the phase transition and microstructure of black holes. On this basis, we
discuss the continuous phase transition of a non-linear charged AdS black hole
to reveal the potential microstructure of a black hole by introducing the order
parameter and using the scalar curvature.
