Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation

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Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation Zilin Yan a,*, Shotaro Hara b, Naoki Shikazono a a

Institute of Industrial Sciences, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan Department of Mechanical Engineering, Faculty of Engineering, Chiba Institute of Technology, 2-17-1, Tsudanuma, Narashino, Chiba 275-0016, Japan

b

article info

abstract

Article history:

Microstructural parameters such as triple phase boundary (TPB) density, surface area

Received 14 February 2017

density, connectivity and tortuosity of different phases strongly influence the performance

Received in revised form

of solid oxide fuel cells (SOFCs). In this study, the effect of the powder morphology on the

16 March 2017

microstructural parameters of a La0.6Sr0.4Co0.2Fe0.8O3 (LSCF) cathode is comprehensively

Accepted 20 March 2017

examined using Kinetic Monte Carlo (KMC) simulations. A number of numerical samples

Available online xxx

consisting of spheres or clumped spheres are created using a Discrete Element Method (DEM), taking into account the powder morphology such as particle size, particle size

Keywords:

distribution, particle aspect ratio and sphericity, and particle orientation. The DEM-

Solid oxide fuel cells

generated numerical structures with different particle morphologies are submitted to the

Powder morphology

KMC simulations. Their effects on relative density, densification rate, surface area density,

Electrode microstructure

tortuosity factor of LSCF phase and tortuosity factor and connectivity of the pore phase are

Sintering

compared and analyzed.

Kinetic Monte Carlo

© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Solid oxide fuel cells (SOFCs) are promising energy conversion systems for their excellent energy efficiency and fuel flexibility [1]. Microstructural parameters such as triple phase boundary (TPB) density, surface area density and tortuosity factors of different phases in electrodes strongly affect the performance of SOFCs [2e8]. The microstructures of electrodes need to be porous but highly percolated to provide sufficient electrochemical reaction sites and conduction of

ion/electron/gas. On the other hand, the electrolyte requires very dense microstructures to prevent gaseous fuel permeation. These microstructures are supposed to possess good thermal stability under long-term operations. Therefore, the design and tailoring of the microstructures (especially the electrodes) in SOFCs is a key technology in the development of the SOFCs [9]. Sintering phenomenon plays an important role in microstructural change of the electrodes during the firing process [10e12] as well as under the operation condition [13e17]. For example, one of the reasons that cause the degradation of electrodes is the coarsening of electrode

* Corresponding author. E-mail addresses: [email protected], [email protected] (Z. Yan). http://dx.doi.org/10.1016/j.ijhydene.2017.03.136 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136

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materials at an elevated operation temperature, typically in the range of 750e900
C for Nickel (Ni)-Yttria stabilized Zirconia (YSZ)jGd0.1Ce0.9O1.95 (GDC)jLa0.6Sr0.4Co0.2Fe0.8O3 (LSCF) SOFCs. These layered structures are usually made initially using tape-casting or screen-printing of slurry consisting of powder and organics, followed by drying and sintering or cosintering processes [18e21]. It is well known that the final microstructures of a sintered body depends on the powder properties in green state and processing parameters such as sintering temperature and sintering time [22]. The initial configuration of particles in the green body involves many variables such as crystallite size, particle size, particle size distribution (PSD), particle shapes, and packing condition. Understanding the effects of these factors on the microstructural evolution is crucial for the electrode design of SOFCs. In recent years, the correlations between microstructures and powder morphologies have been intensively explored both experimentally and numerically for SOFC materials. Zhang et al. [23] showed that YSZ powder with a small particle size and a narrow PSD can obtain dense YSZ electrolyte while YSZ powder with high aggregates resulted in very porous YSZ electrolyte. Song et al. [24] studied the effect of size of La0.7Sr0.3MnO3 (LSM) powder on cathodic performance of nonporous LSM/YSZ composite cathode. They found smaller nano-sized LSM particles were more sinterable and undergo excess grain growth to inhibit TPB formation. Prasad et al. [25] revealed in dilatometric studies that the sintering behavior of GDC powder was a cumulative function of various powder morphologies and, in particular, strongly influenced by the agglomeration. Li et al. [26] found that the Nickel (Ni) e Samaria-doped ceria (SDC) anode electrical conductivity depended strongly on the NiO powder morphology and particle sizes. Fukui et al. [27] showed from the experiments that the morphology of the resultant Ni-YSZ cermet anode was strongly influenced by the particle size and the shape of the € lker et al. [28] suggested powder mixture of NiO and YSZ. Vo that under certain conditions the performance of composite cathodes can be enhanced by using electronic conducting particles of size different from that of the ionic conducting particles when compared to the best possible configuration of monodisperse particles. Sato et al. [29] showed that nanostructured LSM/YSZ formed a large amount of TPBs, giving rise to high-performance of intermediate temperature (IT) e SOFCs. Pharoah et al. [30] found that with respect to closepacked structures, the TPB length, the effective solid phase conductivity and the electrode performance increased with increasing base particle aspect ratio, while the pore phase effective diffusivity decreased with the increase of the base particle aspect ratio. Murata et al. [31] showed in experiments that an LSCF cathode fabricated with finer powder provided better SOFC performance. Alternatively, a number of numerical simulation models have been developed to investigate the relationship between SOFC performance and microstructures. The discrete element method (DEM) [32e36] is widely used to model the electrodes as 3-dimensional (3D) random packing structures composed of electronic and ionic particles. The effective conductivity is calculated by using a resistor network model [32], where the overpotential is obtained using Kirchhoff's current law.

However, none of these references ever reported the impacts of powder morphology on the microstructural characteristics after sintering. Thus, simply assumption the electrode microstructures as overlapped spheres may be not sufficient for quantitative prediction. Wonisch et al. [37] showed in DEM simulations of sintering of alumina powder that the densification rate declined significantly as the width of the PSD increases. Martin et al. [38,39] demonstrated in DEM simulations that the microstructures can be affected by green packing density, packing conditions and agglomeration of powders. With recent advances in the DEM method, irregularly shaped particles can be represented using multisphere approach [40]. This opens up a possibility to consider realistic particles for the DEM modeling of sintering. However, when dealing with the last stage of sintering, the DEM sintering simulation will be fallacious as grain coarsening and contact impingement are hardly captured [39]. The Potts Kinetic Monte Carlo (KMC) method is recently emerging as a powerful tool at the mesoscale to simulate the microstructural evolution caused by sintering [41e43]. It has been proven to be a robust method to deal with all stages of sintering process. Particularly, the KMC method can handle arbitrarily shaped particles while it is so simple to code. Bjørk et al. [44] found that the densification rate and the final density obtained were inversely proportional to the distribution width using KMC simulations. Hara et al. [45] predicted the microstructural characteristics of sintered sub-micrometric Ni powder using KMC simulations, which were verified by focused ion beam-scanning electron microscopy (FIB-SEM) tomography characterizations of sintered real microstructures. Zhang et al. [46] utilized the KMC method to study the thermal stability of LSM/YSZ composite electrode composed of overlapped spheres. They showed that the evolutions of TPB length, porosity, and tortuosity factor of pores are faster for the samples with smaller particles than for the samples with larger particles. In addition, they found that high TPB density can be obtained by using small particles. Yan et al. [47] showed that with calibrated input parameters, the KMC model can predict the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode during sintering in a real-time scale. In this study, we combine the strengths of both DEM and KMC methods to study the influence of the powder morphology on the microstructure of LSCF cathode as a case study during sintering process. In addition, we will describe the workflow for a typical sintering simulation by combining the DEM and KMC models. In Section Results and Discussions, we will address the effect of the morphological factors on the microstructural parameters. And finally, we will summarize this research and point out some directions to future explorations.

Methodologies Workflow in this study In this study, we bridge from the DEM simulations for power packing to the KMC simulations for powder sintering. The workflow in this study is shown in Fig. 1. First, a serial of powder samples with random packings are generated using

Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136

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Fig. 1 e The workflow in this study bridging DEM simulations and KMC simulations.

DEM simulations in an open source code LIGGGHTS [48]. In consideration of the particle shapes, irregularly shaped particles are reproduced using a multisphere approach in DEM simulations. Loose random packings with a packing density of r ¼ 0.1 are generated, and then the packings are compressed gradually in triaxial directions. After each step compression, a system relaxation is applied so that the particles will rearrange to recover the overlapping between particles. Repetitive compression and relaxation are conducted until the sample achieves a packing density of r ¼ 0.55e0.57. Powder packings with different particle size, particle size distribution (PSD), particle aspect ratio (AR), particle sphericity and particle orientation are considered. A cubic representative volume element (RVE) with an edge length of 7.5 mm is sampled from each distinct packing. These RVEs are then voxelized into 150  150  150 voxels as the starting microstructures for the KMC simulations. In this study, each particle is assumed to have a single grain. The microstructures are submitted to an in-house KMC sintering code. Microstructural characteristics such as relative density, surface area density and connectivity and tortuosity factor of different phases are calculated to assess the impacts of the powder morphological factors on the sintered microstructural characteristics.

Discrete element method (DEM) The DEM in this study is based on the soft-sphere approach originally developed by Cundall and Strack [49]. The motions of individual particles are described using the equations of motion, Eqs. (1) and (2). The forces and torques caused by gravity, particle deformation, and friction are considered for a particle i in contact with particle j as follows: mi

Ii

 dvi X n ¼ Fij þ Ftij þ mi g dt

 dui X ¼ Ri  Ftij  trij dt

(1)

(2)

where mi, g, Ii, vi and ui are mass, gravity vector, moment of inertia, translational velocity and rotational velocity of particle i, respectively. Fnij and Ftij are the normal and the tangential forces due to interaction between particle i and j at the current time step as depicted in Fig. 2. Ri is the vector between the center of particle i and the contact point where the tangential force Ftij is applied. trij is the torque due to rolling friction. In this work, an adapted Hertz-Mindlin contact model [50] is utilized to model the powder mechanics in the green packing of a porous electrode. In the fabrication of SOFCs, the electrode is usually formed initially from slurry or ink using either tape-casting or screen-printing. In a real tape-casting setup, also known as doctor-blading, depending on the blade height, reservoir height, and substrate speed, the viscous drag force and gravity will influence the migration of particle during the slip casting to different degree [51]. However, for simplicity, for the time being we assume that the cathode is formed by compaction of dry powder by ignoring both the viscous drag force and gravity which cause uncertainties in particle distribution and orientation. In this sense, under the current conditions we in fact model the green microstructure of an electrode made by die compaction, for example, pellet model electrode. In future, a more sophisticated coupling of DEM with CFD (computational fluid dynamics) will be utilized to assess the exact effects of both the viscosity of liquid and gravity of particles during the tape casting of slurry. When tangential force Ftij is rather mild and Eq. (3) is satisfied, it will cause a small region of slip (termed “microslip”) at contacts.      t   Fij  < ms Fnij 

(3)

where ms is the static friction coefficient between particles. If Eq. (3) is not satisfied, the slip covers all the contact area and this can be referred as “gross sliding” [19]. In this case, the tangential force is given by Eq. (4) according to Coulomb's friction law,

Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136

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Fig. 2 e DEM models: (a) schematic representation for the contact between two particles i and j; (b) representation of the irregularly shaped particle using clumped spheres.

  dt   ij Ftij ¼ ms Fnij    dtij 

(4)

where dtij is the tangential indentation vector at the particle contact. To create samples with non-spherical particles, the multisphere method is employed to approximate irregular shape of a particle by conjoining multiple spheres and integrating them as one rigid body [52], as shown in Fig. 2(b). Mass center and the inertial tensor of the rigid body are calculated using a Monte Carlo method [52]. In this study, we have considered different morphological factors as shown in Fig. 3. Five groups of samples are created using the procedures detailed in Section Workflow in this study: (1) Samples consisting of monosized particles with different particle sizes, i.e., R ¼ 0.2 mm, 0.3 mm, and 0.4 mm. (2) Volume-based lognormal distributed samples with the same size D50 ¼ 0.5 mm, different PSD width, i.e., s ¼ 0.2, 0.4, and 0.6. (3) Samples with ellipsoidal particles of different particle aspect ratio (AR) in the range of AR ¼ 1.0e5.0. The aspect ratio (AR) is defined as the ratio of the largest diameter to the smallest diameter that is orthogonal to former [53], i.e., AR ¼ dmax =dmin . Ellipsoidal particles chosen for the aspect ratio study consist of differently sized spheres. The ellipsoidal particles have the same volume equivalent diameter size Dv ¼ 1.0 mm but differ in AR values, which is calculated as AR ¼ a/b, where a is the major axis and b the minor axis. (4) Samples with particles of the same AR value (AR ¼ 1.0) and the same volume equivalent diameter size (Dv ¼ 1.0 mm) but differing in the sphericity values. Sphericity (F) is defined as F ¼ p1=3 ð6Vp Þ2=3 =Ap , where Vp is the volume of the object, Ap is its surface area [54]. Vp and Ap are calculated by assuming that a multisphere clump has an ideal shape. For example, for a cubic clump Vp ¼ a3 and Ap ¼ 6a2, where a is the edge length. In this study, four particle shapes of tetrahedron

(F ¼ 0.67), cube (F ¼ 0.81), cylinder (F ¼ 0.87) and sphere (F ¼ 1.0) are considered. (5) Samples with aligned packing of ellipsoidal particles in group (4) with AR ¼ 5.0. These high-AR particles are orientated in x direction while in y and z directions, the packing appears isotropic. For a better comparability, we reproduce the packings in each group at a same pre-designed packing density r ¼ 0.55e0.57. This is to minimize the effect of different green density on sintering kinetics so that in each parametric study the effect of the considered variable can be clearly examined. Wonisch et al. [37] employed the same consideration for study on the effect of particle size distribution during sintering in DEM.

Kinetics Monte Carlo simulations of sintering KMC model description In this study, the Potts Kinetics Monte Carlo (KMC) model is used for sintering simulation. It is originally developed in 1950's [55] and is recently pioneered by Tikare and co-workers [41e43,56,57]. In this model, the sample including pores and grains is discretized into 3D voxel grids. A unique state q ¼ 0 is assigned to all the pore sites. A positive integer number qi is assigned to each grain site, which signifies the crystallographic orientation of the grains. Thus, the ensembles of continuous sites with the same qi state define individual crystal grains. In this model, sintering driving force is a reduction of system interfacial energy E that is defined as Eq. (5), E¼

N X 26    1X Jij 1  d qi ; qj 2 i¼1 j¼1

(5)

where N is the total number of sites in the system; 26 is the number of nearest-neighbor sites of site i in a 3D model; Jij is the interaction energy between sites i and j, corresponding to the surface energy Js for pore-grain interaction, and the grain boundary energy Jgb for grainegrain interaction; and d is the Kronecker delta function with d ¼ 0 (qi s qj) or d ¼ 1 (qi ¼ qj). Thus, only boundary or surface can contribute to the energy E. In this study, we employ the same sintering mechanisms for solid-state sintering in Ref. [41]: (i) curvature driven grain

Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136

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Fig. 3 e Numerical samples prepared with DEM.

growth by short range atomic diffusion across the grain boundaries; (ii) pore migration by long range surface diffusion of pores; and (iii) vacancies formation on grain boundaries and annihilation along grain boundaries to cause densification. (I) Grain growth

(III) Vacancy formation and annihilation

To simulate the grain growth, a grain site randomly chosen and its q state is exchanged at random with that of a neighboring grain site. The standard Metropolis algorithm is used to proceed the grain growth attempt with a probability P given by Eq. (6), 8   > < exp DE for DE > 0 KB T P¼ > : 1 for DE  0

grain sites. Pore migration is simulated by exchanging a pore site at random with a neighboring grain site. The same Metropolis algorithm is used to proceed this site exchange attempt based on Eq. (6).

Vacancy formation is achieved simply by pore site and grain site exchange attempted at a much higher simulation temperature. If a vacancy is formed on the grain boundary after the exchange, Eqs. (5) and (6) are used to decide to acceptance probability of the exchange. Vacancy annihilation is conducted by collapsing sites along a chosen direction pointing from the vacancy to surface [43].

(6)

where E is the energy calculated using Eq. (5); KB is the Boltzmann constant and T is the simulation temperature. (II) Pore migration In this model, a pore is defined as ensembles of contiguous pore sites and a vacancy as a single pore site isolated from

Simulation parameters In our KMC models, the sintering temperatures are normalized by interfacial energy or surface energy. For example, grain growth temperature KBTgg value is normalized by grain boundary energy Jgb; pore migration temperature KBTpm value and vacancy formation temperature KBTvf value are normalized by surface energy Js. The surface energies of solids typically fall in a range 0.5e2.0 J m2 [58]. In this study, we

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simulate the sintering of La0.6Sr0.4Co0.2Fe0.8O3 cathode as case study. However, little data are reported for La0.6Sr0.4Co0.2Fe0.8O3. In this study, we set the surface energy Js to 1.8 J m2. This value approximates to the estimation according to Mullin [59] where the Js as the elastic work done to create a free surface and found to be (Y/8)  1010 m, where elastic modulus Y ¼ 152 GPa for La0.6Sr0.4Co0.2Fe0.8O3 [60]. Jgb is expected to be smaller than Js and is set to 1.0 J m2 [61]. The KMC simulation parameters, i.e. the sintering temperatures and frequencies for the three sintering mechanisms, are calibrated against experiments on La0.6Sr0.4Co0.2Fe0.8O3 pellet samples sintered at 1000
C as detailed in our previous work [47]. We use the same calibrated parameters for this simulation study, i.e., KBTgg ¼ 1.16, fgg ¼ 0.68, KBTpm ¼ 1.48, fpm ¼ 0.20, KBTvf ¼ 37.0, and fvf ¼ 0.52. KMC simulations are carried out using an inhouse KMC code on an Intel Xeon Cluster. Sintering simulation time tmcs in Monte Carlo time steps (mcs) is scaled with the physical time tphy using a scaling factor of b ¼ 0.00465 min mcs1, i.e., tphy ¼ 0.00465 tmcs. Table 1 summarizes the parameters used in this study. It is worth mentioning that since the KBT values are normalized by Js or Jgb, their experimentally calibrated values will implicitly correct the errors in Js and Jgb taken from literature, if any.

Microstructural parameters Based on the KMC modeled 3D microstructures, microstructural characteristics such as relative density, surface area density, and tortuosity factors of LSCF and pores, and pore connectivity can be quantified. Relative density is defined as the ratio of the total number of solid voxels to the total voxel number. Surface area density is defined as Sa:v ¼ Sa/V (mm2 mm3), where Sa is the total surface area of solid calculated using a marching cube method [62], and V is the total volume of both solid and pore phases. Tortuosity factors (t) of LSCF and pore phases were calculated using a random walk method as detailed in Ref. [3]. Connectivity of the pores is defined as the ratio of total volume of connected pore phase to the total volume of the pores [45].

Results and discussions Effect of particle size Fig. 4 shows the effect of the particle size in the range of R ¼ 0.2e0.4 mm on the microstructural parameters of LSCF cathode during sintering. It shows that for the same sintering

Table 1 e The parameters used for the KMC simulations. Parameters Voxel size [nm] Surface energy Js [J m2] Grain boundary energy Jgb [J m2] Grain growth temperature KBTgg [e] Grain growth frequency fgg [e] Pore migration temperature KBTpm [e] Pore migration frequency fpm [e] Vacancy formation temperature KBTvf [e] Vacancy formation temperature fvf [e]

Values

References

50 1.80 1.0 1.16 0.68 0.68 1.48 37.0 0.52

e [46] [61] [47] [47] [47] [47] [47] [47]

time, a powder with smaller particle size has higher relative density. As shown in the inset graph in Fig. 4(a), the densification rate, defined as 1=rdr=dt, increases as the particle size decreases in the initial stage. This means that a powder with a smaller particle size has a better sinterability. In solid-state sintering, the sintering driving force is proportional to the inverse of the particle radius [63]. On the other hand, a powder with a smaller particle size has a lower sintering onset temperature [64]. Especially, the onset sintering temperature for nano-sized powder is much reduced than for coarse powder. This suggests that the fabrication temperature for LSCF cathode with smaller particle size need to be reduced to secure sufficient porosity for a SOFC cathode. After about 60 min, the trend is reversed, i.e., a powder with smaller particle size shows a smaller densification rate, in other words, better thermal stability. This is because, after about 60 min, the sample with smaller particle size (R ¼ 0.2 mm) is much denser (e.g., r ¼ 0.95), the densification rate is very slow at the final stage of sintering. In the KMC model, the vacancy formation frequency is intrinsically very small and leads to a very small densification rate at the final stage of sintering. Fig. 4(b) shows that a decrease in the particle size results in an increased surface area density, which will efficiently increase the electrochemical reaction in the cathode during SOFC operation. However, after about 50 min, the trend is reversed. As shown in the inset graph in Fig. 4(b), the degradation rate of the surface area density, defined as dsa:v/dt, is faster for a powder with smaller particle size than for a powder with larger particle size. This trend is reversed after about 50 min. This can be explained by the same reason for the trend change in the density and densification rates, since the surface area density is proportionally associated with the porosity. Fig. 4(c) shows that a powder with smaller particles leads to a lower tortuosity factor for the LSCF phase. However, the effect of particle size on LSCF tortuosity factor is very slight. Fig. 4(d) shows conversely that a powder with a larger particle size leads to a smaller tortuosity factor for the pore phase for the same sintering time. It is obvious that the interparticle contacts separate the pore phase; a higher contact number will result in a lower connectivity of pores and consequently a higher tortuosity factor for pore phase. Before sintering (t ¼ 0), there are more particle contacts in the green packing for the powder with a smaller particle size at the same given packing density (r ¼ 0.55). This explains a slightly larger tortuosity factor (Fig. 4(d)) and lower connectivity of pores (Fig. 4(e)) for the powder with smaller particles (R ¼ 0.2 mm) at the beginning of sintering. As sintering proceeds, the powder with a smaller particle size sinters much faster (cf. Fig. 4(a)), resulting in more contacts and isolated pores and making the even higher tortuosity for pores compared with powder with a larger particle size. The same reason applies to trend in the pore connectivity as functions of sintering time. In conclusion, using a smallerparticle-size powder can enhance the surface area density, but the sinterability or thermal stability of the cathode is also undesirably increased. This also causes a decrease in the LSCF tortuosity factor and an undesired increase in tortuosity factor of pore phase. In literature, nanostructured cathodes [16,65e67] are developed to improve the performance of SOFCs but their thermal stabilities become worse. A proposed solution is to add inert non-sintering nanoparticles [68,69] to

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Fig. 4 e Effect of particle size on the microstructural parameters: (a) relative density and densification rate as functions of sintering time; (b) surface area density and its degradation rate as functions of sintering time; (c) tortuosity factor of LSCF as functions of sintering time; (d) tortuosity factor of pores as functions of sintering time; and (e) pore connectivity as functions of sintering time.

the sintering phase, and these inert particle will serve as a second pinning phase so as to hinder the grain coarsening of the LSCF cathode.

Effect of particle size distribution Fig. 5 shows the effect of the particle size distribution on the microstructural parameters of a LSCF cathode during sintering. It shows in Fig. 5(a) that a powder with a wider PSD (s ¼ 0.6) has a smaller densification rate, which means a better thermal stability. This is because, for the same given packing density and the same D50 size, a wider-PSD powder has a smaller average contact number because the smaller particles can be accommodated in the spaces between bigger particles. Consequently, a wider-PSD powder expects a slower sintering kinetics. The same effect of PSD is found independently by Wonisch et al. [37] in DEM simulations and Bjørk et al. [44] in KMC simulations. Fig. 5(b) shows that the effect of the PSD in this study on the surface area density of the LSCF phase is negligible. It is noticed that the powder with a wider-PSD (s ¼ 0.6) has a very rapid surface area density degradation rate dsa:v/dt as soon as the sintering starts as shown in the inset graph of Fig. 5(b). This is because for a volume-based wide-PSD powder, it contains a large number of fine particles, which sinter very fast. The effect of the PSD on the tortuosity factor of the LSCF phase is not significant as shown in Fig. 5(c). On the other hand, for the same sintering time, the wider-PSD powder provides a better pore phase connectivity and hence a smaller tortuosity factor for the pore phase as

shown in Fig. 5(d) and (e), respectively. This might be because there are much fewer particle contacts, which are separating the pore phase, for a wider-PSD powder compared with a narrower-PSD powder packing. Although there are more fine particles for the wider-PSD powder, they will rapidly sinter and merge, contributing little to the number of particle contacts, which we think is the main factor that influences the connectivity for pore phase. In addition to this, the powder with wider-PSD sinters slower (as shown in Fig. 5(a)), resulting in a relatively higher porosity after the same sintering time. It is well known that a high porosity is associated with a low tortuosity factor of pore phase (Fig. 5(d)) and a high pore connectivity (Fig. 5(e)) in porous media. It is concluded that using a wider-PSD powder can improve the tortuosity factor of the pore phase and thermal stability of cathode, while the surface area density and LSCF tortuosity factor are almost not affected.

Effect of aspect ratio (AR) Fig. 6 shows the effect of particle aspect ratio (AR) on the microstructural parameters of an LSCF cathode during sintering. It is seen in Fig. 6(a) that for the same given particle size, powder with higher aspect ratio (AR) has a higher relative density after the same sintering time. We can see that the powder with spherical particles (AR ¼ 1.0) has the lowest relative density. However, in the range of AR ¼ 1.0e2.0, it seems that the influence of the AR is very slight. From the inset graph in Fig. 6(a), we see that with an increase in particle

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Fig. 5 e Effect of the particle size distribution on the microstructural parameters: (a) relative density and densification rate as functions of sintering time; (b) surface area density and its degradation rate as functions of sintering time; (c) tortuosity factor of LSCF as functions of sintering time; (d) tortuosity factor of pores as functions of sintering time; and (e) pore connectivity as functions of sintering time.

Fig. 6 e The effect of particle aspect ratio on the microstructural parameters: (a) relative density and densification rate as functions of sintering time; (b) surface area density and its degradation rate as functions of sintering time; (c) tortuosity factor of LSCF as functions of sintering time; (d) tortuosity factor of pores as functions of sintering time; and (e) pore connectivity as functions of sintering time. Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136

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AR value, the densification rate increases. This may be because the elongated particles highly interact with each other in the powder with high-AR particles. And for the same given packing density, higher AR powder has larger average contact number, resulting in greater sintering kinetics. Fig. 6(b) shows that higher AR value particles show larger initial surface area density (0e40 min). However, the initial degradation rate is also high for higher AR samples. At about 40 min, this degradation trend reverses. Increase in AR value decreases the tortuosity factor of LSCF phase. This may be because elongated particles can improve the connectivity of LSCF phase. Chen et al. [70] suggested that longer and thinner fibers were more efficient in facilitating both mass and charge transport. However, the effect of the AR value on the LSCF tortuosity factor is not significant in this study. This is because LSCF phase is already highly connected (connectivity of about 0.99) at relative density of above 0.55 in this study. On the contrary, with an increase in the AR, the connectivity of the pore phase decreases (Fig. 6(e)), resulting in an increase in the tortuosity factor of the pore phase (Fig. 6(d)). This result is in agreement with literature report [30]. The effect of the AR value in the range of AR ¼ 1.0e2.0 on all the microstructural parameters is very mild.

Effect of sphericity Fig. 7 shows the effect of particle sphericity on the microstructural parameters for fixed AR ¼ 1.0 and Dv ¼ 1.0 mm. It can be seen in the inset graph of Fig. 7(a), with an increase in the

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sphericity of the particles, the powder's densification rate increases. Thus, for the same sintering time, the sample with the spherical particles (Ф ¼ 1.0) has the lowest relative density; the sample with the tetrahedron shape particles (Ф ¼ 0.67) has the highest density. This is because that decrease in the particle sphericity and increase in the microsurface roughness of particles will lead to greater intimate contacts between particles and increased internal surface area that promotes sintering [71]. Conversely, Dupont et al. [72] showed in experiments that yttria ceramic powder with spherical particles demonstrated good sinterability; grooved particles or very regular particles displayed lesser sinterability, while irregular particles made poor sinterable powders. We notice that in their experiments, the different initial green densities that may have an affect on the sinterability are not considered. Under the same compression condition, the powder with spherical powder which will promote sinterability has higher green density, while the powder with irregular shape has much lower green density. In our simulation study, we hold the green density as a constant. This has showed that one of the advantages of the simulation method over experiments is that the uncertainties can be strictly controlled in numerical simulations. It is shown in Fig. 7(b) that, the surface area density increases with a decrease in the particle sphericity. However, it seems that the effect of particle sphericity in this study on the sintering kinetics and the surface degradation rate is very slight. Fig. 7(c) shows that with a decrease in the particle sphericity, the tortuosity factor of the LSCF phase decreases, especially at the very beginning of the sintering.

Fig. 7 e Effect of particle sphericity on the microstructural parameters: (a) relative density and densification rate as functions of sintering time; (b) surface area density and its degradation rate as functions of sintering time; (c) tortuosity factor of LSCF as functions of sintering time; (d) tortuosity factor of pores as functions of sintering time; and (e) pore connectivity as functions of sintering time. Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136

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Later on, as the sintering continues, the effect of the sphericity seems to be negligible. This may be due to the fact that the curvature of the particle surface decreases as sintering proceeds, and an irregular shape tends to re-shape towards a spherical shape. Fig. 7(d) and (e) shows the effect of particle sphericity on the pore tortuosity factor and pore connectivity, respectively. For the shapes currently chosen in this study, the trend is not clear.

Effect of particle orientation Fig. 8 shows how the orientation of particle influences the microstructural parameters of LSCF cathode. It shows that for the same given packing density, a powder with aligned (particles are orientated orderly in x direction as shown in Fig. 3) particle packing has a lower densification rate (Fig. 8(a)) than the powder which has a random particle packing. Thus, for the same sintering time, the former one has a lower relative density. This means that a powder with an aligned packing can improve the thermal stability of the LSCF cathode. This is probably because for an aligned packing, the average contact number is lower than that for a random packing in which the elongated particles highly interact. Fig. 8(b) shows that the ordered packing has a slightly higher surface area density for the same sintering time. The inset graph in Fig. 8(b) shows that the orderly packed powder has lower surface area density degradation rate. This is because, on one hand, the ordered packing has a lower contact number hence less contact areas, leading to more surface areas. On the other hand, the ordered

packing has a lower densification rate as shown in Fig. 7(a), so after the same sintering, it has a higher porosity and surface area density. An important effect caused by the alignment of elongated particles is that anisotropic tortuosity factors for both LSCF and pore phases are observed in the three different directions as shown in Fig. 8(c) and (d). We can see for the sample with orderly alighted particles, in the alignment direction (x axis), the tortuosity factors for both the pore phase and the LSCF phase are lower than the tortuosity factors in the orthogonal directions (y and z axis). In y and z directions, the tortuosity factors of LSCF and pores are isotropic. In the sample with a random packing, the tortuosity factors of the LSCF and pores are isotropic in all the three directions. Fig. 8(e) shows that at the early stage of sintering the pore connectivity almost shows no difference for the two different configurations. As sintering proceeds, the randomly packed powder reaches a higher density and shows lower pore connectivity, which results in a higher tortuosity factor of the pore phase. In conclusion, using elongated particles and aligned hierarchical structure can improve the thermal stability of the LSCF cathode and can reduce the tortuosity factors of both the LSCF and pore phases, which will improve the electronic and ionic conductivities and gas transport. The existing literatures report mainly on electrochemical performance enhancement of electrodes with randomly interweaved nanofiber and nanotube structures. However, the effect of alignment of elongated particles has not been experimentally addressed yet. Similarly, some researchers [73e75] fabricated cathodes or anodes with hierarchical porous microstructures using a

Fig. 8 e The effect of the particle orientation on the microstructural parameters: (a) relative density and densification rate as functions of sintering time; (b) surface area density and its degradation rate as functions of sintering time; (c) tortuosity factor of LSCF as functions of sintering time; (d) tortuosity factor of pores as functions of sintering time; and (e) pore connectivity as functions of sintering time. Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136

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so-called “freeze-casting” method. The aligned pores (in line with cathode thinness direction) effectively reduce the tortuosity factor of the pores and provide good channels for mass transport. Nagato et al. [75] fabricated Ni/YSZ anode with aligned nickel microstructure under magnetic field. By aligning microstructure path of ion/electron/gas in anode, the power of SOFC is enhanced.

Discussion on applicability of the proposed approach The approach proposed works by interfacing DEM simulations for formation of green powder packing and the KMC simulations of the sintering process. On the DEM side, we simply simulate the cathode as compact of dry powders. However, DEM as a very established numerical technique, and with help of excellent commercial and open source softwares, is widely used for the studies on granular and particulate materials. With calibrated input parameters and validated contact models, DEM tools can be used for predicting industrial problems [76]. By coupling DEM with a CFD solver, solid-fluid two-phase flow problem can also be studied [48]. On side of the KMC simulations, this method is proven to be a robust method to model the sintering and has been validated with 3D in-situ X-ray tomography experiments on sintering of cupper powder [41] and FIB-SEM 3D reconstruction data [45,47]. However, for the KMC model which is based on a phenomenological description, its parameter calibration is a challenging aspect. It requires a lot of trial-and-error simulations to determine in the input parameters [45]. We recently proposed a robust and rigorous method to calibrate the KMC input parameter using artificial neural networks for sintering of La0.6Sr0.4Co0.2Fe0.8O3 cathode [47]. The KMC model with the calibrated parameter provides a good prediction for microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode during sintering. Although we apply this approach to the case study using LSCF cathode, the DEM model and KMC model proposed can be also applied to study other devices that are made via sintering process. However, reliable numerical predictions depend on the accuracy of the model and the model input parameters' values. For the DEM simulation of powder forming step, interested readers may refer to Ref. [76] for guideline on DEM simulation calibration. As for the KMC sintering simulation step, in general, modelers shall calibrate the KMC input parameters (Section Simulation Parameters) by comparing simulations and experiments in terms of microstructural parameters such as porosity, grain size, pore size, surface area, and other user-defined microstructural descriptors (e.g., tortuosity). Extra experiments are necessary to validate the model and the calibrated parameters. In order to conduct a real-time prediction, Monte Carlo time steps in a KMC simulation should be related to corresponding physical sintering time using a linear correlation [41].

Conclusions In this study, we propose a numerical approach to bridge powder packing (forming) to powder sintering by combining the DEM method and the KMC method to study the effect of

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powder morphology on the microstructural characteristics of a porous electrode using a LSCF cathode as case study. The simulation results can serve as suggestions for future experimental research. From the results of this study, following conclusions can be drawn:  The DEM method is a very suited tool to look into the powder forming, which is a preceding process prior to the sintering process. By using the multisphere approximation, complexed shaped particles can be represented in the DEM simulations. Hence, irregularly shaped particles can be considered in the powder packing/forming.  Parametric study shows that the powder morphology has important influence on the microstructural characteristics in the sintered LSCF cathode. Simple assumption of spherical particles in the KMC simulations may overlook the effect of the powder morphology.  Using fine sized powder can improve the surface area density and decrease the tortuosity factor of the LSCF phase. However, the decreased particle size at the same time enhances the sinterability of the LSCF, resulting in a decrease in thermal stability of LSCF material. The decreased particle size can also provide a decreased pore phase connectivity, which is disadvantageous for gas transport in the cathode.  A wider-PSD powder can improve the thermal stability by decreasing the sinterability of the powder. Another consequence for increasing width of PSD is that the tortuosity factor of pore phase decreases, which benefits the gas transport in the cathode. The effect of the width of the PSD on the surface area density and tortuosity factor of the LSCF phase is negligible.  Powder with higher AR particles leads to higher surface area density and lower tortuosity factor for LSCF (better ionic and electronic conductivity). However, it also gives lower thermal stability and higher pore tortuosity factor. AR in the range of AR ¼ 1.0e2.0 seems to have a very limited effect.  Powder with irregular shapes has better sinterability (poorer thermal stability). The tortuosity factors for LSCF and pores seem not to be significantly influenced in the study.  In the case of elongated particles being used, alignment of particles in the green state will lead to lower sinterability of the packing, hence a better thermal stability of cathode. As a consequence of the particle alignments, anisotropic tortuosity factors for LSCF and pores have developed. In the alignment direction, the tortuosity factors appear smaller than the other orthogonal directions. In the current scope, all the morphological factors seem to have both beneficial and adverse effects with respect to different microstructural parameters that are related to the SOFC performance. In order to optimize the powder morphological factors for microstructural control of LSCF cathode, we need to evaluate their overall effect on the electrochemical performance of SOFCs, by coupling with electrochemical modeling [62,77]. In addition, the essence of the proposed numerical approach bridging from DEM to KMC can be also applicable to microstructural modeling of anode and other SOFC materials.

Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136

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As part of future work, we will consider more realistic particle morphology by extracting the 3D geometries of real particles using high-resolution tomography techniques for multisphere approximation. In doing this, we aim to reproduce more realistic microstructures for SOFC modeling. This will be a key step for the roadmap to the modeling from powder to power for SOFCs.

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Acknowledgements This work was partly supported by the NEDO Project and the JST CREST Project (JPMJCR11C2).

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Please cite this article in press as: Yan Z, et al., Effect of powder morphology on the microstructural characteristics of La0.6Sr0.4Co0.2Fe0.8O3 cathode: A Kinetic Monte Carlo investigation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2017.03.136