Influence of Self‐Consistency on the Relaxation near a Vacancy or a Surface in Transition Metals

Abstract

I n the tight-binding approximation a complete intra-atomic screening of the charge is assumed t o evaluate the self-consistent potential near a defect in a transition metal. The importance of this potential on the relaxation near e defect is demonstrated. It can, for instance, invert the sign of the displacements for a nearly empty or full d band where the screening by the d electrons is less efficient. The agreement with the experimental results is notably improved for the vacancy formation volume of platinum.Dans l'approximation des liaisons fortes, le potentiel de self-consistence prhs d'un dbfaut dans un metal de transition est bvalub en supposant un bcrantage oomplet de la charge sur chaque site. On montre l'importance de ce potentiel sur la relaxation atomique prhs d'un dbfaut. Ce terme peut renverser le signe des dbplacements pour une bande d presque pleine ou presque vide lorsque 1'6cran par les blectrons d est moins efficace. L'eccord avec les rbsultats expbrimentaux est am6liorb notamment pour le volume de formation d'une lacune dans le platine.

Vacancies and small vacancy clusters in BCC transition metals : calculation of binding energy, atomic relaxation and electronic and vibrational densities of states

“…BCC transition metals like a-Fe and Mo are known to show small void swelling [16]. Furthermore, these calculations are of significance for the understanding of vacancy conversion process into dislocation loops : Jenkins et al [17] observed both the (al2) I I I > and the a ( 100 ) vacancy loops in BCC transition metals irradiated with heavy ions.…”

“…We use a TB approximation coupled to the moments method [3, 4] to describe the transition metal d-band, and estimate the change in the d-band energy due to the introduction of lattice defects. The local DOS pi(E) of the d-electrons on atom i is approximated by a Gaussian fitted to the first and second moments, J.lli and J.l2i [17]. We take the free atom level as the origin of the energies and take into account the diagonal matrix element Vl = ,ui i) of the self-consistent potential resulting from charge oscillations near the lattice defects [18].…”

“…In deriving equation 2b, we have assumed that the self-consistent potential Vi completely screens the defect and each atom is neutral. In this case, Vi can be given by [17] To account for the repulsive core-core interaction energies at small distances, arising mainly from the increase in sp kinetic energy upon compression, we take a Born-Mayer potential [3] :…”

On the interaction between a vacancy and an interstitial impurity atom in B.C.C. transition metals

“…The transition metal d-band is approximated by a Gaussian fitted to the first p1i and second pzi moments [5, 61. One can calculate the change in the d-band energy AEe due to introduction of lattice defects (i.e., due to the changes in pli and pZi) from [6],…”

A tight-binding derivation of force constants : Application to covalent systems

“…It is to be noted that a similar technique has already been used for transition metals but using a method of moments restricted to the second moment [17][18][19]. Within this context angular terms such as described here are absent but should appear in a complete Green's function treatment of the d orbitals.…”