The normalized pressure dependence method for the evaluation of kinetic rates of metal hydride formation/decomposition

Abstract

An assumption is put forward, here, that the main reason for the large discrepancies between results derived from kinetic measurements, carried out by various investigators, is the fact that the pressure dependence of the overall kinetic flow rates has been given a different interpretation by various investigators. The new approach presented here, the normalized pressure dependence method (NPDM), for the interpretation of the overall kinetic flow rates consists of several main elements: (1) the pressure dependence function, has the general form of F(P)=|Peq-P|/Peq where, P and Peq are the system and equilibrium pressure, respectively. The function F(P) changes continuously with time. (2) F(P) is to be inserted, as a factor, into an integrated rate equation as follows: Ri(α)=−ktF(P) where, α is the reacted fraction and i refers to a particular mechanism or process order. (3) By plotting, for an isothermal experiment, Ri(α)/F(P) vs t an intrinsic kinetic rate constant, k, which depends on temperature only, is derived. (4) From each experimental run, the reacted fraction for a decomposition experiment into vacuum, αv(t), can be calculated, without running an experiment with P=0. It is shown that for a decomposition experiment F(P) changes within the inherent limits, 0<F(P)≤1. Thus F(P) serves as a normalizing factor. Utilizing the NPDM kinetic measurements carried out under different pressure conditions can be compared. The NPDM is considered here, for brittle metal hydrides such as the intermetallics AB5 (LaNi5), AB (TiFe) and pseudo AB2, of Laves phases structure, for concentrations in the two-phase region, α+β. During the so termed, `second activation step', associated with the disintegration of the bulk into powder, the thermodynamic and kinetic parameters of the reaction change and reach, at the end, stable values. The mean particle diameter, Dm, has been shown to reduce sharply at the beginning of a cycling process and to reduce at a slowing down rate with an increasing number of cycles. An important empirical fact is that, upon cyclic hydrogenation, brittle MH materials asymptotically reach a minimal particle size (or rather a size distribution), but do not atomize. Adopting a fracture behavior approach applied to an isotropic, brittle, crystalline material, in the absence of plastic deformation, the qualitative approximation δVVmin∼ΔA(Γ/Ev) was received. Where Vmin is the smallest particle volume, δV is the volume misfit and ΔA the area of the newly formed surface. Γ is the surface energy per unit surface, and Ev is an elastic strain energy, per unit volume associated with the M↔MH phase transformation. The ratio (Γ/Ev) has the dimension of length. Combining these results with the empirical finding of the existence of a minimal particle size, Dm,min, it can be concluded that a particle of a volume smaller than Vmin would not be able to produce a crack by forming two new surfaces. Thus, further fractionating is prevented and the atomizing of the material is excluded. The effectiveness of the NPDM for the determination of kinetic rates is demonstrated for LANi5 at 10°C and for the alloy Ti0.95Zr0.05Mn1.48V0.43Fe0.08Al0.01, labeled C5, at 20°C, assuming a first-order reaction in both cases.