Dynamics of deuterium retention and sputtering of Li–C–O surfaces

https://doi.org/10.1016/j.fusengdes.2011.07.009Get rights and content

Abstract

Chemistry as well as sputtering and reflection dynamics of lithiated carbon material, bombarded by slow hydrogen atoms are studied. We present a realistic method for computational simulation of the dynamics of the polar Li–C–O–H material dynamics. It is based on an approximate, semi-empirical quantum mechanics of electrons and classical mechanics of nuclei. Results are validated qualitatively by comparison with experiments and with a first principle DFT computations. In particular, we explain observed details of the hydrogen bonding chemistry in lithiated carbon, showing that incoming hydrogen interacts preferably with Li-C rather than C structures.

Highlights

► Bonding of lithium with carbon, hydrogen and oxygen is mixed covalent and polar. ► We use approximate quantum-mechanical approach for slow Li-C-O-H dynamics. ► Presence of lithium in carbon increases retention of hydrogen in its neighborhood. ► The simulation findings are validated by the experiments.

Introduction

The use of lithium as a plasma-facing surface in magnetic confinement fusion devices is increasingly becoming popular. Mostly due to its impurity gettering and ability to retain hydrogen (low recycling regimes). National Spherical Torus Experiment (NSTX) [1] uses lithium deposition on graphite substrates to enable important plasma control. One peculiar mystery in the past few years of lithiation efforts in NSTX is how ultra-thin films of lithium can readily affect the tokamak plasma knowing that Li readily intercalates (diffuses) to the graphite bulk. The mechanism of hydrogen (in NSTX deuterium is used) bonding with lithiated graphite is unknown and this paper seeks to elucidate on this mystery. Laboratory experiments by Taylor et al. [2] have demonstrated a complex rich surface chemistry at play and with XPS analyses found that the presence of lithium has significant effects on the fundamental interactions of hydrogen with C and O atoms on the ATJ graphite surface.

Long range interactions when treating molecular dynamics have been readily “avoided” in the past because of the possible prohibitive computational cost. Namely, it is difficult to study the Li dynamics theoretically because of its polarizing features when interacting with other elements. These features are most transparently represented by the quantity called electronegativity, i.e. the chemical property of an element which defines its tendency to attract electrons. Li electronegativity is exceptionally low, one of the lowest in nature, and is low in comparison to the elements readily met in NSTX [1], H, C, O, Mo, W. Thus, according to the Pauling scale [3], Li electronegativity is 0.94 as contrasted to 2.2, 2.4, 3.5, and 1.9 of H,C,O, and Mo, respectively. In consequence of partial charge transfer from Li to other atoms, the dominant long-distance binding force is the Coulomb attraction between opposite charges. Bonding between Li and other atoms is mixed covalent and polar (Fig. 1a). The differences in electronegativity between constituent atoms in Li–C, Li–O and Li–H systems are very large and therefore these systems could be considered as ionic solids.

Long-range nonbonding interactions are typically represented as (a) Coulomb type Ecoul =  i  j>i((qiqj)/rij), as well as (b) Lennard-Jones types [4], ELJ =  i  j>iDij[(σij/rij)12  2(σij/rij)6], resulting in total nonbonding interaction Enob = Ecoul + Elj. Finally the total interaction energy reflects both nonbonding and bonding (covalent, Eb) interactions,Etot=Eb+Enob

We also note that electronegativity and the size of atoms are mutually related, as shown in Fig. 1b. The bond length of the simple diatomic molecules is typically sum of the so-called covalent radii of the constituting atoms. Thus, covalent radius of C is about 0.7 Å, while for Li and H it is close to 1.3 Å and 0.3 Å, respectively. This implies that the density of carbon is lower in lithiated carbon than in a hydrogenated carbon, since Li–C bonds are about twice as long as H–C bonds. Indirect consequence is that the Li–C bond (typically 1.6 eV) could be significantly weaker than the H–C bond (4.5 eV, typically).

However, the charges of the atoms that take part in these polar interactions depend on atomic coordinates. The charges typically change in each simulation step. This narrows down the number of methods that can be used in studies of system dynamics to those that are capable of recalculating accurately the charges at each time step. If the classical molecular dynamics (CMD) is used, with pre-parameterized short range potentials, a semiempirical method like is the Electronegativity Equalization Method (EEM) [5] has to be applied at each step for calculation of the atomic charges. Besides questionable accuracy, this combination of the classical covalent potential with EEM raises a question of numerical efficiency of the approach, and motivates the use of Quantum-Classical Molecular Dynamics (QCMD) as a better candidate for the treatment of the system dynamics.

In the QCMD [6], motion of electrons in the system is treated quantum-mechanically, by solving some form of Schrodinger equation at the beginning of each time step, keeping frozen positions of the nuclei. From this solution the potential energy surface in the hyperspace of all atomic coordinates is found, resulting in instantaneous forces on each atom. Positions of the nuclei are then relaxed, and the whole system is moved during a time step. The main problem is how to solve efficiently the Schrodinger equation for electronic motion. Employing standard Plane Wave (PW) [7] or molecular Density Functional Theory (DFT) to the system of N atoms (scaling  N3) would be too numerically demanding in comparison to the CMD (scaling  N). For example, at a sample of 1000 atoms the DFT would introduce about 106 times slower calculations. Having in mind that analog CMD calculation takes of the order of minutes, this is currently a formidable task.

For the quantum-mechanical part of the approach we employ Self Consistent Charge Density Functional Tight Binding (SCC-DFTB) method [8], developed by the Bremen (Germany) Center for Computational Material Sciences, adapted for the trajectory Monte Carlo calculations in a multi-processor super-computer environment. This is an approximation to DFT, in which only valence orbitals are considered and difficult density integrals are parameterized and fitted in advance. In comparison to other tight-binding methods, this one has self-consistent calculation of atomic charges. The method still scales as N3 (due to diagonalization step), but the corresponding size of basis set (Slater orbitals) is much smaller (up to 10 times) than in first principles DFT. Thus the method is significantly faster, up to a thousand times than first principles DFT, but is also slower than the CMD, falling into the range of current computational capabilities. Parameterization of the pair-parameters for the Li–C–O–H system is provided by the K. Morokuma and S. Maeda [9].

We use a simulation cell of a few hundreds of atoms of lithiated and oxydated amorphous carbon (∼20% of Li, ∼5% of O), at 300 K. This is created by random seeding of Li and O in amorphous hydrogenated carbon, replacing hydrogen by Li and O, followed by quantum-mechanical energy minimization and thermalization to 300 K. This approach also closely resembles the situation in the NSTX where lithium coatings on graphite are used. As expected, during the optimization, the simulation cell swelled about 30% to allow Li and O to create their extended bond lengths (Fig. 2). The swelling decreased the effective carbon density.

The prepared cell was cut into a rectangular box of approximate length of 1.5 nm, xy periodic conditions applied, and then optimization and thermalization of the periodic cell was repeated, resulting into a slab, which was periodic in xy directions with period of 14 Å while its thickness in z-direction was close to 20 Å. The slab was bombarded by 5 eV D and 2.5 eV H atoms, perpendicularly to the free cell interface (in z-direction). 5004 random trajectories were applied to both D and H, each evolving in a separate core of Cray XT5 of NICS (Kraken), with the time step of 0.2 fs. About 24 h was needed for most of the trajectories to finish their evolution, resulting either in reflection (fastest), retention and sputtering (slowest), thus requiring 120,000 CPU hours per impact energy. We note that our simulation had a primary goal to establish the retention chemistry of deuterium with Li–C mixture and was applied to a Li–C–O “virgin” (previously not-hydrogenated and not-bombarded) surface. Realistic experimental conditions would be better approximated if one saturates the Li–C–O surface with deuterium (hydrogen) prior to each prescribed simulation. However, since the saturation process is causal, this would require much more computation effort if done with the SCC-DFTB method. Some combination of the classical MD and the DFTB is a must for creation of a saturated (steady-state) surface [10], and will be a subject of our forthcoming publications.

Section snippets

Results and discussion

Here we study chemistry and sputtering/reflection dynamics in lithiated (and partially oxydated) carbon material, bombarded by slow deuterium (5 eV) and hydrogen (2.5 eV) atoms. The objectives of this research are two-fold: (a) to develop realistic methods for computational simulation of the polar–covalent bonding of Li-C-O-H, validated by experiments; (b) to explain the specifics of the chemistry of deuterium bonding in lithiated carbon. Namely, experiments from Purdue [2] indicate that Li-C/O

Conclusions

We have studied the polar–covalent interactions that emerge in mixtures of lithium with carbon–hydrogen–oxygen. The swelling of the Li–C surface due to the larger size of Li–C bonds is reflected by a increased penetration of D and H into the surface. We found that the influence of O, present in small quantities, is of negligible influence to the dynamics of retention. However Li, present at 20% of the total number of atoms in the cell, substantially changes the retention chemistry,

Acknowledgments

The authors are grateful to K. Morokuma and S. Maeda for useful discussions on the SCC-DFTB method and for providing the DFTB parameters for interaction of lithium with C, H and O. PSK acknowledges support from the US DOE, Office of Fusion Energy Sciences, and the LDRD program of the Oak Ridge National Laboratory (PSK and JD), of DOE INCITE program (PSK) and NSF TERA-GRID program (PSK, JD). JJ acknowledges NSF support through the EPSCoR program. The data were obtained at the ORNL computational

References (15)

  • P.S. Krstić, R.J. Harrison, B.G. Sumpter, Phys. Scr. T124 (2006) 101–107, doi:10.1088/0031...
  • A. Allouche et al.

    B

    Phys. Rev.

    (2006)
    A. Allouche et al.

    J. Chem. Phys.

    (2005)
  • C.H. Skinner, J.P. Allain, W. Blanchard, et al., J. Nucl. Mat (in press, 2011),...
  • M.G. Bell

    Plasma Phys. Control. Fus.

    (2009)
    M. Ono et al., “Recent progress of NSTX lithium program and opportunities for magnetic fusion research”, this...
  • C.N. Taylor et al.

    J. Appl. Phys.

    (2011)
  • L. Pauling

    Nature of the Chemical Bond

    (1960)
  • J.E. Lennard-Jones

    Proc. Roy. Soc. Lond. A

    (1924)
There are more references available in the full text version of this article.

Cited by (20)

  • Sputtering and reflection processes from amorphous lithium surfaces by low-energy impacts of H and D atoms and D<inf>2</inf> molecules

    2022, Journal of Nuclear Materials
    Citation Excerpt :

    Quantum-classical molecular dynamics (QCMD) simulations based on the density functional tight binding (DFTB) method can correctly treat the change of the electron cloud during the classical dynamics of atoms, but this requires excessive computational time and resources [12–14]. While this is feasible for the study of hydrogen retention or chemical sputtering at low energies (≤ 5 eV) [12,13], the study of these processes in a range of energies of 5-100 eV is computationally too intensive, not only because the calculation must be repeated for various energies, but also because higher energies require larger computational cells, i.e., a larger number of Li atoms in a target surface. For this reason, in this work, we chose to use classical molecular dynamics (CMD) based on a reactive bond-order force field (ReaxFF) [15,16], which showed in practice to be two orders of magnitude faster while still providing a similar accuracy [17,18] for the particle-surface processes to the QCMD with Sef-consistent charge DFTB [19] method.

  • Unraveling the surface chemistry processes in lithiated and boronized plasma material interfaces under extreme conditions

    2018, Matter and Radiation at Extremes
    Citation Excerpt :

    In fact, the surface analysis conducted by Taylor et al. showed that lithium began to interact with carbon and oxygen immediately upon deposition [7,71]. The first attempt to describe deuterium retention in lithiated graphite used an atomistic modeling in a Li-O-C-D matrix, and generated a reasonable conjecture on possible mechanisms for the retention of D in lithiated graphite [56]. The electropositive nature of Li and its interaction with the majority of atomic elements suggested that lithium readily binds less electropositive hydrogen and carbon [34].

  • Hydrogen retention in lithium and lithium oxide films

    2018, Journal of Nuclear Materials
    Citation Excerpt :

    We simulated these experiments by using Molecular Dynamics. Amorphous target surfaces of pure Li and Li2O were prepared for a set of temperature values T (90, 300, 400, 500, and 600 K), following the procedure in Refs. [21,22] for each temperature. Computational cells of about 2000 atoms were used.

  • Sputtering of lithiated and oxidated carbon surfaces by low-energy deuterium irradiation

    2017, Journal of Nuclear Materials
    Citation Excerpt :

    The quantum component of the QCMD solves the multielectron eigenvalue problem at each time step of the system evolution, which could be computationally formidable problem even if density-functional theory (DFT) is used. The use of approximations to DFT, like is Self-Consistent-Charge Tight Binding DFT (SCC-DFTB) [16] can make the QCMD problem computationally feasible for study of deuterium retention or chemical sputtering at low energies (5 eV) [12,13]. However, study of chemical sputtering in a range of energies 5–30 eV is computationally too intensive, not only because the calculation has to be repeated for various energies, but also because higher energies require larger computational cells, i.e. larger number of atoms.

View all citing articles on Scopus
View full text