- Zeitschrift für Physikalische Chemie, Bd. 181, S. 393-397 (1993) by R. Oldenbourg Verlag, München 1993 0942-9352/93 $ 3.00 + 0.00 The Diffusion of H in Mg and the Nucleation and Growth of MgH2 in Thin Films* By P. Spatz, H. A. Aebischer, A. Krozer and L. Schlapbach Institute of Physics, University, CH-1700 Fribourg Magnesium hydride / Diffusion / Nucleation andgrowth / Thin film / Interface We have studied the kinetics of hydrogen absorption in thin Mg-layers (20 Â 800 Â) that were UHV evaporated onto a previously hydrided Pd-foil. The Pd-foil acted as a virtually infinite reservoir of atomic hydrogen. In this way we were able to circumvent the problem of the slow dissociation of gaseous hydrogen on the Mg-surface. In order to study the diffusion of hydrogen through Mg and the subsequent nucleation and growth of the hydride we used X-ray photoelectron spectroscopy (XPS) to measure the temporal evolution of the hydride concentration on the vacuum-exposed surface of the Mg-film. Our goal was to develop a simple diffusion model that describes our measured curves in order to determine the overall diffusion coefficient. The model exploits the fact that the hydride is preferentially formed on the PdHr Mg-interface and forms a diffusion barrier for subsequent diffusion of hydrogen particles. This was taken into account by adopting a time dependent boundary condition for the hydrogen concentration on the PdHv Mg-interface. The model curves agreed well with the experimental results. We found an overall diffusion coefficient D 1.1 10"20 m2/s at 305. 1. Introduction The hydrides of Mg and its alloys are of considerable interest in hydrogen technology. Mg is cheap, light, its deposits are abundant on earth, and it is able to absorb 7.6 wt% of atomic hydrogen. However, magnesium hydride (MgH2) forms very slowly. In the last years, many experiments aiming at the determination of the diffusion coefficient of in Mg, and at the identification of the rate-limiting step in its hydriding kinetics were performed [1, 2, 3]. In a recent review article Gérard and Ono [4] wrote that "The results on hydriding/dehydriding of unalloyed magnesium are described in many papers and consist of a series ofcontradictory experimental results and diametrically opposed interpretations." Hydrogen Systems, Funda- * Presented at the International Symposium on Metal mentals and Applications. Uppsala, Sweden, June 8 955 12, 1992.
394 P. Spatz, H. A. Aebischer, A. Krozer and L. Schlapbach Mgls Mgls 1 1r 1308 1304 1300 1308 1304 1300 1308 1304 1300 Binding Energy [ev] Binding Energy [ev] Binding Energy [ev] t 0 ti CU Me PdHx MgH2 Fig. 1. The bottom part of the Figure illustrates our model of the temporal formation of the hydride in the Mg-layer. The top part shows the corresponding XPS-spectra. At the time / 0, no MgH2 has formed in the overlayer. The Mgls-electron emission at 1303.5 ev is characteristic of metallic Mg. At the time tu MgH2 domains that had started to grow on the PdHx Mg-interface have reached the vacuum-exposed surface. The Mgls-level splits into a chemically shifted peak at 1305.8 ev characteristic of MgH2 and a part corresponding to the metallic Mg. At the time r2, the part of the sample close to the PdHxMg-interface is nearly completely hydrided. A large part of the vacuum-exposed surface is hydrided, too. The chemically shifted part of the Mgl.v-peak is now a dominating feature in the spectrum. 2. Experiments and results Our approach to follow the hydride formation in Mg is different from the ones used in previous experiments. To avoid the problems connected with the oxidation of the Mg-surface and of the slow dissociation of gaseous hydrogen we have evaporated a thin layer of Mg in ultrahigh vacuum onto a previously in situ hydrided thick Pd-foil. The Pd-foil served as a virtually infinite reservoir of atomic hydrogen. The Mg-film was thus hydrided through the PdHx Mg-interface. With the aid of X-ray photoelectron spectroscopy (XPS) the presence of MgH2 on the vacuum-exposed surface (down to the probing-depth of approximately 30 Â) could be identified through the chemically shifted Mgls-peak [5], see Fig. 1. The concentration of MgH2 was determined through the ratio of intensities of the shifted 956
Diffusion of H in Mg and Nucleation and Growth of MgH2 in Thin Films 395 0 400 800 Time [min] Fig. 2. This figure shows the experimental ( ) and the theoretical curves (-) of the MgH2-concentration ( 8 2/ 8,)at the vacuum-exposed surface as a function of time. Curves for four different thicknesses' of the Mg-layer, lu l2, h and!4 are shown. (hydride) and the total (Mg-bulk plus hydride) Mgfs-peak. The temporal evolution of the concentration calculated in this way is plotted in Fig. 2. The experiments were carried out in a VG ESCALAB 5 spectrometer at a base pressure of 1 10~10 mbar. Mg ~ was evaporated simultaneously onto a clean hydrided Pd-foil and onto a thickness-and-rate-monitor INFICON- XTC close to the sample position. The thickness of the evaporated layers was determined with three independent methods: (I) an order of magnitude of the Mg-thickness was obtained from the reading of the thickness monitor; (II) for thinner Mg layers, the thickness was determined through the ratio of the intensities of the Mgls- and Pd3i/-core level peaks; (III) after the completion of the experiments the samples were dehydrided (at about 100 C) and Mg was sputtered away with Ar-ions. The thickness of the Mglayer was determined with the aid of a tabulated sputter-rate for Mg. 3. Interpretation by diffusion kinetics A simplified model able to describe the temporal evolution of the concentration of MgH2 is given below. It is known that when Mg is hydrided from 957
396 P. Spatz, H. A. Aebischer, A. Krozer and L. Schlapbach the gas phase, MgH2 starts to grow close to the surface and acts as a diffusion barrier for further diffusion of hydrogen particles [2], see Fig. 1. Consequently, we assumed in our model that hydrogen diffuses only through the non-hydrided part of the Mg-film. We projected all the effects that slow down the formation of MgH2 (diffusion barrier just mentioned, nucleation, and growth, making up the overall diffusion coefficient) onto the PdHx Mg-interface. The surface already hydrided at the time t + dt can be expressed in the form AHyd(t + dt) AHyd(t) + k-df [A0-AHyd(t)l (1) A0 is the total surface available for diffusion at the time t 0. The difference Ao-AUyd{t) describes the surface not yet hydrided at the time t. The constant k describes the overall-rate of Mg-to-MgH2-transition. From Eq. (1) it follows that the surface available for diffusion decays exponentially with time: A(t) Ao-e~kt. (2) We made the additional assumption that the local flux of hydrogen particles through the part of the PdHx Mg-interface not yet hydrided stays constant in time. This leads to the following time-dependent boundary condition for our diffusion problem: C0(/) Co-e-*''. (3) Co(0 represents the hydrogen concentration at the time / on the boundary. Using this boundary condition in Fick's second law [6] we found that the temporal evolution of the MgH2-concentration, C*(x0,t), on the vacuumexposed Mg-surface (at x x0) is given by C y(x0) C(x0,t); 0<t<tmdx C*(*o,0 (4) I? ^ ^ ^max where Co- - " (2/1+1) (-!" / 2«+l \ ' cos- x0 (5) C(x0,t) -à- -j - [exp{ ot exp{ k t}] describes the concentration of dissolved hydrogen on the vacuum-exposed surface of the Mg-layer (D is the diffusion coefficient and / is the layer thickness), and D-(2n+\)2-n2 a- -^2- (6) 958
Diffusion of H in Mg and Nucleation and Growth of MgH2 in Thin Films 397 We further assumed in Eq. (4) that the concentration of the hydride on the vacuum-exposed surface is proportional to the concentration of the hydrogen dissolved on this surface (proportionality factor ^(xo))- The saturation concentration Cs of the hydride was reached after the time rmax. In all the experiments we found that Cs was below one and depended on the thickness of the Mg-layer. This observation can be understood in terms of our boundary condition, Eq. (3), since the hydride concentration on the PdHx Mg-interface is higher than in the interior of the Mg-layer and blocks further H-transport. The experimental curves of the hydrogen concentration as a function of time measured at the vacuum-exposed surface were computer-fitted to our diffusion model. The theoretical curves are in good agreement with the measured ones (Fig. 2). The overall diffusion coefficient of H in Mg at 305 extracted from the fits is D 1.1 10~20m2/s. Acknowledgements This work was supported by the Swiss Foundation for Energy Research (NEFF). References 1. J. Renner and H. J. Grabke, Z. Metallkd. 69 (1978) 639-642. 2. C. M. Stander, Z. Phys. Chem. Neue Folge 104 (1977) 229-238. 3. M. Stioui, A. Grayevsky, A. Resnik, D. Shaltiél and N. Kaplan, J. Less-Common Met. 123(1986)9-24. 4. N. Gerard and S. Ono, "Hydride Formation and Decomposition Kinetics", Chap. 4 in: L. Schlapbach (ed.), Hydrogen in Intermetallic Compounds II. Topics in Applied Physics, Vol. 67 (1992) 165ff. 5. A. Fischer, A. Krozer and L. Schlapbach, "Mg/Pd and Ba/Pd Interfaces With and Without Hydrogen", Proceedings of the 12th European Conference on Solid Surfaces (ECOSS), Stockholm, Sweden, Sept. 9-12 (1991). Surf. Sci. 269/270(1992) 737. 6. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, Oxford (1959). 959