Tight-binding modeling of interstitial ordering processes in metals: Application to zirconium hydrides

Abstract

We present here a theoretical study of ordering processes in metal-hydrogen compounds based on a generalized perturbation method and on tight-binding coherent potential approximation. This approach is illustrated for zirconium hydrides, in which case we demonstrate that a cluster expansion of the ordering energy can be limited to effective pair interactions, the leading one being between hydrogen atoms in third-neighbor positions. These results are quantitatively confirmed by comparison to density functional theory calculations and qualitatively interpreted through orbital symmetry analysis. The method is then applied first to draw a preliminary Zr-H phase diagram and then to characterize the effect of lattice deformation on the ordering processes in zirconium hydrides.

How to take into account local concentration in Ising-based Monte-Carlo: illustration with zirconium hydrides

“…At that point, we can notice that detailed derivation of the Zr-H TBIM (recalled in section 2.2), and a preliminary Monte-Carlo study, have been already performed in Ref. [19]. However, the present investigation is clearly distinct from this previous work.…”

“…This local concentration MC based on TBIM allows us to build a Zr-H schematic phase diagram (section 4), similar to the one obtained on Figure 9 of ref. [19] by global concentration MC based on DFT-fitted Ising model.…”

“…Here is a recap of procedure and results developed in Ref. [31,19], which will be necessary for what follows.…”

“…Formula ( 5) can be generalized for triplets, quadruplets, etc, corresponding to higher order additional terms in perturbative development (3). In practice, we have proven [31,19] that for the Zr-H system, these multiplet interactions are negligible with respect to pairwise interactions.…”

“…In ref. [19], we failed at directly implementing the concentration-dependent TBIM in our MC with the global concentration approach, because of unphysical demixing phenomena. To overcome the problem, we implemented our global concentration approach MC with an alternative Ising model, fitted on DFT calculations by Connolly-…”