The　phase　transition　and　critical　behaviors　of　charged　AdS　black　holes　in　f(R)　gravity　with　a　conformally　invariant　Maxwell　(CIM)　source　and　constant　curvature　are　further　investigated.　As　a　highlight,　this　research　is　carried　out　by　employing　new　state　parameters　(T,Q,Phi)　and　contributes　to　deeper　understanding　of　the　thermodynamics　and　phase　structure　of　black　holes.　Our　analyses　manifest　that　the　charged　f(R)-CIM　AdS　black　hole　undergoes　a　first-order　smalllarge　black　hole　phase　transition,　and　the　critical　behaviors　qualitatively　behave　like　a　Van　der　Waals　liquidvapor　system.　However,　differing　from　the　case　in　Einsteins　gravity,　phase　structures　of　the　black　holes　in　f(R)　theory　exhibit　an　interesting　dependence　on　gravity　modification　parameters.　Moreover,　we　adopt　the　thermodynamic　geometry　to　probe　the　black　hole　microscopic　properties.　The　results　show　that,　on　the　one　hand,　both　the　Ruppeiner　curvature　and　heat　capacity　diverge　exactly　at　the　critical　point,　on　the　other　hand,　the　f(R)-CIM　AdS　black　hole　possesses　the　property　as　ideal　Fermi　gases.　Of　special　interest,　we　discover　a　microscopic　similarity　between　the　black　holes　and　a　Van　der　Waals　liquidvapor　system.