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Three-dimensional microstructural changes in the Ni–YSZ solid oxide fuel cell anode during operation
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Acta Materialia 60 (2012) 3491–3500 www.elsevier.com/locate/actamat
Three-dimensional microstructural changes in the Ni–YSZ solid oxide fuel cell anode during operation George J. Nelson a,b, Kyle N. Grew c, John R. Izzo Jr. a,b, Jeffrey J. Lombardo a,b, William M. Harris a,b, Antonin Faes d,e,1, Aı¨cha Hessler-Wyser d, Jan Van herle e, Steve Wang f, Yong S. Chu g, Anil V. Virkar a,h, Wilson K.S. Chiu a,b,⇑ a HeteroFoaM Center, a DOE Energy Frontier Research Center, USA Department of Mechanical Engineering, University of Connecticut, CT, USA c Sensors and Electron Devices Directorate, US Army Research Laboratory, MD, USA d Interdisciplinary Centre for Electron Microscopy (CIME), Ecole Polytechnique Fe´de´rale de Lausanne, Switzerland e Industrial Energy Systems Laboratory (LENI), Ecole Polytechnique Fe´de´rale de Lausanne, Switzerland f Advanced Photon Source, Argonne National Laboratory, IL, USA g National Synchrotron Light Source II, Brookhaven National Laboratory, NY, USA h Department of Materials Science and Engineering, University of Utah, UT, USA b
Received 16 November 2011; received in revised form 15 February 2012; accepted 21 February 2012 Available online 7 April 2012
Abstract Microstructural evolution in solid oxide fuel cell (SOFC) cermet anodes has been investigated using X-ray nanotomography along with differential absorption imaging. SOFC anode supports composed of Ni and yttria-stabilized zirconia (YSZ) were subjected to extended operation and selected regions were imaged using a transmission X-ray microscope. X-ray nanotomography provides unique insight into microstructure changes of all three phases (Ni, YSZ, pore) in three spatial dimensions, and its relation to performance degradation. Statistically significant 3D microstructural changes were observed in the anode Ni phase over a range of operational times, including phase size growth and changes in connectivity, interfacial contact area and contiguous triple-phase boundary length. These observations support microstructural evolution correlated to SOFC performance. We find that Ni coarsening is driven by particle curvature as indicated by the dihedral angles between the Ni, YSZ and pore phases, and hypothesize that growth occurs primarily by means of diffusion and particle agglomeration constrained by a pinning mechanism related to the YSZ phase. The decrease in Ni phase size after extended periods of time may be the result of a second process connected to a mobility-induced decrease in the YSZ phase size or nonuniform curvature resulting in a net decrease in Ni phase size. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Solid oxide fuel cell; Ni–YSZ anode; Ni coarsening; Degradation; Dihedral angle
1. Introduction Power and electrical efficiency losses in a solid oxide fuel cell (SOFC) can result from changing composition and ⇑ Corresponding author at: Department of Mechanical Engineering, University of Connecticut, CT, USA. Tel.: +1 860 486 3647. E-mail address: [email protected] (W.K.S. Chiu). 1 Present address: Materials and Design Unit, University of Applied Science, Western Switzerland, Switzerland.
microstructure of cell components during operation [1–5]. These changes have been found to reduce the SOFC operating voltage achieved at constant current depending on the cell design and operating conditions [1]. Performance degradation of the SOFC can result from several phenomena, including microstructural changes in the electrode, reactions between materials to form new phases and contamination of active interfaces [2–5]. The coarsening of Ni particles in SOFC anodes is one widely observed example of such deleterious microstructural evolution [1,6–10].
1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.02.041
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Focused ion beam scanning electron microscopy (FIBSEM) and X-ray nanotomography permit three-dimensional imaging of composite electrodes at unprecedented scales [1,11–14], distinguishing them from other imaging techniques applied to explore microstructure and composition in SOFC electrodes. SEM serial sectioning approaches, including FIB-SEM, have fostered a greater understanding of the microstructure and composition in SOFC anodes and cathodes [11,15] and have advanced the understanding of Ni–YSZ anode degradation mechanisms, particularly Ni coarsening behavior [1,6]. However, serial sectioning approaches result in the loss of the imaged sample and are often restricted to ex situ experimental investigations. Full-field X-ray nanotomography permits the non-destructive imaging of anode samples [12,13], with elemental sensitivity achieved for anode microstructures by applying a tunable X-ray source in conjunction with differential absorption imaging across the Ni K-absorption edge [13]. Applying X-ray absorption near-edge structure (XANES) spectroscopy in combination with full-field X-ray nanotomography can expand these capabilities by allowing chemical speciation based on chemical bonding states discerned the XANES spectra [16]. These advances may allow for in situ measurement opportunities with an appropriate environmental chamber [17,18]. The present work extends transmission X-ray microscopy (TXM) techniques to the exploration of degradation in SOFC anodes. X-ray nanotomography measurements of anodes subjected to extended operation have been performed using differential absorption imaging to further elucidate degradation associated with microstructural evolution in the anode phases. Digitized reconstructions of the volumetric data have enabled elemental mapping and microstructural characterization of the Ni, YSZ and pore phases of aged SOFC anodes at a spatial resolution of 32 nm (based on TXM zoneplate characteristics [13]). Ni coarsening is observed as indicated by the statistically significant growth of Ni particle diameters over extended cell operation. Dihedral angle calculations for anode microstructures suggest the Ni–YSZ system performance may decay under long-term cell operating conditions. The particle sizes and dihedral angles are used in a thermodynamic model to provide a hypothesis on the primary modes and mechanisms of microstructural reconfiguration. Specifically, Ni coarsening is found to be driven by particle curvature, which supports primary growth through particle agglomeration. We hypothesize that this growth is constrained by the YSZ phase through a pinning mechanism [19,20]. Furthermore, results suggest that, at long operational times, the decrease in YSZ phase size, possibly linked to Zr or Zr4+ mobility [21,22], may result in a decrease in Ni phase size. 2. Methodology 2.1. Sample preparation and statistical analysis Initial microstructural characterization has been completed on regions taken from SOFC anodes subjected to
extended operation. Microstructural evolution and the associated degradation of these anodes has been previously investigated using SEM [1,6]. Details of the test cell configurations and operational conditions are provided by Faes et al. [1]. The regions measured in the present study were taken from 250 lm thick tape-cast Ni–YSZ anode supports (HTceramix SA, Switzerland). These supports were tested in a short stack configuration with YSZ electrolytes and lanthanum strontium ferrite (LSF) cathodes [1]. The anode regions measured were acquired from anode support pieces extracted from these test cells at set operational time intervals (0 h (reference), 158, 240 and 1130 h). A total of nine regions were measured using X-ray nanotomography combined with differential absorption imaging. The allocation of these regions among the operational times studied is outlined in Table 1. Sectioning was performed with both traditional techniques and FIB milling. An example of a mounted cylindrical sample produced by FIB milling is shown in Fig. 1a. These FIB-milled samples exhibit improved transmission characteristics compared to traditionally sectioned regions, due in part to the more uniform cross-sections achieved. Anode regions extracted using traditional sectioning are designated T##, while regions sectioned with FIB milling are designated F##, where ## is a two-digit region identifier. The anode regions imaged using X-ray nanotomography were segmented into sample volumes 1253 voxels in size, corresponding to a cube approximately 6.6 lm on a side. Details of the segmentation and characterization approach are provided in a later section of this work. To support the microstructural evolution observed in the characterization results, the statistical significance of the operational time as a predictor of microstructural evolution was investigated using a one-way layout analysis of variance (ANOVA) [30]. The statistical test applied in this ANOVA was an F-test with a = 0.05. Samples segmented from each anode region were treated as replicates representing the operational times investigated. The number of samples taken from each operational time considered in the oneway layout ANOVA is given in Table 1. A total of 21 distinct samples were characterized to provide data for this statistical analysis. 2.2. X-ray nanotomography measurements X-ray nanotomography measurements were completed using the TXM at beamline 32-ID-C of the Advanced Photon Source (APS). Details of this TXM configuration and the nanotomography measurements are available in the literature [13,23]. The energy level tuning capability of the TXM at beamline 32-ID-C permits the nondestructive 3D mapping of elemental composition within the SOFC anode by providing access to the Ni K-absorption edge (K-edge) at 8.333 keV. Slightly below this energy level the solid phases in the anode exhibit comparable X-ray transmission behavior, while Ni absorption increases abruptly by a factor of 5 across the edge. Acquiring images above
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Table 1 Overview of data for one-way layout ANOVA testing operational time dependence. Stack
Operational time (h)
Anode regions measured (sample volumes per regions)
Sample volumes characterized
Reference Stack A Stack B Stack C
0 158 240 1130
REFT23 (3), REFT25 (3) SAC4F01 (2), SAC4T01 (2), SAC4T11 (2) SBC1F01 (2), SBC1T27 (3) SCC3F01 (2), SCC3T12 (2) Total number of samples characterized
nRef = 6 nA = 6 nB = 5 nC = 4 ntot = 21
(b)
Phase Size Distribution, µm
(c)
-1
(a)
0.8
t=0h t = 158 h t = 240 h t = 1130 h
(d)
0.6 0.4 0.2
0
0
2
4
Nickel Phase Diameter, µm Fig. 1. A cylindrical SOFC anode sample for X-ray nanotomography measurement (a) is produced using FIB milling. A reconstructed cross-section of a sample (b) taken above the Ni K-edge reveals the Ni and YSZ phases indicated by the red and blue arrows, respectively; black regions are the pore phase. These two-dimensional images are reconstructed from a series of transmission images and analyzed as digitized representative volume elements (c) that map the phases in three dimensions. The mean Ni phase size distributions (d) for the anode samples, calculated from the reconstructed X-ray nanotomography data, show a clear shift in phase sizes for samples subjected to extended cell operation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
and below the K-edge, with 20 eV or 0.25% bandwidth separation, enables elemental mapping of the anode phases, as illustrated in Fig. 1b for a cylindrical anode sample. The Ni phase, displayed as white in this absorption mode image, can be clearly discerned from the gray YSZ phase and the black pore phase. The full-field X-ray nanotomography measurements were completed by collecting a series of transmission images at a fixed energy over a 180° rotation range in 1° increments with exposure times of 1–5 s per transmission image. Differential absorption imaging was applied to enable elemental mapping of samples taken from the aged SOFC anodes. For the present work, measurements were conducted at 8.317 and 8.357 keV from the anodes examined by Faes et al. [1].
2.3. Segmentation and microstructural analysis The TXM transmission images acquired at each energy level were segmented using appropriate software [24]. Following fine alignment to account for minor variations in stage positioning, the nanotomography data sets were cropped to generate a set of distinct sample volumes. A total of 21 samples were sectioned from the volumetric data. For each sample, the volumetric data taken above the Ni K-edge was reconstructed and segmented to isolate the Ni phase from the pore and YSZ phases. Subsequent segmentation of the below-edge data isolated the pore phase. Taking the intersection of the non-Ni phase in the above-edge data and the solid phase in the below-edge data determined the YSZ phase. The final product of the segmentation process
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is a digitized sample volume, illustrated in Fig. 1c, that identifies the phases of interest with unique integer values. This digitized form of the volumetric sample facilitates microstructural characterization. The unique phase identifiers provide a means of tracking the pore, Ni and YSZ phases and facilitate the calculation of phase-specific (particle) size distributions (PSDs), two-phase interfacial areas, phase connectivity, phase tortuosity, triple-phase boundary (TPB) lengths and dihedral angles. To test the operational time as a predictor of microstructural evolution, these characterization results were analyzed using the one-way layout ANOVA outlined in Table 1. The microstructural characterization in the present work focuses on PSDs that elucidate microstructural changes linked to performance degradation [1]. The characterization of these PSDs is based on a ray-shooting routine developed from a three-dimensional lattice Boltzmann method formalism using 19 lattice directions (D3Q19) [25]. This approach provides a measure of phase size similar to particle size distributions that may be obtained using quantitative stereology [26–28], but also maintains sensitivity to the contiguous microstructure without requiring transformation of 2-D data to discern 3-D characteristics. More specifically, the PSD provides a volume-weighted description of the particle sizes within the system, with a unique PSD calculated for each of the constituent phases. The PSD can provide insights into (i) the volume fraction of particles that may be above or below some critical radius and are subject to growth or dissolution; (ii) statistical descriptions of the systems for stability and/or phase-field type models; and (iii) how the statistical description of the particle sizes evolve in samples that have been aged during SOFC operation. The methodology applied to calculate PSDs from the nanotomography data has been described by Grew et al. [25]. Phase contiguity, two-phase interfacial areas and TPB lengths are also addressed in the present work. As with the PSD calculations, the methods for assessing these characteristics are provided by Grew et al. [25,29]. The contiguity of the electrode phases provides a measure of the degree of percolation and is determined using the numeric painting scheme. Phase interfaces are defined by stepping through the voxel-based structure along a preselected principal Cartesian plane, referred to as the search plane. As an interface is recognized, it is recorded for the corresponding interface description. Once all of the planes normal to the search plane have been examined, the process is repeated twice more in the orthogonal planes. This process generates a measure of the two- and three-phase interfaces that is initially based on the voxel size. Knowing the volume of each voxel from the imaging data, these measures can be converted into an area and a line length corresponding to the three-phase interface. Both of these measurements can be recast as an extensive property by dividing by the total volume of the regions examined. These measurements are made for the full structure (nominal measurements) and the structure excluding non-contiguous regions (effective measurements).
In addition to the above microstructural characteristics, dihedral angles are measured from the nanotomography data. A graphical overview of the dihedral angle measurement algorithm is provided in Fig. 2. The dihedral angle measurement begins with a search of the representative volume element (RVE) for TPBs which cycles through the Cartesian planes. When a TPB is identified in the search plane, its coordinates in the geometry file and a TPB indicator number are recorded. With the TPB points identified, a second search is performed for the two-phase interface areas, to determine their position and their orientation with respect to the TPB. The two-phase interface data and TPB points are then organized based on the pre- and post-TPB phase interfaces. This critical step defines the orientation of phases for interpretation of the dihedral angle. A 2-D spline of predetermined type is fitted to the organized interfacial data. The gradient is evaluated to provide the slope of the spline and used to calculate the phase angle via a four-quadrant inverse tangent function. An average slope is calculated using the interpolated points that are defined on the fit over a preset voxel radius relative to the TPB. This radius is set to 3 voxels, approximately 150 nm in the present studies. The dihedral angle corresponding to each individual phase is identified from these slopes, and the data are stored and passed to averaging, standard deviation and histogram generation routines. 3. Results and discussion The mean Ni PSDs for the SOFC anodes operated for 0, 158, 240 and 1130 h are shown in Fig. 1d. A clear shift toward larger phase sizes can be seen in the distributions when comparing the pristine reference case to the cases taken from an operated SOFC (stacks A, B and C). A decrease in the amount of Ni with a phase diameter near 1.0 lm is also observed, as indicated by the shift in the largest peak (near 1.0 lm) to slightly larger particle sizes. This may result, in part, from coarsening and interaction between the anode phases. It has been proposed that the YSZ phase may influence the growth of Ni particles in SOFC anodes [1]. Finally, the number-weighted mean particle diameters calculated from this X-ray nanotomography data are within the experimental error of previously reported Ni coarsening results observed by SEM [1]. This agreement confirms the ability of X-ray nanotomography to accurately capture microstructural details within the SOFC anodes. Ni coarsening behavior has been further investigated in terms of the volume-weighted mean diameter. As with the number-weighted mean results, the volume-weighted mean diameter displays growth behavior comparable to the firstorder, constrained-growth model (Eq. (1)) proposed by Faes et al. [1]. An initial fit of this model to the data was made using a maximum mean phase size, Dmax, of 1.3 lm and a time constant, s, of 110 h, as shown in Fig. 3. The maximum diameter determined in fitting this model is a volume-weighted mean diameter, which is expected to be
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Fig. 2. An overview of the dihedral angle algorithm is provided. TPB points are identified within the digitized representative volume element. These points are further used to track the phase interfaces in the plane orthogonal to the TPB line (unit into the page in the case shown). By fitting splines to these interfaces the relative phase dihedral angles can be determined and used to provide a statistical representation of the structure.
higher than the number-weighted mean diameter [21]. The fitted time constant is lower than time constant values noted by Faes et al. due to a decrease seen in the Ni phase size at the longest operational time. Such a decrease is not accounted for in the growth model described by Eq. (1). However, using the 3-D microstructural data obtained in X-ray nanotomography measurements, the physical phenomena underlying this behavior can be further explored. DðtÞ ¼ D0 þ ðDmax D0 Þ½1 expðt=sÞ:
ð1Þ
Fig. 3. The volume-weighted mean Ni phase diameter (circles and squares) shows an apparent exponential rise with operating time that is comparable to previously measured Ni coarsening behavior described by a constrained first-order growth model (solid black line) [1]. Critical diameters (diamonds) calculated from the YSZ nanotomography data (inset) following Hillert’s form of the Zener equation [19] suggest that the YSZ phase may be restricting the growth of the Ni phase. The Ni phase sizes are generally bounded within the uncertainty associated with the critical diameter (gray dashed lines, based on 1r).
The conditions applied for the extended operation tests suggest particle coarsening is supported by Ostwald ripening [1,31]. Traditionally, such coarsening could be described using the Lifshitz–Slyozov–Wagner (LSW) theory, which results in an equation for unconstrained particle growth with time [32]. However, constrained growth is clearly seen for the Ni phase in Fig. 3, and a slight decrease is seen in the Ni phase diameter at 1130 h, which may be related to the appearance of smaller particles seen in the PSD (Fig. 1d). These particles could form as a means of reducing the complex curvatures of various features within the composite microstructure, as long as the total interfacial energy of the complex sintered microstructure is reduced [33]. It is also possible that a secondary mechanism causes this decrease. The low water content and moderate temperatures should preclude the loss of Ni through volatilization [34]. This mechanism has been suggested based on observed losses of Ni volume fraction at higher water content and flow conditions [10,31,35]. The anodes in the present work were operated in humidified hydrogen (3% H2O) [6]. Based on the fuel utilization measured in the cell tests, the central anode regions from which the samples were taken may have experienced water contents up to 20% [1]. However, thermodynamic calculations suggest negligible volatilization at the temperatures and water contents corresponding to such conditions. The constrained growth observed may result from a Zener pinning mechanism related to the YSZ phase. Considering abnormal growth of the Ni phase [19,20], a critical diameter for coarsening was calculated based on the YSZ nanotomography data. As shown in Fig. 3, the Ni phase diameter approaches this critical diameter over the course of stack
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operation, reaching agreement when coarsening plateaus. The decrease in Ni phase size may be connected to the behavior of the YSZ in the anode (Fig. 3 inset), which displays a decreasing phase size over long-term operation. This decrease may result from changes to the structure [21,22] or mobility [36] of the YSZ. ANOVA was conducted to test operational time as a predictor of Ni phase size. The statistical significance was evaluated based on the ANOVA results and related Pvalues, which quantify the probability that variation in the data is random and not associated with the tested predictor. Significance of operational time as a predictor of the Ni phase size was confirmed by a P-value of 0.0184, suggesting there is less than a 2% chance that changes in the Ni phase size observed for the operational times considered are random. Measurements of the YSZ phase do not show significant influence of operational time, primarily due to spread in the reference (0 h) data. Specifically, the ANOVA resulted in a P-value of 0.1696, which suggests a 17% likelihood that variations observed in the YSZ are due to randomness within the samples and cannot be predicted based on operational time. However, exclusion of the YSZ phase reference (0 h) data results in a P-value of 0.075, suggesting there is less than a 8% chance that changes in the YSZ phase size observed during operation (t > 0 h) are considered random. For this subset of the data, variations in the YSZ phase size are statistically significant when applying an F-test at a level of a = 0.1. Several microstructural characteristics exhibit a dependence on operational time and can be connected to the changes observed in Ni phase size. These characteristics are shown in Fig. 4. The effective TPB length and effective Ni–YSZ contact area (Fig. 4a and b, respectively) decrease during operation. These two characteristics display an exponential decay over the course of operation, indicated by the black lines in Fig. 4a and b, which suggests that the decreases in TPB length and Ni–YSZ contact area are linked to the observed Ni coarsening. As the volume of the Ni particles increases, their surface area available for contact with the pore and YSZ phases will decrease, resulting in reduced interphase contact points. The effective forms of these measurements account for only those TPBs and contact areas connected to contiguous Ni, pore and YSZ networks within the RVE. The loss of effective TPB length therefore results in performance loss during operation that results from reduced electrochemical activity. The contiguity of the Ni phase also displays a marked decrease during operation. An average contiguity of 94% was measured for the Ni phase in the pristine samples. This contiguity decreases to 78% at 1130 h, and a substantial increase is observed in the variance of the contiguity. This increased spread in the data suggests that fewer, but larger, particles may be occupying the RVEs characterized. These disconnected particles suggest that a breakdown in the percolating network within the electrode may also contribute to performance loss during operation. Voltage degradation rates were estimated based on the measured TPB lengths.
For the nominal TPB lengths, these rates agree well with rates estimated from SEM measurements [1]. However, for the 1130 h data the degradation rates show a substantial contribution from the reduced phase contiguity, shifting from 56 to 85 lV h1 when calculated based on the nominal and effective TPB lengths, respectively. The ability to account for the effects of detailed network characteristics is one advantage of the 3-D data obtained by X-ray nanotomography. As with the phase diameter data, ANOVA was performed on the TPB length, interphase contact areas and phase contiguity measurements. Statistically significant dependence on operational time was confirmed for the TPB length (total and effective), Ni–YSZ contact area (total and effective) and the Ni contiguity. The respective P-values for these measurements indicate less than a 2% likelihood that the observed variations are random. Therefore, the dependence of these microstructural characteristics on operational time is considered statistically significant. No significant dependence was seen for the contiguity of the pore and YSZ phases. The mean phase diameters and TPB lengths measured for each operational time are summarized in Table 2. Microstructural stability can be further elucidated by inspecting dihedral angles, shown in Fig. 4d for the anode samples measured. These angles have been calculated using a spline-fitting approach to characterize surfaces near the TPBs. Initial characterization of the samples measured reveals Ni dihedral angles between 140° and 155° near the TPB. This range is substantially higher than existing measurements of the Ni–YSZ contact angle [37]. This discrepancy may be due to differences in experimental methods, curvature in the sintered YSZ structure and possible changes in YSZ phase size [21,22,36]. These dihedral angles support the observation of poor Ni wettability on YSZ [37]. Combining this assessment with the PSD information, a chemical potential difference of the Ni phase can be used to gage the propensity for coarsening. In general, the processes that may contribute to the reorganization of the Ni phase are considered to have two requirements: a difference in chemical potential (i.e. gradient), and a mechanism/carrier to support the transport of material. An analysis of agglomeration and coarsening can be formulated on the basis of these requirements. As a preliminary analysis, the chemical potential difference between Ni particles is assessed for a simplified system based on a free-standing Ni particle. A two-particle approach based on vacancy diffusion has previously been reported by Vaben et al. [38]; however, the approach outlined below calculates a Ni–YSZ surface energy normalized chemical potential difference that is scaled by the volume fraction of particles of diameter D ± DD/2. This scaling weighs the normalized chemical potential difference by the volume available for coarsening. The chemical potential for a single Ni particle leNi ðr; cs ; T ; P Þ may be determined as a function of particle radius r, interfacial surface energy cs, temperature T, and pressure P:
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(a)
(b)
(c)
(d)
Fig. 4. The effective triple-phase boundary length (a) and Ni–YSZ contact area (b) for the aged anode samples measured by X-ray nanotomography display reductions that follow a first-order, exponential decay (indicated by the black lines), which can be attributed to the first-order growth observed in the Ni particle size. The mean contiguity of the Ni phase (c) follows a distinct linear trend (indicated by the black line). The increasing spread seen between individual RVEs as operational time extends suggests the percolating network in the broader electrode may breakdown. Statistically significant changes were observed for these three microstructural characteristics. While dihedral angles measured for each phase show little variation (d), their values support the propensity for Ni coarsening. Mean dihedral angle measurements, calculated by averaging all operational times, are: hNi = 151°, hYSZ = 97°, and hPore = 111°.
Table 2 Mean Ni phase diameters and triple phase boundary (TPB) lengths for the aged anode samples measured by X-ray nanotomography at various operational times. SOFC stack of origin (operational time)
Mean phase diameter (lm)
Reference (0 h) Stack A (158 h) Stack B (240 h) Stack C (1130 h)
1.06 1.28 1.34 1.24
Ni
leNi ðr; cs ; T ; P Þ ¼ loNi ðT ; P Þ þ
2cs V Ni : r
Pore (±0.38) (±0.16) (±0.30) (±0.16)
ð2Þ
Here, loNi ðT ; P Þ is the chemical potential of the particle at a standard reference state and V Ni is the partial molar volume of Ni. The second term on the right-hand side of Eq. (2) dictates the contribution of the curvature of the particle to the chemical potential. This formulation assumes a Young–Laplace description of the difference in pressure between the vapor (pore) phase and the idealized spherical Ni particle. While likely, curvature effects due to a nonsmooth surfaces/features (i.e. inclusion of the second principal axis of curvature on a localized basis) have been excluded in this preliminary analysis. Such contributions will increase the chemical potential of the particle, since they increase the surface area to volume ratio for a given
0.49 0.52 0.55 0.62
TPB length (m/m3) YSZ
(±0.12) (±0.16) (±0.22) (±0.08)
0.85 0.92 0.96 0.81
Nominal (effective) (±0.30) (±0.22) (±0.18) (±0.10)
1.0E+13 7.5E+12 5.3E+12 7.2E+12
(7.8E+12) (5.9E+12) (3.9E+12) (4.5E+12)
surface energy. For isothermal and isobaric conditions, the difference in chemical potential for a two-particle system can be cast in terms of the particle radii r1 and r2 with interfacial energies c1s and c2s : 1 c c2 DleNi ðr1 ; r2 ; c1s ; c2s ÞT ;P ;n ¼ 2V Ni s s : ð3Þ r1 r2 Eq. (3) provides the difference in chemical potential due to the surface energy of the particles. Letting cs ¼ c1s ffi c2s , and assuming that this is the dominant term of leNi , it can be seen smaller particles tend to promote a larger chemical potential difference than larger particles. Therefore, the chemical potential difference will drive the larger particle to grow at the smaller particle’s expense. The magnitude of the chemical potential difference is scaled by cs. Assuming
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sin hY 1 1 Z Ni ðri ; rm ; cNs ;P ; hi ; a; dDÞ ¼ 2aðDi ÞdD sin hP rm ri sin hY 1 1 ¼ 2w ½lm1 : sin hP rm ri
pseudo-equilibrium, a normalized version of this surface energy may be determined by balancing the dihedral angles at the three-phase junction, as shown in Eq. (3): cN ;Y cP ;N cY ;P cN ;Y sin hP cP ;N ¼ ¼ yielding ¼ ; sin hP sin hY sin hN cN ;Y sin hP cN ;Y ¼
sin hY cY ;P sin hN ; ¼ ; sin hP cN ;Y sin hP
This factor applies the PSD function associated with a given phase size, a(Di), to scale the normalized chemical potential. Application of this factor allows the Ni coarsening potential, ZNi, to account for (i) the magnitude of the force driving particle growth that is associated with a given phase size, Di, and (ii) the availability of material within a range phase sizes, Di ± DD/2, that is subjected to this driving force. This concept is illustrated in Fig. 5a. Regions with little volume and regions that do not have an appreciable size difference show low propensity to change size. However, a high volume fraction of particles much smaller than the mean size results in a large propensity for coarsening. A final scenario, proposed by Mendoza et al. [28], permits the appearance of smaller particles for interfaces with complex local curvatures if the appearance of smaller particles leads to a lower interfacial energy for the system undergoing microstructural evolution. The normalized chemical potential difference, calculated for all of the diameters in each PSD, is shown in Fig. 5b. A negative value indicates a chemical potential gradient between particles of disparate size that promotes consumption of the smaller particle. Conversely, a positive value indicates coarsening of the larger particle. A large change in the normalized chemical potential gradient occurs at small Ni diameters with aging. Here, the primary negative peak moves toward larger diameters and reduces in magnitude, suggesting there has been significant volume loss for smaller particles. The shift in this peak indicates that these particles are dissolving and agglomerating with larger
ð4Þ
ci;j 6 cj;k þ ck;i :
ð5Þ
Here cP,N corresponds to the surface energy cs used in Eqs. (2) and (3). In Eq. (4) it is noted that hi is the dihedral angle measured using the method outlined above, rather than a contact angle. To apply this analysis to the nanotomography data, the chemical potential difference can be defined relative to the volume-weighted mean particle radius, rm , determined from the microstructural characterization. This mean radius is taken to represent r1 in Eq. (3). Normalization by the Ni–YSZ surface energy and the molar volume of Ni provides a means of casting the chemical potential difference in terms of dihedral angles and distinct phase sizes, ri, measured directly from the X-ray nanotomography data: DleNi ðrm ; ri ; csN ;P ÞT ;P ;n csN ;Y V Ni
sin hY ¼2 sin hP
1 1 rm ri
½lm1 :
ð6Þ
As a final step, the normalized chemical potential difference defined in Eq. (6) is multiplied by a weighting factor, w = a(Di)dD, and a quantitative measure of the propensity for Ni coarsening is defined according to:
(b)
Propensity for Nickel Particle -1 Growth (+) or Shrinkage (-), µm
(a)
ð7Þ
0.1 0 -0.1 -0.2 -0.3 -0.4
0h 158 h 240 h 1130 h
(+) Net growth (-) Net loss 0
1
2
3
Ni Diameter, µm Fig. 5. A conceptual overview of the propensity for Ni coarsening (a) illustrates that coarsening within the complex electrode microstructure requires both a sufficient size difference, which determines the chemical potential gradient driving a change in particle size, and a sufficient available volume of particles that can undergo size change. Lack of either contributing factor will reduce the propensity for coarsening, quantified by ZNi. Changes in the volumeweighted chemical potential difference for the Ni phase (b) indicate net particle growth for positive values, and net particle loss for negative values. Over operational time, the trend shows general coarsening behavior at longer time scales. A re-emergence of Ni nanoparticles appears at 1130 h probably due to Zener pinning related to the YSZ phase.
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particles. Likewise, the less-pronounced positive peak moves to larger diameters as operating time increases. However, there is a lack of significant variation between the subsequently aged samples. From 0 to 240 h, no additional negative peaks are seen to move toward smaller diameters with increased aging. Rather, the entire distributions, and particularly the negative peaks associated with smaller particles, reduce in magnitude and move towards the volume-weighted particle mean diameter. This suggests that small particles are agglomerating while large particles do not exhibit significant growth. The observation that larger particles do not exhibit growth appears to be consistent with the limiting particle size in accord with the Zener mechanism. Similar details are also reflected in the PSDs. This means that the volume lost from the smaller particles may not be agglomerating with the largest particles, which is most favorable on a curvature basis. We can further note that the volume-weighted mean Ni particle diameter for the aged samples (158, 240 and 1130 h) corresponds to the diameter of the apex of the largest positive peak for the reference sample. Thus the aged samples have agglomerated with the particles most prone to coarsening of the pristine sample. At 1130 h, we do recognize a more negative peak at the smallest Ni particle diameters. This could be (i) formation of new and small Ni particles, and/or (ii) secondary implication of reorganization of the YSZ phase in conjunction with a pinning-type process. 4. Conclusions In summary, X-ray nanotomography with differential absorption imaging was applied to measure the microstructure and composition of SOFC anodes subjected to extended cell operation. Reconstructed microstructural data has been characterized with respect to temporal phase size variations and dihedral angles. These results have been corroborated vs. results obtained using SEM imaging [1], thus demonstrating the validity of X-ray nanotomography as a method for further investigation of degradation mechanisms in electrochemical systems, particularly in situ measurement to track the dynamic process. The 3-D data obtained by X-ray nanotomography provides insight into performance impacts of microstructural characteristics, such as phase contiguity, and the interaction between anode phases which cannot be readily distinguished with two-dimensional SEM imaging. Operational time was found to be a statistically significant predictor of growth in the Ni phase, with mean phase diameters displaying an apparent exponential dependence with time. Using ANOVA, the statistically significant influence of operational time was also confirmed for TPB length, Ni–YSZ contact area and Ni contiguity. Constrained growth observed in the Ni phase agrees well with critical phase sizes predicted based on Zener pinning for abnormal grain growth, which suggests that YSZ influences Ni coarsening behavior. This influence can be seen in corresponding
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decreases in Ni and YSZ phase sizes at long times. For the YSZ this decrease may be caused by Zr or Zr4+ mobility. Initial calculations of dihedral angles for the Ni, YSZ and pore phases support the propensity for Ni coarsening. This propensity has been quantified in terms of the chemical potential for Ni particles in the samples measured. Coarsening in aged samples was found to progress to a Ni phase diameter corresponding to the largest coarsening potential observed in the pristine reference samples. Acknowledgements Financial support from an Energy Frontier Research Center on Science Based Nano-Structure Design and Synthesis of Heterogeneous Functional Materials for Energy Systems (HeteroFoaM Center) funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences (Award DE-SC0001061), and the National Science Foundation (Award CBET-0828612) are gratefully acknowledged. K.N.G. acknowledges mentor Dr. Deryn Chu and financial support from the U.S. Department of the Army and the U.S. Army Materiel Command with work performed through a contractual appointment to the U.S. Army Research Laboratory Postdoctoral Fellowship Program administered by the Oak Ridge Associated University. The authors would like to thank Dr. Roger Ristau for his assistance in preparation of X-ray nanotomography samples and Alex P. Cocco for assistance in data segmentation. Portions of this research were carried out at the Advanced Photon Source supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357, and by the Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886. References [1] Faes A, Hessler-Wyser A, Presvytes D, Vayenas CG, Van herle J. Fuel Cells 2009;9:841. [2] Lee CH, Lee CH, Lee HY, Oh SM. Solid State Ionics 1997;98:39. [3] Hsiao YC, Selman JR. Solid State Ionics 1997;98:33. [4] Tu H, Stimming U. J Power Sources 2004;127:284. [5] Gong M, Bierschenk D, Haag J, Poeppelmeier KR, Barnett SA, Xu C, et al. J Power Sources 2010;195:4013. [6] Tanasini P, Cannarozzo M, Costamagna P, Faes A, Van herle J, Hessler-Wyser A, et al. Fuel Cells 2009;9:740. [7] Iwata T. J Electrochem Soc 1996;143:1521. [8] Simwonis D, Tietz F, Sto¨ver D. Solid State Ionics 2000;132:241. [9] Jiang SP. J Mater Sci 2003;38:3775. [10] Holzer L, Iwanschitz B, Hocker T, Mu¨nch B, Prestat M, Wiedenmann D, et al. J Power Sources 2011;196:1279. [11] Wilson JR, Kobsiriphat W, Mendoza R, Chen HY, Hiller JM, Miller DJ, et al. Nat Mater 2006;5:541. [12] Izzo Jr JR, Joshi AS, Grew KN, Chiu WKS, Tkachuk A, Wang SH, et al. J Electrochem Soc 2008;155:B504. [13] Grew KN, Chu YS, Yi J, Peracchio AA, Izzo Jr JR, Hwu Y, et al. J Electrochem Soc 2010;157:B783. [14] Chen YT, Lo TN, Chu YS, Yi J, Liu CJ, Wang JY, et al. Nanotechnology 2008;19:395302. [15] Wilson JR, Duong AT, Gameiro M, Chen HY, Thornton K, Mumm DR, et al. Electrochem Commun 2009;11:1052.
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[16] Nelson GJ, Harris WM, Izzo Jr JR, Grew KN, Chiu WKS, Chu YS, et al. Appl Phys Lett 2011;98:173109. [17] Hsu PC, Chu YS, Yi JM, Wang CL, Wu SR, Hwu Y, et al. Appl Phys Lett 2010;97:033101. [18] Chen YCK, Chu YS, Yi J, McNulty I, Shen Q, Voorhees PW, et al. Appl Phys Lett 2010;96:043122. [19] Hillert M. Acta Metall 1965;13:227. [20] Manohar PA, Ferry M, Chandra T. ISIJ Int 1998;38:913. [21] Balakrishnan N, Takeuchi T, Nomura K, Kageyama H, Takeda Y. J Electrochem Soc 2004;151:A1286. [22] Hattori M, Takeda Y, Sakaki Y, Nakanishi A, Ohara S, Mukai K, et al. J Power Sources 2004;126:23. [23] Chu YS, Yi JM, De Carlo F, Shen Q, Lee WK, Wu HJ, et al. Appl Phys Lett 2008;92:103119. [24] Rasband, WS. ImageJ. Bethesda (MD, USA). US National Institutes of Health.
[28] Torquato S. Annu Rev Mater Res 2002;32:77. [29] Grew KN, Peracchio AA, Joshi AS, Izzo Jr JR, Chiu WKS. J Power Sources 2010;195:7930. [30] Wu C, Hamada M. Experiments: planning, analysis, and parameter design optimization. New York: Wiley; 2000. [31] Hagen A, Barfod R, Hendriksen PV, Liu Y-, Ramousse S. J Electrochem Soc 2006;153:A1165. [32] Ratke L, Voorhees PW. Growth and coarsening: Ostwald ripening in material processing. Berlin, New York: Springer Verlag; 2002. [33] Mendoza R, Savin I, Thornton K, Voorhees PW. Nat Mater 2004;3:385. [34] Gubner A, Landes H, Metzger J, Seeg H, Stubner R. Electrochem Proc 1997;97–18:844. [35] Pihlatie MH, Kaiser A, Mogensen M, Chen M. Solid State Ionics 2011;189:82. [36] Chen HY, Yu HC, Scott Cronin J, Wilson JR, Barnett SA, Thornton K. J Power Sources 2011;196:1333. [37] Tsoga A, Naoumidis A, Nikolopoulos P. Acta Mater 1996;44:3679. [38] Vaßen R, Simwonis D, Sto¨ver D. J Mater Sci 2001;36:147.
Acta Materialia 60 (2012) 3491–3500 www.elsevier.com/locate/actamat
Three-dimensional microstructural changes in the Ni–YSZ solid oxide fuel cell anode during operation George J. Nelson a,b, Kyle N. Grew c, John R. Izzo Jr. a,b, Jeffrey J. Lombardo a,b, William M. Harris a,b, Antonin Faes d,e,1, Aı¨cha Hessler-Wyser d, Jan Van herle e, Steve Wang f, Yong S. Chu g, Anil V. Virkar a,h, Wilson K.S. Chiu a,b,⇑ a HeteroFoaM Center, a DOE Energy Frontier Research Center, USA Department of Mechanical Engineering, University of Connecticut, CT, USA c Sensors and Electron Devices Directorate, US Army Research Laboratory, MD, USA d Interdisciplinary Centre for Electron Microscopy (CIME), Ecole Polytechnique Fe´de´rale de Lausanne, Switzerland e Industrial Energy Systems Laboratory (LENI), Ecole Polytechnique Fe´de´rale de Lausanne, Switzerland f Advanced Photon Source, Argonne National Laboratory, IL, USA g National Synchrotron Light Source II, Brookhaven National Laboratory, NY, USA h Department of Materials Science and Engineering, University of Utah, UT, USA b
Received 16 November 2011; received in revised form 15 February 2012; accepted 21 February 2012 Available online 7 April 2012
Abstract Microstructural evolution in solid oxide fuel cell (SOFC) cermet anodes has been investigated using X-ray nanotomography along with differential absorption imaging. SOFC anode supports composed of Ni and yttria-stabilized zirconia (YSZ) were subjected to extended operation and selected regions were imaged using a transmission X-ray microscope. X-ray nanotomography provides unique insight into microstructure changes of all three phases (Ni, YSZ, pore) in three spatial dimensions, and its relation to performance degradation. Statistically significant 3D microstructural changes were observed in the anode Ni phase over a range of operational times, including phase size growth and changes in connectivity, interfacial contact area and contiguous triple-phase boundary length. These observations support microstructural evolution correlated to SOFC performance. We find that Ni coarsening is driven by particle curvature as indicated by the dihedral angles between the Ni, YSZ and pore phases, and hypothesize that growth occurs primarily by means of diffusion and particle agglomeration constrained by a pinning mechanism related to the YSZ phase. The decrease in Ni phase size after extended periods of time may be the result of a second process connected to a mobility-induced decrease in the YSZ phase size or nonuniform curvature resulting in a net decrease in Ni phase size. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Solid oxide fuel cell; Ni–YSZ anode; Ni coarsening; Degradation; Dihedral angle
1. Introduction Power and electrical efficiency losses in a solid oxide fuel cell (SOFC) can result from changing composition and ⇑ Corresponding author at: Department of Mechanical Engineering, University of Connecticut, CT, USA. Tel.: +1 860 486 3647. E-mail address: [email protected] (W.K.S. Chiu). 1 Present address: Materials and Design Unit, University of Applied Science, Western Switzerland, Switzerland.
microstructure of cell components during operation [1–5]. These changes have been found to reduce the SOFC operating voltage achieved at constant current depending on the cell design and operating conditions [1]. Performance degradation of the SOFC can result from several phenomena, including microstructural changes in the electrode, reactions between materials to form new phases and contamination of active interfaces [2–5]. The coarsening of Ni particles in SOFC anodes is one widely observed example of such deleterious microstructural evolution [1,6–10].
1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.02.041
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Focused ion beam scanning electron microscopy (FIBSEM) and X-ray nanotomography permit three-dimensional imaging of composite electrodes at unprecedented scales [1,11–14], distinguishing them from other imaging techniques applied to explore microstructure and composition in SOFC electrodes. SEM serial sectioning approaches, including FIB-SEM, have fostered a greater understanding of the microstructure and composition in SOFC anodes and cathodes [11,15] and have advanced the understanding of Ni–YSZ anode degradation mechanisms, particularly Ni coarsening behavior [1,6]. However, serial sectioning approaches result in the loss of the imaged sample and are often restricted to ex situ experimental investigations. Full-field X-ray nanotomography permits the non-destructive imaging of anode samples [12,13], with elemental sensitivity achieved for anode microstructures by applying a tunable X-ray source in conjunction with differential absorption imaging across the Ni K-absorption edge [13]. Applying X-ray absorption near-edge structure (XANES) spectroscopy in combination with full-field X-ray nanotomography can expand these capabilities by allowing chemical speciation based on chemical bonding states discerned the XANES spectra [16]. These advances may allow for in situ measurement opportunities with an appropriate environmental chamber [17,18]. The present work extends transmission X-ray microscopy (TXM) techniques to the exploration of degradation in SOFC anodes. X-ray nanotomography measurements of anodes subjected to extended operation have been performed using differential absorption imaging to further elucidate degradation associated with microstructural evolution in the anode phases. Digitized reconstructions of the volumetric data have enabled elemental mapping and microstructural characterization of the Ni, YSZ and pore phases of aged SOFC anodes at a spatial resolution of 32 nm (based on TXM zoneplate characteristics [13]). Ni coarsening is observed as indicated by the statistically significant growth of Ni particle diameters over extended cell operation. Dihedral angle calculations for anode microstructures suggest the Ni–YSZ system performance may decay under long-term cell operating conditions. The particle sizes and dihedral angles are used in a thermodynamic model to provide a hypothesis on the primary modes and mechanisms of microstructural reconfiguration. Specifically, Ni coarsening is found to be driven by particle curvature, which supports primary growth through particle agglomeration. We hypothesize that this growth is constrained by the YSZ phase through a pinning mechanism [19,20]. Furthermore, results suggest that, at long operational times, the decrease in YSZ phase size, possibly linked to Zr or Zr4+ mobility [21,22], may result in a decrease in Ni phase size. 2. Methodology 2.1. Sample preparation and statistical analysis Initial microstructural characterization has been completed on regions taken from SOFC anodes subjected to
extended operation. Microstructural evolution and the associated degradation of these anodes has been previously investigated using SEM [1,6]. Details of the test cell configurations and operational conditions are provided by Faes et al. [1]. The regions measured in the present study were taken from 250 lm thick tape-cast Ni–YSZ anode supports (HTceramix SA, Switzerland). These supports were tested in a short stack configuration with YSZ electrolytes and lanthanum strontium ferrite (LSF) cathodes [1]. The anode regions measured were acquired from anode support pieces extracted from these test cells at set operational time intervals (0 h (reference), 158, 240 and 1130 h). A total of nine regions were measured using X-ray nanotomography combined with differential absorption imaging. The allocation of these regions among the operational times studied is outlined in Table 1. Sectioning was performed with both traditional techniques and FIB milling. An example of a mounted cylindrical sample produced by FIB milling is shown in Fig. 1a. These FIB-milled samples exhibit improved transmission characteristics compared to traditionally sectioned regions, due in part to the more uniform cross-sections achieved. Anode regions extracted using traditional sectioning are designated T##, while regions sectioned with FIB milling are designated F##, where ## is a two-digit region identifier. The anode regions imaged using X-ray nanotomography were segmented into sample volumes 1253 voxels in size, corresponding to a cube approximately 6.6 lm on a side. Details of the segmentation and characterization approach are provided in a later section of this work. To support the microstructural evolution observed in the characterization results, the statistical significance of the operational time as a predictor of microstructural evolution was investigated using a one-way layout analysis of variance (ANOVA) [30]. The statistical test applied in this ANOVA was an F-test with a = 0.05. Samples segmented from each anode region were treated as replicates representing the operational times investigated. The number of samples taken from each operational time considered in the oneway layout ANOVA is given in Table 1. A total of 21 distinct samples were characterized to provide data for this statistical analysis. 2.2. X-ray nanotomography measurements X-ray nanotomography measurements were completed using the TXM at beamline 32-ID-C of the Advanced Photon Source (APS). Details of this TXM configuration and the nanotomography measurements are available in the literature [13,23]. The energy level tuning capability of the TXM at beamline 32-ID-C permits the nondestructive 3D mapping of elemental composition within the SOFC anode by providing access to the Ni K-absorption edge (K-edge) at 8.333 keV. Slightly below this energy level the solid phases in the anode exhibit comparable X-ray transmission behavior, while Ni absorption increases abruptly by a factor of 5 across the edge. Acquiring images above
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Table 1 Overview of data for one-way layout ANOVA testing operational time dependence. Stack
Operational time (h)
Anode regions measured (sample volumes per regions)
Sample volumes characterized
Reference Stack A Stack B Stack C
0 158 240 1130
REFT23 (3), REFT25 (3) SAC4F01 (2), SAC4T01 (2), SAC4T11 (2) SBC1F01 (2), SBC1T27 (3) SCC3F01 (2), SCC3T12 (2) Total number of samples characterized
nRef = 6 nA = 6 nB = 5 nC = 4 ntot = 21
(b)
Phase Size Distribution, µm
(c)
-1
(a)
0.8
t=0h t = 158 h t = 240 h t = 1130 h
(d)
0.6 0.4 0.2
0
0
2
4
Nickel Phase Diameter, µm Fig. 1. A cylindrical SOFC anode sample for X-ray nanotomography measurement (a) is produced using FIB milling. A reconstructed cross-section of a sample (b) taken above the Ni K-edge reveals the Ni and YSZ phases indicated by the red and blue arrows, respectively; black regions are the pore phase. These two-dimensional images are reconstructed from a series of transmission images and analyzed as digitized representative volume elements (c) that map the phases in three dimensions. The mean Ni phase size distributions (d) for the anode samples, calculated from the reconstructed X-ray nanotomography data, show a clear shift in phase sizes for samples subjected to extended cell operation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
and below the K-edge, with 20 eV or 0.25% bandwidth separation, enables elemental mapping of the anode phases, as illustrated in Fig. 1b for a cylindrical anode sample. The Ni phase, displayed as white in this absorption mode image, can be clearly discerned from the gray YSZ phase and the black pore phase. The full-field X-ray nanotomography measurements were completed by collecting a series of transmission images at a fixed energy over a 180° rotation range in 1° increments with exposure times of 1–5 s per transmission image. Differential absorption imaging was applied to enable elemental mapping of samples taken from the aged SOFC anodes. For the present work, measurements were conducted at 8.317 and 8.357 keV from the anodes examined by Faes et al. [1].
2.3. Segmentation and microstructural analysis The TXM transmission images acquired at each energy level were segmented using appropriate software [24]. Following fine alignment to account for minor variations in stage positioning, the nanotomography data sets were cropped to generate a set of distinct sample volumes. A total of 21 samples were sectioned from the volumetric data. For each sample, the volumetric data taken above the Ni K-edge was reconstructed and segmented to isolate the Ni phase from the pore and YSZ phases. Subsequent segmentation of the below-edge data isolated the pore phase. Taking the intersection of the non-Ni phase in the above-edge data and the solid phase in the below-edge data determined the YSZ phase. The final product of the segmentation process
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is a digitized sample volume, illustrated in Fig. 1c, that identifies the phases of interest with unique integer values. This digitized form of the volumetric sample facilitates microstructural characterization. The unique phase identifiers provide a means of tracking the pore, Ni and YSZ phases and facilitate the calculation of phase-specific (particle) size distributions (PSDs), two-phase interfacial areas, phase connectivity, phase tortuosity, triple-phase boundary (TPB) lengths and dihedral angles. To test the operational time as a predictor of microstructural evolution, these characterization results were analyzed using the one-way layout ANOVA outlined in Table 1. The microstructural characterization in the present work focuses on PSDs that elucidate microstructural changes linked to performance degradation [1]. The characterization of these PSDs is based on a ray-shooting routine developed from a three-dimensional lattice Boltzmann method formalism using 19 lattice directions (D3Q19) [25]. This approach provides a measure of phase size similar to particle size distributions that may be obtained using quantitative stereology [26–28], but also maintains sensitivity to the contiguous microstructure without requiring transformation of 2-D data to discern 3-D characteristics. More specifically, the PSD provides a volume-weighted description of the particle sizes within the system, with a unique PSD calculated for each of the constituent phases. The PSD can provide insights into (i) the volume fraction of particles that may be above or below some critical radius and are subject to growth or dissolution; (ii) statistical descriptions of the systems for stability and/or phase-field type models; and (iii) how the statistical description of the particle sizes evolve in samples that have been aged during SOFC operation. The methodology applied to calculate PSDs from the nanotomography data has been described by Grew et al. [25]. Phase contiguity, two-phase interfacial areas and TPB lengths are also addressed in the present work. As with the PSD calculations, the methods for assessing these characteristics are provided by Grew et al. [25,29]. The contiguity of the electrode phases provides a measure of the degree of percolation and is determined using the numeric painting scheme. Phase interfaces are defined by stepping through the voxel-based structure along a preselected principal Cartesian plane, referred to as the search plane. As an interface is recognized, it is recorded for the corresponding interface description. Once all of the planes normal to the search plane have been examined, the process is repeated twice more in the orthogonal planes. This process generates a measure of the two- and three-phase interfaces that is initially based on the voxel size. Knowing the volume of each voxel from the imaging data, these measures can be converted into an area and a line length corresponding to the three-phase interface. Both of these measurements can be recast as an extensive property by dividing by the total volume of the regions examined. These measurements are made for the full structure (nominal measurements) and the structure excluding non-contiguous regions (effective measurements).
In addition to the above microstructural characteristics, dihedral angles are measured from the nanotomography data. A graphical overview of the dihedral angle measurement algorithm is provided in Fig. 2. The dihedral angle measurement begins with a search of the representative volume element (RVE) for TPBs which cycles through the Cartesian planes. When a TPB is identified in the search plane, its coordinates in the geometry file and a TPB indicator number are recorded. With the TPB points identified, a second search is performed for the two-phase interface areas, to determine their position and their orientation with respect to the TPB. The two-phase interface data and TPB points are then organized based on the pre- and post-TPB phase interfaces. This critical step defines the orientation of phases for interpretation of the dihedral angle. A 2-D spline of predetermined type is fitted to the organized interfacial data. The gradient is evaluated to provide the slope of the spline and used to calculate the phase angle via a four-quadrant inverse tangent function. An average slope is calculated using the interpolated points that are defined on the fit over a preset voxel radius relative to the TPB. This radius is set to 3 voxels, approximately 150 nm in the present studies. The dihedral angle corresponding to each individual phase is identified from these slopes, and the data are stored and passed to averaging, standard deviation and histogram generation routines. 3. Results and discussion The mean Ni PSDs for the SOFC anodes operated for 0, 158, 240 and 1130 h are shown in Fig. 1d. A clear shift toward larger phase sizes can be seen in the distributions when comparing the pristine reference case to the cases taken from an operated SOFC (stacks A, B and C). A decrease in the amount of Ni with a phase diameter near 1.0 lm is also observed, as indicated by the shift in the largest peak (near 1.0 lm) to slightly larger particle sizes. This may result, in part, from coarsening and interaction between the anode phases. It has been proposed that the YSZ phase may influence the growth of Ni particles in SOFC anodes [1]. Finally, the number-weighted mean particle diameters calculated from this X-ray nanotomography data are within the experimental error of previously reported Ni coarsening results observed by SEM [1]. This agreement confirms the ability of X-ray nanotomography to accurately capture microstructural details within the SOFC anodes. Ni coarsening behavior has been further investigated in terms of the volume-weighted mean diameter. As with the number-weighted mean results, the volume-weighted mean diameter displays growth behavior comparable to the firstorder, constrained-growth model (Eq. (1)) proposed by Faes et al. [1]. An initial fit of this model to the data was made using a maximum mean phase size, Dmax, of 1.3 lm and a time constant, s, of 110 h, as shown in Fig. 3. The maximum diameter determined in fitting this model is a volume-weighted mean diameter, which is expected to be
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Fig. 2. An overview of the dihedral angle algorithm is provided. TPB points are identified within the digitized representative volume element. These points are further used to track the phase interfaces in the plane orthogonal to the TPB line (unit into the page in the case shown). By fitting splines to these interfaces the relative phase dihedral angles can be determined and used to provide a statistical representation of the structure.
higher than the number-weighted mean diameter [21]. The fitted time constant is lower than time constant values noted by Faes et al. due to a decrease seen in the Ni phase size at the longest operational time. Such a decrease is not accounted for in the growth model described by Eq. (1). However, using the 3-D microstructural data obtained in X-ray nanotomography measurements, the physical phenomena underlying this behavior can be further explored. DðtÞ ¼ D0 þ ðDmax D0 Þ½1 expðt=sÞ:
ð1Þ
Fig. 3. The volume-weighted mean Ni phase diameter (circles and squares) shows an apparent exponential rise with operating time that is comparable to previously measured Ni coarsening behavior described by a constrained first-order growth model (solid black line) [1]. Critical diameters (diamonds) calculated from the YSZ nanotomography data (inset) following Hillert’s form of the Zener equation [19] suggest that the YSZ phase may be restricting the growth of the Ni phase. The Ni phase sizes are generally bounded within the uncertainty associated with the critical diameter (gray dashed lines, based on 1r).
The conditions applied for the extended operation tests suggest particle coarsening is supported by Ostwald ripening [1,31]. Traditionally, such coarsening could be described using the Lifshitz–Slyozov–Wagner (LSW) theory, which results in an equation for unconstrained particle growth with time [32]. However, constrained growth is clearly seen for the Ni phase in Fig. 3, and a slight decrease is seen in the Ni phase diameter at 1130 h, which may be related to the appearance of smaller particles seen in the PSD (Fig. 1d). These particles could form as a means of reducing the complex curvatures of various features within the composite microstructure, as long as the total interfacial energy of the complex sintered microstructure is reduced [33]. It is also possible that a secondary mechanism causes this decrease. The low water content and moderate temperatures should preclude the loss of Ni through volatilization [34]. This mechanism has been suggested based on observed losses of Ni volume fraction at higher water content and flow conditions [10,31,35]. The anodes in the present work were operated in humidified hydrogen (3% H2O) [6]. Based on the fuel utilization measured in the cell tests, the central anode regions from which the samples were taken may have experienced water contents up to 20% [1]. However, thermodynamic calculations suggest negligible volatilization at the temperatures and water contents corresponding to such conditions. The constrained growth observed may result from a Zener pinning mechanism related to the YSZ phase. Considering abnormal growth of the Ni phase [19,20], a critical diameter for coarsening was calculated based on the YSZ nanotomography data. As shown in Fig. 3, the Ni phase diameter approaches this critical diameter over the course of stack
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operation, reaching agreement when coarsening plateaus. The decrease in Ni phase size may be connected to the behavior of the YSZ in the anode (Fig. 3 inset), which displays a decreasing phase size over long-term operation. This decrease may result from changes to the structure [21,22] or mobility [36] of the YSZ. ANOVA was conducted to test operational time as a predictor of Ni phase size. The statistical significance was evaluated based on the ANOVA results and related Pvalues, which quantify the probability that variation in the data is random and not associated with the tested predictor. Significance of operational time as a predictor of the Ni phase size was confirmed by a P-value of 0.0184, suggesting there is less than a 2% chance that changes in the Ni phase size observed for the operational times considered are random. Measurements of the YSZ phase do not show significant influence of operational time, primarily due to spread in the reference (0 h) data. Specifically, the ANOVA resulted in a P-value of 0.1696, which suggests a 17% likelihood that variations observed in the YSZ are due to randomness within the samples and cannot be predicted based on operational time. However, exclusion of the YSZ phase reference (0 h) data results in a P-value of 0.075, suggesting there is less than a 8% chance that changes in the YSZ phase size observed during operation (t > 0 h) are considered random. For this subset of the data, variations in the YSZ phase size are statistically significant when applying an F-test at a level of a = 0.1. Several microstructural characteristics exhibit a dependence on operational time and can be connected to the changes observed in Ni phase size. These characteristics are shown in Fig. 4. The effective TPB length and effective Ni–YSZ contact area (Fig. 4a and b, respectively) decrease during operation. These two characteristics display an exponential decay over the course of operation, indicated by the black lines in Fig. 4a and b, which suggests that the decreases in TPB length and Ni–YSZ contact area are linked to the observed Ni coarsening. As the volume of the Ni particles increases, their surface area available for contact with the pore and YSZ phases will decrease, resulting in reduced interphase contact points. The effective forms of these measurements account for only those TPBs and contact areas connected to contiguous Ni, pore and YSZ networks within the RVE. The loss of effective TPB length therefore results in performance loss during operation that results from reduced electrochemical activity. The contiguity of the Ni phase also displays a marked decrease during operation. An average contiguity of 94% was measured for the Ni phase in the pristine samples. This contiguity decreases to 78% at 1130 h, and a substantial increase is observed in the variance of the contiguity. This increased spread in the data suggests that fewer, but larger, particles may be occupying the RVEs characterized. These disconnected particles suggest that a breakdown in the percolating network within the electrode may also contribute to performance loss during operation. Voltage degradation rates were estimated based on the measured TPB lengths.
For the nominal TPB lengths, these rates agree well with rates estimated from SEM measurements [1]. However, for the 1130 h data the degradation rates show a substantial contribution from the reduced phase contiguity, shifting from 56 to 85 lV h1 when calculated based on the nominal and effective TPB lengths, respectively. The ability to account for the effects of detailed network characteristics is one advantage of the 3-D data obtained by X-ray nanotomography. As with the phase diameter data, ANOVA was performed on the TPB length, interphase contact areas and phase contiguity measurements. Statistically significant dependence on operational time was confirmed for the TPB length (total and effective), Ni–YSZ contact area (total and effective) and the Ni contiguity. The respective P-values for these measurements indicate less than a 2% likelihood that the observed variations are random. Therefore, the dependence of these microstructural characteristics on operational time is considered statistically significant. No significant dependence was seen for the contiguity of the pore and YSZ phases. The mean phase diameters and TPB lengths measured for each operational time are summarized in Table 2. Microstructural stability can be further elucidated by inspecting dihedral angles, shown in Fig. 4d for the anode samples measured. These angles have been calculated using a spline-fitting approach to characterize surfaces near the TPBs. Initial characterization of the samples measured reveals Ni dihedral angles between 140° and 155° near the TPB. This range is substantially higher than existing measurements of the Ni–YSZ contact angle [37]. This discrepancy may be due to differences in experimental methods, curvature in the sintered YSZ structure and possible changes in YSZ phase size [21,22,36]. These dihedral angles support the observation of poor Ni wettability on YSZ [37]. Combining this assessment with the PSD information, a chemical potential difference of the Ni phase can be used to gage the propensity for coarsening. In general, the processes that may contribute to the reorganization of the Ni phase are considered to have two requirements: a difference in chemical potential (i.e. gradient), and a mechanism/carrier to support the transport of material. An analysis of agglomeration and coarsening can be formulated on the basis of these requirements. As a preliminary analysis, the chemical potential difference between Ni particles is assessed for a simplified system based on a free-standing Ni particle. A two-particle approach based on vacancy diffusion has previously been reported by Vaben et al. [38]; however, the approach outlined below calculates a Ni–YSZ surface energy normalized chemical potential difference that is scaled by the volume fraction of particles of diameter D ± DD/2. This scaling weighs the normalized chemical potential difference by the volume available for coarsening. The chemical potential for a single Ni particle leNi ðr; cs ; T ; P Þ may be determined as a function of particle radius r, interfacial surface energy cs, temperature T, and pressure P:
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(a)
(b)
(c)
(d)
Fig. 4. The effective triple-phase boundary length (a) and Ni–YSZ contact area (b) for the aged anode samples measured by X-ray nanotomography display reductions that follow a first-order, exponential decay (indicated by the black lines), which can be attributed to the first-order growth observed in the Ni particle size. The mean contiguity of the Ni phase (c) follows a distinct linear trend (indicated by the black line). The increasing spread seen between individual RVEs as operational time extends suggests the percolating network in the broader electrode may breakdown. Statistically significant changes were observed for these three microstructural characteristics. While dihedral angles measured for each phase show little variation (d), their values support the propensity for Ni coarsening. Mean dihedral angle measurements, calculated by averaging all operational times, are: hNi = 151°, hYSZ = 97°, and hPore = 111°.
Table 2 Mean Ni phase diameters and triple phase boundary (TPB) lengths for the aged anode samples measured by X-ray nanotomography at various operational times. SOFC stack of origin (operational time)
Mean phase diameter (lm)
Reference (0 h) Stack A (158 h) Stack B (240 h) Stack C (1130 h)
1.06 1.28 1.34 1.24
Ni
leNi ðr; cs ; T ; P Þ ¼ loNi ðT ; P Þ þ
2cs V Ni : r
Pore (±0.38) (±0.16) (±0.30) (±0.16)
ð2Þ
Here, loNi ðT ; P Þ is the chemical potential of the particle at a standard reference state and V Ni is the partial molar volume of Ni. The second term on the right-hand side of Eq. (2) dictates the contribution of the curvature of the particle to the chemical potential. This formulation assumes a Young–Laplace description of the difference in pressure between the vapor (pore) phase and the idealized spherical Ni particle. While likely, curvature effects due to a nonsmooth surfaces/features (i.e. inclusion of the second principal axis of curvature on a localized basis) have been excluded in this preliminary analysis. Such contributions will increase the chemical potential of the particle, since they increase the surface area to volume ratio for a given
0.49 0.52 0.55 0.62
TPB length (m/m3) YSZ
(±0.12) (±0.16) (±0.22) (±0.08)
0.85 0.92 0.96 0.81
Nominal (effective) (±0.30) (±0.22) (±0.18) (±0.10)
1.0E+13 7.5E+12 5.3E+12 7.2E+12
(7.8E+12) (5.9E+12) (3.9E+12) (4.5E+12)
surface energy. For isothermal and isobaric conditions, the difference in chemical potential for a two-particle system can be cast in terms of the particle radii r1 and r2 with interfacial energies c1s and c2s : 1 c c2 DleNi ðr1 ; r2 ; c1s ; c2s ÞT ;P ;n ¼ 2V Ni s s : ð3Þ r1 r2 Eq. (3) provides the difference in chemical potential due to the surface energy of the particles. Letting cs ¼ c1s ffi c2s , and assuming that this is the dominant term of leNi , it can be seen smaller particles tend to promote a larger chemical potential difference than larger particles. Therefore, the chemical potential difference will drive the larger particle to grow at the smaller particle’s expense. The magnitude of the chemical potential difference is scaled by cs. Assuming
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sin hY 1 1 Z Ni ðri ; rm ; cNs ;P ; hi ; a; dDÞ ¼ 2aðDi ÞdD sin hP rm ri sin hY 1 1 ¼ 2w ½lm1 : sin hP rm ri
pseudo-equilibrium, a normalized version of this surface energy may be determined by balancing the dihedral angles at the three-phase junction, as shown in Eq. (3): cN ;Y cP ;N cY ;P cN ;Y sin hP cP ;N ¼ ¼ yielding ¼ ; sin hP sin hY sin hN cN ;Y sin hP cN ;Y ¼
sin hY cY ;P sin hN ; ¼ ; sin hP cN ;Y sin hP
This factor applies the PSD function associated with a given phase size, a(Di), to scale the normalized chemical potential. Application of this factor allows the Ni coarsening potential, ZNi, to account for (i) the magnitude of the force driving particle growth that is associated with a given phase size, Di, and (ii) the availability of material within a range phase sizes, Di ± DD/2, that is subjected to this driving force. This concept is illustrated in Fig. 5a. Regions with little volume and regions that do not have an appreciable size difference show low propensity to change size. However, a high volume fraction of particles much smaller than the mean size results in a large propensity for coarsening. A final scenario, proposed by Mendoza et al. [28], permits the appearance of smaller particles for interfaces with complex local curvatures if the appearance of smaller particles leads to a lower interfacial energy for the system undergoing microstructural evolution. The normalized chemical potential difference, calculated for all of the diameters in each PSD, is shown in Fig. 5b. A negative value indicates a chemical potential gradient between particles of disparate size that promotes consumption of the smaller particle. Conversely, a positive value indicates coarsening of the larger particle. A large change in the normalized chemical potential gradient occurs at small Ni diameters with aging. Here, the primary negative peak moves toward larger diameters and reduces in magnitude, suggesting there has been significant volume loss for smaller particles. The shift in this peak indicates that these particles are dissolving and agglomerating with larger
ð4Þ
ci;j 6 cj;k þ ck;i :
ð5Þ
Here cP,N corresponds to the surface energy cs used in Eqs. (2) and (3). In Eq. (4) it is noted that hi is the dihedral angle measured using the method outlined above, rather than a contact angle. To apply this analysis to the nanotomography data, the chemical potential difference can be defined relative to the volume-weighted mean particle radius, rm , determined from the microstructural characterization. This mean radius is taken to represent r1 in Eq. (3). Normalization by the Ni–YSZ surface energy and the molar volume of Ni provides a means of casting the chemical potential difference in terms of dihedral angles and distinct phase sizes, ri, measured directly from the X-ray nanotomography data: DleNi ðrm ; ri ; csN ;P ÞT ;P ;n csN ;Y V Ni
sin hY ¼2 sin hP
1 1 rm ri
½lm1 :
ð6Þ
As a final step, the normalized chemical potential difference defined in Eq. (6) is multiplied by a weighting factor, w = a(Di)dD, and a quantitative measure of the propensity for Ni coarsening is defined according to:
(b)
Propensity for Nickel Particle -1 Growth (+) or Shrinkage (-), µm
(a)
ð7Þ
0.1 0 -0.1 -0.2 -0.3 -0.4
0h 158 h 240 h 1130 h
(+) Net growth (-) Net loss 0
1
2
3
Ni Diameter, µm Fig. 5. A conceptual overview of the propensity for Ni coarsening (a) illustrates that coarsening within the complex electrode microstructure requires both a sufficient size difference, which determines the chemical potential gradient driving a change in particle size, and a sufficient available volume of particles that can undergo size change. Lack of either contributing factor will reduce the propensity for coarsening, quantified by ZNi. Changes in the volumeweighted chemical potential difference for the Ni phase (b) indicate net particle growth for positive values, and net particle loss for negative values. Over operational time, the trend shows general coarsening behavior at longer time scales. A re-emergence of Ni nanoparticles appears at 1130 h probably due to Zener pinning related to the YSZ phase.
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particles. Likewise, the less-pronounced positive peak moves to larger diameters as operating time increases. However, there is a lack of significant variation between the subsequently aged samples. From 0 to 240 h, no additional negative peaks are seen to move toward smaller diameters with increased aging. Rather, the entire distributions, and particularly the negative peaks associated with smaller particles, reduce in magnitude and move towards the volume-weighted particle mean diameter. This suggests that small particles are agglomerating while large particles do not exhibit significant growth. The observation that larger particles do not exhibit growth appears to be consistent with the limiting particle size in accord with the Zener mechanism. Similar details are also reflected in the PSDs. This means that the volume lost from the smaller particles may not be agglomerating with the largest particles, which is most favorable on a curvature basis. We can further note that the volume-weighted mean Ni particle diameter for the aged samples (158, 240 and 1130 h) corresponds to the diameter of the apex of the largest positive peak for the reference sample. Thus the aged samples have agglomerated with the particles most prone to coarsening of the pristine sample. At 1130 h, we do recognize a more negative peak at the smallest Ni particle diameters. This could be (i) formation of new and small Ni particles, and/or (ii) secondary implication of reorganization of the YSZ phase in conjunction with a pinning-type process. 4. Conclusions In summary, X-ray nanotomography with differential absorption imaging was applied to measure the microstructure and composition of SOFC anodes subjected to extended cell operation. Reconstructed microstructural data has been characterized with respect to temporal phase size variations and dihedral angles. These results have been corroborated vs. results obtained using SEM imaging [1], thus demonstrating the validity of X-ray nanotomography as a method for further investigation of degradation mechanisms in electrochemical systems, particularly in situ measurement to track the dynamic process. The 3-D data obtained by X-ray nanotomography provides insight into performance impacts of microstructural characteristics, such as phase contiguity, and the interaction between anode phases which cannot be readily distinguished with two-dimensional SEM imaging. Operational time was found to be a statistically significant predictor of growth in the Ni phase, with mean phase diameters displaying an apparent exponential dependence with time. Using ANOVA, the statistically significant influence of operational time was also confirmed for TPB length, Ni–YSZ contact area and Ni contiguity. Constrained growth observed in the Ni phase agrees well with critical phase sizes predicted based on Zener pinning for abnormal grain growth, which suggests that YSZ influences Ni coarsening behavior. This influence can be seen in corresponding
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decreases in Ni and YSZ phase sizes at long times. For the YSZ this decrease may be caused by Zr or Zr4+ mobility. Initial calculations of dihedral angles for the Ni, YSZ and pore phases support the propensity for Ni coarsening. This propensity has been quantified in terms of the chemical potential for Ni particles in the samples measured. Coarsening in aged samples was found to progress to a Ni phase diameter corresponding to the largest coarsening potential observed in the pristine reference samples. Acknowledgements Financial support from an Energy Frontier Research Center on Science Based Nano-Structure Design and Synthesis of Heterogeneous Functional Materials for Energy Systems (HeteroFoaM Center) funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences (Award DE-SC0001061), and the National Science Foundation (Award CBET-0828612) are gratefully acknowledged. K.N.G. acknowledges mentor Dr. Deryn Chu and financial support from the U.S. Department of the Army and the U.S. Army Materiel Command with work performed through a contractual appointment to the U.S. Army Research Laboratory Postdoctoral Fellowship Program administered by the Oak Ridge Associated University. The authors would like to thank Dr. Roger Ristau for his assistance in preparation of X-ray nanotomography samples and Alex P. Cocco for assistance in data segmentation. Portions of this research were carried out at the Advanced Photon Source supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357, and by the Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886. References [1] Faes A, Hessler-Wyser A, Presvytes D, Vayenas CG, Van herle J. Fuel Cells 2009;9:841. [2] Lee CH, Lee CH, Lee HY, Oh SM. Solid State Ionics 1997;98:39. [3] Hsiao YC, Selman JR. Solid State Ionics 1997;98:33. [4] Tu H, Stimming U. J Power Sources 2004;127:284. [5] Gong M, Bierschenk D, Haag J, Poeppelmeier KR, Barnett SA, Xu C, et al. J Power Sources 2010;195:4013. [6] Tanasini P, Cannarozzo M, Costamagna P, Faes A, Van herle J, Hessler-Wyser A, et al. Fuel Cells 2009;9:740. [7] Iwata T. J Electrochem Soc 1996;143:1521. [8] Simwonis D, Tietz F, Sto¨ver D. Solid State Ionics 2000;132:241. [9] Jiang SP. J Mater Sci 2003;38:3775. [10] Holzer L, Iwanschitz B, Hocker T, Mu¨nch B, Prestat M, Wiedenmann D, et al. J Power Sources 2011;196:1279. [11] Wilson JR, Kobsiriphat W, Mendoza R, Chen HY, Hiller JM, Miller DJ, et al. Nat Mater 2006;5:541. [12] Izzo Jr JR, Joshi AS, Grew KN, Chiu WKS, Tkachuk A, Wang SH, et al. J Electrochem Soc 2008;155:B504. [13] Grew KN, Chu YS, Yi J, Peracchio AA, Izzo Jr JR, Hwu Y, et al. J Electrochem Soc 2010;157:B783. [14] Chen YT, Lo TN, Chu YS, Yi J, Liu CJ, Wang JY, et al. Nanotechnology 2008;19:395302. [15] Wilson JR, Duong AT, Gameiro M, Chen HY, Thornton K, Mumm DR, et al. Electrochem Commun 2009;11:1052.
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