Determination of effective recombination coefficient by thermodesorption method Int. J. of Hydrogen Energy, 2014, v. 39, pp. 15819–15826 Yu.V. Zaika ∗ , E.K. Kostikova Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, Pushkinskaya st. 11, Petrozavodsk, Russia 185910 Abstract The degassing by thermodesorption method (TDS) of structural material sample previously hydrogen saturated is considered. The mathematical model of TDS-experiment and parametric identification method are presented. The data for nickel and tungsten in numerical simulations are used. The two-peak problem and effect (“derivatives”) of diffusion and desorption parameters on the TDS-spectrum are illustrated. Diffusion coefficient is known but the recombination parameters on surface remain to be estimate. The estimation algorithm needs no special mathematical software and allows to scan a material in wide temperature range. Integral smoothing processing of measurements is applied in the algorithm to secure its noise resistance. Keywords: hydrogen permeability, boundary-value problems of TDS-degassing, parametric identification 1. Introduction Interest in the interactions of hydrogen with various mate- rials is multifaceted [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. It suffices to mention power engineering, protection of metals against hydrogen corrosion, chemical reactor design, rocket engineering. For instance, while a radioactive isotope of hydrogen, tritium, will presumably (in the long term) be ap- plied in thermonuclear reactors, the problem of tritium diffu- sion leakage and its accumulation in structural materials may arise. Hydrides help to retain substantial amounts of hydro- gen. Hence the high expectations attached to the relatively safe hydrogen batteries and motors: no high pressures or low tem- peratures involved. Reversible metal alloyage by hydrogen is the basis for plasticization and thermal hydrogen processing of titanium alloys. Enthusiasts speak not only of hydrogen energy but even of hydrogen economy [5]. Mathematical models of hydrogen isotopes’ interaction with structural materials and methods for their parametric identifica- tion are needed to enhance the performance of experimental re- search, solve applied problems and draw general conclusions. Practice has shown that the limitations are not only diffusion processes inside the metal, but also physical-chemical effects on the surface [2, 3]. Transfer parameters depend on the pro- cess characteristics of producing the material batch, and one needs effective algorithms for processing measured curve in- stead of focusing on “tabular data”. Adsorption, dissolution, diffusion, . . . per se are subjects for theoretical and experimen- tal studies. Each additional coefficient however leads to a leap * Corresponding author Email addresses: zaika@krc.karelia.ru (Yu.V. Zaika), fedorova@krc.karelia.ru (E.K. Kostikova) to a new difficulty level of the inverse problem of parametric identification. We shall focus on the thermodesorption method and take into account only the limiting factors and the informa- tion capacities of the TDS experiment explicated below. 2. Mathematical model Boundary value problem. We consider hydrogen transfer through a test metal sample (plate thickness ℓ ). For brevity we speak of a metal plate, although it may be a multialloy or an intermetallic compound. We assume that heating is relatively slow, well nigh uniform, so that the diffusion flow can be con- sidered proportional to the concentration gradient. Let us as- sume a standard model for diffusion in the bulk [17]: ∂ t c(t, x)= D( T )∂ 2 x c(t, x), (t, x) ∈ Q t* , (1) c(0,x)= ϕ(x),x ∈ [0,ℓ], where t — time, Q t* = (0,t ∗ ) × (0,ℓ); c(t, x) — diffusing hydrogen (monoatomic) concentration; D — diffusion coeffi- cient. For definiteness we assume that D is a function of the temperature T (t) given by the Arrhenius equation with the pre- exponential factor D 0 and the activation energy E D (R is the universal gas constant): D = D 0 exp  −E D /[RT (t)]  . Such f ( T ) relationships are plotted by S-shaped saturation curves. More disaggregate transfer models are known. Among other factors, we can take into account various diffusion channels (transcrystalline, grain boundary, along defects) and the inter- change between them. In the inverse problem (the difficulties involved being commonly known) we focus only on the limiting factors and the feasibility of parametric identification by TDS- method. Some problems of the parametric identification of hy- Preprint submitted to Elsevier January 13, 2015