Electron impact ionisation cross sections of iron hydrogen clusters

Abstract

Abstract.We computed electron impact ionisation cross sections (EICSs) of iron hydrogen clusters, FeHn with n = 1, 2, . . . , 10, from the ionisation threshold to 10 keV using the Deutsch-Märk (DM) and the binary-encounter-Bethe (BEB) formalisms. at 51 eV for the DM method. Cross sections calculated via the BEB method are substantially higher than the ones obtained via the DM method, up to a factor of about two for FeH and FeH2. The formation of Fe-H bonds depopulates the iron 4s orbital, causing significantly lower cross sections for the small iron hydrides compared to atomic iron. Both the DM and BEB cross sections can be fitted perfectly against a simple expression used in modelling and simulation codes in the framework of nuclear fusion research. The energetics of the iron hydrogen clusters change substantially when exact exchange is present in the density functional, while the cluster geometries do not depend on this choice.

Electron impact ionisation cross sections of iron oxides

“…The DM cross sections remain lower at all energies but, in contrast to BEB, appear to be distinctly too low especially at energies far beyond the maxima since in this region the discrepancies between the three approaches should actually become smaller. The BEB cross sections are generally significantly larger (and their maxima are shifted to higher electron impact energies) than the DM cross sections -ranging from a factor of 1.7 in case of Fe 2 O 2 down to 1.4 in case of Fe 3 O 4 -which is in line with a study on iron hydrogen clusters EICSs [22] in which also discrepancies between those two methods were obtained which were larger than previously assumed to be the norm. We note that there have been cases reported in which the DM method resulted in cross sections which were significantly smaller and also showed a faster decrease beyond the maximum than it was the case for cross sections obtained using other methods or experimental ones [66][67][68].…”

“…In an earlier work on iron hydrogen clusters, we also compared BEB cross sections obtained from all-electron calculations and by employing ECPs. There as well, a better agreement of the latter with the DM cross sections was found [22].…”

“…Concerning fusion-relevant species, EICSs were reported earlier for beryllium [16,17], its hydrides [18], tungsten and its oxides [19,20], beryllium-tungsten clusters [21] and iron hydrides were also been covered recently [22]. In this work we report calculated EICSs using both the BEB and the DM methods for neutral iron oxide molecules, in particular for Fe x O x and Fe x O x+1 compounds with x = 1, 2, 3.…”

“…We note that there have been cases reported in which the DM method resulted in cross sections which were significantly smaller and also showed a faster decrease beyond the maximum than it was the case for cross sections obtained using other methods or experimental ones [66][67][68]. In reference [22] the discrepancy between DM and BEB cross sections was related to the different methodological foundations of the methods, and especially to the explicit inclusion of geometric parameters in terms of the radius of maximum radial density of atomic subshells (see also Sect. 2.1) in the DM approach.…”

“…2.1) in the DM approach. It was found that the 4s electrons led to the by far most dominant contribution to the EICS of atomic Fe and as the population of this atomic orbital decreased with increasing number of hydrogen atoms in the iron hydrogen cluster, the discrepancies for the resulting EICSs between DM and BEB decreased also [22]. Hence, we also investigated how the addition of oxygen affects the population of Fe 4s orbital in the considered Fe x O x molecules.…”