Direct modeling of the electrochemistry in the three-phase boundary of solid oxide fuel cell anodes by density functional theory: a critical overview.

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Cite this: DOI: 10.1039/c3cp53943a

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Direct modeling of the electrochemistry in the three-phase boundary of solid oxide fuel cell anodes by density functional theory: a critical overview M. Shishkin* and T. Ziegler The first principles modeling of electrochemical reactions has proven useful for the development of efficient, durable and low cost solid oxide full cells (SOFCs). In this account we focus on recent advances in modeling of structural, electronic and catalytic properties of the SOFC anodes based on density functional theory (DFT) first principle calculations. As a starting point, we highlight that the adequate analysis of cell electrochemistry generally requires modeling of chemical reactions at the metal/oxide interface rather than on individual metal or oxide surfaces. The atomic models of Ni/YSZ and Ni/CeO2 interfaces, required for DFT simulations of reactions on SOFC anodes are discussed next, together with the analysis of the electronic structure of these interfaces. Then we proceed to DFTbased findings on charge transfer mechanisms during redox reactions on these two anodes. We provide a comparison of the electronic properties of Ni/YSZ and Ni/CeO2 interfaces and present an

Received 18th September 2013, Accepted 11th November 2013

interpretation of their different chemical performances. Subsequently we discuss the computed energy

DOI: 10.1039/c3cp53943a

of DFT studies combined with microkinetic modeling as well as the results of kinetic Monte Carlo

pathways of fuel oxidation mechanisms, obtained by various groups to date. We also discuss the results simulations. In conclusion we summarize the key findings of DFT modeling of metal/oxide interfaces to

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date and highlight possible directions in the future modeling of SOFC anodes.

1. Introduction Solid oxide fuel cells (SOFCs) offer a promising solution for the realization of power efficient, fuel flexible and low cost energy producing devices.1–3 Operating stages of SOFC are illustrated in Fig. 1. The cell consists of three basic parts: cathode and anode electrodes and the electrolyte. Under operation conditions, oxygen gas is supplied into the cathode compartment of the cell. Here the oxygen molecules are reduced into individual ions that are subsequently incorporated into the solid electrolyte. This process is electrochemical, as oxygen incorporation into the electrolyte is accompanied by transfer of electronic charge from the cathode to the electrolyte.4 In the second stage the oxygen ions migrate through the ion-conducting electrolyte (the most common choice to date is yttria-stabilized zirconia (YSZ)) towards the anode. In the third stage, the fuel, which is supplied into the anode compartment of the cell is oxidized. This stage is also electrochemical, as fuel oxidation is accompanied by transfer of electronic charge from the electrolyte to the anode.5 Department of Chemistry, University of Calgary, University Drive 2500, Calgary, AB, T2N 1N4, Canada. E-mail: [email protected]

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Fig. 1 Operating stages of SOFC: (1) oxygen reduction at the TPB of the cathode, resulting in incorporation of oxygen into electrolyte, accompanied by transfer of charge from the cathode to the electrolyte; (2) oxygen migration through the electrolyte; (3) hydrogen oxidation at the anode TPB, accompanied by transfer of electronic charge from the electrolyte to the anode.

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Unfortunately, the efficiency of SOFCs is challenged at all three described stages of device operation. Efficiency losses are caused by high activation energies of oxygen reduction in the cathode compartment and ionic transport through the electrolyte, requiring high operating temperatures (700–1000 1C).6 Moreover anode operation is not stable due to redox cycling at high operating temperatures.7 Additionally, if hydrocarbons are used as fuel, the metallic (Ni) surface of the anode is rapidly covered by a graphitic film (coke formation), which is particularly manifested at high temperatures.8 Much experimental and some theoretical efforts have been made to resolve these problems in the past.6,9–11 Experimental measurements are usually capable of providing the observable characteristics, such as the impact of temperature on current–voltage characteristics or microstructure of the anode cermet. For this reason the atomic level mechanisms of fuel oxidation reactions remain elusive for these techniques, at least to date. In this respect, ab initio modeling of chemical and electrochemical steps can be considered as a unique tool for providing the insights on the cell electrochemistry on atomic level. In this account we focus on the recent progress in modeling of electrochemical oxidations of fuel molecules in the anode compartment of the SOFCs as well as the analysis of electronic structure of anode cermets. A large amount of works has addressed interactions of fuel (e.g. H2, CO, CH4, etc.) with the metallic part of the anode cermet (see recent comprehensive review in ref. 12). These include the studies of fuel oxidation on Ni, which is the most common choice for anode material, as well as other metals, such as Cu,13 Pd14 and Co.15 Oxidation of fuel molecules have been studied on the flat terrace and defect stepped surfaces.16–18 Moreover several groups performed an analysis of fuel interactions with metallic alloys, such as Ni/Sn, Ni/Co, Ni/Cu and Au/Ni.19–22 The theme of this review, however, will concentrate on some relatively recent ab initio studies of electrochemical reactions at the anode triple phase boundary: the point where the fuel molecules meet the metal/oxide (e.g. Ni/YSZ) interface. In the subsequent sections we present the highlights of our main findings on electronic structure of anode cermets and electrochemical reactions, occurring on SOFC anodes. We also provide a critical analysis of our results and discuss relevant findings, published by other groups. The review is organized as follows. In the next section we discuss the atomic models of Ni/YSZ, which have been published in the literature. Then we proceed to the analysis of findings on the electronic structure of Ni/YSZ as well as the Ni/CeO2 interfaces. Based on the differences in electronic structures of these two interfaces, the possible explanation of the different electrochemical performances of these two anodes are provided. In the subsequent section we discuss the published results on kinetic pathways of fuel (predominantly hydrogen) oxidation at the Ni/YSZ TPB. The results of coupled DFT/microkinetic modeling and kinetic Monte Carlo simulations are discussed subsequently. In the conclusion section we discuss the challenges in modeling of metal/oxide interfaces as well as possible directions for future studies of anode electrochemistry using ab initio methods.


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2. Modeling of Ni/YSZ and Ni/CeO2 anode interfaces using DFT 2.1

The models of Ni/YSZ and Ni/CeO2 interfaces

The first attempt of modeling the fuel interactions with the Ni/YSZ anode using first principle methods dates back to the work of Anderson and Vayner, where the cluster calculations have been applied to the analysis of H2 oxidation.23 A rather small model (B15 atoms of YSZ) was used, moreover the Ni part has been modeled by only a single Ni atom. Later studies, undertaken by us, have used larger models of both YSZ and the Ni parts (70 or 140 atoms of YSZ and 18 atom of Ni).24,25 One of these models, containing 70 atoms of YSZ is presented in Fig. 2. Here the YSZ is exposed to the vacuum by a (111) termination, that is generated from the bulk crystal with the lowest number of broken bonds as compared to (100) and (110) terminations. The YSZ used in these models has been constructed by incorporation of pairs of Y atoms and vacancies (one vacancy for each pair of Y) to provide 9 mol% concentration of Y2O3 in ZrO2. The Ni cluster is periodic in one direction. This is desirable as actual Ni components should be continuous through the entire Ni/YSZ network to account for electrical conductivity of the cermet. The Ni cluster is exposed to the gas phase by (111) terminations. Starting from a (100) surface led invariably to a (111) termination during the optimization process (Fig. 2). Two comments have to be made about this property of the employed Ni cluster. First, subsequent calculations have shown that hydrogen oxidation path on the Ni surface of the Ni/YSZ model is very similar to the respective oxidation path on the pure Ni surface.24 This indicates that the employed model should provide reliable results at least for adsorption of light molecules. Secondly, however, it has been

Fig. 2 The model of Ni/YSZ interface (Ni atoms are represented by the dark blue balls, whereas Zr, Y and O are represented by gray, green and red balls). The Ni cluster is obtained by a cut of the fcc Ni bulk cell along the (100) plane (a). Upon mounting on the YSZ substrate, the (100) of Ni is transformed into a (111) face, thus the Ni cluster is exposed to the gas phase by (111) terminations (b). The YSZ substrate is constructed by adding two pairs of substitutional Y and introducing two vacancies, denoted as open circles (b). YSZ is exposed by (111) termination to the gas phase. The model enlarged in y-direction is shown in (c).


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Fig. 3 The model of a Ni/CeO2 anode. Similar to the Ni/YSZ model (Fig. 2), the Ni cluster (dark blue balls) is mounted on top of fluorite ceria (light blue and red balls correspond to cerium and oxygen atoms respectively).

reported recently that upon adsorption of a sulfur atom on the Ni surface, the sites of (111) termination undergo transformation back into a (100) facet.26 This indicates that more energetic interactions with the Ni surface of the Ni/YSZ model may cause a backward reconstruction of the surface to a (100) termination. Thus the model is suitable for analysis of ‘‘weak’’ interactions (e.g. hydrogen adsorption and oxidation), whereas the study of reactions, involving larger molecules (e.g. sulfur adsorption on the Ni surface or oxidation of molecules, such as CH424) may require a larger computational cell. Such a larger system has been used by Cucinotta et al.27 Their model consists of 219 atoms of YSZ and 46 atoms of Ni, where both Ni and YSZ face the gas phase by (111) terminations. The model has been employed for the study of hydrogen oxidation mechanisms, as we shall discuss in the following subsections. A possible deficiency of this model is the absence of periodicity in any horizontal direction on the YSZ plane (judging based on Fig. 1 of ref. 27). More recently An and Turner analyzed the stability of Ni-based nanorod clusters on a YSZ substrate.28 Their calculations favored nanorods, derived from a Oh-nanocluster, over those derived from Ih-nanoclusters. They also found that Ni(6,3) nanorods have a stability, competitive to Oh-derived nanorods. An and Turner further determined a very high reactivity of nanorods toward binding of O, C, and S atomic species. Additionally, alloying of Ni with other metals (Fe, Co and Cu) was found to suppress S and C binding on a metallic surface.28 The models of alternative anode cermets have been proposed as well in the past.29–31 However, in this work we present a detailed analysis to Ni/YSZ and Ni/CeO2 anodes exclusively. The model for Ni/CeO2 has been constructed by simply replacing the YSZ with cerium oxide, as both materials have a fluorite structure.29 The model for Ni/CeO2 is depicted in Fig. 3. 2.2 Analysis of the electronic structure of Ni/YSZ and Ni/CeO2 at the interface To characterize the charge migration between the metal and oxide upon the interface formation, the total charges on Ni and


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the oxide atoms have to be calculated. The Bader analysis is quite instrumental for the calculation of the total charge on atoms,32,33 although other methodologies, such as Mulliken population analysis or the Hirshfeld scheme can be used. However, we find that the Bader approach is more suitable, as it generally predicts higher bond ionicity and thus is more sensitive as compared to Hirshfeld or Mulliken analysis. This is important, as we are interested in monitoring even a small amount of transferred charge in response to electrochemical reaction steps. It has been found that for a Ni–YSZ system, only a small amount of charge (0.1 e) is transferred from Ni to YSZ upon interface formation.14,15 In contrast, a similar analysis for Ni/CeO2 (Fig. 3) shows a transfer of a substantial charge (2 e) to CeO2, which is quite surprising as the oxide here is also stoichiometric.29 It should be noted that a similar effect of charge transfer from the metal atoms (e.g. Pd) to stoichiometric ceria has been reported previously.34 Charging of the ceria substrate and partial reduction of the oxidation state on one cerium atom upon adsorption of one Pd atom on a ceria surface have been observed on the basis of DFT + U calculations.34 Moreover reduction of the cerium oxidation state has been observed as well experimentally, confirming the validity of ab initio modeling.34 Thus one can see that even prior to reactions on the Ni–YSZ and Ni–CeO2 systems, quite different properties for the electronic structure of these two cermets are already observed. The aforementioned differences can be explained on the basis of a PDOS analysis of Ni/YSZ and Ni/CeO2 interfaces.29 The respective energies of the highest occupied orbitals (HOMO) localized on Ni and YSZ for Ni/YSZ interface as well as on Ni and CeO2 for the Ni/CeO2 interface have been evaluated. To simplify the comparison, all three HOMO levels are shown on the same diagram, where HOMO of Ni is used as a reference (horizontal blue lines in Fig. 4). Additionally the energies of the vacancyinduced states (on a pure CeO2 and YSZ without Ni) have been shown (broken red lines on Fig. 4). Moreover the energies of the

Fig. 4 The diagram of energy levels for the Ni/YSZ and Ni/CeO2 interfaces. The HOMO localized on Ni, YSZ and CeO2 are denoted by the blue horizontal lines (the energy scale is provided on the left to indicate the relative values of all displayed energy levels). The Ni HOMO is used as a reference with the relative energy equal to zero. Vacancy induced states for both YSZ and CeO2 are denoted by the red broken lines. The state, introduced upon vacancy of YSZ, approached close to Ni/YSZ interface (see Fig. 5 and the text for details) is denoted by a brown solid line. Additionally, the metal-induced state of ceria is also denoted by a solid brown line.


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Fig. 5 The electronic structure of the surface, close to interface and interfacial vacancies of Ni/YSZ. The additional introduced vacancy is denoted by an open square, whereas stoichiometric vacancy of YSZ, caused by doping with yttria, is denoted by circle. The vacancies of all three types are shown at the left. The degree of localization of d-electrons, localized on the Zr atoms, adjacent to the removed oxygen is shown on the right. The gap states are present for the surface and close to the interface vacancies, whereas no gap state is present for interfacial vacancy.

vacancy-induced state, caused by the vacancy, created near the interface (Fig. 5, middle) in case of Ni/YSZ, and the metalinduced state in case of Ni/CeO2 have been presented as well by brown lines in Fig. 4. These will be discussed in the analysis of oxygen removal from the oxides in the next subsection. The diagram provides an explanation for the miniscule charge transfer from Ni to YSZ. Indeed, although the HOMO of Ni is higher than the HOMO of YSZ, the energy of a vacancyinduced state (which should be occupied by the extra charge, transferred from Ni) is much higher than the HOMO of Ni. Thus the transfer of charge from Ni to stoichiometric YSZ is energetically unfavorable and only a small amount is transferred possibly due to structural transformations in response to the interface formation. The situation is very different for Ni/CeO2. Here the energy of a defect-induced state is actually lower than the HOMO of Ni (Fig. 4). This explains a substantial transfer of charge from Ni to CeO2 (as indicated by the green arrow on Fig. 4), resulting in reduction in the oxidation state of some cerium atoms. Clearly, a correct evaluation of the orbital energy of the metal-induced state in this case is crucial for an adequate description of the electronic properties of the Ni/CeO2 interface. This emphasizes the need for inclusion of Hubbard corrections (DFT + U method), for an accurate evaluation of the metal-induced state. For instance in the case when U = 0.0 eV (thus making DFT + U method identical to regular DFT), no charge transfer and hence no formation of Ce3+ is predicted for the Pd–CeO2 system35 in sharp disagreement with the experimentally observed reduction of the oxidation state of Ce atoms upon adsorption of Pd nanoclusters.34 Moreover, DFT + U method also predicted charge transfer across the Pt/CeO2 interface with partial reduction of cerium oxidation state.36 The challenges, associated with modeling of metal/oxide interfaces, used for SOFC applications, have been discussed


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¨rketun et al.37 These authors as well in a recent work of Bjo stated that for the adequate description of the electronic structure of metal/oxide interface, the metal work function should be lower than the oxide ionization potential and higher than electron affinity of the oxide. This requirement essentially states that the Fermi level (i.e. HOMO orbital) of the metal should be positioned between the energies of HOMO and LUMO of the oxide to avoid non-physical charge transfer between the oxide and the metal. Clearly Ni/YSZ satisfies this criteria (Fig. 4) and charge transfer between Ni and YSZ is almost fully suppressed. However, in the general case, the criteria formulated in ref. 37 cannot be considered valid for any type of metal/oxide interface. Indeed, in case of the Ni/CeO2 interface, the energy of the metal-induced state is below the HOMO of Ni and charge transfer from the metal to ceria occurs even for stoichiometric oxide (Fig. 4, the electron migration from Ni HOMO to ceria metal-induced state is shown by the green arrow). It should be mentioned however that the possibility for the occurrence of charge transfer, describing a valid physical process, was still ¨rketun et al. envisaged in the work of Bjo 2.3 Reduction/oxidation of the oxide in Ni/YSZ and Ni/CeO2 anodes: impact on the charge transfer to Ni 2.3.1 The case of Ni/YSZ. Reduction and oxidation of YSZ as part of the Ni/YSZ cermet have been studied previously by us.24 These processes are essential outcomes of fuel oxidation (anode compartment) and oxygen incorporation (cathode compartment) respectively. With regard to reduction, two types of vacancies have been differentiated: surface- and interface-vacancies.24 A surface vacancy is defined as a vacancy formed by means of removal of surface oxygen, not bonded to Ni. The interface vacancy is formed if the oxygen atom, bonded to Ni is removed (surface and interface vacancies are shown on the left in Fig. 5). For Ni/YSZ it is interesting to monitor the change in charge on Ni and the vacancy formation energy as the surface vacancy is ‘‘approaching’’ the interface.24 The vacancy formation energy (Evac) is defined as: Evac = E(Ni/YSZ + vac) E(O) E(Ni/YSZ) where E(Ni/YSZ + vac) and E(Ni/YSZ) are the DFT calculated total energies of the Ni/YSZ slabs with reduced and stoichiometric YSZ respectively. The E(O) is the energy of a single O atom, evaluated by DFT in a triplet ground state. The vacancy formation energy may be evaluated using other references, accounting for an energy of a single oxygen atom, e.g. the half energy of an oxygen molecule. Indeed the difference of Evac for various sites rather than the absolute values are important for understanding which oxygens are easier to remove from the oxide surface. Although other choices are also valid and can be made, in our works we used the definition presented above to indicate that we are only interested to determine the energy of oxygen extraction from YSZ, rather than to study the possibility of O2 gas formation. Overall, three types of vacancies have been considered: (a) a surface vacancy, infinitely far from the Ni/YSZ interface; (b) a surface vacancy, close to the interface; (c) vacancy at the


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interface (Fig. 5, left). A surface vacancy, formed infinitely far from the interface, has been modeled using a YSZ slab without Ni.24 DFT modeling finds that the Evac does not change as the vacancy ‘‘approaches’’ the interface (vacancy on Fig. 5, middle) and decreases only when the vacancy becomes interfacial (respective values are 210, 210, 185 kcal mol1). The Bader analysis shows that the electronic charge on Ni increases by 0.5 e as the vacancy approaches the interface (Fig. 5, middle) and than by 1 e, when the surface vacancy is transformed into the interface vacancy (Fig. 5, bottom).24 The transfer of charge to Ni upon oxygen removal can be explained, using the diagram of electronic levels, Fig. 4.29 Upon surface vacancy formation, the high energy vacancy-induced state is introduced B3 eV above the YSZ HOMO (Fig. 4). When the vacancy approaches the interface, the energy of respective vacancy-induced state decreases (compare positions of red broken line and brown line for YSZ in Fig. 4). If the vacancy migrates to the Ni/YSZ interface (Fig. 5, bottom), the electrons of the vacancy-induced state can be transferred to a lower energy Ni LUMO orbitals (this transfer is indicated by a green arrow in Fig. 4). This explains the increase of the total charge on the Ni cluster, as observed by the Bader analysis.24 Thus DFT modeling shows that fuel oxidation, which always leads to removal of oxygen form the Ni/YSZ interface, results in accumulation of additional electric charge on the metal (Ni) part of the anode. This additional charge will eventually flow from the anode to the cathode through the external circuit, accounting for electric current under operating conditions. The transfer of charge to Ni can be corroborated by the analysis of charge localization of the vacancy-induced state (Fig. 5, right). The degree of localization of a charge distribution for each electronic band is defined as the projection of the band on the atomic orbitals (s,p,d), where integration is performed in the atomic spheres of the metals (Zr or Y), surrounding the vacant site. One can see a highly localized vacancy-induced gap state for the surface vacancy (Fig. 5, top, right). Then upon approaching the Ni/YSZ interface (Fig. 5, middle, right), the magnitude of the gap state decreases (alongside with the increase of charge on Ni, as calculated by the Bader’s approach). The interface vacancy does not give rise to a vacancy-induced state since the electrons of this state are fully transferred to Ni. This provides the reason of a more favorable vacancy formation at the Ni/YSZ interface as opposed to the pure YSZ surface. We have also evaluated the change of electronic charge on Ni upon YSZ oxidation.24 If the stoichiometric vacancy of YSZ is filled by an extra oxygen atom (formation of the so called YSZ + O), the Bader charge on Ni decreases by 1 e. This process is relevant for the modeling of cathode electrochemistry. Thus simulations reveal that reduction/oxidation of the YSZ results in the accumulation/depletion of charge on the metal (Ni).24 Moreover, using DFT modeling of the electronic structure of the Ni/YSZ interface, the shift of the Fermi level of Ni in response to YSZ reduction/ oxidation has been also monitored (Fig. 6).24 In such modeling the Fermi level of the deep bulk YSZ has been used as a reference. Employing elongated cells of Ni/YSZ we have shown that the local DFT potential is practically indistinguishable for deep atomic


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Fig. 6 The shift of the Fermi level of Ni with respect to the YSZ bulk. The p-state of the ‘‘deep’’ oxygen of YSZ is shown prior to (a) and after (b) oxygen addition at the Ni/YSZ interface. It is clear that the position of the p-state and the edge of the peak (denoted by a solid vertical line) is not affected by oxygen addition. The PDOS of d-states and the Fermi level of the Ni part, also shown by solid vertical line is presented on (c). Clearly there is an downshift of the Fermi level (with respect to the edge of oxygen p-band, (a) and (b)) upon oxygen addition to the interface (d) and an upshift upon oxygen removal (e).

layers of YSZ if an oxygen atom is added to the Ni/YSZ interface.24 Using the upper edge of the oxygen p-band of deep-laying atoms as the reference (Fig. 6), the position of the Fermi level of a Ni cluster has been monitored upon oxygen addition/removal. Fig. 6 shows that if an oxygen is added at the Ni/YSZ interface, the Fermi level of Ni is downshifted to the lower energies with respect to the top of p-band of deep oxygen atoms (Fig. 6d). Similarly, if oxygen is removed from the YSZ (this process consists of oxygen migration from the bulk to the Ni/YSZ interface and subsequent formation of interface vacancy), the Fermi level of Ni is upshifted (Fig. 6e).24 2.3.2 The case of Ni/CeO2. Formation of surface and interface vacancies on Ni/CeO2 (the model in Fig. 3) has been investigated as well.29 DFT calculations revealed that in sharp contrast to the Ni/YSZ interface, formation of the surface vacancy is more favorable for the case of Ni/CeO2 as compared to formation of the interface vacancy. This property can be explained using the diagram of energy levels on Fig. 4. Indeed vacancy formation on a ceria surface gives rise to the vacancyinduced state, which is lower in energy than the HOMO of Ni in


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contrast to Ni/YSZ, where a vacancy-induced state is above the HOMO of Ni (Fig. 4). Therefore the presence of Ni does not result in a more favorable vacancy formation in ceria. Moreover, as has been mentioned in the previous section, some cerium atoms, close to Ni, are already in the reduced state, even prior to the vacancy formation. As a result the energy interfacial vacancy formation is even higher (by 28 kcal mol1) than the respective value for the surface vacancy formation in Ni/CeO2.29 The energy level diagram (Fig. 4) allows for the formulating of a general principle of activity of metal/oxide cermet. If the energy of the vacancy-induced state of the oxide is above the HOMO of the metal, than the oxidation of fuel molecules is more favorable at the metal/oxide interface, resulting in formation of interfacial vacancy (the case of Ni/YSZ). On the other hand, if a vacancy-induced state of the oxide is below the HOMO of the metal, than oxidation of fuel molecules is more favorable on the oxide surface, resulting in formation of surface vacancy (the case of Ni/CeO2). The full electrochemistry of a Ni/CeO2 anode with a YSZ electrolyte has been investigated recently using both experimental and theoretical approaches.30 Experimental measurements have shown that maximum current is observed when most of the cerium atoms (close to 100%) of the oxide adopt lower (Ce3+) oxidation state.30 This is quite surprising as the vacancy formation energy of a fully reduced ceria (213 kcal mol1) is even slightly higher than the respective value on stoichiometric YSZ surface (which is 210 kcal mol1).30 Moreover NEXAFS measurements also revealed that the ceria stoichiometry is much closer to CeO2, rather than to Ce2O3 under SOFC operating conditions.30 It has been shown that the impact of ceria reduction on the upshift of the Ni Fermi level can be interpreted based on a recently proposed three-step mechanism, which is illustrated in Fig. 7.30 First step is the ceria surface reduction as a result of oxidation of fuel ˜ (in this molecule. Denoting a general fuel molecule as F analysis the specific type of fuel molecule is not important), ¨ger–Vink notations as: this step is expressed using Kro ~ þ O þ 2Cesurf )" FO ~ þ V CeO2 þ 2Ce0 "F CeO2 surf O¨ Two cerium atoms in the reduced oxidation state are formed (these are denoted as Ce0surf ). The position of the Fermi level on Ni, CeO2 and YSZ (which is used as an electrolyte) has been monitored as well for each discussed reaction step (Fig. 7). Upon formation, the vacancy migrates through ceria towards the electrolyte (YSZ). The ceria reduction results in a slight downshift of both ceria and the Ni Fermi levels with respect to their positions prior to the vacancy formation (those are used as references). The second step includes migration of a vacancy (formed as a result of step 1) through ceria bulk into YSZ across the ceria/YSZ interface (Fig. 7). The total energy of the system is found to decrease when a vacancy migrates from ceria to YSZ. Moreover, hopping of a vacancy to YSZ also causes an increase of a negative charge on ceria (with concomitant decrease of negative charge on YSZ), as is attested by the Bader’s approach. Additionally the second step leads to restoration of ceria stoichiometry back to CeO2. Although stoichiometry of ceria


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Fig. 7 The three-step mechanism of fuel oxidation for the case of Ni/CeO2 anode and YSZ electrolyte. Each step occurs in the part of the figure, highlighted by the green, broken line rectangular, with respective step number provided in parenthesis. For description of each step, see the text. The position of the Ni, CeO2 and YSZ (ZrO2) Fermi levels are shown prior to and after each step, which are indicated by the numbers in parenthesis.

is restored, the oxidation state of a pair of cerium atoms is still reduced as is indicated by the characteristic occupied f-state in ¨ger–Vink notations this PDOS of these cerium atoms. Using Kro step is denoted as: ZrO2 0 2 VOCeO þ 2Cebulk þ O ZrO2 ) OCeO2 þ 2Cebulk þ VO¨ ¨

Upon restoration of the ceria stoichiometry, the Fermi level of both Ni and ceria is found to undergo an upshift with respect to the reference levels. We find that the energies of these Fermi levels will increase with migration of more vacancies through the ceria–YSZ interface. As the energy of a Fermi level of Ni will increase, the electrons will eventually flow from Ni to the cathode through the external circuit. Depletion of electrons from Ni will cause hopping of electrons from ceria


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(which is both stoichiometric and charged negatively in response to the step 2). As a result, the cerium atoms in a reduced oxidation state are again transformed back into regular cerium atoms. This third step is denoted as: 0 0 O CeO2 þ 2Cesurf ) OCeO2 þ 2Cesurf þ 2e

From this point, the process can restart from step one. Thus using DFT modeling it has been shown that in contrast to the Ni/YSZ interface, where vacancy formation results in the transfer of charge to Ni and the upshift of the Ni Fermi level, a more complicated three-step mechanism has to be considered for the case of Ni/CeO2 anode. Using DFT modeling we have also provided an explanation for the high activity of Ni/ceria cermet, when cerium atoms are in a low oxidation state. 2.4 Hydrogen oxidation reactions on the Ni/YSZ interface: insights from DFT modeling Hydrogen oxidation at the Ni/YSZ can be subdivided into the three groups of reaction steps: (1) hydrogen adsorption either on Ni or YSZ; (2) spillover exchange reactions of adsorbed species between Ni and YSZ; (3) water formation and desorption.24 Each of these steps can include various possible pathways. For instance hydrogen adsorption can occur on either the Ni or YSZ surfaces, whereas adsorbed hydrogen ions can migrate from Ni to YSZ or in the opposite direction (hydrogen spillover). Moreover, oxygen atoms may also migrate from YSZ to Ni (oxygen spillover). Possible scenarios of the three reaction steps are provided below: mH2 2 *HNi + *HNi

(1a)

mH2 2 *HYSZ + *HYSZ

(1b)

*OYSZ 2 *ONi

(2a)

*HNi 2 *HYSZ

(2b)

*OHYSZ 2 *OHNi

(2c)

*HNi + *ONi 2 *OHNi

(3a)

*OHNi + *HNi 2 *H2ONi 2 mH2O

(3b)

*HYSZ + *OYSZ 2 *OHYSZ

(3c)

*OHYSZ + *HNi 2 *H2OYSZ 2 mH2O

(3d)

Understanding of the hydrogen oxidation pathways is crucial for modeling of the SOFC operation and calculations of observable manifestations such as the dependence of voltage– current characteristics on the H2 and H2O partial pressures. Using a kinetic modeling approach Bessler and coworkers performed several studies of hydrogen oxidation reactions, fitting the results of their modeling to the measured polarization resistances and Tafel plots for pattern anodes.38–40 In this study the best fit to experimental measurements is achieved if hydrogen spillover reactions (from Ni to YSZ) with subsequent water formation on the YSZ surface are adopted for a description of hydrogen electrochemical oxidation.40 The process essentially includes steps (1a) + (2b) + (3c) + (3d) from the reaction list given above. Assuming other scenarios, such as oxygen or hydroxide spillovers ((2a) and (2c) respectively), were not able to provide a


good fit to the measured data.40 Therefore it has been proposed that a mechanism associated with hydrogen spillover from Ni to YSZ is the most relevant for the hydrogen oxidation reaction. It should be noted that another work of Rossmeisl and Bessler, based on ab initio DFT calculations, led to a different conclusion.41 In this case oxygen adsorption energy correlates quite well with the activity of a wide range of metal catalysts, whereas no such correlation was observed for the hydrogen adsorption energy.41 Therefore it was concluded that hydrogen oxidation, which includes an oxygen spillover step (2a), is a more realistic pathway. Kinetic modeling of hydrogen electrochemisty has also been performed by Goodwin et al., who claimed that the mechanism, associated with hydroxyl spillover from YSZ to Ni provided the best fit to the experimental measurements (the included steps were (1a) + (2b) + (2c) + (3b)).42 Therefore, no consensus exists on a key mechanism of the hydrogen oxidation reaction. Clearly, hydrogen oxidation on the Ni/YSZ interface of the SOFC anode had also to be addressed by DFT calculations. As already mentioned, in the first attempt of Anderson et al. a very small model of Ni/YSZ was used for such a study.23 Therefore hydrogen oxidation pathways had to be revisited using periodic DFT calculations and larger models of both the Ni and YSZ parts. Such a study has been performed by us.24,25 The two systems, namely Ni/YSZ and Ni/YSZ + O, where an extra oxygen atom is transported from the bulk of the electrolyte to the metal/oxide interface, have been considered. We have shown that although fuel oxidation is more favorable on a Ni/YSZ + O interface, the overall energy of the reaction is higher for this model, as oxygen migration to the interface increases the enthalpy by 25–30 kcal mol1.25 Therefore we limited the further analysis to the study of hydrogen oxidation on the Ni/YSZ interface.25 With regard to the first group of reaction steps (hydrogen adsorption, steps (1a) and (1b)) the ab initio calculations clearly show that hydrogen adsorption is only possible on a Ni surface of the cermet (exothermic by 22 kcal mol1), whereas adsorption on the YSZ surface is prohibitively costly (endothermic by 30 kcal mol1).24 As for the second group of reaction steps, we have demonstrated that sequential spillover of two hydrogens from Ni to the Ni/YSZ interface with subsequent oxidation and formation of the interface vacancy corresponds to the most favorable free energy profile (the reaction steps are shown in Fig. 8) as compared to other scenarios, including oxygen or hydroxyl spillovers to Ni.25 Moreover, initial hydrogen migration from the Ni/YSZ interface to the surface of YSZ with subsequent oxidation is found to be very unfavorable energetically. The latter finding is not that surprising as we have established that interfacial vacancy formation is more favorable than formation of the surface vacancy. This work also demonstrated that oxidation of fuel molecules at the Ni/YSZ interface and YSZ surface should be differentiated for future kinetic modeling of the electrochemical reactions.25 We have also established that the final step of water desorption from the interface is electrochemical in the sense that it is associated with charge transfer from YSZ to Ni. All preceding steps are not associated with charge transfer according to our Bader analysis.25


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ions through the electrolyte and hydrogen oxidation. Wang et al. determined that oxygen reduction is the dominant step, followed by oxygen ion migration through the electrolyte with hydrogen oxidation at the anode being the third dominant process.44 A potential mechanism of hydrogen oxidation, including migration of protons through the Ni bulk into the YSZ has been analyzed recently for a Ni(100)/YSZ(100) model with the help of DFT calculations.45 This study revealed that migration of hydrogen on the Ni surface is associated with much lower barriers, as compared to the migration pathways including penetration of protons into the bulk of Ni and YSZ. Therefore hydrogen oxidation should most likely include surface reactions, whereas reaction steps, including the bulk phased should be disfavored.

Fig. 8 Hydrogen oxidation mechanism at the Ni/YSZ TPB. Stages include: (a) hydrogen on the Ni surface; (b) spillover of one hydrogen to the oxygen of the Ni/YSZ interface; (c) formation of a water molecule at the Ni/YSZ interface; (d) desorption of water.

Hydrogen oxidation has been investigated as well using DFT modeling by Cucinotta et al.27 These authors also found that hydrogen spillover from Ni to the Ni/YSZ interface is a more favorable reaction path as compared to the scenarios involving oxygen or OH spillover to Ni.27 Moreover it has been shown that water molecules, adsorbed on the YSZ surface (rather than Ni/YSZ interface) can facilitate oxidation of interfacial hydrogen. The mechanism includes concerted migration of interfacial OH to the hydrogen, spilled over to the interface, mediated by the surface hydroxyl of the adsorbed water molecule. Moreover the energy can be even further decreased if the formed interfacial vacancy is filled by the bulk oxygen. Hydrogen oxidation reactions have been studied as well using a combined DFT/microkinetic modeling approach by Ammal and Heyden.43 In agreement with previous reports, hydrogen oxidation via the hydrogen spillover step to the interface was found more favorable than the mechanisms, involving O or OH spillover to Ni.43 In contrast to Cucinotta et al., calculations of Ammal and Heyden have shown that interface vacancy formation is more favorable than bulk vacancy formation. Therefore according to Ammal and Heyden, water formation at the interfaces is not facilitated by filling of the vacant oxygen site (formed as a result of OH migration on atop Zr position) by the bulk oxygen. Moreover, half-cell microkinetic modeling (limited to the analysis of oxygen migration through the electrolyte and hydrogen oxidation at the anode) revealed that at low temperature (o1300 K) oxygen migration through the electrolyte is a rate-limiting step in the SOFC electrochemistry, whereas at high temperatures (>1300 K), hydrogen spillover becomes a rate-limiting step.43 These findings are also in agreement with kinetic Monte Carlo simulations by Wang et al.,44 who performed a full cell study, including oxygen reduction at the cathode, migration of oxygen


3. Summary of DFT modeling of various metal/oxide anode cermets In spite of an obvious need for a better understanding of fuel oxidation at the TPB of the anodes, the applications of ab initio calculations to the study of such reactions have emerged only within the last five years. In part, the lack of interfacial reaction studies can be explained by more complex atomic models required in comparison to those needed for a description of fuel oxidation either on the metal or oxide surfaces. Nevertheless, the published works have already provided additional insights, which would not be possible if analysis of fuel interactions would be limited to a single metal or oxide surface. This includes finding that hydrogen oxidation is most favorable at the Ni/YSZ interface rather than on Ni or the YSZ surfaces. To date this conclusion is shared by the groups, who applied DFT calculations to the analysis of hydrogen oxidation on Ni/YSZ anodes. Moreover DFT calculations have been used as well for interpretation of a more favorable hydrogen oxidation at Ni/YSZ interface as compared to YSZ surface, using the electronic structure analysis (Fig. 4). Additionally DFT modeling demonstrated a clear difference in electronic structure and catalytic properties of Ni/CeO2 and Ni/YSZ interfaces. In agreement with experimental findings, DFT calculations have shown that in contrast to Ni/YSZ, fuel oxidation is actually favorable on the oxide (CeO2) surface in case of the Ni/CeO2 anode.29 Again, using electronic structure analysis (Fig. 4) it has been shown that vacancy formation in ceria results in introduction of a vacancy induced state, which is lower in energy than the Ni Fermi level, thus explaining that the reaction on a ceria surface is at least as favorable as the metal/oxide interface in a sharp contrast to Ni/YSZ anode. Moreover a complex three-step mechanism of fuel oxidation in a Ni–CeO2–YSZ system has been proposed by DFT.30 A peculiar observation of the highest activity of the fully reduced ceria has been also interpreted on the basis of DFT analysis of Ni/CeO2 and CeO2/YSZ interfaces. Very recently DFT calculations have been applied to the study of other metal/oxide interfaces, relevant for the modeling


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of SOFC anodes. For instance the role of doping of zirconia with various aliovalent metal ions in the sulfur tolerance of Ni part of the anode have been analyzed using DFT.26 It has been shown that doping of zirconia with Sc2O3 would result in higher energy of sulfur adsorption on the Ni surface, explaining experimentally observed higher sulfur tolerance of the scandia-doped anode, as compared to a conventional Ni/YSZ.26 Another recent work based on DFT modeling of sulfur removal from the Ni/YSZ has been reported recently.46 The authors of ref. 46 have shown that sulfur adatom is not stable at the Ni/YSZ interface if its capture is not facilitated by interfacial vacancies. However if present, the interfacial vacancy traps the S adatom, which is hard to remove via the hydrogen sulfidation reaction (formation of H2S). A DFT study of hydrogen oxidation on the Ni/BaZrO3 interface has been reported recently.47 It has been determined that hydrogen adsorption is very favorable at the TPB of the Ni/BaZrO3 anode, whereas subsequent migration of protons into the perovskite bulk results in the enthalpy increase by about 1 eV.47 Recently we performed a DFT study of the coke-tolerant Ni/BaCe1xYxO3d anode,31 using it as a prototype of Ni/BaZr0.1Ce0.7Y0.2xYbxO3d anodes for which resistance to coke formation in humidified (3 vol% of H2O) atmosphere has been observed experimentally.48 We have demonstrated that carbon removal from the TPB of a Ni/BaCe1xYxO3d anode via interactions with adsorbed water molecules is significantly more favorable than from conventional Ni/YSZ anode.31 Similarly, carbon oxidation with the help of an adsorbed water molecule has been demonstrated in a DFT study of Ni anodes with BaO nanoclusters in full agreement with experimentally observed coke tolerant of Ni/BaO anodes in a humidified atmosphere.49 Additionally, DFT modeling helped to unravel a peculiar increase of anode activity in H2/H2S atmosphere at low temperatures (T = 500 1C).50 Again an analysis of oxide reduction close to the interface with the metal was required for interpretation of the experimentally observed activity boost.50

4. Possible directions of future work To end this account we wish to discuss possible directions of future DFT modeling of metal/oxide anode cermets. First, the models of interfaces used in the published works to date are constructed without any attempts of validation of their atomic structure by experimental measurements. Indeed the pathway of fuel oxidation would in principle depend on such structural properties as dopant concentration on the YSZ surface, bond topology at the Ni/YSZ interface, presence of structural interfacial defects, caused by the lattice mismatch and etc. Although validation of the full Ni/YSZ model does seem to be realistic in a near future, recent experimental findings, for instance on dopant segregation in YSZ has to be incorporated in the construction of future models of Ni/YSZ interface.51 Secondly, current studies of fuel oxidation on the metal/ oxide interface are performed without taking into account the change of the Ni potential under experimental conditions.


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Theoretical frameworks, which allow analysis of molecule interactions with the metal surface under applied voltage has been proposed in the past.52–55 It should be noted that the effect of the applied field was not negligibly small and found to affect the energy pathways of molecular interactions with the metal surface. A similar analysis for the case of metal/oxide cermet still needs to be performed. Moreover explicit calculations of reaction free energy, as a function of chemical potentials of reactant and products should also be taken into account in the future studies. Such data would be very useful for the microkinetic or kinetic Monte Carlo modeling of experimentally observed current/voltage dependencies, taking applied potential, partial pressure of involved gases and temperature as parameters. The well known limitations of DFT, such as poor accuracy in evaluation of the electronic gaps and positions of defectinduced energy levels, may also cause a problem in the modeling of metal/oxide interfaces. For instance the inaccurately defined position of the vacancy-induced state may be the reason for the inadequate modeling of electronic charge transfer through the interface upon oxygen vacancy formation. Moreover, relative positions of the Fermi levels of a metal and an oxide (the valence band offset) have to be calculated precisely for correct modeling of the electrochemical reactions. One possible solution to these problems might be a recourse to more precise hybrid DFT functionals, although computational limitations (much higher computational cost as compare to the local DFT) may render this approach impractical at least for the near future. As DFT modeling of electrochemical reactions on the metal/ oxide interface is already capable of providing useful and nontrivial insights, the future research should also focus on proposing new avenues for development of more durable and efficient anodes. This would include a design of coke and sulfur tolerant anodes and the anodes stable to redox cycling under operating conditions. For instance in our recent work on coke tolerant Ni/BaCe1xYxO3d anodes,31 we were able to formulate a general principle for selecting of an oxide with higher ability of water capture, which is crucial for the development of coke tolerant anodes in the wet atmosphere. In summary, DFT modeling proved to be very effective in the analysis of the mechanisms of fuel oxidation on the Ni/YSZ and Ni/CeO2 anodes. The energy pathways of fuel oxidation and the charge transfer mechanisms have been studied. Moreover the differences in electrochemical properties of Ni/YSZ and Ni/CeO2 cermets have been interpreted by comparison of electronic structure of these two interfaces. We have also discussed the deficiencies of the current modeling approaches and presented possible new directions for the future research in this exciting area.

Acknowledgements This research was supported through funding to the NSERC Solid Oxide Fuel Cell Canada Strategic Research Network from


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the Natural Science and Engineering Research Council (NSERC) and other sponsors listed at www.sofccanada.com. Tom Ziegler thanks the Canadian government for a Canada Research Chair in theoretical inorganic chemistry.

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Density functional theory in the solid state.

YSZ anodes in solid oxide fuel cells.

Detailed Multi-dimensional Modeling of Direct Internal Reforming Solid Oxide Fuel Cells.

Nanotubular array solid oxide fuel cell.

In situ optical studies of methane and simulated biogas oxidation on high temperature solid oxide fuel cell anodes.

Revealing the photorelaxation mechanism in a molecular solid using density-functional theory.

Tailoring the Microstructure of a Solid Oxide Fuel Cell Anode Support by Calcination and Milling of YSZ.

Boosting properties of 3D binder-free manganese oxide anodes by preformation of a solid electrolyte interphase.

Modeling the Photoelectron Spectra of MoNbO2(-) Accounting for Spin Contamination in Density Functional Theory.

Nanocrystalline ceria coatings on solid oxide fuel cell anodes: the role of organic surfactant pretreatments on coating microstructures and sulfur tolerance.

Enhanced sulfur tolerance of nickel-based anodes for oxygen-ion conducting solid oxide fuel cells by incorporating a secondary water storing phase.

X-ray micro Laue diffraction tomography analysis of a solid oxide fuel cell.

Density functional theory of electrowetting.

Insight into the structure and functional application of the Sr0.95Ce0.05CoO3-δ cathode for solid oxide fuel cells.

carbon nanotube-coated scaffold.

Solid oxide fuel cell interconnect design optimization considering the thermal stresses.

Multi-functional reactively-sputtered copper oxide electrodes for supercapacitor and electro-catalyst in direct methanol fuel cell applications.

A novel approach for analyzing electrochemical properties of mixed conducting solid oxide fuel cell anode materials by impedance spectroscopy.

Micro-tubular solid oxide fuel cell based on a porous yttria-stabilized zirconia support.

Density functional theory study of the oligomerization of carboxylic acids.

Density-functional theory of the electronic structure of molecules.

Nanodrop on a smooth solid surface with hidden roughness. Density functional theory considerations.

First-time electrical characterization of nanotubular ZrO2 films for micro-solid oxide fuel cell applications.

Periodic subsystem density-functional theory.