Abstract
Abstract This research paper presents a black hole solution with a rational nonlinear electrodynamics source within the Rastall gravity framework. The paper analyzes the thermodynamic properties of the solution in normal phase space and explores its critical behavior. The phase structure is examined using the extended first law of thermodynamics, with the cosmological constant Λ serving as pressure P. The isotherms exhibit van der Waals behavior at small values of horizon r +. The paper also investigates the Gibbs free energy behavior and finds two critical points with two pressures where the re-entrant phase transition occurs and disappears. We also explore the prevalent microstructure of black holes in Ruppeiner geometry, uncovering significant deviations in the nature of particle interactions from conventional practice. Moreover, the thermodynamic geometry is analyzed using the Ruppeiner formalism, with the normalized Ricci scalar indicating possible point-phase transitions of the heat capacity, and the normalized extrinsic curvature having the same sign as the normalized Ricci scalar. The three-phase transitions of the heat capacity are those that we find for the normalized Ruppeiner curvatures. Thus, there is an absolute correspondence.