Ca-Doping Cobalt-Free Double Perovskite Oxide as a Cathode Material for Intermediate-Temperature Solid Oxide Fuel Cell.

Solid oxide fuel cells (SOFCs) are emerging as energy conversion devices for large-scale electrical power generation because of their high energy conversion efficiency, excellent ability to minimize air pollution, and high fuel flexibility. In this context, this critical review has focussed on the recent advancements in developing a suitable electrolyte for SOFCs which has been required for the commercialization of SOFC technology after emphasizing the literature from the prior studies. In particular, the significant developments in the field of solid oxide electrolytes for SOFCs, particularly zirconia- and ceria-based electrolytes, have been highlighted as important advancements toward the production of sustainable and clean energy. It has been reported that among various electrolyte materials, zirconia-based electrolytes have the potential to be utilized as the electrolyte in SOFC because of their high thermal stability, non-reducing nature, and high mechanical strength, along with acceptable oxygen ion conductivity. However, some studies have proved that the zirconia-based electrolytes are not suitable for low and intermediate-temperature working conditions because of their poor ionic conductivity to below 850°C. On the other hand, ceria-based electrolytes are being investigated at a rapid pace as electrolytes for intermediate and low-temperature SOFCs due to their higher oxygen ion conductivity with good electrode compatibility, especially at lower temperatures than stabilized zirconia. In addition, the most emerging advancements in electrolyte materials have demonstrated that the intermediate temperature SOFCs as next-generation energy conversion technology have great potential for innumerable prospective applications.

Solid-state oxygen ion conductors are of paramount importance to solid oxide fuel cells and electrolytic cells. However, with the oxygen ion conductors proposed to date, these technologies require too high (close to 800 oC) temperatures to operate, leading to technological challenges and high costs. Therefore, it is of primary importance to design faster oxygen ion conductors at intermediate and low temperatures (below 400 oC) that can enable sustainable energy technologies to mitigate climate change. Descriptors for oxygen ion conduction are highly desirable to identify promising materials, which can be done by leveraging fast-growing statistical and machine learning approaches for screening of material databases [1]. Recently, computational tools combined with experiments have allowed researchers to gain atomistic insights and relate ion transport to features of the lattice dynamics [2] and electronic structure [3] of a given material. In this work, building upon the previous literature, we leverage both the lattice dynamics and electronic structure to predict the migration barrier for oxygen migration in pure and mixed electronic ionic conductors and search for promising oxygen ion conductors.Using density functional theory simulations, we model oxygen migration in perovskite, rutile, fluorite, and Ruddlesden-Popperoxides. We analyze oxygen ion transport in pure and mixed electronic ionic conductors and oxygen vacancies with and without charge. We study changes in the electronic structure during oxygen migration within the solid host lattice in different oxides. By analyzing trends of migration barrier and electronic density of states, we relate the migration barrier to the electronic structure of the transition state. Our results show that the migration barrier depends on the capability that the host lattice has of screening charge associated with the mobile ion in the transition state, which if increased would lower the localization of charge around the mobile ion and in turn the oxygen migration barrier. In pure ionic conductors – where no charge is associated with the mobile ion - the migration barrier is largely dependent on the M-O strength. Based on the mechanistic understanding derived by these initial analyses, we further relate oxygen ion conductivity to the lattice dynamics. We show that in pure ionic conductors, increasing migration barrier follows trends of increasing oxygen vibrational frequency based on phonon-electron coupling, which also relates the prefactor of Arrhenius law with the migration barrier. However, when trying to predict trends of the migration barrier across different crystal structures or mixed ionic conductors, no single descriptor can capture the complex physiochemistry behind oxygen migration. Thus, we leverage statistical learning tools to identify multivariate descriptors and analyze specific features of lattice moieties that improve oxygen ion conduction. The results of this work provide mechanistic understanding of oxygen ion migration and strategies to accelerate the designs of fast oxygen ion conductors.

Ni-Sm 2O 3 cermet anodes for intermediate-temperature solid oxide fuel cells with stabilized zirconia electrolytes

Bi 0.5Sr 0.5MnO 3 as cathode material for intermediate-temperature solid oxide fuel cells

Four oxides belonging to the perovskite series of nominal stoichiometry LaNi1−xMoxO3, x = 0.10, 0.15, 0.20, 0.25 (LNMO), have been tested as cathode materials for solid oxide fuel cells (SOFC). The electrodes were supported on a 300-μm-thick pellet of the electrolyte La0.8Sr0.2Ga0.83Mg0.17O3−δ (LSGM) with Sr2MgMoO6 (SMMO) as the anode and LNMO as the cathode. The test fuel cells gave a maximum power density of 660 mW/cm2 at 850 °C and 565 mW/cm2 at 800 °C for the x = 0.25 cathode material and exhibited high cyclability and low cathodic overpotential losses with pure H2 as fuel. All the cathode materials were characterized by X-ray diffraction (XRD) and electrical conductivity measurements while the test fuel cell cross-section was examined by scanning electron microscopy (SEM). The X-ray data indicate that all the cathode materials exhibit a perovskite phase with an additional impurity phase present in LNMO x = 0.20, 0.25 materials. Molybdenum (Mo)-poor LNMO x = 0.10 exhibits a purely metallic behavior in...

Lowering the operating temperature of the high-temperature, solid oxide fuel cell (SOFC) improves both the thermodynamic efficiency and the lifetime of this energy efficient technology. Unfortunately the rate of oxygen-ion transport through the solid electrolyte is temperature dependent, and materials previously employed as electrolytes in the high-temperature SOFC perform poorly at intermediate temperatures. Therefore new oxygen-ion conductors with enhanced ionic conductivity at intermediate temperatures are required. The bulk of the existing literature on high-temperature SOFCs has focussed on zirconia-based binary systems as electrolytes, due to their high ionic conductivity and negligible electronic conductivity. Only select compositions within the zirconia-scandia system have demonstrated acceptable ionic conductivity levels at intermediate temperatures; however unstable phase assemblage and the high economic cost of scandia are clear disadvantages. Ceria-based binary systems have demonstrated improved oxygen-ion conductivity at intermediate temperature compared to many zirconia systems, however significant levels of n-type electronic conductivity are observed at low oxygen partial pressures. Consequently it was thought unlikely that significant increases in ionic conductivity would be found in existing zirconia- and ceria-based binary systems, therefore another approach was required in an attempt to improve the performance of these established fluorite systems. The fluorite systems Zr0.75Ce0.08M0.17O1.92 (M = Nd, Sm, Gd, Dy, Ho, Y, Er, Yb, Sc) were prepared and investigated as possible, intermediate-temperature SOFC electrolytes in an attempt to combine the higher conductivity found in the ceria systems with the low electronic conductivity observed in the zirconia systems. Also it was anticipated that systems containing dopants not previously observed to confer high ionic conductivity in either zirconia- and ceria-based binary systems, might exhibit enhanced ionic conductivity with expansion of the zirconia lattice resulting from the addition of ceria. All the as-fired Zr0.75Ce0.08M0.17O1.92 compositions possessed the face-centred cubic structure and lattice parameter measurements revealed the anticipated unit cell enlargement as the size of the dopant cation increased. No unusual microstructural parameters were identified that could be expected to interfere with the ionic transport properties in the as-fired compositions. The electrical conductivity was found to be influenced by the dopant-ion radius, the presence of ceria, low oxygen partial pressures and, in some compositions, the formation of poorly conducting, ordered-pyrochlore microdomains dispersed amongst the cubic defect-fluorite matrix. In a second approach to the formulation of new oxygen-ion conductors suitable for the intermediate-temperature SOFC, compounds possessing structures other than the fluorite structure were considered. An examination of the literature for oxides having the pyrochlore, scheelite and perovskite structures showed that the Sr+2- and Mg+2-doped LaGaO3 perovskites (LSGM) possessed ionic conductivity equal to the highest conducting, zirconia and ceria binary compounds. Therefore the perovskite systems La0.9Sr0.1Ga(0.8-x)InxMg0.2O2.85 (X = 0, 0.05, 0.1, 0.2, 0.4, 0.6, 0.8) (I-LSGM) were prepared and examined, the objective being to favourably influence structural parameters believed responsible for optimal ionic conductivity, namely the unit cell symmetry and volume. It was found that In+3 systematically substituted for Ga+3 on to the B-site of LSGM at least up to the X = 0.4 composition. While In+3 was found to replace the Ga+3 as expected, Mg+2, which occupies the same crystallographic site, was also replaced by In+3. Up to the X = 0.2 composition, at least two trace level secondary phases were observed to form along with the bulk I-LSGM phase. For I-LSGM compositions with X > 0.2, significantly larger concentrations of the secondary phases were identified. Evidence of a strontium-rich, high-temperature liquid phase was observed also near the grain boundaries on as-sintered and thermally etched surfaces in LSGM and I-LSGM compositions. It is believed that the observed, high sintered density in the complex, doped-LaGaO3 systems is due to the formation of this high-temperature liquid phase. Increasing levels of diffuse scatter and superstructure formation were observed in electron diffraction patterns in the I-LSGM bulk phase (up to X = 0.2), indicating a possible decrease in vacancy concentration and reduced, localised unit cell symmetry. The electrical conductivity in the I-LSGM compositions was believed to be influenced by the distortion of the oxygen-ion conduction path, a reduction in vacancy concentration, formation of stronger dopant-vacancy associates at low temperature and the presence of ordered structures. In addition, phase instability, in the form of subtle ordering in specific crystalline planes, was observed to influence the electrical conductivity as a function of time at intermediate temperatures.

Cathode material SmBaCoFeO5+δ (SBCF) was synthesized by a combined EDTA-citrate complexing sol-gel method and characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), AC impendence spectroscopy, respectively. The results showed that the SBCF cathode had an orthorhombic perovskite-structure and formed a good contact with the Ce0.9Gd0.1O1.95 (GDC) electrolyte after sintering at 950°C for 2h. Based on symmetric cell test, area specific resistance of SBCF on GDC electrolyte was as low as 0.1Ω cm2 at 800°C. The maximum power densities of a cell using the SBCF cathode are 431 mWcm−2, 313mWcm−2 and 200mWcm−2 at 800°C, 750°C and 700°C, respectively. Preliminary results demonstrate that SBCF is a very promising cathode material for application in intermediate-temperature solid oxide fuel cells (IT-SOFCs).

CeO2-based materials have been studied intensively as anodes for intermediate temperature solid oxide fuel cells (IT-SOFCs). In this work, pristine and europium (Eu)-doped CeO2 nanowires were comprehensively investigated as anode materials for IT-SOFCs, by a combination of theoretical predictions and experimental characterizations. The results demonstrate: (1) Oxygen vacancies can be energetically favorably introduced into the CeO2 lattice by Eu doping; (2) The lattice parameter of the ceria increases linearly with the Eu content when it varies from 0 to 35 mol.%, simultaneously resulting in a significant increase in oxygen vacancies. The concentration of oxygen vacancies reaches its maximum at a ca. 10 mol.% Eu doping level and decreases thereafter; (3) The highest oxygen ion conductivity is achieved at a Eu content of 15 mol.%; while the 10 mol.% Eu-doped CeO2 sample displays the highest catalytic activity for H2-TPR and CO oxidization reactions. The conducting and catalytic properties benefit from the expanded lattice, the large amount of oxygen vacancies, the enhanced reactivity of surface oxygen and the promoted mobility of bulk oxygen ions. These results provide an avenue toward designing and optimizing CeO2 as a promising anode for SOFCs.

Solid Oxide Fuel Cells (SOFCs) are one of the most attractive energy conversion and storage devices, which can be applied for decentralized energy applications. However, the high operating temperature making SOFCs still unmarketable, which indicates that lowering the working temperature of SOFCs while still maintaining a high-power output is very crucial. For Intermediate-Temperature Solid Oxide Fuel Cells (IT-SOFCs), new cathode materials with high electrocatalytic activity and stability are necessary to provide a stable and high performance of cells. Perovskite-structured oxide (ABO3−δ) is one group of the most interesting material candidates for IT-SOFCs, presenting great potential in chemical composition modifications, yielding the design and gain of desired physicochemical and electrochemical properties [1]. The simple perovskite LaCuO3 is one of the well-studied Cu-content oxides with a high conductivity (106 S·cm−1), but it can be hardly obtained and suffers with stability issues in air [1, 2]. To stabilize the perovskite structure and to improve electrochemical properties of Cu-content oxides A-site and B-site modification strategy can be applied. It has been noted that Cu- and Ni-containing LaNi0.5Cu0.5O3−δ simple perovskite possesses low cathodic polarization of 0.056 Ω·cm2 at 800 °C, and a high power output of 870 mW·cm−2 at 900 °C [1, 3]. The generation of oxygen vacancies by strontium doping contributes to the increase of ionic conductivity component, and the Sr dopant can reduce the oxygen vacancy formation energy and increase the ionic conductivity of La1−xSrxMO3−δ (M = Fe, Mn) perovskites [1,4]. Therefore, in this work, Cu-content La1−xSrxNi1−yCuyO3−δ oxides with strontium doping at the A-site were evaluated as very promising Co-free cathode material candidates for IT-SOFCs.In this work, all La1−xSrxNi1−yCuyO3−δ compounds have been successfully obtained using soft chemistry. The room-temperature crystal structure of all oxides was assigned to the R-3c trigonal system. The substitution of La with Sr lowers the phase transition temperature from the R-3c space group to Pm-3m simple perovskite while increases the oxygen non-stoichiometry and the thermal expansion coefficient of studied materials. All investigated materials are chemically compatible with GDC-10, while unstable in contact with LSGM and 8YSZ. The manufactured anode-supported IT-SOFC with the La0.95Sr0.05Ni0.5Cu0.5O3−δ cathode presents an excellent power density of 445 mW·cm−2 at 650 °C in humidified H2. The results confirmed that La1−xSrxNi1−yCuyO3−δ perovskites can be potentially qualified as promising cathode candidates for IT-SOFCs, yielding promising electrochemical performance in the intermediate-temperature range [1].

Performance of an improved combination unit of Pd-membrane methane steam reformer and intermediate temperature solid oxide fuel cell (C-Pd-ITSOFC)

One of the most promising next-generation energy conversion technologies is the solid oxide fuel cell (SOFC), which is more efficient and less polluting than conventional internal combustion engines (ICEs). However, in order to commercially compete with ICEs, SOFCs must be cost-competitive and operation-reliable. To achieve this goal, lowering the operating temperature of a SOFC from the current 700-1000oC to ≤ 600oC is vitally important. The realization of such intermediate-temperature SOFCs (IT-SOFCs) depends critically upon the availability of high-conductivity electrolytes and high-activity electrode catalysts. In recent years, significant progress has been made in the area of cathode catalysts through new material discovery and microstructural optimization, which has demonstrated a polarization resistance (area-specific resistance) as low as 0.1 W×cm2 even at 500oC. 1 2 In contrast, the development of high-conductivity oxide-ion conductors significantly lags behind that of IT-SOFC cathodes. Therefore, identification of new IT solid-state fast oxide-ion conductors is in high demand. A practical criterion for an electrolyte to be suitable for an IT-SOFC is its oxide-ion conductivity so ≥0.01 S/cm at an operating temperature < 600oC. None of the existing chemically stable oxide-ion conductors can satisfy this requirement at a temperature ≤500oC. Recently, the Goodenough group at the University of Texas at Austin discovered a new class of oxide-ion conductors that can meet this conductivity-temperature requirement. These new oxide-ion conductors have a generic formula Sr3-3xNa3xSi3O9-1.5x (or SNS hereinafter) and layered structure as shown in Fig.1 (a). 3 4 The oxide-ion conductivity of SNS is so»0.01 S/cm at 500oC, Fig.1 (b), the highest among all known chemically stable oxide-ion conductors. More importantly, it is stable over a broad pO2 range of approximately from 10-30 to 1 atm and an extended lifetime, making it an ideal electrolyte for IT-SOFCs. 5 Despite the exciting discovery of this superior ion conductor, so far very little is known about the transport mechanisms governing the high oxide-ion conductivity in the SNS. This study investigates the origin of high oxide-ion conductivity by probing the local structure and dynamics of ionic motion with high-temperature multinuclear (17O, 23Na, and 29Si) solid-state NMR techniques. It reveals the inhomegeneity of chemical phases in this electrolyte. The increased level of Na-doping has led to increased degree of amorphorization in structure, which may be correlated to the enhancement in ionic conductivity. The foundational knowledge gained from this research may have significant impact on understanding the critical structure-conductivity relationship and designing new solid-state fast ion conductors for advanced electrochemical energy conversion and storage systems. References (1) Liang, F. L.; Zhou, W.; Li, J.; Zhu, Z. H.: Microwave-plasma induced reconstruction of silver catalysts for highly efficient oxygen reduction. J Mater Chem A 2013, 1, 13746-13749. (2) Zhu, Y. L.; Chen, Z. G.; Zhou, W.; Jiang, S. S.; Zou, J.; Shao, Z. P.: An A-Site-Deficient Perovskite offers High Activity and Stability for Low-Temperature Solid-Oxide Fuel Cells. Chemsuschem 2013, 6, 2249-2254. (3) Singh, P.; Goodenough, J. B.: Monoclinic Sr1-xNaxSiO3-0.5x: New Superior Oxide Ion Electrolytes. J Am Chem Soc 2013, 135, 10149-10154. (4) Singh, P.; Goodenough, J. B.: Sr1-xKxSi1-yGeyO3-0.5x: a new family of superior oxide-ion conductors. Energ Environ Sci 2012, 5, 9626-9631. (5) Wei, T.; Singh, P.; Gong, Y. H.; Goodenough, J. B.; Huang, Y. H.; Huang, K.: Sr3-3xNa3xSi3O9-1.5x (x=0.45) as a superior solid oxide-ion electrolyte for intermediate temperature-solid oxide fuel cells. Energ Environ Sci 2014, 7, 1680-1684.

The high-temperature solid oxide fuel cells (SOFCs) are the most efficient and green conversion technology for electricity generation from hydrogen-based fuel as compared to conventional thermal power plants. Many efforts have been made to reduce the high operating temperature (>800 °C) to intermediate/low operating temperature (400 °C<T<800 °C) in SOFCs in order to extend their life span, thermal compatibility, cost-effectiveness, and ease of fabrication. However, the major challenges in developing cathode materials for low/intermediate temperature SOFCs include structural stability, catalytic activity for oxygen adsorption and reduction, and tolerance against contaminants such as chromium, boron, and sulfur. This research aims to provide an updated review of the perovskite-based state-of-the-art cathode materials LaSrMnO3 (LSM) and LaSrCOFeO3 (LSCF), as well as the recent trending Ruddlesden-Popper phase (RP) and double perovskite-structured materials SOFCs technology. Our review highlights various strategies such as surface modification, codoping, infiltration/impregnation, and composites with fluorite phases to address the challenges related to LSM/LSCF-based electrode materials and improve their electrocatalytic activity. Moreover, this study also offers insight into the electrochemical performance of the double perovskite oxides and Ruddlesden-Popper phase materials as cathodes for SOFCs.

This paper reports a new approach to develop functional solid oxide fuel cells (SOFC) electrolytes based on nanotechnology and two-phase nanocomposite approaches using non-oxygen ion or proton conductors, e.g., lithium aluminate-lithium sodium carbonate, with great freedom in material design and development. Benefited by nanotechnology and nanocomposite technology, the lithium aluminate-lithium sodium carbonate two-phase composite electrolytes can significantly enhance the material conductivity and fuel cell performance at low temperatures, such as 300 degrees C-600 degrees C compared to non-nano scale materials. The conductivity mechanism and fuel cell functions are discussed to be benefited by the interfacial behavior between the two constituent phases in nano-scale effects, where oxygen ion and proton conductivity can be created, although there are no intrinsic mobile oxygen ions and protons. It presents a new scientific approach to design and develop fuel cell materials in breaking the structural limitations by using non-ionic conductors on the desired ions i.e., proton and oxygen ions, and creating high proton and oxygen ion conductors through interfaces and interfacial mechanism.

Fuel cells have developed of excessive interest as a probable economical, efficient, and clean candidate for alternative and environmental friendly power generation services. Solid Oxide Fuel Cell (SOFC) is an elevated temperature fuel cell, dealing with power generation as well as heat. Up to now many studies have been made to replace platinum, Pt, with a new cathode catalyst for intermediate temperature-solid oxide fuel cells (IT-SOFC) (500 °C&amp;lt;T) range but research has become inadequate. Since Pt sources are limited and very expensive, they could not meet the supply for the commercial fuel cells, the scientists started for searching new materials. There are two important aspects about SOFC cathodes, different cathode materials effect on the electrode electrochemical performance and the oxygen reduction reaction (ORR) kinetics. Understanding in these concepts would lead to improvements of SOFC systems. The production of novel and supreme cathode electrodes used in IT-SOFC is aimed to employ cheaper metals (Fe, Co, Cr, Mn, Gd, and V) by using superior properties of perovskite structure. The reduction of oxygen on metal oxide surface is achieved within the complicated mechanism. The completion of these steps depends on the nature of oxide ion carrier in cathode, atomic formation in crystal structure, and microstructure of cathode materials. The analysis of the impedances required the use of three to four (RQ) circuits in series in the equivalent circuit model. Of the four cathodes synthesized, the vanadium doped cathode on YSZ showed the highest area specific resistance.

In recent years, various environmental problems such as rising temperature, droughts, and extreme weather events have become more serious in many parts of the world because of global warming. One of the causes of the global warming is an increase in emissions of greenhouse gases such as CO2, CH4, and N2O, those are emitted during a combustion of fossil fuels such as coal, oil, and natural gas in thermal power generation. As energy consumption accelerates year by year, the depletion of fossil fuels is also becoming an issue. Therefore, hydrogen energy is attracting attention. Hydrogen is known as a clean energy because it reacts with oxygen to produce only water and chemical energy.Fuel cells are attracting attention as a new power generation device that produces electricity from hydrogen energy. Fuel cells generate electricity directly through chemical reactions, resulting in minimal power generation loss from energy conversion. Solid oxide fuel cells (SOFC), in which solid oxide electrolyte membrane (SOEM) is used as the electrolyte membrane, have particularly high-power generation efficiency. On the other hand, the operating temperature of SOFCs is extremely high (over 1000 K), which accelerates degradation of SOEM. Therefore, it is necessary to lower the operating temperature from high to medium (about 700 K) while maintaining high power generation efficiency.To solve this problem, we focus on dual-phasing and nano-structuring of SOEMs. Previous studies of SOEM have shown that dual-phase membranes have better ion transport performance than a single-phase membrane. For example, a dual-phase SOEM is composed of SSC (SrSc0.1Co0.9O3-d) with perovskite structure and SDC (Sm0.2Ce0.8O2-d) with fluorite structure. One the other hand, nano-structuring are nano-thin film and nano-crystalline. Nano-thin film is a method of forming an electrolyte film of several μm by layering nano-films of several nm in size. Nano-crystalline is a method to reduce a crystal size to several tens of nanometers. By these nano structures, the resistance of ion conduction is reduced, and ion conductivity is improved.However, the number of interfaces in dual-phase SOEM and nano structured membrane is expected to increase. Previous studies have reported a decrease in ion conductivity near the interface between different structures of membrane. This decrease in ion conductivity at the interface is caused by an increase in the energy barrier as the conduction path passes through the interface. The correlation between the reduction of ion conductivity and nano structures in membrane has not been clarified clearly.In this study, we analyze the mechanism of oxygen ion conductivity reduction near the interface by numerical simulations. Molecular simulations are performed to build up information by multi-scale analysis. Specifically, density functional theory (DFT), molecular dynamics (MD), and kinetic Monte Carlo (kMC) are performed in a bottom-up manner. First, MD simulations were performed using a potential model constructed from the energy states in the atomic arrangement at the interface obtained by DFT. We analyzed the ion conductivity at the interface and its crystal size dependence. We also create a hopping model of oxygen ions moving from site to site for kMC simulations. Next, kMC simulations are performed to analyze the oxygen ion conductivity in the dual-phase SOEM including interface, on a time and spatial scale similar to that of a real SOEMs.In this presentation, we report on the results of MD simulation. A dual-phase SOEM model consisting of SSC and SDC was used as the simulation model (Fig.1(a)). The diffusion coefficient of oxygen ions was obtained as an indicator of ionic conductivity. Because the ionic conductivity is determined by the balance between the energy barrier of the conduction path and the kinetic energy of the ions involved in ionic conduction. In this study, the activation energy for the diffusion was calculated as the energy barrier. The activation energy was estimated from Arrhenius relation of diffusion coefficient. The number of unit cells in the dual-phase SOEM model was varied to change the crystal size. As a result, both the diffusion coefficient and activation energy increase as the crystal size of SSC increases. On the other hand, as the crystal size of SDC increases, although the diffusion coefficient decreases, the activation energy increases (Fig.1(b)). These results show the dependence of the diffusion coefficient and activation energy on the crystal size in a dual-phase SOEM. Figure 1