To understand the effects of radiation on the perfor­mance of permeation barriers, we need to first exam­ine how barriers work. For tritium to permeate through a material with or without a coating, the tritium must absorb on the surface, dissociate into atoms, dissolve into the material, diffuse through the material, and then recombine into molecules on the downstream side. In the simple case in which diffa — sion through the structural material is rate limiting, the permeation rate is controlled by the ratio of the permeability and the thickness of the pressure boundary (eqn [16]); as described earlier, the perme­ability is the product of the diffusivity and the solu­bility, which can be thought of as the velocity times capacity. These parameters are dependent on tem­perature, and should not be affected by radiation effects or nominal surface cracking. In the simple case of diffusion-limited permeation through the structural boundary, the experimental result deter­mined in the laboratory cannot be extrapolated to the radiation environment.

Permeation barriers, by their basic nature, consist of a thin layer adhered to the structural material. The performance of barriers depends on the integrity of the barrier as well as the physical interaction of the barrier material with tritium. What is it about many barriers and how they operate that causes labo­ratory and reactor data to disagree? In their review, Hollenberg et al}15 considered these aspects of bar­riers and their performance in radiation, proposing three models that describe distinct physics of the interactions between tritium and the barrier material. The most basic model is the Composite Diffusion Model, in which hydrogen transport is diffusion — controlled in both the barrier and the base metal. The steady-state permeation rate (Q1) through a pressure boundary in this case is

Fb Fm

where A is the surface area of the boundary, and the subscripts B and M refer to the barrier and structural metal, respectively. Considering the intent of the barrier, the ratio tB/FB should be much larger than tM/FM, thus the permeation is controlled simply by the permeation through the barrier.

The second model proposed by Hollenberg et al. considers the barrier to be effectively impermeable to tritium and is called the Area Defect Model. In this case, hydrogen is transported through the metal, reaching the metal surface through a limited number of cracks or other defects in the barrier layer. The permeation rate for this case is

Qi = Ad— ppTT [23]

teff

where Ad is the area of the defects and teff is the effective distance the hydrogen isotope must traverse to reach the other side of the metal.

The third model proposed by Hollenberg et a/. is the Surface Desorption Model, in which case, perme­ation is controlled by the recombination rate of hydrogen isotope atoms into molecules on the back surface and the recombination-limited flux of tritium is described by eqn [19]. Surface desorption does not make sense by itself; as show, it is actually part of the Area Defect Model.

As reported by Hollenberg eta/.175 and as revealed by a review of the literature on barriers and oxides,196,223-225 the activation energy of permeation is generally not altered by the addition of the barrier layer onto the substrate. This means that, in practice, the permeation process itself is being controlled by the substrate, not the barrier, strongly supporting the Area Defect Model described earlier. In short, the barrier works simply by limiting the area of the metal exposed to the driving pressure.

Pisarev et a/.226 provide particularly intriguing insights into the effects of cracks on permeation barriers. Their report showed that permeation reduc­tion for the Area Defect Model is difficult to achieve when the distance between defects is not larger than the combined thickness of the barrier and substrate. Inherent in this conclusion is the assumption that the dissociation rate at the defect is sufficiently fast to maintain the equilibrium concentration dictated by Sievert’s law. If this condition is not met, then the activation energy for the process would be that asso­ciated with the dissociation, and not that of perme­ation through the substrate. Thus, barriers that can provide a significant permeation reduction in the laboratory must be essentially defect free.

The physics of hydrogen transport in metals with permeation barriers can be further understood by examining the pressure dependence of perme­ation. As discussed earlier, diffusion-controlled per­meation through metals is proportional to the square root of the hydrogen partial pressure. Perujo et a/.227 reported that the pressure dependence of permeation through MANET plasma sprayed with aluminum changed from the classic square root dependence to linear as the pressure was decreased below 20 000 Pa. Mcguire228 also noted the transition to near-linear pressure dependence in the pressure range from 200 to 1000 Pa. Linear pressure dependence is symp­tomatic of permeation limited by absorption or recombination. For example, if recombination limits permeation, the concentration of hydrogen in the metal will be almost constant and uniform, and it will be established by equilibrium at the upstream side of the pressure boundary. Thus, Sievert’s law (eqn [7]) can be substituted into eqn [24], leading to linear pressure dependence:

Jr = kTK2p tt [24]

While the same relationship will be found if the permeation is limited by absorption on the upstream surface, known values for the recombination-rate constant for MANET can explain the linear pressure dependence seen in permeation measurements.128 The conclusion is that a combination of the Area Defect Model and the Surface Desorption Model is needed to properly model permeation though barrier materials.

If barriers work by limiting the area available for the gas to contact the underlying metal surface, and possibly by creating low enough permeation to have recombination even further reduce the permeation, how does radiation affect this process? One possible answer is by increasing the porosity or cracking of the barrier. According to Arshak and Korostynska229 properties of metal oxide materials are directly or indirectly connected to the presence of defects, oxy­gen vacancies in particular. Oxygen vacancies are also known as color centers, and these color centers are stabilized by hydrogen trapped at the defects. The hydrogen can come from preexisting OH~ groups or from hydrogen isotopes migrating through the oxide, possibly increased by the enhanced electrical con­ductivity generated by the radiation damage and the oxygen vacancies. While cracking was not considered by Arshak and Korostynska, one can speculate that the radiation damage with increased oxygen vacan­cies and trapped hydrogen would lead to a more brittle oxide layer. In metals, lateral stress from hydrogen or helium trapping can lead to blisters.230 Without the required ductility to allow blistering, the oxide layer could experience significantly increased cracking. The cracking would then increase the area available for hydrogen to reach the metal surfaces.