Quantum chemical study of the reactivity of boron-doped graphite layers towards water formation

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Quantum chemical study of the reactivity of boron-doped graphite layers towards water formation A. Jeleaa,b,*, F. Marinellia, A. Allouchea a

Physique des Interactions Ioniques et Mole´culaires, CNRS et Universite´ de Provence, Campus Universitaire de Saint Je´roˆme, Service 242, 13397 Marseille Cedex 20, France b Institute of Physical Chemistry ‘‘IG Murgulescu’’, Romanian Academy, Spl. Independentei 202, Bucharest, Romania

A R T I C L E I N F O

A B S T R A C T

Article history:

Density functional calculations were used to study some fundamental features of boron-

Received 4 October 2007

doped graphite layers (CxBy) and the boron influence on the mechanisms leading to the for-

Accepted 17 January 2008

mation of water molecules on the CxBy graphite like layers. The Langmuir–Hinshelwood

Available online 1 February 2008

reactions leading to water formation on the graphite-like layers containing 12 at% boron take place with activation energies 3–5 times lower than on pure graphite ones. For the Eley–Rideal mechanism, the activation energies are always very low whether or not the graphite contains boron. Similar results were observed for 25 at% B doping. As a consequence, the oxygen and hydrogen can be more easily eliminated from the doped surfaces in the form of water molecules than from the corresponding pure ones. The CxBy layers with high boron content or having accumulations of boron, lose their planar structure. Two such parallel layers strongly interact through the boron atoms with the formation of a B–B bond and the displacement of the boron atoms into the inter-layer space. As a whole the system deviates from the graphite-like structure.  2008 Elsevier Ltd. All rights reserved.

1.

Introduction

One of the promising methods for generating energy is by deuterium–tritium nuclear fusion. A tokamak-type International Thermonuclear Experimental Reactor (ITER) to generate 1500 MW has been designed for this purpose. The idea is to obtain and confine inside of the reactor, a deuterium–tritium plasma, ‘‘hot’’ enough, that the crossing of the activation barrier corresponding to the fusion reaction occurs. The edge plasma interacts with the reactor walls with negative consequences on the conditions in the core plasma. Thus, finding a material resistant enough to the erosion is one of the key issues for the success of the ITER project. The erosion is caused mainly by the deuterium and tritium, which represent the fusion fuel, or by the oxygen atoms present in the boundary plasma as impurities.

The carbon is the material currently used in the tokamaks in the form of armor tiles protecting the plasma-facing components (PFC) from the intense heat load and particle flux coming from the plasma. It was preferred for its low atomic number and high-thermal shock resistance. However, its strong affinity with hydrogen (and its isotopes deuterium and tritium) and oxygen, is largely responsible for the carbon erosion mechanisms in the tokamak [1]. By erosion, volatile species form, as hydrocarbons and carbon oxides, which pollute the boundary plasma. The use of boron as doping element for the carbonaceous materials [2–6] has been proved to be a good modality to reduce the formation of hydrocarbons and to enhance both the retention of hydrogen and the formation of H2 (or D2) molecules [7–11]. In a theoretical study, Ferro et al. [12] show that the adsorption energies of CHn (n = 0–3) fragments and of

* Corresponding author: Address: Physique des Interactions Ioniques et Mole´culaires, CNRS et Universite´ de Provence, Campus Universitaire de Saint Je´roˆme, Service 242, 13397 Marseille Cedex 20, France. Fax: +33 4 91 41 89 16. E-mail address: [email protected] (A. Jelea). 0008-6223/$ - see front matter  2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2008.01.024

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hydrogen atoms on a graphite surface are larger in the case the surface is doped with boron, this being consistent with the enhancement of hydrogen retention and with the reduction of erosion yields. The enhancement of the molecular hydrogen formation is explained elsewhere by the same authors by the catalyst effect of boron on the recombination of hydrogen on the graphite basal plane [13]. Chen et al. [11] explain that a CH4 yield reduction is observed in boron-doped graphite because the enhancement of the H2 recombination implies a diminution of the hydrogen available for the formation of the CH4 molecules. The doping with boron has also an effect on the oxidation of the graphite materials: an inhibition of the oxidation has been observed in the boron-doped graphite compared to the pure graphite [14–16]. Three mechanisms have been proposed [14,15] to explain the oxidation rate diminution: the catalyst effect of boron on the graphitization [17] – thus crystalline graphite structures resistant to oxygen form, the modification of the p electrons density by doping and the blocking of the active sites by the formation of a B2O3 layer. We have seen above that the effects of boron doping on the hydrogen or oxygen interactions with graphite have been relatively well studied, but the situation when both of them are present is poorly treated, at least from a theoretical viewpoint. The study of the reaction mechanisms of oxygen and hydrogen on the pure or doped graphite is particularly interesting because the oxygen was proposed as detritiation agent of the carbonaceous walls of tokamaks, and experiments have proved its high reactivity towards the hydrogenated carbon [18–20]. In a previous study [21], we analyzed the mechanisms for the formation of water molecules on pure graphite, implying atoms of oxygen and hydrogen adsorbed or in the gas phase. The present paper has two aims: the first one is to reveal the influence of boron on the oxygen–hydrogen reactions taking place on graphite-like boron–carbon layers and the second one is to explore, within the limits of our models, the deviation from the graphite-like structure of the BxCy systems. The paper is structured as follows: Section 2 describes the technical part of our calculations; in Section 3, after a short analysis of the structural properties of graphite-like layers containing boron with implications on reactivity, the formation of water on these layers is studied. Section 4 is a study of the limits of the graphite-like structure for the boron–carbon systems. Finally, the main results of this study are discussed in Section 5.

2.

Table 1 – Test parameters calculated using the Troullier– Martins pseudo-potentials

˚) a graphite (A graphite (kJ/mol) Ecoh ˚) a boron a-rhomb (A (kJ/mol) Eboron coh Ebond(O2) (kJ/mol) ˚) dOO (A Ebond(H2) (kJ/mol) ˚) dHH (A Ebond(OH) (kJ/mol)

Abinit

Exp [25]

2.456 748.0 5.080 572.7 562.7 1.219 436.9 0.741 432.7

2.461 716.7 5.060 562.7 498.0 1.208 453.6 0.741 463.0

The calculations on graphite were carried out considering a 36 kpoints sampling (6 · 6 · 1) and for boron a 16 k-points sampling (4 · 4 · 1) of the BZ. Experimental results are given for comparison.

parameters were considered as follows: for carbon and boron, the cohesion energies and the cell parameters (cell vectors modulus and angles) corresponding to the allotropic modifications graphite (elementary cell of four carbon atoms) and a-rhombohedral boron (elementary cell of 12 boron atoms), respectively, and for hydrogen and oxygen, the binding energies and the bond lengths in the diatomic molecules of hydrogen, oxygen and the hydroxyl radical (OH). The calculated values are in good agreement with the experimental ones, the pseudo-potentials we tested being appropriate to be used in the subsequent calculations. All the calculations were carried out using an energy cutoff of 25 Hartree (680 eV). The tolerance on the difference of total energy for the SCF iterations was of 106 Hartree and the tolerance on the maximal force for geometry optimization of 103 Hartree/Bohr. The spin polarization was taken into consideration because some of our systems contain unpaired electrons. The first Brillouin zone (BZ) sampling is based on the Monkhorst–Pack technique [26]. In these quantum calculations, both deuterium and tritium were assimilated with hydrogen because of their identical chemical properties. Hydrogen atoms play also the role of all the hydrogenous ions coming from the thermonuclear fusion plasma and interacting with carbon walls. This is based on the assumption that the surface is an electron reservoir and each hydrogen ion arriving on the surface is immediately neutralized.

3.

Carbon–boron with graphite-like structure

3.1.

Boron-doped graphite layers

Computational method

All the calculations were carried out within the frame of the density functional theory (DFT) formalism and using the ABINIT computer code [22]. The exchange–correlation term is described by the non-empirically constructed Perdew–Burke– Ernzerhof (PBE) [23] gradient corrected functional. The Kohn–Sham orbitals are represented in a plane wave basis associated to Troullier–Martins pseudo-potentials [24]. In Table 1 are listed both experimental and calculated values of different parameters chosen for testing the pseudopotentials used in the calculations. By element, the ‘‘test’’

CxBy compounds with the concentration in boron up to 25 at% [4,5] were synthesized using the chemical vapor deposition (CVD) method. These compounds have a graphite-like structure with the carbon atoms substituted in different proportions by boron (doping by substitution). The substitution is easily explained because the covalent radius of boron (0.98) is very close to that of the carbon (0.91) [15]. Moreover, in these compounds the boron atom has its characteristic sp2 hybridization with the corresponding trigonal planar geometry.

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This section is dedicated to the surface properties of the boron–carbon compounds with a graphite-like structure. The calculations were carried out on periodically repeated one layer cells. Some carbon atoms from the one-layer hexagonal super-cell of pure graphite (C8) represented in Fig. 1 were replaced by boron atoms, therefore creating boronized layers (CxBy) with different concentrations in boron. The cell vectors ‘‘a’’ and ‘‘b’’ are oriented along the CxBy surface and they were optimized for each concentration in boron. The cell vector ‘‘c’’ is perpendicular to the graphite plane and in the frame of our model it measures the distance between two CxBy layers belonging to different neighboring cells. Its modulus was cho˚ in order to avoid the interactions between sen equal to 15 A the layers. The substitution of one and two carbon atoms by boron led to two systems, C7B and C6B2 (a more familiar formula of C3B will be used in the present paper) containing 12.5 and 25 at% B, respectively (see Fig. 1). The C7B structure is unique. However, the double substitution led to three different configurations. In the C3B(1, 2) structure, the boron atoms were directly connected. In the C3B(1, 3) and C3B(1, 4), the boron atoms were separated by one and two carbon atoms, respectively. The cell parameters corresponding to C7B and C3Bs were optimized. The cohesion energy corresponding to one CxBy layer was calculated using the formula Ecoh ¼

1 ðECx By  xEC  yEB Þ: xþy

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ð1Þ

ECx By is the total energy of the CxBy system and EC, EB are the energies of the isolated carbon and boron atoms in their ground state, triplet and doublet, respectively. The variation of the cohesion energy versus ‘‘a’’ parameter for the C7B, C3B(1, 2) and C3B(1, 4) structures is represented in ˚ (C7B) Fig. 2. The energy minima were reached for a = 5.03 A ˚ and 5.16 A (the C3B structures). The corresponding cohesion energies (Table 2) were decreasing with the concentration in boron. The opposite effect is observed for the ‘‘a’’ parameter. The same tendencies have been shown by the DFT–LDA calculations of Tomanek et al. [27] or by the experimental works of Lowell [2]. The angle made by ‘‘a’’ and ‘‘b’’ vectors keeps its

˚) Fig. 2 – Cohesion energies (kJ/mol) versus the a (A parameter corresponding to the C7B, C3B(1, 2) and C3B(1, 4) systems.

Table 2 – Cohesion energies (kJ/mol) and optimized ˚ ) corresponding, respectively, to the pure parameters (A (C8) and boron-doped graphite layers Structure C8 C 7B C3B(1, 2) C3B(1, 3) C3B(1, 4)

Ecoh (kJ/mol) 747.7 707.3 665.2 671.1 685.9

˚) a (A 4.91 5.03 5.16 5.16 5.16

value of 120 from the pure graphite. Consequently, the cell structure remains hexagonal. The empty pz orbitals of boron induce the decrease of the p electrons density above the layer, which leads to the weakening of the p bonds and then to the increasing of the interatomic distances [28] with the number of the boron atoms in the system. This result fits very well the values of the bond ˚ ) < B–C (1.52 A ˚ ) < B–B (1.65 A ˚ ). lengths: C–C (1.42 A As regards to the three C3B configurations the results are similar to those reported in [29]: the most stable configuration

Fig. 1 – Graphite layers with different boron contents.

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is (1, 4) with the most uniform distribution of the boron atoms. The least stable configuration is (1, 2), which presents a boron accumulation generating a B–B bond. Magri [30] proved also in her study on the stability of different CxBy structures that the B–B bonds are energetically unfavorable when the concentration of boron is less than 25 at%. However, the difference in stability (Table 2) between the (1, 4) and (1, 2) configurations, respectively, the most and the least stable, is very thin (20 kJ/mol). This could explain the results of the NMR-11B measurements of Shirasaki et al. [31], who observed an important number of B–B bonds in systems containing less than 25 at% B. Moreover, the number of these bonds increases with the concentration in boron. The densities of states (DOS) corresponding to the C8, C7B and C3B(1, 2) and (1, 4) layers, with the contributions from the carbon and boron atoms, are presented in Fig. 3a–d. The contributions to the r bands are marked with a continuous line and to the p bands with a dotted line. The origin of the energies is taken at the Fermi level (EF). The gap between the valence band and the conduction band for the C8 system is of approximately 0.7 eV. This is why, this system behaves like a semi-conductor. In this case,

the last valence band is p type one and the first conduction band is of a p* type. The DOS corresponding to the C7B system (Fig. 3b) shows a displacement of the Fermi level to the middle of the p band. Because of this semi-occupied band, the system should behave like a metal. From a chemical point of view it should have an affinity for species able to fill this semi-occupied band, like the radicals. The most important contribution to this band comes from the boron atom. The peak at 1.3 eV from the DOS of C7B and which exists also for the C3B systems belongs to the valence band and is due to the directly connected boron and carbon atoms. Thus, this band is associated to the B–C bond. As regards the C3B structures (Fig. 3c and d), the Fermi level is situated between the r and the p bands. Similar results on the C3B systems have been reported in [32]. The gap corresponding to the configuration (1, 4) is approximately 0.4 eV characteristic to a semi-conductor. The DFT–LDA calculations of Tomanek et al. [27] led to a close value of 0.7 eV. The (1, 2) configuration presents a superposition of the r and p bands at the Fermi level. The increasing of the DOS at the Fermi level is due to a new band at 0.4 eV. This band is attributed to the B–B bond, because the boron atoms are the

Fig. 3 – (a) DOS(PDOS) corresponding to the C8 system (pure graphite layer); (b)–(d) DOS(PDOS)’s corresponding to the C7B, C3B(1, 2) and C3B(1, 4) systems. The contribution of carbon and boron atoms to the r (continuous line) and p (dotted line) bands are also represented. C1 are the carbon atoms directly connected to the boron (B) and C2 the carbon atoms connected only to carbon. The Fermi level (EF) is in the origin.

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635

only ones that significantly contribute to it. The semi-empirical calculations of Lee et al. [32] determined a 0.2 eV gap for the (1, 2) configuration and from 1.4 to 1.8 eV for (1, 4). Our results, agreeing with those of Tomanek, have us think that these values are overestimated. However, qualitatively our results agree with those of Lee et al. as regards the rapprochement of the r and p bands in the C3B(1, 2) system. The reduction of the gap induces the increasing of the chemical reactivity [33]. Therefore, the C3B(1, 2) layers are more reactive than C3B(1, 4). Moreover, the decrease of the gap in the boron doped layers compared to the pure graphite induces an increased reactivity of the previous ones.

3.2.

Formation of water on the boron-doped graphite layers

3.2.1. Adsorption of atomic hydrogen and oxygen on the boron-doped surfaces The adsorption energies of one hydrogen atom on the C7B and C3B(1, 2) layers as calculated in the present work are 231.3 and 269.1 kJ/mol, respectively. They are much larger than for the pure graphite: 71.5 kJ/mol. The preferred adsorption sites are the carbon atoms directly connected to the boron in the first case and the two boron atoms from the B–B bond in the second one. Ferro et al. [13,34,35] have shown, on the cluster type [34] or periodical [13] models, that the hydrogen is adsorbed on the boron-doped graphite layers with higher energies than on the pure graphite ones. The adsorption energy on a C7B layer calculated by these authors using a periodical model (228.0 kJ/mol) is very close to ours. It was already shown [21,36–41] that on the defect less graphite layer the oxygen atom is adsorbed preferentially on the bridge sites, situated above the middle of a C–C bond (bridge-CC sites). The pure graphite has only CC such sites, but the boronization makes the creation of other kinds of bridge sites possible: BC and sometimes BB. The same boron-doped surface could have many non-equivalent CC and BC sites. In the present work, it was studied the adsorption of the oxygen atom on all of the CxBy layers presented in Fig. 1 and on all of the non-equivalent CC, BC or BB sites of each one. The absolute values of the adsorption energies are presented in Fig. 4. Whether the site is CC or BC the adsorption energy increases with the concentration in boron. This tendency is shown on the figure by the vertical arrows. At the same concentration in boron, the adsorption energy increases with the number of boron atoms from every site. Indeed, on the same doped surface, the CC sites are less reactive; they are followed by BC and finally the most reactive, the BB sites. Other calculations have also shown that the adsorption energy of the atomic oxygen increases with the concentration in boron [36].

3.2.2. Formation of OH radicals on the boron doped layers: the Eley–Rideal and Langmuir–Hinshelwood mechanisms Whether the mechanism is Eley–Rideal (ER) or Langmuir–Hinshelwood (LH), the reactions between hydrogen and oxygen take place in two stages: the first stage is the formation of

Fig. 4 – Adsorption energies of an oxygen atom on different sites (CC, BC and BB) belonging to pure and boron-doped graphite surfaces.

the hydroxyl radicals and the second is the formation of the water molecules (see also [21]). The potential energy surfaces (PES) corresponding to the ER reaction between the hydrogen and oxygen atoms on the C7B layer are presented in Fig. 5. The PES from Fig. 5a corresponds to the vertical attack of a hydrogen atom on the oxygen adsorbed on a BC site. The reaction is barrier-less and as result an O–H bond forms and the O–C bond breaks. This is represented on the AB segment of the reaction profile. The energy of the system is calculated versus OH distance, which represents here the reaction coordinate (RC). In every point of the PES the coordinates of the hydrogen and oxygen atoms were not relaxed. Given the constraints we had to impose, the B point of the PES is not the absolute minimum. In order to obtain it (point C on the PES) one had to remove the constraints imposed to the U angle formed by the O–H and B–O bonds. Finally, the new formed OH group remains bound to the boron atom. The reaction has a strong exothermic effect (424.9 kJ/mol). Fig. 5b presents the inverse situation with an oxygen atom from the gas phase attacking the hydrogen which is adsorbed on a carbon neighboring the boron atom. The reaction product is an OH radical which leaves the surface. This reaction is less exothermic than the previous one. To the difference of 225.1 kJ/mol between the reaction energies DE of the two reactions contributes also the adsorption energy of the OH radical on a boron atom. The PES corresponding to the LH mechanism on C7B is shown in Fig. 6. The oxygen is initially adsorbed on a BC site, as in the previous situation and the hydrogen is adsorbed on a carbon atom neighboring the boron. The step-by-step displacement of the hydrogen atom along the B–C bond, towards the oxygen, leads, after crossing of a 27.3 kJ/mol potential barrier, to the formation of an OH radical, adsorbed on the boron atom. The decrease of the activation energy compared to the pure graphite (Ea = 138.6 kJ/mol) [21] is remarkable. The activation energies for the two mechanisms, but on the C3B(1, 4) layer, presented in Table 3, were obtained in a similar manner. The activation energies corresponding to

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Fig. 5 – The ER mechanism for the formation of OH radicals on a C7B layer. (a) Reaction between an hydrogen atom coming from the gas phase and an adsorbed oxygen atom. (b) Reaction between an oxygen atom coming from the gas phase and an adsorbed hydrogen atom.

Fig. 6 – LH mechanism for the formation of an OH radical on the C7B layer. Reaction coordinate (RC) is the displacement of the hydrogen atom with respect to its initial position on the carbon atom neighboring the boron.

the ER mechanism remain very low and those associated to the LH mechanism are close to the previous situation. However, if the oxygen is adsorbed on the BB site (the case when the surface is C3B(1, 2)) the LH formation of OH radicals takes place with a higher energy than in the two previously analyzed situations (Fig. 7).

None of the strong B–O bonds breaks during this reaction and therefore the newly formed OH group remains adsorbed on the bridge site, above the middle of the B–B bond. The calculated adsorption energy of the OH radical on this site is 308.6 kJ/mol, much larger than on a pure graphite surface (50 kJ/mol [21]).

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Table 3 – Activation (Ea) and reaction (DE) energies corresponding to the formation of the OH radicals and water molecules on the C7B, C3B(1, 4) and C3B(1, 2) layers Reaction product

Surface (mechanism)

Ea (kJ/mol)

OH OH OH OH OH OH H 2O H 2O H 2O H 2O H 2O

C7B (ER) C7B (ER) C7B (LH) C3B(1, 4) (ER) C3B(1, 4) (LH) C3B(1, 2) (LH) C7B (ER) C7B (LH) C3B(1, 4) (ER) C3B(1, 4) (LH) C3B(1, 2) (LH)

0 0 27.3 16.9 39.7 101.6 4.9 25.5 10.8 0 4.7 ðE1a Þ 29.7 ðE2a Þ

DE (kJ/mol) 424.9 (H + Oacls) 199.8 (O + Hacls) 139.0 223.7 139.5 54.4 297.5 146.2 351.2 – +1.4(E2  E1) 21.0 (E3  E2)

The bridge site (site B) is not the only one. The PES from Fig. 8, corresponding to the displacement of the OH radical along the B–B bond, shows the existence of a second type of site (site A) situated above each one of the two boron atoms. The difference in adsorption energy on the two types of sites is very low (20.8 kJ/mol) thus facilitating the migration of the OH radical from a site to another.

3.2.3. Formation of water molecules on the boron-doped graphite layers: ER and LH mechanisms The OH radicals formed in the first stage remain generally adsorbed, with adsorption energies significantly increased with respect to the adsorption on the pure graphite layer [21].

Fig. 8 – PES corresponding to the displacement of the OH radical along the B–B bond. With A and B are denoted the sites situated, respectively, above one of the boron atoms and above the middle of the B–B bond.

The formation of water on the C7B layer takes place with very low activation energies either the mechanism is ER or LH. For the ER case, the activation barrier is 4.9 kJ/mol (Fig. 9a) and the newly formed water molecule spontaneously desorbs. The doping with boron significantly decrease the activation energy for the LH mechanism from 76.5 kJ/mol on the pure graphite [21] to 25.5 kJ/mol (Fig. 9b). On the C3B(1, 4) surface (Table 3) the ER formation of water by vertical attack of the hydrogen atom on the OH radical adsorbed on a boron atom requires an activation energy of 10.0 kJ/mol while in the LH case the reaction is barrier-less. In both cases, the newly formed water molecules desorb.

Fig. 7 – LH mechanism for the formation of the OH radicals on the C3B(1, 2) layer. Reaction coordinate (RC) is the displacement of the hydrogen atom with respect to its initial position on the carbon atom neighboring the boron.

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Fig. 9 – PES corresponding to the ER (a) and LH (b) mechanisms for the formation of water on the C7B layer.

The LH reaction on the C3B(1, 2) layer has two stages (Fig. 10). The OH radical is initially adsorbed between two boron atoms, as described in the previous section, and the hydrogen is adsorbed on a carbon atom neighboring the boron. During the first stage the E2 intermediate forms with a positive DE of 1.4 kJ/mol. Ea for this stage is very low: 4.7 kJ/mol. In the E2 intermediate, the hydrogen atom is situated above the C–B bond while the OH radical remains adsorbed

on only one of the boron atoms. It was previously shown that the OH radical can easily migrate from a bridge site (site B) to the A site situated above a boron atom. This explains the low activation energy of the first stage. In the second stage, the system evolves towards the formation of the water molecule. For this stage, Ea = 29.7 kJ/mol. Thus, the activation energies on the boron-doped graphite layers have very low values, this facilitating the formation of

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Fig. 10 – LH mechanism for the formation of the water molecules on the C3B(1, 2) layer. Reaction coordinate (RC) is the displacement of the hydrogen atom with respect to its initial position.

water and finally the elimination of oxygen and hydrogen from the surface. However, some local effects can be observed, as for the case of the C3B(1, 2) layer which presents accumulations of boron.

4.

Limits of the graphite-like structure

All of the surface models from the previous section were built based on the assumption that we have to deal with materials with graphite-like structure. The purpose of the present section is to investigate the limits of the graphite-like structure and to see to what extent our results can be reported to the experiment. The XRD (X-ray diffraction) determinations of Hach et al. [17] have shown that for concentrations in boron of 17 at% B and more, the boron atoms leave the substitution sites to occupy the interstitial ones, situated between the graphite layers, thus, provoking structure modification. However, the C5B systems (17 at% B) synthesized by Way et al. [5] have a graphite-like structure with the boron atoms occupying the substitution sites. The fact that we observe non-graphite structures at concentrations as low as 17 at% B can be explained by the uneven distribution of the boron in the material, because such structures occur in boron-rich systems [42]. Moreover, it has been previously shown (Section 3.1) that local accumulations of boron atoms are possible even if the corresponding configurations are less stable energetically. In the present work, two situations will be considered: (1) The situation we have large accumulations of boron: thus the system can be divided into boron-rich regions and graphite-like regions with a very low boron content. From a macroscopic point of view this system is heterogeneous: there is an interface between the boron-rich and boron-poor zones.

(2) The situation where we have accumulations in boron as small as a couple of atoms. From a macroscopic viewpoint, this system can be considered as homogeneous. The model proposed for representing a boron-rich CxBy layer, is built from the one-layer cell of the pure graphite (C8 from Fig. 1) where four carbon atoms have been replaced by boron. The four boron atoms are distributed in a such a manner that they form clusters consisting in one boron atom surrounded by the three others (Fig. 11; left). The structure presents also identical clusters, but only with carbon atoms. Thus, the CB model with 50 at% B consists in a mosaic of carbon clusters surrounded by three boron clusters and vice versa. The cell parameters, ‘‘a’’, ‘‘b’’ and the angle they form, together with the atoms coordinates have been all relaxed. ˚ (more Thus the value of the optimized ‘‘a’’ parameter is 5.21 A than for the pure graphite) while the angle keeps its value of 120 from the pure graphite. However, the optimized CB layer looses its planar structure. The boron and carbon atoms situated in the middle of the corresponding clusters leave the plane in the opposite direction. The displacement of the ˚ for boron and 0.20 A ˚ for caratoms along the z axis is +0.70 A bon. This loss of the planar structure was not observed for the C7B and C3B optimized layers. The displacement of the boron atom induces an elongation of the B–B bond to the value of ˚. 1.70 A For a system consisting of parallel CB layers, the loss of the planar structure of the layers could induce strong interactions between them. In order to study this kind of interactions, a second CB layer, identical to the previous one, was added in the system. The distance between the two layers is initially ˚ , the same as for the pure graphite. The layers are 3.35 A superposed following an ABAB stacking similar to that from the graphite crystal. This system was then optimized.

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Fig. 11 – Optimized one-layer CB system (left); optimized two-layer CB system (right). Some too long B–B bonds are not shown in the figure.

The interaction energy (Eint) between the two layers is given by the formula Eint ¼ E2L  2EL ;

ð2Þ

where E2L and EL are, respectively, the total energies of the optimized two-layer and one-layer systems in their singlet ground state. The optimized two-layer system (Fig. 11; right) shows the ˚ ) between boron atoms formation of a B–B bond (dBB = 1.62 A belonging to different layers and situated in the middle of the corresponding clusters. This chemical bond implies a large interaction energy: Eint =  215.3 kJ/mol. It implies also that the boron atoms occupy interstitial sites. The perturbation of the electronic structure of the system is described by the DOS of the one-layer and two-layer systems, but also by the PDOS of the boron atoms forming the inter-layer bond (Fig. 12). In the one-layer system (Fig. 12; left), the boron atoms situated in the middle of the cluster contributes with the 2s, 2px and 2py orbitals to the r bands ranging from 15 to 2 eV. The most significant participation at the Fermi level (p bands) comes from the 2pz orbitals. There is also a contribution in

this region from 2px and 2py, but a very weak one. This is due to the deformation of the CB layer as has been previously shown. In the two-layer system (Fig. 12; right), the PDOS peaks corresponding to the orbitals of the same boron atom have a shift generally towards higher energies. Thus, they have no contribution in the region ranging from 15 to 10 eV. The 2px and 2py orbitals participate identically to the bands situated at the Fermi level. Only the 2pz level has a shift towards lower energies. At the origin of these modifications could be the creation of a B–B bond similar to that from the B2 molecule. Actually, the bond length of this bond is the same as for the B2 mole˚ ). The B2 ground state configuration is: 1r2g cule (1.62 A 2 2 2 1ru 2rg 2ru 1p1u 1p1u [43]. Each one of the 2rg and 2ru molecular orbitals is the result of the superposition of the 2pz and predominately 2s atomic orbitals. The last two semi-occupied levels of a p type are formed by identical contribution of 2px and 2py orbitals, respectively. The first unoccupied level, rg type is formed also by a 2s–2pz combination but with a significant contribution from 2pz. In all the previous commentaries, one considered the B–B bond is oriented along to the z axis.

Fig. 12 – DOS corresponding to the one-layer (left) and two-layer (right) systems. The PDOS corresponds to the boron atoms situated in the middle of the cluster.

CARBON

4 6 (2 0 0 8) 6 3 1–64 3

641

Fig. 13 – Optimized one-layer C7B2 system (left); optimized two-layer C7B2 system (right). Some too long B–B bonds are not represented in the figure.

In the two-layer case, the band close to the Fermi level, formed by 2px and 2py contributions from the two boron atoms, is associated to the p type B–B bonds as in the B2 molecule. From the comparison with the B2 molecule one should expect that the contribution of the 2pz orbitals was significant to a r band higher in energy than the p band. However, the opposite is observed. This is due to the strong interactions of these orbitals with the carbon–boron layers. In order to study the formation of B–B inter-layer bonds in systems with less than 50 at% boron a periodic model representing a layer with 22.2 at% B was used. This model was built from a one-layer super cell of pure graphite of 18 carbon atoms, where four carbon atoms were substituted by boron. The four boron atoms form a cluster similar to that previously described: a central atom surrounded by the other three. This system (Fig. 13; left) has the ‘‘molecular’’ formula C7B2. The ˚ , larger than optimized ‘‘a’’ parameter of this cell is 7.470 A ˚ . The boron for the corresponding pure graphite cell: 7.368 A atom from the center of the cluster moves out from the plane ˚ and the bond length of the B–B bond with approximately 1.3 A ˚. becomes 1.7 A The two-layer cell is built by the superposition of two such layers following an ABAB stacking with the boron clusters situated one above the other. The distance between the layers ˚ . Following the optimization of this strucwas initially 3.35 A ˚ ) forms in a similar manner ture, a B–B inter-layer bond (1.59 A with the system containing 50 at% B (Fig. 13; right). The interaction energy, calculated with formula (2), is 277.7 kJ/mol. Thus, the B–B inter-layer bonds can also form in systems with less than 50 at% B with the condition that there are regions with high concentration in boron (uneven distribution of boron in the material). The formation of such inter-layers bonds is accompanied by the displacement of the boron atoms from the substitution sites into the interstitial ones.

5.

Conclusions and discussion

We have presented the results of a DFT study on some properties of the boron-doped graphite layers. The one-layer model was used when treating surface reactions on planar CxBy layers. This kind of model is sustained by the fact that the interactions between the layers in graphitelike materials are very weak and consequently the influence

of the bulk on the surface processes is not important. This was already shown by Ferro et al. [44]. Then, the study of the oxygen–hydrogen reactions on the CxBy one-layer model surfaces showed that, following the LH mechanism, the water forms more easily on the borondoped graphite layers than on the pure ones. On the C7B (12.5 at% B) layer, the OH radicals and water molecules formation through LH mechanism takes place with activation energies 3–5 times lower than on the pure graphite layer. The works of Ferro et al. [13] proved a similar effect for the recombination of hydrogen. Increasing the concentration of boron to 25 at% B (C3B) does not imply any improvement compared to the C7B case: for the formation of OH radicals Ea = 39.7 kJ/mol (slightly higher than on the C7B) and the formation of water is a barrier less reaction. The activation barriers corresponding to the ER mechanism are always very low. Thus, concerning this mechanism, the doping with boron brings practically no modification in respect to the pure graphite case. The formulas (3) and (4) allow the coarse estimation of the rates of the reactions leading to water formation on C7B and C3B(1, 4): sffiffiffiffiffiffiffiffiffiffiffiffiffi kT ER ER NA eEa =RT cA csB ¼ rER f ER cA csB v ¼r ð3Þ 2pmH and LH

v

sffiffiffiffiffiffiffiffiffi Ea pkT ¼r NA eRT csA csB ¼ rLH f LH csA csB : 2l LH

ð4Þ

T is the absolute temperature, k is the Boltzmann’s constant, NA is the Avogadro’s constant, l is the reduced mass and mH the mass of the hydrogen atom, cA is the volume concentration (mol/m3) of the reactant A (H), csA and csB are the concentrations at the surface (mol/m2) of the reactants A (H) and B (O or OH). rER (m2) and rLH (m) are the cross-sections corresponding to the ER and LH mechanisms, respectively: rER = ˚ ; RO = 0.60 A ˚ and p(RA + RB)2 and rLH = RA + RB; RH = 0.25 A ˚ . The factor ‘‘f’’ (m/mol s) is the frequency by mol ROH = 1.0 A of the reactive collisions, multiplied by the distance covered by the particle in one second. The formulas (3) and (4) are derived from the collision theory as presented in [45]. The ER mechanism is seen as the

642

CARBON

4 6 ( 2 0 0 8 ) 6 3 1 –6 4 3

Table 4 – Calculated ER and LH ‘‘f’’ factors (mol1 s1 m) corresponding to the formation of OH radicals and water molecules at temperatures of 500 and 700 K, respectively Surface C 7B C3(1, 4)

fER(OH) 26

fLH(OH) 26

4.8 · 10 5.8 · 10 8.3 · 10243.2 · 1025

24

fER(H2O) 25

2.2 · 10 1.7 · 10 1.1 · 10232.1 · 1024

collision of the hydrogen atoms with a wall (the surface containing the adsorbed oxygen atoms or OH radicals). From all of the colliding hydrogen and oxygen atoms (or OH radicals), only those with the kinetic energy surpassing the activation energy will react. In the LH case, the displacement of the reacting atoms can be considered as taking place in two dimensions. Consequently, the reasoning [45] allowing the calculation of the rate constants for the reactions taking place in the volume was adapted to the two-dimensional situation: two-dimensional velocities and one-dimensional crosssection. The ‘‘f’’ factors corresponding to the ER and LH mechanisms are presented in Table 4. They were calculated for the temperatures of 500 and 700 K (the hydrogen release by oxygen ventilation was carried out in TEXTOR within this range of temperatures [46]). The frequency factors corresponding to the ER mechanism are larger than for the LH case. One can infer that ER is the main mechanism leading to the formation of OH radicals and water molecules on the CxBy surfaces. Some experimental results on the formation of water molecules but on different surfaces are in agreement with this conclusion [47,48]. However, the formation of water on the C3B(1, 4) seems to be faster following the LH mechanism. The reaction product, the water molecules, weakly interacts with the CxBy layers thus, leaving the surface (within the limits of the DFT methods in correctly predicting the van der Waals interactions [49], it seems that the water molecules do not adsorb on the pure graphite or C7B, C3B(1, 2) or C3B(1, 4) layers). The two-layer model was used only when the layers presented deviations from the planar structure thus, opening the possibility for a strong in-bulk interaction. By using this model it was shown that, for the systems with high concentration in boron, the boron atoms from the CxBy layers leave their in-plane position in order to occupy the inter-layer sites. In this situation, B–B bonds forms, indicative of a structure modification. Thus, one can expect the structure of boronrich systems to be very different from the graphite-like one. Moreover, the works of Vast et al. [50] proved that a system with high concentration in boron, as B4C, has a structure very close to the rhombohedral boron. It was also shown that structure deviations from the graphite-like one are present at concentrations in boron as low as 22.2 at% B, even if the structure is not as distorted as that corresponding to 50 at% B. This happens for the systems presenting accumulations in boron. Though not energetically favored, accumulations in boron occur at low concentrations. This is due to the fact that the difference in stability between the most stable configurations, with the boron uniformly distributed and those with accumulations in boron, is very small. For the system with 25 at%

26

fLH(H2O) 26

1.5 · 10 2.5 · 10 3.6 · 10259.0 · 1025

3.2 · 10242.4 · 1025 1.6 · 10271.9 · 1027

B, studied in the present work, such difference in stability is 20 kJ/mol.

Acknowledgements This work was supported by the Euratom-CEA Association in the framework of the LRC (Laboratoire de Recherche Conventionne´). The calculations were performed at the ‘‘Centre Re´gional de Compe´tence en Mode´lisation Mole´culaire de Marseille’’ and at CCRT, the CEA (Commissariat a` l’Energie Atomique) computing center.

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