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

An assumption is put forward, here, that the main reason for the large disc repancies between results derived from kinetic measurements, carried out by various investigators, is the fact that the pressure dependence of the ove rall kinetic flow rates has been given a different interpretation by variou s investigators. The new approach presented here, the normalized pressure d ependence method (NPDM), for the interpretation of the overall kinetic flow rates consists of several main elements: (1) the pressure dependence funct ion, has the general form of F(P)=\P-eq-P\/P-eq where, P and P-eq are the s ystem and equilibrium pressure, respectively. The function F(P) changes con tinuously with time. (2) F(P) is to be inserted, as a factor, into an integ rated rate equation as follows: R-i(alpha) = -ktF(P) where, alpha is the re acted fraction and i refers to a particular mechanism or process order. (3) By plotting, for an isothermal experiment, R-i(alpha)/F(P) vs t an intrins ic kinetic rate constant, k, which depends on temperature only, is derived. (4) From each experimental run, the reacted fraction for a decomposition e xperiment into vacuum, alpha(v)(t), can be calculated without running an ex periment with P=0. It is shown that for a decomposition experiment F(P) cha nges within the inherent limits, 0<F(P)less than or equal to 1. Thus F(P) s erves as a normalizing factor. Utilizing the NPDM kinetic measurements carr ied out under different pressure conditions can be compared. The NPDM is co nsidered here, for brittle metal hydrides such as the intermetallics AB(5) (LaNi5), AB (TiFe) and pseudo AB(2), of Laves phases structure, for concent rations in the two-phase region, alpha+beta. During these termed, 'second a ctivation 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, D-m, has been show n 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 empir ical fact is that, upon cyclic hydrogenation, brittle MH materials asymptot ically reach a minimal particle size (or rather a size distribution), but d o not atomize. Adopting a fracture behavior approach applied to an isotropi c, brittle, crystalline material, in the absence of plastic deformation, th e qualitative approximation delta(v)V(min)similar to Delta A(Gamma/E-v) was received. Where V-min is the smallest particle volume, delta(v) is the vol ume misfit and Delta A the area of the newly formed surface. Gamma is the s urface energy per unit surface, and E-v is an elastic strain energy, per un it volume associated with the M<->MH phase transformation. The ratio (Gamma /E-v) has the dimension of length. Combining these results with the empiric al finding of the existence of a minimal particle size, D-m,D-min, it can b e concluded that a particle of a volume smaller than V-min would not be abl e to produce a crack by forming two new surfaces. Thus, further fractionati ng is prevented and the atomizing of the material is excluded. The effectiv eness of the NPDM for the determination of kinetic rates is demonstrated fo r LANi(5) at 10 degrees C and for the alloy Ti0.95Zr0.05Mn1.48V0.43Fe0.08Al 0.01, labeled C5, at 20 degrees C, assuming a first-order reaction in both cases. (C) 1999 Elsevier Science S.A. All rights reserved.