Available online at www.sciencedirect.com ScienceDirect Physics Procedia 71 (2015 ) 30 34 18th Conference on Plasma-Surface Interactions, PSI 2015, 5-6 February 2015, Moscow, Russian Federation and the 1st Conference on Plasma and Laser Research and Technologies, PLRT 2015, 18-20 February 2015 Ab-initio simulation of hydrogen atom interaction with tungsten N. Degtyarenko*, A. Pisarev National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe shosse 31,115409, Moscow, Russia Abstract The results of calculations of stable configurations of atomic hydrogen in the tungsten bulk, in the presence of vacancies, as well as on the surface (100) and in the near-surface layers are given. Activation barriers for interstitial diffusion, on-surface diffusion, trapping in a vacancy, detrapping from the vacancy, and transitions between on-surface and under-surface sites are calculated. Hydrogen-vacancy interaction is considered for the case of several H atoms trapped in a vacancy. 2015 The Authors. Published by Elsevier by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Peer-review Physics Institute) under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute). Keywords: Tungsten; hydrogen; potential energy; diffusion; defects; surface; trapping; detrapping. 1. Introduction Hydrogen in tungsten is a serious problem of plasma-surface interactions in ITER from the point of view of radiation safety and material longevity. Various aspects of the problem have been examined both theoretically and experimentally. All the main processes devoted to hydrogen in tungsten were analyzed theoretically: adsorption, desorption, diffusion over the surface, absorption, diffusion in the bulk, formation of clusters, and various aspects of interaction with defects [Heinola K. et al. (2010), Arnold M. et al. (1997), Johnson and Carter (2010), Liu et al. (2011), Ventelon et al. (2012), Xu and Zhao (2009), Kong et al. (2015)]. Different methods were used for particular tasks. The results obtained in various works are sometimes in agreement but sometimes they are contradictive. This * Corresponding author. Tel.: Tel.: +7-495-788-5699 (ext.9753). E-mail address: nndegtyarenko@mephi.ru 1875-3892 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) doi:10.1016/j.phpro.2015.08.307
N. Degtyarenko and A. Pisarev / Physics Procedia 71 ( 2015 ) 30 34 31 work is an attempt to analyze all the above mentioned aspects of H-W interaction within a single approach. Quantum-mechanical modeling based on densities functional theory (DFT) is used here. 2. Method Adequate method of calculation is quantum- mechanical modeling. In this work, the calculations were performed in the approximation of the density functional theory (DFT - GGA) using the correlation - exchange functional PW91. For tungsten atoms pseudopotential was used. The calculations involved 6 electrons from each W atom. The crystal (supercell) for simulation of the W bulk and its surface contained up to 120 atoms. Periodic conditions were established on the crystal boundaries. A free ( 100) surface was formed by removing several atoms and subsequent relaxation of the crystal. Search of stable atomic configurations with and without hydrogen was performed on the principle of minimization of the total energy of the system. Transitions from one configuration to another were modeled by the method of linear and quadratic synchronous transits (LST/QST) along the path. The first step of the search (LST) was to calculate the potential energies along the straight line between the two sites to find the approximate position and potential of the saddle point. The second step (QST) was to optimize the configuration of H and W atoms in this area to minimize the energy and find the exact position of the saddle point and exact potential barrier. 3. Results 3.1. Crystal, vacancy, and surface The optimized initial configuration of the bcc tungsten crystal was characterized by the binding energy of 5.3 ev/atom. Creation of a vacancy by removing a W atom from the crystal bulk leads to relaxation of the system to a new atomic configuration. Fig. 1 demonstrates the electron density surface at the level of 0.2 near the vacancy. The density is less within this surface, being about zero in the center, and larger outside this surface. Linear dimensions of this area are of about 3 Å. Displacements of the nearest W atoms are almost symmetric, being only 0.1% towards the center of vacancy. The dilation volume due to relaxation of W atoms around a vacancy VW W -5.2 Å 3, while the specific volume for an atom ω 16.4 Å 3 /atom. Fig. 1. Isosurface of electron density at a level of 0.2 near the vacancy having the shape of polyhedron with 6 square and 8 hexagonal faces. A free (100) surface after relaxation demonstrated no surface reconstruction effects, which were mentioned by Heinola and Ahlgren (2010). The distance between two top layers 3.16 Å was found to be less than the distance between layers far from the surface c 3.20 Å. A small contraction of the first W(110) plane of the order of 3% was calculated by Arnold et al. (1997).
32 N. Degtyarenko and A. Pisarev / Physics Procedia 71 ( 2015 ) 30 34 3.2. Interstitial hydrogen The equilibrium position of a hydrogen interstitial atom is the center of the pyramid formed by 4 tungsten atoms (tetrahedral position). The distance from H atom to these W atoms is 1.85 Å. The functional form of the local partial density of electron states (LPDOS) on an interstitial hydrogen atom depends on the position of the hydrogen atom. The maxima on LPDOS map are determined by s-electrons of the nearest tungsten atoms. Transition of the H atom between two neighbor interstitial sites takes place along a curvilinear trajectory and needs the activation energy dif 0.35-0.38 ev, which is the activation energy for diffusion. 3.3. Adsorbed hydrogen The energy gain between the energy of a crystal with hydrogen atom far from the surface and the crystal with hydrogen atom in the adsorption state was ε ads 3 ev. No barrier for transition of the atom from vacuum to the on-surface state was found. Tungsten atoms relax around H atom, which occupy a short bridge position over the surface between two relaxed W atoms. The position of the H atom is not symmetric with respect to the two W atoms; H atom is closer to one of the W atoms to be in the region with a certain electron density The energy barriers for transition of H atom between two adsorption sites were estimated for different paths of transition. Two of them are shown in Fig. 3. A longer jump to an equivalent site separated by 3.1 Å needs the energy Sdif1H 0.9 ev, while the shorter jump to a site separated by 2.1 Å needs a smaller energy barrier Sdif2 2H 0.4 ev. The trajectory is curvilinear around a W atom. 3.4. Transition through the surface Transition through the surface was modeled in two directions (from the bulk on the surface and backward). The transition from an on-surface site to an under-surface site (solution or absorption) needs activation energy inp H 1.41 ev. The transition from the under-surface site to the on-surface site (dissolution or re-adsorption) needs activation energy out H 0.34 ev. Fig. 2. (a) The relaxed top surface W(100) with an adsorbedd H atom in the short bridge position. (b) Two trajectories of diffusion (long and short) over the surface. Colored map is a 2D electron density map. 3.5. The net near-surface diagram The net potential energy diagram is given in Fig. 3. One should mention that the potential energy at the saddle- sites in point for transition between the on-surface and under-surface sites is less than that between two interstitial the W bulk.
N. Degtyarenko and A. Pisarev / Physics Procedia 71 ( 2015 ) 30 34 33 Fig. 3. The potential diagram near the surface. 3.6. Hydrogen atom and vacancy If an H atom is in the nearest interstitial position to a vacancy, it can be trapped by the vacancy, while an H atom in the vacancy can be detrapped back to the nearest interstitial position. One vacancy can contain several H atoms. Activation energies for trapping and detrapping depend on the number of H atoms in the vacancy. These energies are given in Fig. 4. Fig. 4. Energy barriers for hydrogen trapping in a vacancy (1) and detrapping from a vacancy (2) as a function of number of hydrogen atoms in the vacancy. Two isosurfaces with the electronic density at the level of 0.2 are shown on the left and on the right for a vacancy containing six and seven atoms of hydrogen, respectively. The barrier for trapping is less than the activation energy for diffusion and increases with the number of atoms in the vacancy. The energy of detrapping is much higher and only slightly depends on the number of atoms in the vacancy. The maximum number of H atoms in a vacancy equals n=6 (the detrapping barrier becomes less than the trapping barrier at n=7). The configuration of H atoms inside a vacancy changes with the number of H atoms as shown in Fig. 5. If one H atom is trapped in a vacancy, it is placed far from the center of vacancy closer to W atoms in the configuration similar to that one in the adsorption state. Two atoms form a dumb-bell with the length of 1.02 Å. Threee atoms give a regular triangle. Four atoms are arranged in an equilateral pyramid. Five atoms make a regular pyramid. In all the cases, the distance between the H atoms is 2 3 times longer than that in the hydrogen molecule.
34 N. Degtyarenko and A. Pisarev / Physics Procedia 71 ( 2015 ) 30 34 Fig. 5. Equilibrium configurations of H atoms in a vacancy. 4. Conclusions Features of hydrogen atom adsorption, solution, diffusion and interaction with defects were modelled using DFT within a unified approach. A good agreement with previous works was obtained for The energy gain for atomic hydrogen adsorption on (100) tungsten surface ads 3 ev [Heinola and Ahlgren (2010)]. The activation energy for interstitial diffusion of hydrogen in tungsten bulk dif 0.35-0.38 ev [Heinola and Ahlgren (2010), Johnson and Carter (2010)]. The activation energy of hydrogen diffusion over the (100) surface Sdif2H 0.4 ev [Heinola and Ahlgren (2010)]. The maximum number of H atoms in a single vacancy n=6 [Johnson and Carter (2010), Heinola et al. (2010)]. Acknowledgements This work was partially supported by Contract 14.Y26.31.0008 with the Ministry of Education and Science of RF. References Arnold, M., Hupfauer, G., Bayer, P., Hammer, L., Heinz, K.., Kohler, B., Scheffler, M., 1997. Hydrogen on W (110): an adsorption structure revisited. Surface Science 382, 288-299. Heinola, K., Ahlgren, T., 2010. First-principles study of H on the reconstructed W (100) surface. Physical Review B 81, 073409. Heinola, K., Ahlgren, T., 2010. Diffusion of hydrogen in bcc tungsten studied with first principle calculations. Journal of Applied Physics 107, 113531. Heinola, K., Ahlgren, T., Nordlund, K., Keinonen, J., 2010. Hydrogen interaction with point defects in tungsten. Physical Review B 82, 094102. Johnson, D.F., Carter, E.A., 2010. Hydrogen in tungsten: Absorption, diffusion, vacancy trapping, and decohesion. Journal of Materials Research 25, 315-327. Kong, X.-S., Wang, S., Wu, X., You, Y.-W., Liu, C.S., Fang, Q.F., Chenand, J.-L., Luo, G.-N., 2015. First-principles calculations of hydrogen solution and diffusion in tungsten: Temperature and defect-trapping effects. Acta Materialia 84, 426 435. Liu, Y.-L., Zhou, H.-B., Zhang, Y., 2011. Investigating behaviors of H in a W single crystal by first-principles: From solubility to interaction with vacancy. Journal of Alloys and Compounds 509, 8277-8282. Ventelon, L., Willaime, F., Fu, C.-C., Heran, M., Ginoux, I., 2012. Ab initio investigation of radiation defects in tungsten: Structure of selfinterstitials and specificity of di-vacancies compared to other bcc transition metals. Journal of Nuclear Materials 425, 16-21. Xu, J., Zhao, J., 2009. First-principles study of hydrogen in perfect tungsten crystal. Nuclear Instruments and Methods in Physics Research, Section B 267, 3170-3174.