Downstream analytics quantification of ion release during high-voltage anodisation of niobium

In operando quantification of field-assisted ion release during high-voltage anodisation (up to 100 V SHE) of Nb in 0.1 M sulphuric acid was performed. Electrochemical high-field oxide formation under both potential and current control was studied separately. The quantification of in situ ion release via ICP-MS revealed an increase of the oxide dissolution factor (from 337 to 422 fm V^?1) when decreasing the potential scan rate from 200 to 100 mV s^?1. Dissolution rates measured during galvanostatic oxide formation allowed measuring oxide dissolution factors of 719 and 837 fm V^?1 for current densities of 1.0 and 0.5 mA cm^?2, respectively. As compared to the potentiodynamic case, higher dissolution rates and oxide dissolution factors were measured for galvanostatic anodisation. The overall fraction of the charge used for generation of soluble Nb species was below 0.4% for all oxide growth regimes. Cross-sectional SEM imaging proofs an oxide formation factor of 2.1 nm V^?1. The surface of anodised films was extremely smooth and featureless without any cracks or voids. Based on X-ray diffraction, the films were found to be amorphous, indicating that no field crystallisation is occurring under the applied oxide growth conditions even at higher voltages.

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Graphical abstract Schematic live immaging of Nb dissolution during anodization and its quantification via ICP-MS.

     

New improvements of the Stirling formula

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We recast the Dirichlet boundary conditions satisfied by the displacement field of the middle surface of a linearly elastic shell as boundary conditions satisfied by the corresponding linearized change of metric and of curvature tensor fields. This in turn allows us to give an intrinsic formulation of the linear shell model of W.T. Koiter with these two tensor fields as the sole unknowns.     

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