PHYSICAL REVIEW B VOLUME 29, NUMBER 10 15 MAY 1984 Kinetics of hydrogen absorption in transition metals and subsurface bonding M. Lagos and G. Martinez Facultad de Fisica, Pontificia Universidad Catolica de Chile, Casilla 114-D, Santiago, Chile Ivan K. Schuller Materials Science and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received 22 February 1984) We have modified the kinetic equations for the absorption of hydrogen in transition metals to include the effects of strong subsurface bonding. The new equations show that the subsurface, self-trapped hydro- gen acts as a valve for the admission of hydrogen into the bulk. The explanation for a number of experi- mental facts, not well understood before, neatly follows. Discrepancies between theory and experiments found earlier are explained by the inclusion of the subsurface term into the kinetic equation. INTRODUCTION The absorption of hydrogen in transition metals has been a subject of recent theoretical and experimental interest. In a series of experiments' 4 it was found that the absorption of hydrogen in the bulk is critically related to the details of the surface. In particular, it was shown that the Nb(110) surface covered with less than two monolayers of Pd ab- sorbs hydrogen very slowly. However, when it is covered by more than three monolayers of Pd(111) the absorption into the bulk of niobium increases considerably. This is conventionally attributed to an increase in the electronic density of states at the Fermi level which enhances the dis- sociation of molecular hydrogen to atomic hydrogen. The absorption kinetics (i.e. , time dependence) is, howev- er, very difficult to explain in a self-consistent manner. Pick et al. ' have solved a series of kinetic equations, origi- nally written down by Conrad, Ertl, and Latta, assuming H exchange between the gas, surface, and bulk of the Nb sam- ple. They obtain a good fit to the experimental, high- temperature, bulk uptake rates assuming a small value of the initial sticking coefficient. However, later experiments which observe directly the surface coverage, found the ini- tial sticking S to be large. For instance, for Nb(110), S =0. 3 compared with Pd(111) which has a sticking coeffi- cient S =0.1. Smith7 has measured the time dependence of hydrogen absorption by the Nb(110) surface and analyzed his data us- ing the Pick et al. model. His conclusions are the following: (i) The experimental time dependence does not follow the model at any temperature, i.e. , the charging curve saturates too fast. (ii) The time dependence of the surface coverage implies high sticking rates and slow or no equilibration between the surface and bulk. (iii) In the temperature range 400 K & T & 600 K the system follows reversibly the equilibrium equations derived from Pick's model. (iv) At room temperature the saturation value of the sur- face coverage coexists with a very small bulk concentration which is far from equilibrium. This implies that the surface and the bulk are decoupled at room temperature and below. We have shown earlier' that due to the interaction of the hydrogen with the surface vibrations, in certain cases, the hydrogen's binding energy increases considerably close to the surface. Quite recently, experimental evidence has also been found ' which is claimed to prove conclusively the existence of subsurface bonding, in accordance with our theoretical predictions. As a consequence, the subsurface can be saturated with tightly bound hydrogen thereby block- ing the diffusion of hydrogen through the surface into the bulk. This implies that the subsurface acts as a valve, which controls the passage of H between the surface and bulk. In the present paper, we show the consequences of the strong subsurface bonding for the absorption kinetics. The ex- istence of subsurface bonding in Nb(110) solves all the dif- ficulties encountered by Smith in comparing the experimen- tal data with the model of Pick et aL It also explains the coexistence of very high sticking coefficients and very low bulk uptake rates exhibited by clean Nb(110) surfaces in H2 atmosphere. In addition, generalizing the kinetics equations of Pick, we predict the existence of a critical temperature below which the surface is decoupled from the bulk and above which the surface "valve" opens thereby allowing diffusion of hydrogen through the surface into the bulk. KINETICS Since considerable experimental data are available for the absorption of hydrogen by the Nb(110) surface we will re- strict ourselves to comparing our results with experiments in this system. However, the qualitative conclusions are of a general nature and depend only on the existence of subsur- face bonding. Our earlier calculations have shown that for Nb(110) the first subsurface self-trapping energy is quite large ( — 0.56 — 0.86 eV). This is comparable to the chem- isorption energy of (0.55 eV) and, consequently, has to be taken into account. Therefore the energy of a hydrogen atom approaching the Nb(110) surface is shown schemati- cally in Fig. 1. This model is similar to that of Pick et al. ' except that they do not include the deep subsurface potential well. The 5979 1984 The American Physical Society 54