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In this paper, we study the small-large black hole phase transition andconstruct the Ruppeiner geometry for the five-dimensional chargedGauss-Bonnet-AdS black hole in the grand canonical ensemble. By making use ofthe equal area law, we obtain the analytical coexistence curve of the small andlarge black holes. Then the phase diagrams are examined. We also calculate thechange of the thermodynamic volume during the small-large phase transition,which indicates that there exists a sudden change among the black holemicrostructures. The corresponding normalized scalar curvature of the Ruppeinergeometry is also calculated. Combing with the empirical observation of scalarcurvature, we find that for low electric potential, the attractive interactiondominates among the microstructures, while a high electric potential producesrepulsive interactions. In the reduced parameter space, we observe that onlyattractive interaction is allowed when the coexistence region is excluded. Thenormalized scalar curvature also admits a critical exponent 2 and a universalconstant $-\frac{1}{8}$. In particular, the value of the normalized scalarcurvature keeps the same along the coexistence small and large black holecurves. So in the grand canonical ensemble, the interaction can keep constantat the phase transition where the black hole microstructures change. Theseresults disclose the intriguing microstructures for the charged AdS black holein the Gauss-Bonnet gravity.

Phase transition and microstructures of five-dimensional charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble