Electron impact ionisation cross sections of iron oxides

Eur. Phys. J. D (2017) 71: 335 DOI: 10.1140/epjd/e2017-80308-2 THE EUROPEAN PHYSICAL JOURNAL D Regular Article Electron impact ionisation cross sections of iron oxides? Stefan E. Huber 1,2,a , Andreas Mauracher 1 , Ivan Sukuba 1,3 , Jan Urban 3 , Thana Maihom 4 , and Michael Probst 1 1 Institute of Ion Physics and Applied Physics, University of Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria Institute for Basic Sciences in Engineering Science, University of Innsbruck, Technikerstraße 13, 6020 Innsbruck, Austria 3 Department of Nuclear Physics and Biophysics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, 84248 Bratislava, Slovakia 4 Vidyasirimedhi Institute of Science and Technology, School of Energy Science and Engineering, 555 Moo 1 Payupnai, Wangchan, Rayong 21210, Thailand 2 Received 6 May 2017 / Received in final form 26 September 2017 Published online 19 December 2017 c The Author(s) 2017. This article is published with open access at Springerlink.com Abstract. We report electron impact ionisation cross sections (EICSs) of iron oxide molecules, Fex Ox and Fex Ox+1 with x = 1, 2, 3, from the ionisation threshold to 10 keV, obtained with the Deutsch-Märk (DM) and binary-encounter-Bethe (BEB) methods. The maxima of the EICSs range from 3.10 to 9.96 × 10−16 cm2 located at 59–72 eV and 5.06 to 14.32 × 10−16 cm2 located at 85–108 eV for the DM and BEB approaches, respectively. The orbital and kinetic energies required for the BEB method are obtained by employing effective core potentials for the inner core electrons in the quantum chemical calculations. The BEB cross sections are 1.4–1.7 times larger than the DM cross sections which can be related to the decreasing population of the Fe 4s orbitals upon addition of oxygen atoms, together with the different methodological foundations of the two methods. Both the DM and BEB cross sections can be fitted excellently to a simple analytical expression used in modelling and simulation codes employed in the framework of nuclear fusion research. 1 Introduction Plasma-wall interaction (PWI) is regarded as one of the key issues in nuclear fusion research. In nuclear fusion devices, such as the JET or the ITER tokamak (presently under construction), first-wall materials are those parts of the devices that will be directly exposed to plasma components. In ITER, the first-wall is envisaged to be coated with beryllium and tungsten [1]. After ITER, in the fusion program DEMO and beyond it in industrial applications of nuclear fusion, it seems likely that the highly toxic and hence difficult to handle beryllium will be avoided. The use of special stainless steels (i.e. the Eurofer steel envisaged for DEMO [2,3]) for some portions of the main wall may then come into consideration. Erosion of first-wall materials is an inevitable consequence of the impact of hydrogen and its isotopes as main constituents of the hot plasma [4,5]. Besides the formation of gas-phase atomic species in various charge states, also molecular species are expected to be formed via PWI processes. Disturbance of the fusion plasma and unfavourable re-deposition of materials and composites ? Supplementary material in the form of one pdf file available from the Journal web page at https://doi.org/10.1140/epjd/e2017-80308-2. a e-mail: in other areas of the vessel are expected to be some of the undesired consequences [6–9]. Hence, detailed knowledge and quantification of interactions between atoms, molecules and the plasma as well as of the transport of impurities is of considerable interest for modelling and simulation of fusion plasmas [10]. Collisions of atoms and molecules with plasma electrons are one important class of such processes. They are mainly characterised by the respective electron-impact ionisation cross sections (EICSs) and their knowledge is especially important for modelling the plasma energy balance. Apart from magnetic confinement fusion, EICS data also are quite valuable due to the role of electron-induced reactions in astrophysics and in a variety of other applications such as low-temperature processing plasmas, gas discharges, and in chemical analysis [11]. During the past few decades, a number of semiempirical methods that typically use electronic structure information from quantum chemical calculations as input have been developed in order to derive absolute EICSs for various molecules. Their accuracy is usually in the same range as the one of experimental data. Among those, the most-widely used methods are the binary-encounterBethe (BEB) theory of Kim et al. [12,13] and the DeutschMärk (DM) formalism [14]. These methods have been successfully applied to atoms, molecules, clusters, ions and radicals [15]. Page 2 of 8 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 Fex Ox and Fex Ox+1 compounds with x = 1, 2, 3. Small amounts of oxygen are inevitably present in fusion plasma as are elements of similar atomic weight like nitrogen and argon. Moreover, such oxygen atoms will interact with surface iron or with sputtered iron atoms since the formation of iron oxide is highly exothermic. Electron impact cross sections and EICSs for some of the considered molecules (FeO, Fe2 O3 and Fe3 O4 ) were estimated earlier [23] by applying the additivity rule, i.e. by simply summing the respective cross sections of the atoms constituting a molecule. This can be seen as an upper limit for the EICSs calculated by us which will be discussed further in Section 3.2. Photoionisation studies [24,25] suggest that the most prevalent neutral iron oxide clusters in the gas-phase are of the form Fex Ox , Fex Ox+1 and Fex Ox+2 with the more oxygen rich clusters being favoured for larger values of x. Especially for small values of x < 10, the most abundant iron clusters are suggested to be of the stoichiometry Fex Ox and Fex Ox+1 which is why we are focusing on these clusters in the present work. Moreover, collision induced dissociation studies of small iron oxide cluster cations [26] revealed that predominant decomposition pathways are related to the loss of neutral O2 and of FeO, FeO2 , Fe2 O2 and Fe2 O3 fragments which makes the latter especially interesting to study in the framework of PWI processes. Due to the unique properties of iron oxide nanoparticles and their applications [27–30], iron oxide clusters, as their building blocks, were subject to numerous theoretical studies focusing on energetic, geometrical and magnetic properties, see e.g. references [31–37]. While the structures reported by Jones et al. [32] were used by us as input for structural optimisation (Sect. 2.3), the mentioned studies allowed us (...truncated)