  In this paper, we visit the thermodynamic criticality and thermodynamic
curvature of the charged AdS black hole in a new phase space. It is shown that
when the square of the total charge of the charged black hole is considered as
a thermodynamic quantity, the charged AdS black hole also admits an van der
Waals-type critical behavior without the help of thermodynamic pressure and
thermodynamic volume. Based on this, we study the fine phase structures of the
charged AdS black hole with fixed AdS background in the new framework. On the
one hand, we give the phase diagram structures of the charged AdS black hole
accurately and analytically, which fills up the gap in dealing with the phase
transition of the charged AdS black holes by taking the square of the charge as
a thermodynamic quantity. On the other hand, we analyse the thermodynamic
curvature of the black hole in two coordinate spaces. The thermodynamic
curvatures obtained in two different coordinate spaces are equivalent to each
other and are also positive. Based on an empirical conclusion under the
framework of thermodynamic geometry, we speculate that when the square of
charge is treated as an independent thermodynamic quantity, the charged AdS
black hole is likely to present a repulsive between its molecules. More
importantly, based on the thermodynamic curvature, we obtain an universal
exponent at the critical point of phase transition.

General Relativity and Quantum Cosmology;High Energy Physics - Theory