Interaction between interstitial-interstitial and interstitial-substitutional solute atoms in d-band metals

Abstract

Résumé. 2014 On étudie, dans l'approximation des liaisons fortes, la contribution électronique à l'énergie d'interaction entre atomes interstitiels en solution dans les métaux de transition (interaction I-I). La Abstract. -The electronic contribution to the interaction energy between interstitial solute atoms (I-I interaction) in transition metals is investigated within the tight-binding approximation. The theoretical method used in this study closely parallels that developed by Einstein and Schrieffer for the adatom interaction. The method permits us to study the solution of the gas atom in the octahedral sites as well as in the tetrahedral sites and also allows us to investigate the interaction between the interstitial and substitutional solute atoms (I-S interaction). Calculations have been carried out as a function of band filling, solute atom energy level, an impurity potential matrix element V0 on the substitutional atom site, and a général hopping potential Va between an interstitial atom and the nearest neighbour host atoms. The numerical results generally indicate the importance of the electronic contribution to the interaction énergies (both I-I and I-S interaction). Under reasonable conditions, our simple model of the I-S interaction is shown to agree well with the experimental data for Fe-based ternary alloys containing the simple gas atoms such as N or C. The angular position dependence of the I-I interaction energy is often weak and the possibility of the interstitial condensation (03B1-03B1' phase transition) observed in a Nb-H system is discussed. Contact is also made with the solute (I-I) interaction based on the elastic theory.

The Palladium‐Silver‐Hydrogen System: A Quasi‐Chemical Approach

“…Demangeat et al [23] developed a more general description for the electronic structure of an interstitial atom in a transition metal matrix and proved that, as a first approximation, the electronic interaction energy between the interstitial and a substitutional impurity is proportional to the difference of charge between the substitutional impurity and the matrix ionic cores. This result is again in qualitative accord with those derived by Friedel [21], and Masuda and Mori [22]. So, they corroborate the present thermodynamic analysis.…”

“…This is also consistent with Friedel's screened proton model and his conclusion that hydrogen is repelled at short range by impurities on the right of the matrix in the periodic table and attracted by impurities on the left 1211. Masuda and Mori [22] arrived at similar conclusions after calculating the electronic interaction between substitutional and interstitial atoms in transition metals. Demangeat et al [23] developed a more general description for the electronic structure of an interstitial atom in a transition metal matrix and proved that, as a first approximation, the electronic interaction energy between the interstitial and a substitutional impurity is proportional to the difference of charge between the substitutional impurity and the matrix ionic cores.…”

Chemical binding energies of point defects in palladium doped with hydrogen and d impurities

“…Also, using equation 2.15and expanding up to first order with respect to 5v, we recover the well known perturbing limit i.e. ilEas(À, Ru) is proportional to 5Zjl(EF) [3,11] ; but this limit is not valid in the present case. Let us note that a similar behaviour as figure 3 (i.e.…”

“…and references therein]. This type of result suggests to us that the origin of the hydrogen-hydrogen interaction, in palladium for example, is the sum of a long-ranged elastic part [1,2] and a short-ranged chemical part [3]. However, as shown by Dietrich and Wagner [5] this type of separation may not be valid in coherent palladium systems (see for example table 1 of [5]).…”

“…-Since the work of Alefeld [1] it is often assumed that the dominant contribution to the interaction energy between hydrogen atoms in a transition metal is of an elastic nature, especially in a coherent metalhydrogen system [2]. However Masuda and Mori [3] showed that chemical binding energies, i.e. electronic contributions, might be as large as elastic energies and that the sign depended drastically on the filling of the host d bands under consideration.…”