Modeling hydrogen entry and exit in metals exposed to multiple charging processes
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I.
INTRODUCTION
THERE has been recent interestt~'2j in hydrogen absorbed from industrial processes, such as electrocleaning, electropickling, and plating. These processes operate at high-current densities (0.5 to 12 kA/m 2) and significant electrolyte flow rates (line speeds of 90 to 150 m/min). The processes are typically applied in tandem so that metal sheets are subjected to multiple conditions of charging and discharging of hydrogen. A need exists to predict the hydrogen concentration in metal sheets exposed to such processes. A. Early Models Since Devanathan and Stachurskit31 first applied the permeation technique to metallic foils, there have been many models proposed to understand the hydrogen interaction with a metal electrode. Early modelst4,5] and some mathematical variationst6-91 have been applied to permeation data to obtain hydrogen diffusivities and surface solubilities in metals. Other studies~~ have considered the additional effects of hydrogen traps upon hydrogen permeation. Furthermore, some models t~2j have used permeation information to calculate kinetic rate constants for the hydrogen surface reactions occurring on the surface of a polarized electrode. More recently, a model 1~3]has been proposed that evaluates the S . L AMEY, Admixture Cementitious Product Development Manager, is with Master Builders, Inc., Cleveland, OH 44122. G.M. MICHAL, LTV Steel Professor, and J.H. PAYER, Professor and Chairman, are with the Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH 44106-7204. Manuscript received June 2, 1992.
METALLURGICAL AND MATERIALS TRANSACTIONS A
hydrogen behavior during permeation by consolidating all surface reactions into a single term. Using the foregoing models, a wide variety of situations may be studied. However, all of these models avoid high-current densities. High-current densities may result in permeation curves that are more complex and multifarious factors may arise, such as a change in the metal surface or substantial hydrogen evolution may occur, u41 Such complicating phenomena make the calculation of detailed surface-reaction rate constants uncertain for those modelst~21 that emphasize surface effects. For the modelst3-~~l that do not account for surface effects, these phenomena question the applicability of a model's boundary conditions. The Makhloutll3J model alone bridges the gap between surface and bulk effects, but the model's requirement of a palladium film on the entry surface limits the charging conditions (e.g., pH = 2 H 2 S O 4 with ic --- - 1 mA/cm 2 will remove the coating) that can be analyzed. Furthermore, as noted by others, 17j a useful model to evaluate processes must be able to predict the amount and distribution of hydrogen in a metal sheet for one or more short (on the order of seconds) process steps. The objective of this work is to develop a model for hydrogen entry and exit behavior in metals that is applicable to a wide range of charging conditions. As an illustration, the model will be applied to expe
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