  We investigate the thermodynamics and critical phenomena for four dimensional
RN-AdS and Kerr-AdS black holes in the canonical ensemble both for the normal
and the extended phase space employing the framework of thermodynamic geometry.
The thermodynamic scalar curvatures for these black holes characterizes the
liquid-gas like first order phase transition analogous to the van der Waals
fluids, through the $R$-Crossing Method. It is also shown that the
thermodynamic scalar curvatures diverge as a function of the temperature at the
critical point.
