The efficacy of the model is ascertained by first applying it to Pd and Pd-Cu membranes, for which much literature exists. Of course, for these membranes, typically Sieverts’ law is assumed, which is limited to high temperatures (> 300 ºC) and low hydrogen pressures, when diffusion (step, s3) is controlling, and hydrogen concentration in bulk metal is low. Over a broader range of temperatures spanning the crystallographic phase-transition in the Pd-H and Pd-Cu-H systems, in fact, the slopes are very different at low and high temperatures, and also there is a pronounced peak in permeability in the intermediate temperature range. The latter behavior has not yet been theoretically explained.
Our approach considers the 5-step network in analogy to an electrical circuit and describes well the permeation behavior of hydrogen in Pd and Pd-Cu membranes, including the peak at intermediate temperatures. Further, it can adequately describe the absorption isotherms of the metal-hydrogen system. A comparison of step resistances also allows a systematic reduction to a three-step (adsorption, diffusion, and desorption control) model that is adequate over a broad range of temperatures and pressures.
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