Abstract
To reduce global warming, many countries are shifting to sustainable energy production systems. Solid oxide electrolysis cells (SOECs) are being considered due to their high hydrogen generation efficiency. However, low faradaic efficiency in scaling SOEC technology affects costs and limits large-scale adoption of hydrogen as fuel. This review covers SOECs’ critical aspects: current state-of-the-art anode, cathode, and electrolyte materials, operational and materials parameters affecting faradaic efficiency, and computational modeling techniques to resolve bottlenecks affecting SOEC faradaic efficiency.
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Introduction
During the Industrial Revolution, overdependence and overutilization of fossil fuels led to an increase in greenhouse gas (GHG) emissions, such as carbon dioxide, methane, etc. Due to this increase, the average global temperature also has increased by 1.2 °C since 1880—with the greatest changes coming in just the late twentieth century1. In order to tackle this issue, many countries are reviewing energy transition strategies to shift towards carbon neutrality1,2. For instance, almost all members of the United Nations signed the Paris Agreement in 2016 to keep the average global temperature rise to below 2 °C by 2100 as compared with pre-industrial levels and pursue efforts to limit this increase to just 1.5 °C3. Consequently, many countries are transitioning towards clean and low-carbon energy to promote decarbonization1.
Hydrogen (H2) has received significant attention as a clean energy carrier from both researchers4 and policy makers5, and is an important part of the energy mix in a low-carbon energy future6. Green H2 is the cleanest form of H2 with zero carbon emissions, which is produced using renewable energy1. An increased use of renewable energy is important to achieve a sustainable green H27. Currently, renewable energy H2 production technologies include water electrolysis and biogas steam reforming. Electrolysis using wind- or hydro-generated electricity is considered to be one of the best green H2 production sources8. Electrolysis can be performed using three types of electrolysis cells: (1) alkaline electrolysis cells (AECs); (2) proton exchange membrane (PEM) electrolysis cells; and (3) solid oxide electrolysis cells (SOECs)9. Among these, SOECs can generate H2 with the highest efficiency10,11,12. Despite the merits of SOECs, the major drawbacks in scaling SOEC technology are their low faradaic efficiency and high energy costs—or costs per kilogram of H2—that limit the large-scale adoption of H2 as a fuel.
This current review focuses on various operating and materials factors affecting the faradaic efficiency of SOECs, the recent advances in the computational materials science aimed to model various SOEC intrinsic processes, and the needed future computational developments that would complement the ongoing experimental efforts and generate new ground-breaking knowledge required to improve the SOEC faradaic efficiency. In particular, SOEC electrolyte materials are investigated deeply.
Materials used in the SOECs
In this section, the state-of-the-art materials for electrodes (e.g., cathode and anode) and electrolytes (e.g., oxygen-ion conducting and proton-ion conducting) are reviewed. The first subsection describes the advanced electrode materials, while the second subsection provides an update on recent developments in common electrolyte materials.
Electrodes
In SOECs, the selection of two electrodes—anodes and cathodes—is a vital parameter in determining the overall performance of H2 gas production. Electrodes in SOECs should have the following properties: (a) high ionic conductivity for allowing geometric extension of reaction zone in the entire volume of electrode; (b) high electronic conductivity to improve collection of electrons; (c) a highly porous microstructure for promoting the diffusion of gas, which is a fundamental parameter for oxidation/reduction reactions that ultimately results in increasing the efficiency of SOECs; and (d) high catalytic activity. The active reaction site occurs at the triple-phase boundary, which is the interface between the electronic conductor, the ionic conductor, and the gas diffusion pore10,11,12.
The most common cathode materials that are used in SOECs are nickel (Ni)-based composite materials with yttria (Y2O3)-stabilized zirconia (ZrO2) (YSZ) and yttrium (Y)-doped barium cerate zirconate (BCZY)10,11,12. The main advantages in using Ni-based cathode electrodes are their high electronic conductivity, that they are excellent reforming catalysts, and that they are an electrocatalyst for the electrochemical reduction of water. The Ni-composite electrode acts as a fabrication of supported cell geometry, which allows for the formation of a thin electrolyte, a reduction in ohmic losses, lowering the activation potential, and promoting the electrochemical activity during SOEC operation. Cathode electrode materials are chosen based on the following properties: (1) optimal properties at high temperatures; (2) chemical stability in reducing atmosphere; and (3) a minimal mismatch of thermal and chemical expansion coefficients relative to those of the electrolyte material to prevent mechanical stress. Despite the investigation of different cathode materials, no material exists to meet all of these requirements. One of the most promising strategies for improving stability and electrochemical catalytic activity is the addition of doping materials like manganese (Mn), neodymium (Nd), iron (Fe), and chromium (Cr).
Commonly used anode materials are perovskite (ABO3)-based materials10,11,12. The A-site is occupied by large trivalent lanthanide ions (e.g., La3+, Pr3+, Sm3+, Gd3+) and is substituted by divalent alkali earth ions (e.g., Ca2+, Sr2+, Ba2+) in order to increase the electronic and ionic conductivities13. The B-site is substituted by small trivalent or tetravalent three-dimensional (3D) transition metal ions (e.g., Mn3+/4+, Fe3+/4+, Co3+/4+, Ni3+/4+). Strontium-based lanthanum manganite (LSM) is the most commonly used anode electrode material. LSM has a thermal expansion coefficient close to one of the electrolytes, which stabilizes the cell mechanism. LSM is known to have a high electronic conductivity, but a poor ionic conductivity. Other perovskite-based materials—such as double-perovskites and Ruddlesden-Popper (RP)-based materials—also are widely used as anode electrode materials due to their high potential stability and improved performance under a redox atmosphere. The RP-based materials show a higher oxygen-ion conductivity than regular perovskite materials10,11,12. In double-layered perovskite materials (e.g., AA0B2O5+δ), the A-site is normally occupied by a trivalent lanthanide ion and the A0-site by barium (Ba) or strontium (Sr), while the B-site is a mixture of the first-row transition metal ions.
Electrolytes
The most important electrochemical system component is the electrolyte. It has a large impact on cell performance through its contribution to the ohmic internal resistance. The ideal electrolyte used in SOECs should possess a high ionic conductivity, a negligible electronic conductivity, a good thermal and chemical stability, a matching thermal coefficient, a lower activation energy, a high density, and a minimum reactant crossover13.
SOECs can be further subdivided into two categories—oxygen-ion conducting cells and proton-ion conducting cells, as shown in Fig. 1. The most distinct difference between the proton-ion and oxygen-ion SOEC is the electrolyte-conducting ion, which further results in different working principles. In the case of the proton-ion conducting electrolyte, H+ ions/protons are transported from the anode electrode to the cathode electrode, where H2 gas is produced. In the case of the oxide-ion conducting electrolyte, the oxygen ions migrate from the cathode side of the cell to the anode side. Steam is fed to the anode side in the case of the proton-ion conducting electrolyte; however, for the oxygen-ion electrolyte, it is fed to the cathode side. There are several advantages of using a proton-ion electrolysis cell, such as dry and pure H2 gas that can be directly produced at the cathode side of the fuel, which further simplifies the system and reduces operational costs. Compressed H2 can be directly produced through increasing the operating pressure. Thus, in-situ electrochemical compression can potentially increase the total energy efficiency14. The operating temperature of the proton-ion electrolysis cell is around 673 to 973 K, which is lower than that of the oxygen-ion electrolysis cell of 973 to 1273 K. The lower operating temperature leads to a lower cost in sealing materials and interconnection, which increases the overall durability of the cell. A detailed description of the different oxygen-ion and proton-ion electrolyte materials is provided in ref. 15.
a A proton-ion conducting electrolyte; and b an oxygen-ion conducting electrolyte.
Oxygen-ion conductivity arises due to the mobility of oxygen point defects, which can be oxygen vacancies or the transport of oxygen in the positions of the interstitials via a hopping mechanism16. Zirconia- and ceria-based materials are widely investigated as potential candidates for the oxygen-ion conducting electrolyte. In the case of ceria-based material, partial electronic conductivity at elevated temperatures and a reduced atmosphere occurs, which is due to the reduction of the Ce4+ to Ce3+ ions. Such partial electronic conductivity causes a decrease in faradaic efficiency17. YSZ is commonly used as an oxygen-ion conducting electrolyte because it can be used in high temperature applications16. YSZ is developed by using cubic fluorite structure yttria (Y2O3) as a dopant within the zirconia (ZrO2) structure. Despite having excellent conductivity during SOEC operation, the degradation of material and a reduction in the performance of SOEC hindered the further investigation and development of YSZ material. The degradation issues and low ionic conductivity of YSZ has led to the development of scandia (Sc2O3)-stabilized zirconia (ScSZ) material, which shows higher ionic conductivity than YSZ at intermediate temperatures. In addition, the current density of ScSZ-based electrolytes is approximately twice that of the YSZ-based electrolytes18. However, the cost of Sc in addition to small Sc ion size would lead to diffusivity and separation into impurity phases19. LaGaO3-based materials have shown high conductivity and a high transfer number of O2− ions, thus making them a promising electrolyte candidate at intermediate temperatures18. However, the incompatibility of the Ni-based cathode and LaGaO3-based electrolyte is a major issue in LaNiO3 formation20.
In summary, due to the high operating temperatures of oxygen-ion conducting electrolytes, the degradation of the cell occurs at a faster rate. Even the current state-of-the-art YSZ oxygen-ion conducting electrolyte suffers degradation in the high corrosive environment of electrolysis and shows a lower ion conductivity and lower catalytic activity at lower operating temperatures17. Most of the delamination failure occurs at the interface region between the cathode electrode and the electrolyte, which is primarily caused due to the mismatch of the thermal expansion coefficient of the materials20. For this reason, the trend has shifted towards the proton-ion conducting electrolyte materials, which offer more advantages as mentioned earlier.
Due to their easy synthesis, high thermal stability, and low cost, perovskite crystal structure (ABO3)-based proton-ion conducting electrolytes, as observed in Fig. 221, have gained more attention than fluorite (AO2) and pyrochlore (A2B2O7)-based electrolytes22. In a typical perovskite structure, the A-site is occupied by an alkaline-earth element (e.g., Ba, Sr, Ca), while the B-site is occupied by a tetravalent element—usually Ce or Zr. For an electrolyte, protonation is required, which increases the number of charge carriers while still keeping the material neutral. Thus, to promote protonic conductivity, it is important to dope the B-site with trivalent elements (e.g., Y, Nd, Sm, Yb, In, Eu, Gd, etc.). Doping with trivalent elements leads to the formation of oxygen vacancies that play a crucial part in the formation and mobility of protons. Protons are transported through three major steps: (1) dissociative adsorption; (2) Grotthuss mechanism; and (3) rotational diffusion. With dissociative adsorption, oxygen defects are created after the addition of trivalent elements to keep a neutral charge in the system. For every two dopant atoms, one oxygen vacancy is created. In the presence of water vapor, these oxygen vacancies are occupied by the hydroxyl ions that are formed by dissociation of water into H2 (protons) and hydroxide ions, as shown in Fig. 3. With the Grotthuss mechanism, the mobile protons or the H2 ions interact to form a weak bond with oxygen atoms, as seen in Fig. 4. With rotational diffusion, the protonic defect rotates and reorients itself to facilitate the transport of protons from one oxygen atom to the neighboring oxygen atom16, as shown in Fig. 4.
In a Perovskite crystal structure (ABO3), red spheres represent A-site cations, the grey sphere is the B-site cation, and the blue spheres are oxygen ions.
Blue sphere represents oxygen ions, grey spheres are the B-site cations, and orange-colored spheres are the doping elements.
(Adapted with permission from ref. 15 under Copyright Clearance Center Inc).
The most commonly investigated proton-ion conducting electrolyte materials are barium cerate (BaCeO3) and barium zirconate (BaZrO3). Among these two materials, BaCeO3 has a high proton conductivity23,24,25; however, it also has a low chemical stability, which makes it unsuitable for applications. On the other hand, barium zirconate-based electrolytes exhibit good chemical stability under carbon dioxide and a water-containing atmosphere. However, due to the refractory nature of BaZrO3, high sintering temperatures (e.g., >1600 °C) are required, which makes the fabrication of this material highly unfeasible.
In general, further research and developments in proton-ion conducting electrolytes can make the ideal choice as the electrolyte materials, which will have high ionic conductivity, negligible electronic conductivity, and good thermal and chemical stability.
Factors affecting the efficiency of SOEC
A much-desired electrolyte material property is negligible electronic conductivity. Unfortunately, non-negligible charge carriers—other than protons—are known to exist26,27,28,29. Fig. 5 schematically illustrates the charge carriers in a proton-ion conducting electrolyte. The existence of partial charge carriers—such as an oxide-ion, hole, and electron—decreases the protonic transfer number and overall efficiency of the cell. In the oxidizing environment, the formation of electron holes occurs, and the presence of holes causes the internal leakage current, which further results in a decrease of the faradaic efficiency29,30,31,32.
A schematic representation on the existence of partial charge carriers.
Iwahara et al.33 reported that the faradaic efficiency of the proton-ion conducting electrolyte is between 50 and 95%. Babiniec et al.34 measured a faradaic efficiency of only 32% at 100 mA and 973 K for the cell having a thin BCZY27 electrolyte layer and a Ni-BCZY27 fuel electrode. Using BZY20 as the electrolyte material, the faradaic efficiency ~63.6% at 1.3 V and 873 K was reported by Lei et al.35 Details of more faradaic efficiencies with a variety of electrode and electrolyte materials can be found elsewhere36. Low faradaic efficiency decreases the overall performance of the electrolysis cell. In order to tackle this issue, studying different factors influencing the efficiency is paramount.
An important factor in increasing faradaic efficiency is to reduce the electronic conductivity of the electrolyte material. The effects of temperature, O2 partial pressure, H2O partial pressure, chemical composition, and external current (externally applied voltage) on the electronic conductivity have been studied thoroughly in the literature32. In addition to the above factors, additional strategies are discussed that help in increasing the faradaic efficiencies.
Temperature
The activation energy for the electronic conductivity is greater than the oxygen-ionic and protonic conductivities37,38. Thus, as the temperature increases, a significant increase in the electronic conductivity is observed. To reduce the unwanted effects of electronic contribution, lowering the operational temperature of the electrolysis cell can be the best option to consider39. This strategy is an ongoing process by developing new electrolyte materials38,40,41,42, novel thin film technologies43,44,45, and an innovative highly active electrode system46,47,48. It has been demonstrated theoretically and experimentally that decreasing the operating temperature decreases the electronic conductivity for BZY, BCZY, and BCY materials39,49. In addition, lowering the operational temperature helps in maintaining the low ohmic resistance of the electrolyte and low polarization resistance of the electrode.
Water and oxygen partial pressure
Under humidifying atmosphere, protons are formed due to the dissociation of water. The oxygen vacancies (\({V}_{o}^{..}\)) that were previously generated by acceptor doping are occupied by the hydroxide ion, thereby forming a protonic defect (\({{OH}}_{o}^{.}\)) which leads to the formation of a weak bond between proton and the regular lattice oxide-ion, as observed in Fig. 2. The hydration reaction is as follows32,50:
While in an oxidizing atmosphere, the oxygen occupies the \({V}_{o}^{..}\), which leads to the appearance of electronic holes (\(\dot{h})\). The redox reaction is as follows32,50:
Heras-Juaristi et al.49 investigated the partial conductivity of oxygen-ion (\({\sigma }_{v}\)), proton (\({\sigma }_{H})\) and electron hole (\({\sigma }_{h})\) as a function of partial pressure of water (pH2O) in the BCZY27 material, as observed in Fig. 6. At high temperature (800 °C) and high partial pressure of oxygen (pO2 = 0.2 atm), as shown in Fig. 6a, \({\sigma }_{h}\) was the main contributor towards the total conductivity (\({\sigma }_{{total}})\) of the material. While at lower pO2 (~10−5 atm), as seen in Fig. 6b, the contribution of \({\sigma }_{h}\) towards the \({\sigma }_{{total}}\) decreases. This means that the high pO2 leads to larger electronic conductivity, which can be explained by Eq. 2, where higher pO2 is thermodynamically favorable for the formation of more electrons. In all four cases, as shown in Fig. 6a through Fig. 6a, a decrease in \({\sigma }_{h}\) with an increase in the pH2O is observed, which is due to the suppression of electron-hole formation, while an increase in \({\sigma }_{H}\) as a function of pH2O also was observed due to the formation of a thermodynamically stable proton defect as explained in Eq. 1.
a At 800oC and pO2 = 0.2 atm; b at 800oC and pO2 = 10-5 atm; c at 600oC and pO2 = 0.2 atm; d at 600oC and pO2 = 10-5 atm. [Reprinted figure with permission from ref. 49. Copyright (2017) Elsevier].
Similar trends were observed for other materials. A study carried out by Oishi et al.51 found a decrease in hole conductivity with an increase in pH2O for the BaCe0.9Y0.1O3-δ material. Ji et al.52 investigated BaZr0.85Y0.15O3-δ material and obtained conductivity measurements across wide ranges of pO2 and pH2O at 800 °C. The experiments demonstrated that at higher pO2, conductivity decreases with an increase in pH2O, while it increases at a lower pO2. The decreasing behavior is mainly attributed to the major contributor of \({\sigma }_{h}\). Demin et al.53 found that an increase in pH2O from 0.003 to 0.32 atm (pO2 = 10−5 atm, T = 600 °C) led to an increase in the proton transport of BaZr0.8Y0.2O3-δ material. On a similar material, Han et al.54 investigated transport properties across a wide range of pO2 (10−25 to 1 atm) with pH2O varying from 0.03 to 0.51 atm. The authors found that humidification resulted in a gradual increase in the ionic conductivity. In simple terms, increasing pH2O and decreasing pO2 helps in increasing the overall faradaic efficiency.
Chemical compositions
Chemical compositions play an important role in the overall conductivity of SOEC materials. In this section, studies related to the effect of A- and B-site doping on the protonic/hole conductivities are included.
Layageva et al.55 studied the BaCe0.8-xZrxY0.2O3-δ (BCZY) materials. The authors found that increasing the Zr content leads to an increase in hole conductivity, while a decrease in ionic conductivity was observed. At 750oC and a Zr-enriched phase (x = 0.8), hole conductivity is predominant. A possible explanation for this behavior is related to: (1) the grain boundary features, where decreasing the grain size results in an increase in both grain boundary density and resistance to ionic transportation, while no detrimental effect on electronic transport is observed; and (2) the grain features, where in case of more packed perovskite structures, the ionic conductivity decreases, while the relative contribution of p-type electronic conductivity increases32. Zhang and Zhao56 studied the transport properties of isovalent substitution of Ba in BaCeO3. The authors investigated the protonic and oxygen conductivity variations in Ba1-xSrxCe0.9Nd0.1O3-δ systems (x = 0, 0.1, 0.2). They observed that by decreasing the ionic radius in A cations, with substitution of Sr, results in the structural distortion in the ABO3 materials, which reduced the oxygen-ion conductivity, while an increase in the proton transport was observed. Kato et al.57 studied the transport properties of zirconates formed with various alkaline-earth elements (e.g.,AZr0.9Y0.1O3-δ, A = Ca, Sr, Ba, or Ba/Sr). They found that when the A-site is substituted by Ba, the material becomes predominant electronic conduction, as the hole transfer number is equal to 0.72. While, when the A-site is substituted by Sr and Ca, the hole transfer number is equal to 0.33 and 0.15, respectively. These results suggest that a notable difference in the electronic transport variations is observed due to modification in the A-site and B-site of the ABO3 structures. The conductivity of ABO3 materials is inversely proportionate to the electro-negativity of the A and B elements28. Han et al.58 investigated the effect of doping elements (e.g., Y, In, Ho, Er, Tm, Yb) on the transport number in BaZrO3. The authors observed that the lowest transport number of electron hole was found for the doping element ‘Y.’ Furthermore, both Ba-excess and Ba-deficiency led to an increase in the electron hole transport number. The doping element tends to distort the ideal cubic structure to become orthorhombic; further, an increase in the orthorhombic parameter is observed with an increase in the size of the dopant ion. However, Y shows a contrasting trend that yields a smaller parameter, which in turn reduces strain energy and increases defect mobility59.
External current
Finally, the external current or external applied voltage also have a significant impact on faradaic efficiency. Therefore, many recent studies have focused on investigating the effect of external current on faradaic efficiencies. Zhu et al.36 developed a model to predict faradaic efficiency as a function of electrolysis cell operating conditions. They found that faradaic efficiency increases as imposed current density increases. This is because the cell behaves as a concentration cell at an open circuit (e.g., zero imposed current), driving the protons towards the steam side and resulting into reverse proton flux, which leads to a decrease in faradaic efficiency. A similar trend was observed from other studies60,61,62,63. However, for the same materials and operating conditions, an opposite trend was reported64,65,66,67. A possible explanation was that as the imposed current density increases, the ohmic heating within the membrane and charge transfer polarization at the electrode–electrolyte interface increase leading to an increase in temperature and a decrease in faradaic efficiency36. This discrepancy suggests that there is a knowledge gap, and no published paper explains the discrepancy that can be qualitatively assessed. Thus, more efforts and research are required to study this problem.
Other factors
In addition to the above strategies of lowering the operating temperature, an increase in the partial pressure of H2O, the doping strategy, and two additional approaches can be used to mitigate electron leakage: (1) the use of an electron-blocking layer between the electrode and the electrolyte, which protects the grains of the electrolyte from reduction and consequently reduces the electronic conductivity;68,69 and (2) a double-layer electrolyte strategy, especially in the case of Ce-based electrolyte, to block the electron conductivity due to a reduction in Ce68,70,71.
Current modeling and simulation efforts
Computational modeling is a powerful tool that has allowed researchers to physically understand and explain the mechanism behind the experimentally observed properties and trend. Modeling at the atomic/molecular level (e.g., microscale) plays a vital role in understanding the different reaction pathways. It is an effective way to understand or reveal the interaction mechanisms between reactants and the catalytic surface. For this reason, the microscale modeling technique—density functional theory (DFT) – ab initio molecular dynamics (AIMD), molecular dynamics (MD), Monte Carlo (MC), and multiscale modeling approaches are reviewed in detail in the following subsections.
DFT and AIMD modeling
One of the main problems with SOECs is the stability of the materials72. DFT has been used in studying the stability and degradation of the materials. Rashkeev et al.73 developed the DFT and thermodynamic model to investigate the mechanisms of oxygen delamination in SOECs consisting of a YSZ electrolyte and an LSM oxygen electrode. The authors found that the diffusion of atoms across the interface at high temperature significantly affects the structural stability of materials and interfaces. In addition, La and Sr substitutional defects in the ZrO2 oxide and at the interfaces significantly change the oxygen transport, which may lead to the development of pressure at the interface and eventually leading to the delamination process. Nikolla et al.74 investigated the stability and degradation of Ni in the presence of carbon-based fuels. They found that alloying the Ni surface increases carbon tolerance by oxidizing the C atoms rather than forming C-C bonds. Similar simulations on Ni and Cu (111) and (211), as well as Cu-Ni and Cu-Co alloys in the presence of CH4, were carried out by Galea et al.75. Despite the fact that C was discovered to have a very high thermodynamic and kinetic barrier to CH4 dissociation, C was discovered to strongly adsorb onto the Ni (211) surface and grow graphitic carbon over the terrace. This dissociation barrier prevents breakdown and creates possibilities for electrochemical oxidation occurring directly. The Cu-Ni and Cu-Co alloys demonstrated that Ni and Co have little impact on the Cu surface and that the Cu enrichment of the alloy surface limits stability. Raja et al.76 studied the stability of BaZrO3 at high temperature using AIMD. This study revealed that the high-temperature stability of BaZrO3 is mainly due to the phonon contribution to the free migration energy of the O vacancy. Ribeiro et al.77 used AIMD-based calculations to study the temperature-dependent phase change in YSZ as a function of Ti content. The results from this study suggest that YSZ structures doped with small amount of Ti are both energetically and kinetically more stable than the undoped YSZ structures, and ideal proportion being 3% TiO2 for every 1% of Y2O3 doping.
DFT-based methods are also used to study hydration, adsorption, dissociation, and diffusion at the interface and in the bulk region. The adsorption, dissociation, and diffusion of hydrogen in pure Ni and the Ni/YSZ slab with two different interfaces (Ni/cation and Ni/O) were studied by Weng et al.78 using DFT. The H-atom binds preferentially at the hollow site on the Ni surface with an adsorption energy of −2.68 eV, while the H2 molecule gets adsorbed on the top site of the Ni surface with an adsorption energy of −0.34 eV. The calculated energy barrier for H2 dissociation on both surface is 0.1 eV. Comparing the diffusion energies of H through the surface and bulk suggests that the surface path is more favorable. In addition, the author found that the barrier for the H migration through Ni/O greater than through Ni/cation. Bhatia et al.79 used DFT calculations to examine the behavior of hydrogen on three flat Ni surfaces—Ni(100), Ni(110), and Ni(111)—and two stepped Ni surfaces—Ni(531) and Ni(210). It was found that hydrogen diffuses faster on the flat surfaces, but the stepped surface showed a greater mobility in comparison to the diffusion into the metal from the surface layer. Jing et al.80 performed DFT calculations to investigate the hydration process in yttrium-doped strontium zirconate (SZY) and YSZ materials. The authors found that the SRO(001) surface of SZY and the Ni(111) surface of YSZ is more favorable for water absorption. In the case of proton migrations from surface to bulk, DFT calculations showed that the energy barrier for YSZ is larger than that of SZY for both hydroxide ion migration and proton-hopping. While in the case of proton migration in both bulk structures, the energy barriers are relatively small and comparable. Klarbring et al.81 used non-equilibrium AIMD to study the diffusion and ionic conductivity in Sm-doped ceria using color diffusion algorithm. In the case of ionic conductivity, the results from AIMD showed good agreement with the experimental values. In case of O–diffusion, the external field used did not influence site preference of the Sm-dopants, which previous studies showed that O-vacancies prefer positions close to Sm atoms82,83. AIMD calculations were performed by Fronzi et al.84 to investigate the proton diffusion in the undoped BaZrO3 cubic structure. Three strain conditions were applied – fully relaxed, isometric tensile strength and compressive strain conditions. The authors found that applied external strain has no-linear effect on the proton diffusion constant and an enhancement in the proton diffusion was observed under compressive strain conditions. Zhu et al.85 studied the proton diffusion behavior caused by presence of \({V}_{o}^{..}\) in Ca doped BZY2 material using experimental techniques, DFT and AIMD-based calculations. Experimental study suggested that Ca2+ can be successfully doped at the B-site forming the BZCa1Y2. Due to the weak bond strength of Ca-O bonds, oxygen vacancies tend to form next to Ca, according to DFT simulations. Calculations using AIMD have shown that BZCa1Y2 has a greater diffusion coefficient than BZY2, which is supported by the much-decelerated trapping effect with the presence of \({V}_{o}^{..}\).
DFT-based calculations have been used to investigate the role of catalysts on the electrocatalytic activity in electrode-based materials, which affect the electrochemical performance86. Using the DFT model, Cadi-Essadek et al.87 assessed the stability of various Ni cluster configurations on ZrO2 and YSZ. The authors found that the formation of an Ni-Ni bond was easier than an Ni-electrolyte interaction. This results in the formation of preferred pyramidal shape instead of flat structures. The stability of Ni clusters was affected by temperature and resulted into the aggregation of Ni-other atoms or clusters. Ingram et al.88 used DFT calculations and kinetic modeling to investigate relevant reactions associated with the direct utilization of methane on different electrocatalysts. This allowed to compare relative activity of different materials and identify the optimal performing material. The author found that a family of materials (e.g., Ni, Co, Rh, Ru, Ir) offer maximum activity for all relevant reactions. Using DFT-based calculations, Muñoz-García et al.89 investigated catalytic activity of both Zr substitution with Fe and Mn in a barium zirconate (BZO) environment for oxygen reduction (ORR) and oxygen evolution (OER) reactions. Their study showed that the lowest overpotential as the ORR catalyst was obtained by BZM, while Fe in the stoichiometric BZF surface appears to be insufficient for both ORR and OER. In DFT, the oxygen p-band center has been used for fundamental understanding of an array of perovskite compounds for use in catalyzing the ORR and OER. Properties predictions using the O p-band includes catalytic properties, such as a high-temperature surface exchange rate for the ORR90,91, binding energies of reaction thermodynamics for ORR and OER92,93, and overpotentials of ORR and OER in basic solutions94. Choi et al.95 used quantum mechanical calculations (DFT and AIMD) to study the ORR on Sr-doped LaMnO3. The authors found that B cations are more active than A cations for oxygen reduction on a number of perovskite-type ABO3 cathodes is supported by the fact that O2 species are preferentially adsorbed on the Mn site rather than the La site. A DFT-based study carried out by Jacobs et al. 96 suggests that under a consistent computational framework, robust linear correlations between a variety of significant metrics of catalytic activity and the oxygen p-band bulk descriptor can be found. More DFT-based studies on different aspects of electrode materials can be found elsewhere97.
DFT calculations have been used in investigating defect chemistries and thermodynamics, which gives insights about SOEC materials in operating conditions. Bjørheim et al.98 for the first time, used first-principle calculations to investigate the phonon contribution to the defect thermodynamics (\({V}_{o}^{..}\) and \({{OH}}_{o}^{.}\)) of the ZrO2 terminated (001) surface of BaZrO3 material. The vibrational formation entropy of the surface \({V}_{o}^{..}\) is significantly higher than that of the bulk \({V}_{o}^{..}\), which is due to the smaller structural relaxations. However, in case of the \({{OH}}_{o}^{.},\) it displays near identical vibrational spectra at the surface and in the bulk structure. Using first-principle DFT calculations, Bjørheim et al.99 investigated the impact of phonons on the hydration and defect thermodynamics of undoped and acceptor (e.g., Sc, In, Y, Gd) doped BaZrO3 material. They found that for all of the dopants, the vibrational formation entropy of oxygen vacancy is significantly lower than the protonic defect, which is also the dominant contributor to the entropy of hydration. In addition, the calculated hydration entropy becomes more negative in the order of Y < Gd < In < Sc, because both the formation energy and vibrational formation entropy of oxygen vacancy and protonic defect become more negative with increasing dopant ion size. In addition, Bjørheim et al.100 also investigated the structural, electronic and thermodynamic properties of neutral and positively doubly charged oxygen vacancies in BaZrO3 using AIMD calculations. The author observed that, due to both the charged oxygen vacancy’s severe deformation of the local structure and its substantial negative formation volume, phonons are demonstrated to contribute significantly to the charged oxygen vacancy’s formation energy at high temperatures (1 eV at 1000 K). The ensuing lattice distortions for the neutral vacancy, and consequently the phonon contributions to the free formation energy, are much less. As a result, from 0 K to 1000 K, the charge transition level for oxygen vacancies (+2/0) varies from 0.42 to 0.83 eV below the conduction band bottom due to phonon effects on the relative stability of the two defects. By combining the ab initio results with thermodynamics modeling, defect formation at finite temperature and pressure were investigated by Björketun et al.101, who found that protonic defects are thermodynamically stable only at low temperatures, which is in agreement with the empirical results. By taking into account the configuration of complex defects, Takahashi et al.102 investigated the influence of fundamental factors that affect the hydration of BaZrO3 doped with trivalent cations (e.g., Al, Sc, Ga, Y, In, Lu). They found that Al- and Ga-doped BZOs are more likely to form oxygen vacancies, which results in low hydration energies and stable proton sites at the closest neighbor (1NN). However, BaZrO3 that have been doped with Y, In, and Lu prefer protons at the second nearest neighbor (2NN). DFT-based thermodynamic modeling was performed by Lee et al.103 to investigate the effect of humidity and pressure of H2/O2 gas on the defect chemistry and transport characteristics of BZY in the temperature range of 800 to 1200 K. The authors found that oxygen vacancies formed to compensate for extra Ba vacancies may cause a slight increase in protonation, while a decrease in overall proton diffusivity was observed due to trapping of protons near the Ba vacancies. DFT and AIMD-based calculations have also been used to study the generation, migration, dissociation and transport of electron-hole pairs in photovoltaic or solar cells104,105. Similar studies can also be performed to study the electron-hole pair migration and interactions in the SOECs.
Screening new materials and performing fundamental research can be easily enabled through the Material Genome Initiative (MGI)106,107 database, and DFT and AIMD-based studies have been successfully using the MGI database in exploring new materials108,109. MGI is of significant importance to expedite the material discovery and development process.
The main issue with DFT and AIMD-based studies is the limit on the number of atoms that can be efficiently simulated. In addition, temperature-dependent phenomena and harsh environmental chemistries (e.g., electron migration energy calculations, secondary chemistry calculations with explicit electrons in the system) that tend to lower the faradaic efficiency cannot be simulated using DFT. Also, the timescale that DFT simulations could access is another limiting factor.
MD modeling
In recent years, MD studies have played a crucial role in studying the effect of grain boundaries (GBs) on the oxygen diffusion pathway and proton diffusion in different SOEC materials, especially electrolyte materials. Chang et al.110 studied the GB effect of ionic transport at higher temperatures using Buckingham potential in MD. This study also showed the presence of GBs, degraded ion transport characteristics. At lower temperatures, GBs dominate ion transport, while at higher temperatures, the influence of GBs was eliminated because the migration energy barrier was overcome. Fisher et al.111 studied the oxygen diffusivity in pure zirconia and 8 mol% YSZ over a temperature range of 1273 to 2673 K using MD. The authors found that open GB enables oxygen transport and the rate of diffusion in the bulk structure of YSZ crystals is slow. A number of intrinsic vacancies are present at the interface of pure ZO2 bicrystals, according to MD simulations, and these promote GB diffusion at elevated temperatures112. An MD study by Fisher et al.113 investigated the structure and ion transport properties of three interfaces in 8 mol% YSZ, which included tilt and twist GBs. The authors found that symmetrical tilt GB decreases the overall conductivity because of the trapping of vacancies in the GB region. However, twist GB enables rapid diffusion with an opportunity to provide means for enhancing the ionic conductivity of YSZ ceramics. Gonzalez-Romero et al.114 studied the physical characteristics (e.g., GB energies and oxygen diffusion) of Σ3, Σ5, Σ11, and Σ13 GBs in model of YSZ bicrystals as a function of the concentration of yttria and temperature. Lee et al.115 performed a hybrid MC-MD modeling study on the defect distribution near tilt GBs in YSZ and gadolinia-doped ceria (GDC) materials. They found that in both materials, oxygen vacancy segregation precedes dopant segregation near the GB. Moreover, GDC showed a stronger dopant segregation than YSZ despite a smaller size mismatch between host and dopant cations. From this result, the authors made a conclusion that dopant segregation is initiated by vacancy segregation and largely controlled by dopant-vacancy association. Similarly, many MD studies on the GBs of YSZ material have been studied116,117,118,119.
MD studies have successfully been used to describe how the concentration of doping elements can affect oxygen migration, oxygen diffusivity, and defect interactions. Using Buckingham-type potentials in MD, Devanathan et al.120 studied the effect of doping concentration on oxygen migration and defect interactions in YSZ. They found that with 6 to 25 mol% yttria in YSZ, the activation energy of oxygen diffusion was found to be 0.6 to 1.0 eV. Also, the formation of \({\rm{Y}}-{V}_{o}^{..}-{\rm{Y}}\) with a binding energy of −0.85 eV could play an important role in any conductivity degradation of YSZ. Oxygen vacancy migration properties were studied by Kilo et al.121 by using experimental and MD methods (Buckingham potential). The authors found that experimentally, the oxygen diffusion was highest for the 10 mol% yttria in YSZ. While MD results consistently showed higher diffusion coefficient values than the experiments, the MD predicted activation enthalpy of migration showed a good agreement with the experimental results. Araki et al.122 studied the oxygen diffusion in 4, 8, and 14 mol% yttria (e.g., 4YSZ, 8YSZ, 14YSZ) in YSZ subjected to uniaxial tension in the [100], [110], and [111]. An increase in the oxygen diffusivity along the tensile direction in all three cases (e.g., [100], [110], [111]) was observed for 4YSZ and 8YSZ. However, in the case of 14YSZ, the oxygen diffusivity remained unchanged, probably due to the higher yttria content. Shimojo et al.123 investigated the structural and dynamical properties of YSZ for the three dopant concentration—4.85, 10.2, and 22.7 mol% yttria in YSZ. The authors found that dopant Y ions play a significant role in oxygen diffusion. At lower dopant concentration, Y ions promote the migration of O ions; however, as the concentration increases, a decrease in diffusion constant was observed. The restriction by the Y-Y edge causes a decrease in the diffusivity with an increase in the dopant concentration124.
In addition, phase composition and structural stability were analyzed using MD. Ogawa et al.125 modeled zirconia polycrystal and investigated the microscopic mechanism of high-temperature deformation. The material was deformed at 1500 K under tensile stress up to 8 GPa. The model was found to be stable up to 2 GPa, and largely elongated at stresses above 6 GPa. A disordered layer at the GB was observed and seemed to play an important role in the deformation process. Chang et al.126 investigated the effect of the cubic/monoclinic phase composition on the oxygen-ion diffusion in zirconia-based solid electrolytes using Born-Meyer-Buckingham potential in MD. They found that due to the presence of an unfavorable monoclinic structure for small-ion penetration, the pure cubic-phase system had more effective thermal motions with extended and continuous movements than the dual-phase system. The diffusion coefficient analysis revealed that the pure monoclinic structure was unaffected by the material composition, while the phase and material composition controlled the diffusion mechanisms.
Most of the above MD studies used short-range Buckingham potential and long-range Coulombic potential for investigating different aspects in the SOEC materials. The Buckingham potential is a simplified version of the Lennard-Jones potential, which cannot accurately capture the effects of temperature and pressure on the interaction between atoms. On the other hand, the reactive potential - ReaxFF developed by van Duin et al.127 includes many-body interactions, which allows for accurate interactions between the atoms. ReaxFF also considers the effect of temperature and pressure on the interactions between atoms, which is of significant importance in case of accurate predictions of SOEC materials in different conditions.
In 2008, van Duin et al.128 developed a ReaxFF to study proton diffusion across the GB using the MD simulations. This study paved the way for decades-long simulations using ReaxFF. Cammarata et al.129 studied the structural changes and proton mobility for the undoped, singly, and doubly Y-doped BaZrO3 with varying temperatures ranging from 100–1200 K using ReaxFF MD. The MD results well-reproduced the behavior already observed by the quantum mechanics (QM) calculations where two important conclusions were inferred: (1) the clustering of yttrium in BZY were seen; and (2) out of the three oxygen site sets, two yttrium-clustered models acted as multilevel protonic traps, which delayed the protonic diffusion in the bulk. This was due to the large number of proton-hopping events that occurred between those oxygen atoms that were surrounded by clustered yttrium atoms. Thus, proton conductivity in these materials can be improved by avoiding such clustering. Li et al.130 studied the O2− transport properties, as well as the migration mechanism in Y doped BaZrO3 with/without edge dislocations using ReaxFF MD. In addition, they studied the effect of dopant concentration and temperature on thermodynamic and kinetic properties of bulk and dislocation system. The authors found that below 20 mol% Y content in BZY, O2− ion conduction is promoted, while the maximum O2− conductivity was observed for the model having 30 mol% Y doped in dislocated BZY. Moreover, dislocations in the model accelerate the O2− diffusion when the temperature is less than 1173.15 K due to the formation of double-bottle diffusion channels. Using ReaxFF MD, Ottochian et al.131 studied the effect of isotropic and biaxial strain on proton conduction in Y-doped BaZrO3 at different temperatures (e.g., 1500–2000 K). They observed that compressive pressure led to an increase in the proton conductivity, while the effect of biaxial strain is more complex. In the case of intermediate biaxial strain, an increase in the proton conductivity was observed because of the shortened O-O distance. However, an opposite trend was observed in case of higher compressive biaxial strain, due to strong localization of proton far from the B-site cations. Merinov et al.132 developed a ReaxFF force field for studying the electrode–electrolyte interface. These parameters have facilitated to re-calculate the primary energy barrier for proton diffusion in BZY which shows a good agreement with experimental values. More MD-based studies with different FF can be found elsewhere133.
The inaccuracy in predicting the electron affinity or ionization potential restricts the applicability of ReaxFF in redox reactions134. This led to the development of an electron version of ReaxFF termed ‘eReaxFF.’135 In this potential, electrons-like or hole-like particles are explicitly included. This method has been successfully used to simulate the electronic motion in carbon-based135, lithium-electrolyte136, Ag metal137, and polyethylene electrical breakdown systems138.
As mentioned previously, electron holes (e.g., electronic conductivity) significantly decrease faradaic efficiency. Therefore, to simulate electronic current leakage, the electrons/hole pair should be explicitly included, which is currently not involved in almost all force fields, except for the eReaxFF. However, the parallel version is only incorporated in the Amsterdam Density Functional package139. Since the parallel version is still not available in most MD software packages, the dependency of the serial version is increased, which ultimately limits the size of the eReaxFF MD that can be efficiently simulated.
In addition to the classical interatomic force fields, recently, machine-learned force fields (MLFF) have emerged as an ideal solution to drastically augment length and timescales accessible to MD simulations and retaining first-principle accuracy. Verdi et al.140 developed a MLFF based on MD and Bayesian interface to describe the thermodynamic properties of zirconia. This MLFF accurately captured the temperature-induced phase transformation below the melting point. Guan et al.141 recently developed a global neural network potential (G-NN) for the YSZ. They carried long-time molecular dynamics simulations for YSZ at 6.7, 8, 10, and 14.3 mol % over a wide temperature range (800–2000 K). In addition, Guan et al.142 developed a stochastic surface walking global exploration with G-NN potential (SSW-NN) to investigate changes in the microstructure of YSZ with different concentrations of Y. Wang et al.143 developed a MLFF to investigate anisotropic fracture behavior of BaZrO3 material. The author observed that the fracture strength in the [110] crystal orientation is more significant than the [100] crystal orientation. Niu et al.144 using AIMD and machine learning molecular dynamics (MLMD) studied the proton migration in Y-doped BaZrO3 material. The author observed that at shorter time, the performs superdiffusion through the O–H, while at longer time, proton diffusion first becomes subdiffusive due to OH ion rotation and then gradually turns to normal diffusion. Kholtobina et al.145 investigated the temperature dependencies of surface energies for (111) and (110) CeO2 with extended two-stage up-sampled thermodynamic integration using Langevin dynamics (TU-TILD). This method was used together with machine learning potentials called moment tensor potentials (MTP). The authors found that the increase in the temperature from 0 to 2100 K led to the decrease of the Helmholtz free energy of (111) CeO2 from 0.78 to 0.64 Jm−2.
MC modeling
This section includes a review of MC-based studies on the order of reaction mechanism, oxygen diffusivity, conductivity, electrode degradation, and defect interactions. Some important processes and aspects of cell physics occur on a timescale much longer than the MD timescale (e.g., in nanoseconds). MC methods, which are at a larger length and timescales are suited to study these phenomena. MC-based modeling does not include identifying new reaction pathways, but rather focuses on the complexities associated with the interaction of particles146. Modak and Lusk146 used kinetic MC (KMC) techniques to simulate open circuit voltage and an electrical double layer of doped electrolyte. The study was mainly focused on electrical-physical processes and the results from KMC modeling showed a good agreement with the predictions from the analytical model. The main idea for developing these algorithms was to use it as a sub-model in a more complex and realistic KMC simulator, which accounts for oxidation reaction on the surface of the anode.
KMC has also been used to investigate the reaction mechanism and oxygen-ion diffusion conductivity. Pornprasertsuk et al.147 performed KMC simulations based on DFT-calculated barrier energies to determine the dopant concentrations dependency on the oxygen self-diffusion coefficient in (Y2O3)x (ZrO2)(1-2x) with x varying from 6 to 15%. DFT results suggest that a decrease in the conductivity with a higher dopant concentration is due to the higher migration energy required to travel across two adjacent Y-Zr and Y-Y pairs. While the KMC results reveal that the increase in migration energy is due to the higher probability of oxygen vacancies encountering Y-Zr and Y-Y pairs. Another study by Pornprasertsuk et al.148 used quantum calculation-based KMC to study oxide-ion diffusion process and the space charge double layer at the electrode–electrolyte interface subject to applied alternating potentials, as well as the dependence of impedance and double layer capacitance on the thickness of the electrolyte. The simulation showed that at lower frequencies, oxide ions have sufficient time to migrate across the electrolyte and accumulate at the electrode–electrolyte interface creating a double layer with a space charge. Longer time is needed for thicker electrolytes to reach the same level of oxide-ion vacancies at the electrode–electrolyte interface. Wang et al.149 developed a KMC model based on a series of reversible elementary steps for simulating ORR at the cathode-electrolyte interface and hydrogen-oxidation mechanism near the anode-electrolyte interface. They found that increasing applied bias voltage, operating temperature, and relative permittivity YSZ and decreasing the thickness of YSZ increased the ionic current density and efficiency of the cell. Krishnamurthy et al.150 developed a DFT-based KMC model to study the diffusion of oxygen in YSZ. Oxygen diffusivity was found to increase with an increase in the yttria mole fraction before attaining a maximum value of ~0.1 mole fraction yttria. To understand the physical mechanisms underlying the observed behavior, analytical models were developed. Based on the analyses, two factors that explained the observed behavior were: (1) an increase in the number of high migration energy Y-Zr and Y-Y edges; and (2) an increased dopant induced and vacancy dopant correlations at higher yttria content. Dholabhai et al.151 used a DFT-based kinetic lattice Monte Carlo (KLMC) model to investigate the optimal dopant concentration in GDC for maximum ionic conductivity. They found that higher dopant concentrations increase the vacancy concentration, which thus increases ionic conductivity. However, at higher concentrations, vacancy-vacancy repulsion impedes the diffusion process, which thus reduces the ionic conductivity. At a 20 to 25% mole fraction of Gd, the maximum ionic conductivity was predicted. Gunn et al.152 developed hybrid MC (HMC) and adaptive KMC (AKMC) models based on Buckingham potentials to study the thermodynamic equilibrium and kinetic properties in the gadolinium-doped ceria (GDC). HMC demonstrated the movement of oxygen vacancy from bulk to surface, while the AKMC was crucial in finding multi-atom concerted diffusion mechanisms spanning over large distances.
Other factors like the aging of electrodes and defect interactions were also studied using MC. The KMC simulation model developed by Zhang et al.153 was used to study the thermal aging of infiltrated electrodes by considering the surface diffusion mechanism. The effects of temperature, infiltration loading, wettability, and electrode configuration were studied, as well as the geometric parameters, which included the infiltrate particle size, the total and percolated quantities of the three-phase boundary length and infiltrate surface area, and the tortuosity factor of the infiltrate network. This parametric study led to the following conclusions: (1) lowering the temperature can slow the degradation kinetics of triple-phase boundaries (TPB) and the surface area of the infiltrate particle; however, it can lead to a high level of tortuosity factor of the infiltrate network and slow the electrode reaction kinetics; (2) increasing the infiltration loading accelerates the coarsening rate of infiltrate particles; (3) increasing the wettability increases the coarsening rate of the infiltrate particles and decreasing rate of TPB; and (4) the tortuosity factor of the infiltrate network decreases with time and eventually attains stability. Eisele et al.154 developed a DFT-based Metropolis MC (MMC) model to estimate the influence of defect interactions on the hydration of BZY. The results that were obtained concluded that the non-ideal experimental behavior for the varying yttrium fraction, proton fraction, and temperature were due to the ionic defect interactions. The DFT-based KMC model developed by Gomez et al.155 showed that the proton conduction can be hampered by the presence of other protons. Using the thermogravimetric and a.c. impedance study, similar behavior was observed by Yamazaki et al.156.
KMC models usually use physical property data generated by DFT, MD, or experimental analyses. If inaccurate parameters are selected at the DFT level, then the output from the KMC studies will yield inaccurate results. In the case of a large number of variables confined to different constraints, KMC can be computationally inefficient.
Multiscale modeling
The operation of a cell depends on complex interactions between multi-physics, such as multi-phase fluid flow, mass transport, heat transfer, and electrochemical reactions. Multiscale modeling provides an opportunity to give a mechanistic description of material performance, and thus to guide optimization designs of material and structure. Therefore, handshaking of different length-scale studies, as observed in Fig. 7, will improve the understanding of SOEC properties and their effects on the SOEC behavior.
Schematic diagram of exchange of information between different length-scale models.
Ma et al.157 developed a multiscale model combining DFT, transition state theory (TST), and continuum modeling for the oxygen-based reactions at the electrode to elucidate critical steps and predict device performance. The reaction rates predicted from TST were used as an input in the continuum model for obtaining overpotential-current density relations. The proposed multiscale model yields a quantitative agreement with the overpotential-current density data from the experiments. A new hybrid molecular-continuum model-pointwise coupling methodology was presented by Asproulis et al.158. The atomistic models were utilized to calculate transport properties, provide accurate boundary conditions, and substitute constitutive relations for the pressure among others, while the solution was advanced through the continuum solver. The calculation of the macroscopic variables was performed through averaging the corresponding microscopic properties. Ren et al.159 investigated the effect of oxygen vacancy location on CO2 reduction reaction at the three-phase boundary of Ni/samarium-doped ceria surface using DFT calculations. Moreover, based on the DFT results, the microkinetic model was developed to determine the rate-controlling step under different operating voltages at 1000 K. The results reveal that in case of interface oxygen vacancy, CO desorption is the rate-controlling step regardless of electrode overpotentials. However, in the case of non-interface oxygen vacancy, the rate-controlling step will change with an increase in cathode overpotential.
A multiscale approach was developed by Khaleel et al.160, in which the microscale electrochemistry model (e.g., Lattice-Boltzmann algorithm) calculates the performance of the porous electrode material based on the distribution of reaction surfaces, the material structure at the microstructure level, and the oxygen-ion transport through the material. The macroscale calculations (MARC software) were used to calculate the current density, cell voltage, and heat production after the microscale electrochemistry modeling has calculated the total fuel cell current-voltage relation. Studies by Cheng et al.161 and Pasaogullari and Wang et al.162 also showed the usage of the multiscale modeling approach; however, the integration of different scales is not mentioned. Other multiscale modeling approaches and modeling studies at a higher length-scale (e.g., cell and stack level, system level) can be found elsewhere163,164.
The development of methods for multiscale multi-physics modeling that consider the coupling of fluid flow, heat transfer, species transport, and electrochemical kinetics is a challenge for future studies as this multiscale modeling coupling is rare165,166,167.
Future perspectives and path forward
Despite the advantageous capabilities of SOECs for green H2 production, its use is still limited on the industrial scale. The selections of materials for the cathode, anode, and electrolyte all play a crucial role in the performance of a cell. At the individual level, each component of the cell needs to be 100% effective and efficient to utilize the promising features of SOECs.
The main issue with electrolyte materials is current leakage due to a non-negligible electron conduction, which decreases faradaic efficiency. A computational model is a powerful tool that can be used to systematically study, analyze, and understand the problems related to current leakage within electrolytes. On the atomistic level, DFT studies can be performed to understand the surface chemistries and electron-hole mobility, which is directly related to current leakage. On the other hand, MD studies can be used to investigate the effect that temperature has on electron/hole formation, as well as mobility and bulk chemistries, by using methods that explicitly include electron/hole pair modeling such as AIMD and eReaxFF. Explicit electron/hole pair modeling also can be useful in understanding the factors affecting the faradaic efficiency of the cell and H2 generation. In addition, MC simulations in combination with DFT/MD can be used to investigate the defect evolution and accumulation on a larger timescale. Finally, the multiscale modeling approach plays a significant role in understanding complex processes at a different length scale. The handshaking of a different length-scale study will help in solving the current problems like faradaic efficiency related to SOECs.
In addition to a different length-scale study, the implementation of parallel methods like the graphics processing unit in a different length-scale software package such as MD will help computational modelers in the future to simulate larger models. Incorporating the MGI database with machine learning techniques and data analysis will expedite the process of investigating and exploring new materials related to SOECs, which will significantly help the scientific community.
Data availability
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
Code availability
No underlying code was developed for this study.
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Work supported through the INL Laboratory Directed Research& Development (LDRD) Program under DOE Idaho Operations Office Contract DE-AC07-05ID14517.
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P.G. and G.P. conceived the idea and developed the manuscript outline. G.P. led the collaboration. P.G. wrote a major part of the manuscript. All authors (P.G., K.M., Y.S., A.V.D., and G.P.) reviewed and edited the manuscript.
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Gaikwad, P.S., Mondal, K., Shin, Y.K. et al. Enhancing the Faradaic efficiency of solid oxide electrolysis cells: progress and perspective. npj Comput Mater 9, 149 (2023). https://doi.org/10.1038/s41524-023-01044-1
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DOI: https://doi.org/10.1038/s41524-023-01044-1
