The effect of pressure modulation on the flow of gas through a solid membrane: Surface inhibition and internal traps
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I.
INTRODUCTION
IN design studies for fusion reactors a number of problems have emerged which call for estimates of the rates at which hydrogen and its isotopes flow through solids. For this work the common assumption that fluxes may be represented by diffusion limited permeation through a homogeneous material is not appropriate. More detailed descriptions are needed. Account must be taken of surface reaction rates and processes of internal trapping. Conventional descriptions of macroscopic flow in the solid state relate phenomenological coefficients to two series of measurements: one is of the steady flows through a foil produced by specified pressures of gaseous diffusant; the other is of the time varying flows which follow a step change in diffusant pressure. Methods are well established. Early descriptions of steady flows follow from the work of Richardson ~ and then of Wang. 2 Time varying flows were first investigated by Daynes 3 and then Barrer. 4 Recent accounts of a full steady-state and time-dependent analysis are well exemplified in the work of Fromm et al. 5 Unfortunately, measurements of steady-state and stepchange flows are not strongly characteristic of the processes which determine their values. As pointed out by LeClaire, 6 detailed analysis over a wide pressure range is required to establish the coefficients which describe the flows controlled by surface reactions, while internal trapping, as described, for example, by Iino 7 or Shah et al. ,8 shows only as a small change in the pattern of time-dependent flows. A measure of the difficulty experienced in establishing the parameters of a particular flow may be seen in the inconsistency in estimates of diffusion coefficients noted by Volkl and Alefeld 9 in their review of hydrogen diffusion in metals. In this case, surface dependent techniques provide data significantly different from that coming from measurements based on internal rearrangement or individual atomic motion. There is a clear need for a form of analysis which will demonstrate whether macroscopic flows of gaseous dif-
D. L. CUMMINGS, Research Fellow, and D. A. BLACKBURN, Director, are with The Open University, Oxford Research Unit, Foxcombe Hall, Berkeley Road, Boars Hill, Oxford, OX1 5HR, England. Manuscript submitted November 6, 1984. METALLURGICAL TRANSACTIONS A
fusant are diffusion limited or are subject to modification by processes of surface reaction or internal trapping. One possibility is to use a different form of time-dependent flow. This has led a few experimenters ~~ to use periodic modulation and frequency analysis to obtain detailed information of the parameters governing flow. Their work shows this approach to have considerable potential for the identification of rate determining processes. The function of this paper is to present an analysis of how harmonic modulation of diffusant flow through an experimental foil is modified from its diffusion limited form by the effects of surface reaction and of internal trapping. The approach is a general one and depends on the u
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