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International Journal of Mass Spectrometry 365–366 (2014) 248–254

Contents lists available at ScienceDirect

International Journal of Mass Spectrometry

journa l h om epage: ww w.elsev ier .com/ locate / i jms

odeling the intrusion of molecules into graphite: Origin and shapef the barriers

tefan E. Huber ∗, Michael Probstnstitute of Ion Physics and Applied Physics, University of Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria

r t i c l e i n f o

rticle history:eceived 19 November 2013eceived in revised form5 December 2013ccepted 16 December 2013

a b s t r a c t

We performed density functional theory calculations to explore the energetic and geometric aspects of thepermeation of H2, BeHx, OHx (x = 1, 2) and CHy (y = 1–4) through the central hexagon of coronene. Coroneneserves as a cluster model for extended graphene which can be regarded as the first layer of a graphite(0 0 0 1) surface. We compare the energy barriers encountered by these molecular projectiles with theones that are obtained for atomic H, Be, C and O. The barriers are substantially lower if projectiles possess

vailable online 25 December 2013

eywords:lasma-wall interactionraphiteydrides

free valences that can bind to the carbon entity. Furthermore, for some of the species fragmentation isobserved. Implications with respect to plasma-surface interaction are discussed.

© 2014 The Authors. Published by Elsevier B.V. Open access under CC BY-NC-ND license.

FT

. Introduction

Plasma-wall interactions (PWI) are the basis of plasma coating1] and of the use of microplasmas for medical applications [2]. Inhermo-nuclear research [3,4] they must be understood in termsf material degradation. PWI comprises how atoms and moleculesnd their ions in the plasma interact with surface materials in con-act with them. Important aspects of PWI are how projectiles fromhe plasma or a hot gas in front of the wall can penetrate throughhe surface. In case of molecular projectiles, eventual fragmenta-ion of the molecules is an issue either. The interaction of atomsnd molecules with carbon materials is an especially importantssue in thermo-nuclear research. Carbon fiber composites (CFC)re possibly used in the ITER (International Tokamak Experimen-al Reactor) device as partial coverage of the first wall [5]. There isast experience with this material from earlier fusion experiments6,7]. The main drawback of CFC is its high reactivity with respect toydrogen [6]. It is expected that the latter will eventually lead to a

ubstantial amount of tritium retained in the wall material as wells to the formation of hydrocarbon impurities polluting the fusionlasma and re-depositing at other parts of the wall [6]. The use of

∗ Corresponding author. Tel.: +43 0512 507 52733; fax: +43 0512 507 2932.E-mail addresses: s.huber@uibk.ac.at (S.E. Huber), michael.probst@uibk.ac.at

M. Probst).

387-3806 © 2014 The Authors. Published by Elsevier B.V. ttp://dx.doi.org/10.1016/j.ijms.2013.12.015

Open access under CC BY-NC-ND

beryllium at the main wall of ITER [5] is expected to lead to the for-mation of beryllium hydride molecules forming another source ofimpurities. A rest concentration of oxygen will have the same effectleading to the formation of hydroxyl radicals and water molecules.Furthermore, recombination of hydrogen atoms leads to the forma-tion of hydrogen molecules. Hence, the rather low temperatures ofabout 2–3 eV in the divertor region due to the realization of par-tial detachment [8,9] will give rise to a complex mixture of hydridemolecules interacting with the CFC surface. For this reason, we wantto explore some aspects of the interaction of such molecules withcarbon sheets (as a model for the graphite structures of which CFCconsists) in this work.

The interaction of molecular projectiles with fusion-relevantwall materials has been subject to a variety of experimen-tal studies conducted in the last years [10–20]. Especially thegroups of Hermann and of Märk conducted several mass-spectrometric experiments with respect to molecule/surfaceinteractions [12,13,16–20]. They let deuterated hydrocarbon ionsinteract with stainless steel [10,19], carbon [11–15,17–20], beryl-lium [18] and tungsten [16,18]. All of these surfaces are of relevancein thermo-nuclear fusion research. The impact energies range froma few eV to hundreds of eV. Analyzed were the fragmentation pro-cesses of the incident molecules, sputtering of the material andeffects due to heating of the surface. However, interpretation ofexperimental results is complicated due to technical difficulties

such as contamination of the surfaces in course of their fabricationand unknown details of the surface structure which hinders theinterpretation of the microscopic processes governing the investi-gated systems.

license.

dx.doi.org/10.1016/j.ijms.2013.12.015http://www.sciencedirect.com/science/journal/13873806http://www.elsevier.com/locate/ijmshttp://crossmark.crossref.org/dialog/?doi=10.1016/j.ijms.2013.12.015&domain=pdfmailto:s.huber@uibk.ac.atmailto:michael.probst@uibk.ac.atdx.doi.org/10.1016/j.ijms.2013.12.015http://creativecommons.org/licenses/by-nc-nd/3.0/http://creativecommons.org/licenses/by-nc-nd/3.0/

S.E. Huber, M. Probst / International Journal of Mass Spectrometry 365–366 (2014) 248–254 249

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ig. 1. (a) Coronene used as cluster model for extended graphene and (b) schematic oronene. H and C atoms are depicted as light blue and yellow spheres, respectivelyo the web version of the article.)

In contrast, simulations and (numerical) modeling can work onhe atomistic level. Thus, PWI has also attracted a lot of interestrom the theoretical side. Especially the interaction of hydrogenand/or isotopes) with carbon-based materials has been stud-ed extensively employing both force-field approaches [21–34] as

ell as quantum-chemical methods [35–43]. Also the interactionf molecules with fusion-relevant surfaces has been explored toome extent, mostly by employing force-field based simulations28,30,34,44,45].

This study is of the quantum-chemical type. In particular, we useensity functional theory (DFT) to explore the energetics of perme-tion of the small hydrides Hx, BeHx, OHx and CHy with x = 1,2 and

= 1–4 through the center of coronene (C24H12). The latter moleculeerves as a model of an extended graphene sheet. We are particu-arly interested in the effect of the saturation of free valences viahe addition of hydrogen atoms on the energy barrier associatedith the permeation process. The processes studied are far from

hemical equilibrium and thus are difficult to describe quantita-ively accurate. Hence, we rather aim for a qualitative exploration.evertheless, we will show that the trends explored indicate sub-

tantial differences in the energy barriers for atomic and molecularrojectiles. This might eventually lead to a better understanding ofome types of PWI.

The work is structured as follows. In Section 2, we summarizeur method. In particular, in Section 2.1 we describe the clusterodel used to represent the graphite (0 0 0 1) surface. In Section 2.2,e describe the quantum chemical methods employed. In Section

.3, we describe how the energy barriers are obtained and how theyan be decomposed further in order to aid their interpretation. Inection 3, we discuss our results. We begin with the discussion ofhe differences between the energy barriers for permeation of Hnd H2 in Section 3.1. This is followed by analogous discussionsoncerning the projectiles BeHx, CHy and OHx with x = 0, 1, 2 and

= 0–4 in Sections 3.2–3.4, respectively. In Section 4, we discussmplications of our results in terms of conditions eventually met inuture nuclear fusion applications. In Section 5, we summarize ouronclusions.

. Method

.1. Cluster model

In order to model extended graphene sheets (serving per se as model for a graphite (0 0 0 1) surface) we use a cluster approach.n particular, we use the polycyclic aromatic hydrocarbon (PAH)oronene (C24H12) as model. The molecule is depicted in Fig. 1(a).

n an earlier theoretical work, it has been shown that althoughoronene appears rather small it is large enough to yield essentialrends governing the interaction of atoms with extended graphene43]. In this work, we adopt the strategy of this earlier investigation,

ion of the procedure used to obtain the energy barrier for permeation of H2 throughinterpretation of the references to color in this figure legend, the reader is referred

but now we move molecules rather than atoms through the centerof the central hexagon of coronene. By calculating the energy ateach step we determine the barrier for permeation at this site.Except for the hydrogen atoms at the edge of coronene all atomicpositions are relaxed corresponding to the adiabatic interactionregime, see reference [43]. This corresponds to a velocity of theprojectiles which is small enough for the carbon atoms constitutingthe graphite surface to adapt instantly. This appears as a reason-able assumption given the low temperature of about 2–3 eV in thedivertor of a nuclear fusion scenario as envisaged for ITER. This wasmodeled by moving the approaching molecule along the C6 axis ofcoronene (the z-axis), thus performing a relaxed potential energysurface scan of the system. The z-coordinates of the coronenehydrogen atoms are fixed at z = 0 and the z-coordinate of one atomof the approaching molecule is changed in steps of �z = −0.2 Åand is also fixed while the remaining z-coordinates and all x andy coordinates of all other atoms are allowed to relax. The atoms ofthe approaching molecules with fixed z-coordinates have been (a)one hydrogen atom in H2, (b) the beryllium atom in BeH and BeH2,(c) the carbon atom in CHy (y = 1–4) and (d) the oxygen atom inOH and H2O. A schematic depiction of this adiabatic permeation isshown in Fig. 1(b) for H2.

2.2. DFT calculations

In order to obtain the energy profiles and intermediate geome-tries for permeation as described in the foregoing section we useunrestricted DFT calculations using the B3LYP [46] and PBE0 [47]functionals. Both are hybrid functionals and include a mixture ofHartree–Fock exchange and DFT exchange-correlation. The widelyused B3LYP functional has been constructed semi-empirically byfitting its three parameters to experimental data. The parameter-free PBE0 functional is based on the fulfillment of a number ofphysical constraints. The independent and complimentary designof these functionals makes it worth to compare their results. Asbasis sets 6-31G [48] and 3-21G [49] have been chosen in conjunc-tion with B3LYP and PBE0, respectively. Although they are smallbasis sets, it has been shown in earlier work [43] that basic trendsare well preserved in them, compared with larger ones. The mainreason for the choice of these functionals and basis sets is the com-parability with a former work on the interaction of bare atomswith cluster models for the graphite (0 0 0 1) surface [43]. To ourknowledge, it has never been investigated which combination offunctional and small basis set would be the best for barriers. A com-parison of thermochemical data obtained from a large number ofdensity functionals combined with small basis sets has found func-

tionals without HF-exchange to perform best [50]. On the otherside, it is known that with basis sets like 6-31G* barriers can becalculated more accurately if more HF-exchange than 20 or 25%(PBE0 and B3LYP, respectively) is incorporated like in BH&HLYP

2 l of Mass Spectrometry 365–366 (2014) 248–254

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6

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Fig. 2. Energy barriers obtained for the permeation of H and H through coronene

50 S.E. Huber, M. Probst / International Journa

51,52]. For future studies on larger systems it might well be bene-cial to check if functionals without HF-exchange perform equallyood or better with the specific basis set for barriers and for otherigh-energy geometries like small interatomic distances or largeistortions.

Using the mentioned model chemistries, the geometries of thearget molecule coronene as well as the molecular projectiles haveeen optimized and then used as input for the calculation of thenergy barriers. Another important issue is the choice of the spinonfiguration of the total system. It has been reported [43] thatdiabatic barriers are lowest if the total system exhibits the low-st possible spin multiplicity. Our interest is also to find the lowestarriers and the spin configurations have been chosen accordingly.n case of C, O, CH and CH2 the lowest spin configurations, i.e. sin-let, singlet, doublet and singlet, respectively, correspond to excitedtates (rather than the ground state configurations, i.e. triplet,riplet, quartet and triplet, respectively) of the projectiles for largeistances between them and the target molecule. At a temperaturequivalent to 2–3 eV, these excited spin states are accessible viaollision induced electronic transitions. These states might there-ore be at least partially occupied. For most of the other species like, H2, Be, BeH2, OH2 and CH4, electronically excited states are notccessible at such temperatures. They may be more relevant for theemaining radicals BeH, OH and CH3. Electronic excitations in theurface model coronene are also not of interest in this temperatureange due to the HOMO-LUMO gap of about 9 eV [53]. For the staticalculations of the present work we restricted ourselves to the sin-let and triplet cases mentioned. A more thorough analysis wouldequire more demanding theoretical methods. All calculations wereerformed using the Gaussian 09 suite of programs [54].

.3. Energy decomposition

The planar coronene becomes distorted when the projectileeither an atom or a molecule) approaches. In most cases, it bendsway from the projectile, ‘outward’ of the original molecular plane,n order to reduce the repulsion between the electrons. The energyarrier Eb is then

b = Etot(M − C) − Etot(C) − Etot(M), (1)here Etot(M − C) is the total energy of the (relaxed) system con-

isting of the projectile and the (deformed) coronene molecule,tot(C) is the energy of the isolated coronene molecule in its equilib-ium geometry and Etot(M) is the energy of the isolated projectile.oreover, Eb can be decomposed into the energy required for the

eformation, Edef > 0, of the coronene molecule and the rest energyontaining contributions from temporary bonding and the defor-ation of the projectile molecule, �E, i.e.

b = Edef + �E. (2)The deformation energy Edef was calculated by using the

eformed coronene geometries at each scan step. Subtraction ofhis energy from Eb then yields �E. The latter quantity has proveno be helpful for the interpretation of the individual processes as itccounts for eventually attractive interactions between the projec-ile and coronene, see particularly Sections 3.2–3.4.

. Results and discussion

.1. Energy barriers for H and H2

The energy barriers for adiabatic permeation of H and H2hrough the center of coronene are depicted in the top panel ofig. 2. First, we note that both model chemistries employed, i.e.BE0/3-21G (black lines in the top panel of Fig. 2) and B3LYP/6-31G

2

(top panel). Natural charges as obtained using PBE0/3-21G (bottom panel). (Forinterpretation of the references to color in the text, the reader is referred to theweb version of the article.)

(red lines in the top panel of Fig. 2) yield very similar results. Second,we note that the energy barrier for H2 as projectile (dashed lines)is substantially higher than for the projectile H (solid lines), morespecifically, it is about twice as high. This is a consequence of thedifferent electronic configuration of these two projectile species.H is an open-shell doublet and H2 is a closed-shell singlet. It canbe assumed that the latter projectile is thus chemically much moreinert and this is nicely seen also in the bottom panel of Fig. 2. There,the natural charges as obtained from a natural bond orbital analysis[55] are plotted against the position of the projectile. In the centralregion of the barrier, H donates a significant fraction of its elec-tronic density to the coronene molecule. It acquires thus a positivecharge of about 0.6 e, see the black line (augmented with black cir-cles) in the bottom panel of Fig. 2. In contrast, in H2 such a donationdoes not take place (dashed blue line augmented with squares inFig. 2). By decomposing the total natural charge on H2 into individ-ual contributions from the two hydrogen atoms (dashed red andgreen lines augmented with diamonds and triangles, respectively,in Fig. 2), we find that this is the case for each of the two atomseither rather than a cancelation between them. In summary, per-meation of H is facilitated via temporary bonding, but this is notthe case for H2 which has a much higher barrier.

3.2. Energy barriers for the Be, BeH and BeH2

In Fig. 3, we depict the energy barriers for permeation of (a)Be, (b) BeH and (c) BeH2 through the center of coronene (blacklines augmented with circles). For simplicity, we plot only the bar-riers obtained at the PBE0/3-21G level of theory (solid lines) as thecurves obtained at the B3LYP/6-31G level of theory yield gener-ally very similar results. In Fig. 3(b), however, we show also thedata obtained with B3LYP/6-31G as for the PBE0/3-21G calculationsbeyond z = 1.2 Å no SCF-convergence could be achieved.

Again, the total energy barrier was decomposed into the contrib-utions Edef (red lines augmented with squares) and �E (blue linesaugmented with diamonds and denoted simply as “difference” in

the figure) according to Eq. (2). This helps significantly to inter-pret the results. In contrast, a natural bond orbital analysis as donefor the projectiles H and H2 in Section 3.1 turns out to be rathercomplicated and difficult to interpret in this case.

S.E. Huber, M. Probst / International Journal of Mass Spectrometry 365–366 (2014) 248–254 251

-4 -3 -2 -1 0 1 2 3 4z [Å]

0

2

4

6

8

Ene

rgy

[eV

]

02468

10

Ene

rgy

[eV

]

Be + C24 H12 C24 H12 + Be

C24 H12 + Be + H

BeH + C24 H12

BeH2 + C24 H12

C24 H12 + Be + H2

(a)

(b)

(c)

0

2

4

6

8

Ene

rgy

[eV

]Total barrierDeformation energyDifference

Fig. 3. Energy barriers obtained for the permeation of (a) Be, (b) BeH and (c) BeH2through coronene. The total barriers are decomposed into the deformation energyEdef accounting for geometrical changes in the coronene molecule and the restefr

ceoaoptc

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Fig. 4. Energy barriers obtained for the permeation of (a) C, (b) CH, (c) CH2, (d) CH3and (e) CH4 through coronene. The total barriers are decomposed into the deforma-tion energy Edef accounting for geometrical changes in the coronene molecule andthe rest energy �E according to Eq. (2). The latter contribution is denoted simply

nergy �E according to Eq. (2). The latter contribution is denoted simply as “dif-erence” in the figure. (For interpretation of the references to color in the text, theeader is referred to the web version of the article.)

For the permeation of the atomic projectile Be throughoronene, depicted in Fig. 3(a), we note that both the deformationnergy Edef and the rest energy �E are positive in the central regionf the barrier. The local minima in front of the barrier at z = −0.6 Ånd after the barrier at z = 1.0 Å indicate at least a slight adaptationf the electronic configuration of the atomic projectile facilitatingermeation. Nevertheless, the 2s subshell of Be would need energyo be promoted into a hybrid orbital before bonding and so bothontributions carry a positive sign.

The situation is different for BeH for which the barrier and thewo contributions to it are plotted in Fig. 3(b). Here, slightly attrac-ive forces beyond z = −1.8 Å become apparent. They are much moreronounced for PBE0/3-21G but it is well known that B3LYP has dif-culties with the reproduction of small attractive energies. Theseontributions lead to a somewhat lower energy barrier, comparedo the atomic case. Furthermore, permeation (accompanied by flip-ing of the sheet) occurs later compared to the atomic case, at

= 1.2 Å. Upon permeation of Be, the H atom is stripped off BeHeading to isolated Be and H atoms in the outgoing channel. Due tohis fragmentation process both the total energy as well as the restnergy �E are positive by the amount of binding energy of BeH (athis level of theory) on the right side of the barrier in Fig. 3(b). Inontrast, the deformation energy Edef goes smoothly back to zerondicating that the coronene molecule remains undamaged.

In Fig. 3(c), the energy barrier for BeH2 is depicted. BeH2 is alosed-shell singlet species and as in the atomic case we observeo attractive contributions from �E as well as no local minimum in

ront of the barrier in Fig. 3(c). Both contributions to the total barrierre strictly positive over the entire range. However, in analogy toeH, both H atoms are stripped off the BeH2 molecule. The local

inimum after the barrier corresponds to the one observed for the

tomic case. After the barrier, a positive total energy remains whichs identical to the fragmentation energy required to dissociate BeH2nto Be and H2.

as “difference” in the figure. H and C atoms are depicted as light blue and yellowspheres, respectively. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of the article.)

3.3. Energy barriers for the hydrocarbon projectiles CHx, x = 0, . . .,4

For the analysis of the results concerning (a) C, (b) CH, (c) CH2, (d)CH3 and (e) CH4 we adopt the same strategy, as for the BeHx speciespresented in Section 3.2. The energy barriers and contributions Edefand �E are depicted in Fig. 4.

For atomic C a strong attractive contribution accompanied bya strong repulsive deformation energy in the central region of thepermeation barrier can be seen in Fig. 4(a). We find that in this casepermeation is facilitated by temporary bonding which is reflectedalso in the intermediate geometry of the total system shown on theright of Fig. 4(a). The formation of three C C bonds upon approachof the projectile is in line with the amount of negative energyof about −10 eV contained in �E. The resulting distortion of thecoronene molecule, however, significantly overcompensates thisgain in energy due to temporary bonding.

For CH, we observe similarities with the atomic case, occurringat a somewhat closer distance to the sheet: Energy is gained dueto temporary bonding of CH to three adjacent C atoms of the tar-get molecule. This is again accompanied by a strong distortion ofthe coronene molecule as shown in Fig. 4(b) to the right. Afterpermeation of the C atom from CH the H atom is stripped off aswas observed already for the BeH species, see Section 3.2. How-ever, when the C atom departs from the target molecule, one of

the C atoms of coronene remains attached such that a rather highdeformation is remaining over the rest of the scan range. How-ever, it can be expected that this situation becomes more andmore unfavorable as the C atom departs further such that for larger

2 l of Mass Spectrometry 365–366 (2014) 248–254

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-5

0

5

10

15

20

Ene

rgy

[eV

]

0

5

10

15

Ene

rgy

[eV

]

0

5

10

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rgy

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(b)

(c)

O + C24H12 C24 H12 + O

OH + C24H12

OH2 + C24 H12 C24 H12 + OH2

Total barrierDeformation energyDifference

Fig. 5. Energy barriers obtained for permeation of (a) O, (b) OH and (c) OH2 throughcoronene. The total barriers are decomposed into the deformation energy Edefaccounting for geometrical changes in the coronene molecule and the rest energy

Fg

52 S.E. Huber, M. Probst / International Journa

istances a partially hydrogenated coronene and an isolated C atomill remain.

For the projectile CH2 temporary bonding to three C atoms of theoronene molecule is not favorable. This is also nicely reflected inig. 4(c). During permeation the central hexagon of coronene is cutn two pieces. The permeating CH2 molecule forms a temporaryentagon with four of the C atoms, while the other two C atomsxhibit a stronger bonding than in the original situation.

For CH3 temporary bonding can facilitate permeation only viahe formation of one C-C bond as can be seen in the region beyond

= 1 Å in Fig. 4(d). Beyond z = 1.8 Å fragmentation of into CH2 and Hakes place. For larger z values no convergence could be achieved,ut it is expected that for the remaining part of the scan range theoronene molecule would flip back and one would remain with24H13 and CH2. In general, if the geometry and thus the wave-unction changes substantially and abruptly, it can be difficult tochieve convergence in the SCF procedure.

For the projectile CH4, we observe a relatively early fragmen-ation into CH2 and H2 upon approaching coronene, see Fig. 4(e).fter this fragmentation the permeation is facilitated by the for-ation of two temporary C C bonds as in the case of CH2discussed

bove but in a somewhat more symmetrical manner.

.4. Energy barriers for the projectiles OHx, x = 0,1,2

For the chosen nomenclature and representation of our resultsee Section 3.2. The energy barriers and contributions Edef and �Eor the projectiles (a) O, (b) OH and (c) OH2 are depicted in Fig. 5.

The atomic projectile O exhibits significantly negative �E con-ributions in the central region of the barrier, see Fig. 5(a). Similaro the case of CH2 discussed in Section 3.3, this is accompaniedy temporary bonding between O and two C atoms of the centralexagonal ring in coronene as well as enhanced deformation of thearget molecule.

For OH, we observe a jump in the �E contribution at larger val-es than for the atomic projectile O, see Fig. 5(b). This strongerepulsion for smaller values of z is also familiar from the so fariscussed hydrogenated species. Unfortunately, we could not cal-ulate the data for values of z larger than 1.4 Å. However, our resultst least indicate that for these values the O atom will have passedhe coronene molecule while the H atom is stripped off as it wasbserved already for BeH and CH.

For water as projectile, i.e. OH2, we note for z < 1.2 Å also atrongly enhanced repulsion, see Fig. 5(c). This can be expectedrom the closed-shell configuration of the water molecule. Beyond

= 1.2 Å, however, we observe a significant attractive contributionrom �E indicating temporary bonding in the region between 1.4nd 2.0 Å. The mechanism underlying this feature is depicted inig. 6. At z = 1.2 Å the coronene is strongly distorted and repelled

ig. 6. Permeation mechanism of water through the center of coronene. H, C and O atomiven in Å. (For interpretation of the references to color in this figure legend, the reader is

�E according to Eq. (2). The latter contribution is denoted simply as “difference”in the figure. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of the article.)

by the water molecule. At z = 1.4 Å, however, one of the H atoms(light blue sphere in Fig. 6) of the water molecule is donated toone of the carbon atoms (yellow spheres in Fig. 6) of the centralhexagon of coronene. At z = 1.6 Å both of the hydrogen atoms havebeen donated and O (red sphere in Fig. 6) binds to two C atoms.This situation remains also for z = 1.8 Å. At z = 2.0 Å the departing Oatom re-captures the two H atoms and a water molecule is formedagain.

4. Discussion

We note for the total energy barriers for permeation of the dif-ferent species through coronene, discussed in Sections 3.3 and 3.4,

that these barriers generally exhibit various local maxima. One ofthose is usually located in front of the region in which temporarybonding as discussed above occurs. In the cases of CH2, CH3 andOH2, these maxima are also the global maxima, whereas in all other

s are depicted as light blue, yellow and red spheres, respectively. Values for z are referred to the web version of the article.)

S.E. Huber, M. Probst / International Journal of Ma

0 1 2# of H atoms

0

5

10

15

20

25

Ene

rgy

[eV

]

BeHx CH x OH x

0 1 2 3 4# of H atoms

z=0 Åz=0.2 Å

z=0.4 Å

z=0.6 Å

z=0.8 Å

z=1.0 Å

0 1 2# of H atoms

Fig. 7. Comparison of barrier heights at different positions of the impact referenceatom in dependence of the number of hydrogen atoms in the BeHx , CHx and OHxsfi

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B. Lipschultz, R. Doerner, R. Causey, V. Alimov, W. Shu, O. Ogorodnikova, A.

pecies considered in this work. (For interpretation of the references to color in thisgure legend, the reader is referred to the web version of the article.)

ases they are at least of similar height with the global ones. Hence,rojectiles with energies well below these pre-barrier maxima wille repelled way before they could be subject to fragmentation. In auclear fusion scenario corresponding to partial detachment with

temperature of a few eV in the divertor region, most of the projec-iles will have such low energies. Their dynamics is then governedy these pre-barriers.

For the reason given above, we collect the values of the energyarriers for the range of positions of the projectile species BeHx, CHynd OHx corresponding to z = 0.0–1.0 Å in Fig. 7. These results cane interpreted as follows. From H and H2, (not included in Fig. 7),e have already observed that the permeation barrier depends

trongly on the electronic configuration. For atomic H temporaryonding is possible when approaching the coronene molecule, butot for H2 due to its closed-shell nature. The same holds for theore complex molecules. As noted in Section 3.2, Be exhibits a

losed subshell, while BeH exhibits a valence electron allowingemporary bonding, and BeH2 corresponds to a closed-shell species.his is reflected in the pre-barriers in Fig. 7. In particular, the bar-iers are smaller for BeH than for Be, and larger for BeH2 than foreH, see the left panel in Fig. 7. The exception for z = 1.0 Å in Fig. 7

s due to the different locations of the barrier maxima for the dif-erent species. At this z value, Be and BeH2 have already passed theoronene molecule, whereas this happens later for BeH.

For the CHy species, we note that both C and CH allow tempo-ary bonding to three C atoms of the coronene molecule. However,or the CH molecule the repulsion between the projectile and thearget molecule can be expected to be bit larger due to higher elec-ron density due to its C H bond. Attaching two/three H atomso C, which results in a CH2/3 molecule reduces the number ofossible temporary bonds to two/one in contrast to the fore-oing cases. The expected order of permeation barriers is thusb(CH3) > Eb(CH2) > Eb(CH) > Eb(C). This is indeed the case as can beeen from the central panel in Fig. 7. The early fragmentation of CH4nto CH2 and H2 upon approaching the coronene surface could leado the expectation that it would resemble CH2. However, the costor breaking two C H bonds is not fully compensated by the forma-ion of the H2 molecule and thus the resulting barrier is betweenhe ones for CH2 and CH3 (Fig. 7).

For the last species considered in this work, OHx with x = 0, 1,, we observe that the barriers are the higher the more of the freealences of the projectile are saturated. In particular, the atomicrojectile O yields two free valences, whereas the hydroxyl radicalH yields one, and the water molecule, OH2 exhibits a closed-

hell configuration. Inspection of Fig. 7 shows that the permeationarriers for these projectiles yield the thus expected order, i.e.b(OH2) > Eb(OH) > Eb(O).

Concerning the relevance of the work to fusion setups like ITER,hich will exhibit a complex materials mixture [5,6], the obser-

ation of large differences in permeation capability of species in

ss Spectrometry 365–366 (2014) 248–254 253

a chemical equilibrium with each other might eventually haveimplications for the use of carbon in the divertor region. Assumedthat low temperatures accompanied by high gas densities andhigh recombination rates are present in this region, a signifi-cant fraction of the impurities in front of the wall will consist ofneutral molecules, rather than atomized or ionized species [56].Those molecular species will then experience a stronger repulsionupon approaching the surface due to their limited number of freevalences, as our results indicate. Hence, the situation in such ascenario might be substantially different from exploratory experi-ments in which materials are exclusively bombarded by energeticions. In especially, we expect that effects like material degradation,tritium retention and impurity production will be rather sensitiveto operation parameters such as the degree of detachment realizedin the reactor.

5. Conclusion

We calculated energy barriers for the adiabatic permeation of H,H2, BeHx as well as CHy and OHx with x = 0, 1, 2 and y = 0–4 throughthe central hexagon of coronene. We find that the permeation bar-rier can be lowered by temporary bonding depending strongly onthe electronic configuration of the projectile species. In many cases,we observe energetically driven fragmentation processes, generallyoccurring already upon close approach to the target molecule. Thedynamics of projectiles with energies of a few eV is governed bybarriers that are found to be lowered in cases of temporary bond-ing which is in turn enabled by free valences in the projectiles. Forcomparable systems, the strength of the bonding is related to thenumber of free valences. In particular, some barriers are found to beas much as twice as high for fully hydrogenated species as for thecorresponding bare atoms. It is argued that therefore caution mustbe exercised when experiments using ion beams are compared tothe scenario in plasmas of a few eV ion temperature.

Acknowledgments

This work was supported by the Austrian Ministry of Sci-ence BMWF as part of the UniInfrastrukturprogramm of theForschungsplattform Scientific Computing at LFU Innsbruck, by theFWF (Austrian Science Fund) via the DK+ on Computational Inter-disciplinary Modeling (W1227-N16) and the RFBR-FWF project(No. 11-03-01186-ɑ and I200-N19) and by the European Commis-sion under the Contract of Association between EURATOM andthe Austrian Academy of Sciences within the framework of theEuropean Fusion Development Agreement. The views and opinionsexpressed herein do not necessarily reflect those of the EuropeanCommission.

We thank Prof. Kersti Hermansson and Dr. Andreas Mauracherfor excellent suggestions and inspiring discussions.

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