Electron impact ionisation cross sections of iron hydrogen clusters

Eur. Phys. J. D (2016) 70: 182 DOI: 10.1140/epjd/e2016-70292-4 THE EUROPEAN PHYSICAL JOURNAL D Regular Article Electron impact ionisation cross sections of iron hydrogen clusters Stefan E. Huber1 , Ivan Sukuba2 , Jan Urban2 , Jumras Limtrakul3 , and Michael Probst1,a 1 Institute of Ion Physics and Applied Physics, University of Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria Department of Nuclear Physics and Biophysics, Faculty of Mathematics, Physics and Informatics, Comenius University, 84248 Bratislava, Slovakia 3 Department of Materials Science and Engineering, School of Molecular Science and Engineering, Vidyasirimedhi Institute of Science and Technology, Rayong 21210, Thailand 2 Received 26 April 2016 / Received in final form 31 May 2016 Published online 6 September 2016 c The Author(s) 2016. This article is published with open access at Springerlink.com  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. The maxima of the cross sections for the iron hydrogen clusters range from 6.13 × 10−16 cm2 at 60 eV to 8.76 × 10−16 cm2 at 76 eV for BEB-AE (BEB method based on quantum-chemical data from all-electron basis sets) calculations, from 4.15 × 10−16 cm2 at 77 eV to 7.61 × 10−16 cm2 at 80 eV for BEB-ECP (BEB method based on quantum-chemical data from effective-core potentials for inner-core electrons) calculations and from 2.49 × 10−16 cm2 at 43.5 eV to 7.04 × 10−16 cm2 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. 1 Introduction Plasma-wall interaction (PWI) remains one of the key issues in nuclear fusion research. In nuclear fusion devices, such as the JET tokamak or the International Thermonuclear Experimental Reactor (ITER; presently under construction), first-wall materials will be directly exposed to plasma components. In ITER, the first-wall is envisaged to be coated with beryllium (at the main wall) and tungsten (in the divertor) [1]. JET has demonstrated successful plasma operation using this combination of materials which strongly supports this choice for ITER [2]. Taking a longer term perspective, such as in the fusion program DEMO and beyond it in industrial applications of nuclear fusion, it would be far better, however, to avoid the highly toxic and hence difficult to handle beryllium. The use of stainless steel (i.e. the Eurofer steel envisaged for DEMO [3,4]) for some portions of the main wall may  Supplementary material in the form of one pdf file available from the Journal web page at http://dx.doi.org/10.1140/epjd/e2016-70292-4 a e-mail: then come into consideration. Erosion of first-wall materials is a consequence of the impact of hydrogen and its isotopes as main constituents of the hot plasma [5,6]. Besides the formation of gas-phase atomic species in various charge states, also di- and polyatomic molecular species are expected to be formed via PWI processes. These compounds may profoundly disturb the fusion plasma and may also lead to unfavourable re-deposition of materials and composites in other areas of the vessel [7–10]. Detailed knowledge and quantification of interactions between atoms, molecules and the plasma as well as of the transport of impurities is thus of considerable interest for modelling and simulation of fusion plasmas [11]. Collisions of atoms and molecules with electrons are an important example of such processes. They are mainly characterised by the respective electron-impact ionisation cross sections (EICSs). Their understanding is especially important for modelling the plasma energy balance. Apart from magnetic confinement fusion, EICS data also plays a role in astrophysics and in a variety of other applications, such as low-temperature processing plasmas, gas discharges, and in chemical analysis [12]. Page 2 of 8 Eur. Phys. J. D (2016) 70: 182 Generally speaking, FeHn molecules and clusters are rather unstable, compared to other metal hydrides. Iron hydride, FeH, has only been identified in the gaseous state and in matrices. It is of considerable astronomical importance and has been subjected both to experimental and theoretical investigations [13]. Its so-called Wigner-Ford band, an IR peak at 990 nm, has been found in the spectrum of the sun. FeH2 has a 5 Δg ground state. The frequency of its vibrational bending mode is 226 cm−1 , characteristic of a very floppy angular bending [14], while the asymmetric Fe-H stretching frequency at 1674 cm−1 indicates bonds of medium strength [15]. In addition, FeH2 is normally only stable as a diluted gas or in matrices, although recently [16] a solid high-pressure phase with the stoichiometry of FeH2 has been synthesised. All other FeHn clusters from FeH3 onwards can be thought to consist of FeH or FeH2 with H2 molecules bound to them. In the following, we simply call all FeHn assemblies iron hydrogen clusters. Takahashi et al. [17] report data on a number of these clusters from plane-wave DFT calculations. Their findings on geometries agree mostly with ours, although there are small discrepancies (see Sect. 3.1). During the past few decades, a number of semiempirical methods that typically use quantum-chemically calculated electronic structure information as input have been developed in order to derive absolute EICSs for various molecules. Their accuracy is usually in the same range as corresponding experimental data. Among them, the most-widely used methods are the binary-encounter-Bethe (BEB) theory of Kim and Rudd [18], Kim et al. [19] and the Deutsch-Märk (DM) formalism [20]. These methods have been successfully applied to atoms, molecules, clusters, ions and radicals [21]. In the context of fusion-relevant species, EICSs were reported earlier for beryllium [22,23], its hydrides [24], tungsten and its oxides [25,26] and beryllium-tungsten clusters [27]. In this work we report calculated EICSs using both the BEB and the DM method for neutral iron-hydrogen clusters, in particular for FeHn with n = 0, 1, 2, . . . , 10 compounds, since iron is the main component of steels. To the best of our knowledge there is no such cross section data available for iron-hydrogen clusters up to now. We also report parameters obtained by fitting the calcul (...truncated)