Papers by Author: A. Lodder

Abstract: The driving force on an ion in a metal due to an applied electric field, called the electromigration force, is built up out of two contributions, a wind force and a direct force. The wind force is due to the scattering of the current carrying electrons off the ion. The direct force works on the effective charge of the ion. In the present work we concentrate on the direct force on a migrating proton embedded in an electron gas. For this force a sign change is obtained as soon as a bound state is formed. In recent calculations hardly a sign change was seen, although a bound state was found in a self-consistent-potential for lower electron densities. Here we show that a supplementary term shows up, as soon as one accounts for the bound state explicitly. By this the problem has been solved regarding a possible lack of completeness of the published formalism. The results presented are based on square-well model potentials. By using different depths it is possible to show results for potentials without a bound state and accommodating one bound state.

Abstract: In this review the current status of research on electromigration of hydrogen in metals and alloys is determined. Experimental data and theoretical developments over the past 16 years are gathered and are put in perspective with older literature. Theory has reached a level at which the current induced wind force on a proton in a metal can be estimated quantitatively. At the same time empirical data have become more decisive as well. In experiments on a number of alloys the wind force could be effectively eliminated, revealing information on the direct force in electromigration. In metals, as a function of increasing temperature or sample resistivity, the effective valence of hydrogen slowly approaches unity. Combining theoretical and experimental results, s· strong support in favour of a direct force on a proton in an electron gas in presence of an electric field is found. The direct valence is close to unity or somewhat less due to screening effects. Theoretical analysis shows that only in the dilute limit, at low temperatures, complete screening of the external electric field is expected. At elevated temperatures a gradual break-down of the screening by the electron gas is found to be intimately related to the electron-phonon interaction gaining in strength. As far as the hydrogen-deuterium isotope effect in the effective valence of hydrogen in metals is concerned, results from different experiments are often found to be inconsistent. Combination of a zero point motion model with isotope dependent lattice deformation seems to be most promising in explaining some of the observations.