Hydrogen absorption in thin metal films clamped to rigid substrates results in mechanical stress that changes the hydrogen's chemical potential by Delta mu(H)(sigma) = -1.124 sigma kJ/mol(H) for sigma measured in [GPa]. In this paper we show that local stress relaxation by the detachment of niobium hydrogen thin films from the substrate affects the chemical potential on the local scale: using coincident proton proton scattering at a proton microprobe, the hydrogen concentration is determined with mu m resolution, revealing that hydrogen is not homogenously distributed in the film. The local hydrogen solubility of the film changes with its local stress state, mapping the buckled film fraction. In niobium hydrogen thin films loaded up to nominal concentrations in the two-phase coexistence region, the clamped film fraction remains in the solid solution phase, while the buckles represent the hydride phase. These results are compared to a simple model taking the stress impact on the chemical potential into account. Copyright (C) 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.