  We suggest a new thermodynamic curvature, constructed via adiabatic
compressibility, for examining the internal microstructure of charged black
holes in an anti-de Sitter (AdS) background. We analyze the microscopic
properties of small-large phase transition of black holes with pressure and
volume as the fluctuation variables. We observe that strong repulsive
interactions dominate among the micro-structures of near extremal small black
holes, and the thermodynamic curvature diverges to positive infinity for the
extremal black holes. At the critical point, however, thermodynamic curvature
diverges to negative infinity.
