CermakJ., Kufudakis A., Lewis***F. A.
*Institute of Physics Na Slovance 2,182 21 Praha 8, Czech Republic **Nuclear Research Centre "Demokritos" Aghia Paraskevi, Attiki, Greece ***School of Chemistry The Queen's University of Belfast Belfast BT9 5AG, Northern Ireland, UK
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Performance and interpretation of measurements of hydrogen diffusivity in metals have been improved steadily in regard to emphasizing the role of initial and boundary conditions at interfaces, the state of perfection of the crystal lattice of the solvent metal, the concentration of hydrogen and the strain-induced component of the diffusion flux. This paper presents an attempt to estimate the relative influence of the afore-mentioned factors on the diffusivity of hydrogen in a -Pd at 50 °C in three diffusion-elastic processes, over courses of electrolytic charging with respective subsequent equilibration and electrolytic discharging processes. Comparison of available data has suggested some non-negligible influences of regularly neglected systematic errors.
1. INTRODUCTION
The diffusion-elastic effect, as noted in its simplest form in 1909 by Stoney [1] can be regarded for study of processes of absorption, equilibration and descorption, for different initial and boundary conditions, in the sense of a classification [2] as a direct instantaneous response of a standard linear solid to a time- and co-ordinate-dependent stress field developed during diffusion of impurities/interstitials/in a crystal matrix. Stoney's experimental technique has since been generalised and experimentally developed [3,4] in terms of the simple geometry of uniaxial bending of a strip during one-dimensional diffusion [3,4]. Such a generalised diffusion-elastic effect has thus proved to be an effective and sensitive experimental tool for the investigation of, for example, the diffusion of hydrogen in metallic structures under very different initial and boundary conditions including absorption, equilibration within, and desorption of hydrogen from samples of the strip. Values of diffusion coefficient of the matrix material of the strip could then be derived from the time dependence of the bending deformation related directly to the diffusion process of the hydrogen interstitials through the thickness of the strip. The technique was absolute in the sense that it required no calibration. For determination of the hydrogen diffusion coefficient it was only necessary to record the deflection of the free end of the strip as a function of time and to know the other geometrical characteristics of the experimental system. No adjusting parameters need to enter the subsequent calculations.
It is important here to state explicitly that the associated bending distortions could also be expected to induce consequent Gorsky effect migration processes [5-8]. Thus from a detailed comparison of the diffusion-elastic (DE) and Gorsky effect (GE) in [9] it is impor-
tant to restate here at least two differences between the operation of the two effects:
a) the DE effect can be classified as a primary elastic effect while GE is correspondingly classified an anelastic effect;
b) the sensitivity of the diffusion elastic effect to changes of concentration distribution of interstitials should be expected to be at least two orders of magnitude higher that the sensitivity of the GE [9]. The second statement (b), has allowed the GE to
have been effectively neglected in measurements of dif-fusivity obtained by the DE technique in conditions of current experimental precision, since the GE can never properly develop to its full theoretical magnitude during the course of the DE measurements. This fact further reduces conditions of description according to Ze-ner's classification [2], and so to any contribution of the GE to DE, and has fully justified neglecting the Gorsky effect in this connection in all regard to the following considerations below. On the other hand Gorsky effect influences have been fully taken into account in specialised measurements with tubular membranes of palladium alloys as, for example, in the studies of refs. [10, 11 and 12].
1.1. Scope of the present paper
On turning towards somewhat more specific attentions to the DE effect, it should be noted that the DE technique has been successfully applied to measurements of diffusion parameters of hydrogen in nickel [9,13], iron [14], platinum [15] and a series of palladium-platinum alloys [16]. Its reliability has been justified by overall agreement of results obtained in these studies [13-16] and results alternatively derived by other methods. In addition, the DE technique has been successful in obtaining results under difficult combinations of experi-
mental conditions, where more conventional methods would either have been very difficult to apply or would have proved inefficient as, for example, has been the case in measurements of hydrogen diffusion coefficient in platinum at 30 0C [15] which were the only ones available at that particular time.
All the earlier results that have been mentioned above, have referred to a single-phase solid solution of hydrogen in a homogeneous isotropic metallic matrix. However, in order to verify the principal assumptions of the model that have been previously outlined in full in [3] and [13], a more complicated system of a bimetal double-layer consisting of two parallel metallic strips of nickel and copper has also been experimentally investigated [4,17] and a reasonable agreement has been obtained with available related data, for hydrogen diffu-sivity in the cases of both the involved metals.
In all of the cases quoted here above, experimentally measured bending deflection against time curves have been analysed and compared to appropriate theoretical relation by a least-squares procedure, in terms of a model briefly summarised in ref. [13] where unified boundary conditions had included assumptions of perfect permeabilities of both entrance and exit surfaces together with other prescribed conditions of constant surface concentrations of hydrogen both at beginnings and also over the courses of the entire diffusion process.
In the case of studies with a Pd-H specimens, close examination of bending deflection against time curves (BDT curves) for various electrolytic regimes, had early indicated a need for essential differences in assumptions as compared to those previously applied to the other measured metals [8, 9, 13-15]. In the case of Pd-H specimens [18], the piceine-coated surface of the palladium specimens had to be considered to be effectively impermeable to hydrogen and also that both preanod-ized and palladized surfaces had to be highly efficient both for the initial absorptions and retentions of elec-trolytically discharged hydrogen at 50 0C and also with considerations of the relatively low prescribed current densities of 20 Am-2. It should also be emphasised here, that the piceine coating of one outer surface had assumed a primary purpose of preventing this surface of experimental samples, from actually contacting the electrolyte. An effective combined impermeability to hydrogen of this piceine coating, in the measurements with palladium may also be associated with the generally lower values of hydrogen chemical potentials recorded over the whole course of the palladium studies.
A general survey of the variety of such influences observed in the DE measurements with palladium, including consequences of a ^ f phase transition possibilities, has been presented qualitatively in refs [18 and 24], and has served as a reliable basis for the present more quantitative analysis.
The scope of the present paper, corresponds to a further presentation of results of the DE measurements of diffusivity of hydrogen in a Pd-H at 50 0C obtained in conditions of the operation of three different processes of hydrogen diffusion namely: hydrogen absorption, hydrogen content equilibration and hydrogen desorption respectively, in the electrochemical regime [24]. Possible influences of lattice defects and hydrogen content concentration are also to be discussed. The particular influences of the choice of initial and boundary conditions on the descriptions and results of experiments, are also to be analysed.
2. EXPERIMENTAL
The essential arrangements have been described in previous papers as, for example, in refs. [3, 4, 13]. Long Pd strips, dimensions 60x10x0.3 mm2 of purity 3N as supplied by Safina, had first been annealed for two hours at 1000 0C in vacuum. Specimens were next clamped at one end and a mirror was attached to an arm extended from the other free end positioned to reflect a light beam from a projection lamp on to photographic paper held on a rotating drum.
After the coating of one face of specimens with pi-ceine hydrocarbon wax, the other surface could then be activated by electro-deposition of a thin layer of palladium black from a solution of 2% PdCl2 in 0.1 N HCl. Finally after immersion in an electrolyte solution of 1 N H2SO4 at 50 oC + 0.1 oC, hydrogen could be introduced or removed electrolytically through an estimated effective active surface area of 50x10 mm2 at current densities of 20 A.m-2 or 200 Am-2 alternatively. A platinum sheet was employed as a counter electrode.
Examples of well defined experimental bending deflection-time (BDT) curves obtained for the three different experimental processes are presented in Figs. 1-4. With reference to these BDT curves, a sequence of procedures had to be applied [13], based on physicochemical reasoning concerning surface conditions applying to transmission of hydrogen through the electrolyte-Pd electrode interface to be discussed further below in Section 7.2.
Hydrogen concentrations cH(n) = nH/npd (where nH and nPd are the volume densities of atomic ratios of hydrogen and palladium atoms respectively) were restricted to below a limit of cH(n) = 0.01, in order to ensure limitations of cH(n) values to the a -phase structure composi
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