Evolution of electrochemical interfaces in solid oxide fuel cells (SOFC): a Ni and Zr resonant anomalous ultra-small-angle X-ray scattering study with elemental and spatial resolution across the cell assembly

Abstract

Electrochemical interfaces are key to the direct conversion of fuels to electrical energy and lend energy converters like solid oxide fuel cells (SOFC) their functionality. Over extended operation at high temperatures, the microstructure of the underlying component materials in the cathodes, anodes and electrolytes evolve to an extent that these interfaces become affected and ultimately impaired, giving rise to performance degradation. We present anomalous ultra-small-angle X-ray scattering (anomalous USAXS) measurements to quantify the component phase interfacial surface areas as a function of position within the electrodes and electrolyte of a SOFC assembly. Using USAXS at a 3rd generation X-ray synchrotron facility, the primary microstructural parameters obtained are the mean feature size, size distribution and surface area, determined over a contiguous length scale from nanometers to micrometers in a single measurement at a given position. Here, a spatial resolution of <20 μm has been achieved perpendicular to the SOFC electrode and electrolyte layers. Anomalous USAXS measurements at X-ray energies just below the Ni and Zr K-absorption edges have enabled the electrochemically-active solid components and their associated void morphologies to be distinguished from each other close to the electrode/electrolyte interfaces. The anomalous variation of the X-ray scattering contrast with X-ray energy has been exploited to distinguish Ni-rich or Zr-rich component microstructures from adjacent phases, and to determine the interfacial surface areas both between specific solid phases and between each phase and the void network. Such information provides improved insights for relating the morphology of the SOFC triple phase boundary (TPB, where the reactant gas, electron-conducting and ion-conducting phases coincide) to the various component interfaces in the adjacent microstructure. We demonstrate how such measurements determine the electrochemically-active interface response to SOFC service life, especially in the anode with and without sulfur present in the fuel. Our approach can be generalized to address degradation issues at a quantitative level in other electrochemical systems such as batteries and photo-electrochemical cells.

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Introduction

Much attention has been given in recent years to ceramic solid oxide fuel cell (SOFC) development, because of its potential for energy conversion and possible inclusion of SOFCs in carbon capture and sequestration fuel cycles.¹ Key SOFC properties such as voltage and power density, over-potential or polarization resistance, as well as operational lifetime without significant degradation due to impurities or poisoning effects, are determined by electrochemical reactions occurring in the anode and cathode close to the electrode/electrolyte interfaces, by ionic conduction across the electrolyte, and by the evolution under load of the porous electrode and dense electrolyte morphologies at the elevated service temperatures.^1–3

Whereas the fundamental electrochemistry, ion and electron conduction properties of promising SOFC materials and interfaces have been explored at the molecular level,^4–9 progress in quantifying the statistically representative microstructure evolution has proven more challenging.^2,5,10,11 This is due to the disordered and stochastic evolution under load of the anode and cathode pore/solid morphologies,^12,13 the strong multi-component microstructure and composition gradients encountered close to the electrode/electrolyte interfaces,¹⁰ and the large range of length scales associated with these morphologies.¹¹ Perhaps of greatest interest is the evolving triple phase boundary (TPB)¹⁴ within the anode and the cathode where the percolating pore network (the gas phase), the electron conducting phase, and the ion conducting phase coincide. Recent use of focused ion beam (FIB) thinning techniques in high-resolution scanning electron microscopy (HRSEM) and nanotomography have provided striking images of SOFC TPB structures,^15,16 which comprise a tangle of disordered 1D string-like features. Computed X-ray nanotomography has provided equally effective visualization of SOFC TPB structures,^17,18 and has successfully related aspects of the TPB morphology to electrochemical performance.^19,20

One requirement for improving SOFC designs is a better and more predictive understanding of how TPB performance is related to the surrounding microstructure within a given anode or cathode. At the anode TPB, oxygen O²⁻ ions that have migrated across the electrolyte combine with the fuel as the fuel combustion reactions take place, and electrons are released to the electron conducting phase (i.e., the external electric circuit).¹ Meanwhile, at the cathode TPB, electrons arriving from the external circuit are combined with oxygen to form O²⁻ ions that then migrate across the electrolyte.^1,13 While the electrochemical reactions take place primarily at the interface between the pore network and the solid components, the ions involved can migrate along the interface between the electron and ion conducting phases.^21,22 Thus, the changing state of the interface between the electron and ion conducting phases and between each of these phases and the pore network govern the SOFC performance evolution, as well as the condition of the TPB itself. It follows that, in addition to characterizing the TPB morphology and the active TPB fraction (where all three defining phases percolate to the electrolyte, external electric circuit or external gas supply),²³ the SOFC morphology must itself be characterized, its component phases distinguished, and the phases in intimate interfacial contact identified.

Small-angle X-ray or neutron scattering (SAXS or SANS) methods have become well established techniques for the quantitative microstructure characterization of heterogeneous materials in the size range from 1 nm to 100 nm.²⁴ Ultra-small-angle X-ray scattering (USAXS),^25,26 which incorporates Bonse-Hart crystal optics to extend the size range upper limit, can provide microstructure characterization from ≈1 nm to several micrometers in a single scan. Furthermore, when USAXS is employed at a 3rd generation X-ray synchrotron facility, acceptable signal-to-noise is achievable using a beam size as small as (0.4 to 0.5) mm × (10 to 20) μm. Thus, depending on the thickness of the SOFC electrode and electrolyte layers, the SOFC sample can be aligned to provide a spatial resolution perpendicular to the SOFC electrode/electrolyte layers sufficient to interrogate the microstructure gradients present.¹⁰ Meanwhile the (0.4 to 0.5) mm beam size parallel to the SOFC layers permits a statistically representative sampling of the SOFC microstructure in each layer. Recently, we have applied USAXS methods to provide a basic microstructure characterization of the solid/pore morphology in a suitable SOFC system, and have determined the effects on this microstructure of service life with both sulfur-enriched and sulfur-free fuels.¹¹ Using a single X-ray energy it was not possible to distinguish the internal component phases and interfaces that define the TPB and determine SOFC performance, but it was established that USAXS measurements cover the broad feature size range relevant to SOFC systems.

Anomalous SAXS methods exploit resonant scattering effects^27,28 at photon energies just below a given X-ray absorption edge. These cause the scattering contrast factor to vary as a function of X-ray energy, and in turn the strength of the scattering from structural features containing the element associated with the absorption edge^29,30 within a multi-component microstructure. In the present case, we have carried out anomalous USAXS studies on the same SOFC sample suite for which a basic microstructure characterization was completed previously.¹¹ The anomalous USAXS measurements have been made as a function of position and X-ray energy in the electrodes and electrolyte at just below the Ni K- and Zr K-absorption edge X-ray energies. This has enabled the separate electron conducting and ion conducting phase components to be distinguished in the anode and cathode, and the associated internal and external interfacial surface areas to be quantified. Thus, anomalous USAXS studies can be used to complement electron or X-ray nanotomography measurements of the TPB morphology, as well as techniques such as spatially-resolved, energy-dispersive X-ray diffraction for component phase characterization.³¹ It has been possible to quantify the effects of service life on the microstructure as a function of position, and to evaluate the effects on the anode and cathode of the presence of sulfur in the fuel. The effect of sulfur within the fuel in degrading the microstructure and performance of the anode is currently one of the concerns in SOFC development.^6,32,33 In the sections that follow, we demonstrate how anomalous USAXS studies can interrogate the generic electrochemical interface gradients within SOFCs or similar advanced energy systems.

Experimental

SOFC materials studied

A range of engineered SOFC materials and designs are currently under development.^34,35 For planar SOFC systems, the anode is typically a porous ceramic cerium gadolinium oxide (CGO) or yttria-stabilized zirconia (YSZ) matrix, containing a concentration of small (<1 μm) Ni or Ni-alloy particles, which catalyze the oxidation of hydrocarbon fuel gases entering the anode. The cathode is typically a porous lanthanum strontium manganite (LSM) ceramic or, sometimes, lanthanum strontium cobalt ferrite (LSCF) that catalyzes the dissociation of oxygen from the air flowing through it. The porosity within the electrodes allows the gaseous species to diffuse and percolate to the TPB. In contrast, the electrolyte is a dense, gas-tight layer of YSZ to prevent direct gas mixing and reaction of cations and anions – which would cause a short circuit. Specific material selection depends on the required operating conditions, the fuel type and the SOFC geometry – and whether the electrodes or electrolyte provide structural support. The use of Ni/CGO anodes in electrolyte-supported SOFC systems is of interest for intermediate temperature applications.

The SOFC test materials studied here are discussed in detail elsewhere.^6,11 The samples are summarized in Table 1.³⁶ The cells were fabricated using industrial standard screen-printing and tape-casting techniques, to give a multi-layer anode–electrolyte–cathode cell assembly of five layers with a total thickness of 200 μm. Of the five layers, the anode is a porous Ni/CGO cermet, the electrolyte is dense YSZ, and the cathode is porous LSM. To protect the structural integrity of the assembly during service life, thin inner anode and cathode layers were added, as specified in Table 1. The three identical SOFC samples were treated as follows: sample A (A filter): run at 950 °C for 1000 h with desulfurized fuel (negligible S in fuel), sample B (B sulfur): run at 950 °C for 1000 h with natural gas fuel (S in fuel), and sample C (C pristine): not run – retained in its pristine state.

Table 1 Summary of SOFC samples studied

Sample:	A filter	B sulfur	C pristine
Outer anode	≈25 μm thick; 60% mass Ni, 40% mass CGO; ≈20% porosity; [CGO = Ce0.9Gd0.1O1.95]
Inner anode	≈7 μm thick; 60% mass Ni, 40% mass CGO; ≈10% porosity; [solid = 55% volume Ni, 45% volume CGO]
Electrolyte	≈140 μm thick; 3% mass Y2O3, 97% mass ZrO2 (YSZ); dense
Inner cathode	≈10 μm thick; 50% mass LSM, 50% mass YSZ; ≈15% porosity [solid = 49% volume LSM, 51% volume YSZ]
Outer cathode	≈20 μm thick; 100% LSM; ≈30% porosity [LSM = La0.8Sr0.2MnO3]
Service time	1000 h	1000 h	None
Service temperature	950 °C	950 °C	N/A
Fuel	Desulfurized (no sulfur in fuel)	Natural Gas (sulfur in fuel)	N/A

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Sample sections of each assembly were cut for the USAXS measurements and an image of such a section is shown in Fig. 1a. The thickness of the section perpendicular to the image determines the degree of X-ray beam attenuation by absorption within the sample, the sample volume available for scattering, and also the amount of multiple scattering in the measurements.³⁷ Although the earlier studies with 16.9 keV X-rays were carried out with section thicknesses of ≈80 μm, this was found to be too large for the present measurements at the lower X-ray energies close to the Ni K-absorption edge (8.333 keV). In order to minimize sample absorption and multiple scattering, new SOFC sections were prepared, thinned to a thickness of 30 μm and supported in a light resin. It was determined experimentally that the resin does not produce significant scattering.

Fig. 1 (a) Optical micrograph image of SOFC section showing X-ray beam size (red box) and position rastering direction; and (b) schematic of USAXS instrument at APS sector 32-ID (recently moved to APS sector 15-ID ChemMatCARS).

Ultra-small-angle X-ray scattering (USAXS)

USAXS measurements were carried out using the USAXS facility^25,26 at the Advanced Photon Source (APS) sector 32-ID. A schematic of the instrument is shown in Fig. 1b. With the small beams used (see below), this instrument can measure the small-angle scattering from SOFC samples in the momentum transfer, Q, range from 0.001 nm⁻¹ to 1 nm⁻¹, where Q = (4π/λ)sin(φ_S/2), λ is the X-ray wavelength and φ_S is the scattering angle. This Q range is sufficient to quantify microstructures in the scale range from a few nanometers to a few micrometers. In a USAXS scan the analyzer crystal stage is rotated through and away from the Bragg condition for passing the incident X-ray beam. Once rotated away from the incident beam Bragg condition, the incident beam intensity is no longer transmitted through the analyzer crystal stage. However, X-rays scattered by the sample are transmitted if scattered downwards (Fig. 1b) by the same scattering angle as the analyzer stage has been rotated from the incident Bragg condition. Thus, the direction of Q, which bisects the incident and scattered beam directions is also downwards. By measuring the scattering intensity at the photodiode detector as a function of the analyzer stage rotation, USAXS intensity data are obtained as a function of the scattering angle, or Q. Here, a complete USAXS scan takes ≈15 min.

In the present studies the USAXS entrance slits were set to give an incident X-ray beam size of 20 μm wide by 0.5 mm high, as indicated in Fig. 1a, and each sample was rastered horizontally to obtain the scattering at selected positions relative to the SOFC electrode/electrolyte boundaries. Each USAXS scan was corrected for sample absorption, a normalized empty beam blank was subtracted out, and the intensity data absolute-calibrated with respect to the primary beam using first principle methods.²⁶ The data were reduced and analyzed using the Indra and Irena tool suites for USAXS data reduction and analysis.³⁸ These data are intrinsically slit-smeared, not in the vertical direction defined by the X-ray entrance slits, but in the horizontal direction defined by the angular collimation conditions. This is because the vertical collimation conditions are defined by the collimating and analyzer crystal diffraction optics (vertical full width at half maximum, FWHM ≈ 10 μrad), whereas the horizontal collimation conditions are defined simply by the angle subtended by the photodiode detector aperture at the sample position (horizontal FWHM ≈ 15 mrad).²⁶ While reduced and calibrated slit-smeared USAXS data are frequently desmeared before further analysis, this numerical procedure introduces artefacts if significant data noise is present. For the quantitative comparison here of many datasets measured at different X-ray energies using model functions with a limited number of fit parameters, the slit-smeared model functions were fitted directly to the slit-smeared data.

For all measured locations in the SOFC assembly, the measured USAXS data were fitted assuming a two-component lognormal volume fraction size distribution of scattering features,³⁹ as illustrated in Fig. 2. Most of the data in the Q range could be fitted with a single (main) lognormal size distribution plus a flat background with just the fit to the high Q data improved by including a second small population of fine nanoscale features. In Fig. 3a, the X-ray transmission profiles are presented for the three SOFC sections showing the sample position locations used in the anomalous USAXS studies carried out at both the Ni and Zr K-absorption-edge X-ray energies. The two-component lognormal size distributions are shown in Fig. 3b for each position measured in all three SOFC samples at a X-ray energy just below the Zr K-absorption edge of 17.998 keV and assuming a scattering contrast factor, |Δρ|², of 2000 × 10²⁸ m⁻⁴, close to that for voids in LSM, YSZ or CGO. The scattering contrast at the void/solid interfaces dominates the scattering intensity, although other solid/solid interfaces give some scattering contrast, and hence contribute to the fitted feature size distributions. Nevertheless, previous SEM studies have indicated that the principal solid phases and void features are sufficiently comparable in size to be accommodated within the main lognormal size distribution discussed here.¹¹

Fig. 2 (a) Typical reduced and calibrated USAXS data with 2-component lognormal size distribution fit; and (b) apparent volume fraction size distributions obtained. In (a) and in following figures, the vertical bars represent the estimated or computed standard deviation uncertainties for each measurement point.

Fig. 3 (a) Transmission profiles of SOFC sections studied showing measurement positions within the anode, electrolyte and cathode for each of the three SOFC samples studied: A filter, B sulfur, and C pristine; and (b) corresponding apparent volume fraction size distributions obtained using the 2-component lognormal model. In (a) and in following figures the vertical dashed lines indicate the inner anode and cathode layers.

A simple hard-sphere scattering form-factor was assumed to model the individual scattering features, including voids.^24,40 Each lognormal size distribution can then be defined in terms of a volume fraction, Φ, a volume-weighted minimum diameter, D_MIN, mode diameter, D_MODE, and median diameter, D_MED.³⁹ From these parameters can be derived a volume-weighted mean diameter, D_MEAN, given by (D_MEAN − D_MIN) = (D_MED − D_MIN)^3/2/(D_MODE − D_MIN)^1/2, and a surface-weighted mean diameter, D_SURF, given by (D_SURF − D_MIN) = ((D_MED − D_MIN)(D_MODE − D_MIN))^1/2. The total surface area per unit sample volume for a lognormal population of hard spheres, S_V, is given by: S_V = 6Φ/D_SURF. Thus, the lognormal size distributions, fitted directly to the slit-smeared USAXS data over all Q, provided a caliper for obtaining the feature surface area per unit sample volume. This was considered more reliable than desmearing the data (potentially introducing artefacts) and then applying the Porod scattering law⁴⁰ to obtain the surface area empirically from relatively poor signal-to-noise data at high Q.

Since several measurements were made at a given location in each SOFC cell assembly as a function of X-ray energy, great care was taken to ensure consistency (within experimental uncertainties) among the fits at the different energies close to each X-ray absorption edge, and also between the fits near the Zr K-absorption and those near the Ni K-absorption edge. This was achieved, subject to the lower X-ray energies near the Ni K-absorption edge requiring significantly greater multiple scattering correction (even for 30 μm sections) than needed near the higher Zr K-absorption-edge energy. This correction was made by integrating the data for both empty beam blank and sample, over the incident beam profile out to a small Q value. The ratio of these integral values was then used to determine the sample transmission in place of the ratio of the intensities measured only at Q = 0. It was found that the apparent volume fraction and surface area of the main feature population exhibit systematic variations with X-ray energy at both absorption edges studied.

For the nanoscale feature size distributions, it was not possible to obtain acceptable consistency in the fitted volume fractions or derived surface areas. The nanoscale populations were found to represent between 2% and 5% of the total volume fraction, which is smaller than reported previously¹¹ and consistent with the new sample preparation because more of the scattering from the thin sections is accommodated within the main population. Here, the nanoscale components refine the overall fits to the data for Q > 0.1 nm⁻¹. What remains of the fitted volume fractions and derived surface areas of the nanoscale population vary stochastically with position, energy and background subtraction, and so this particular component is not suitable for further study using the anomalous USAXS technique. We have confined our discussion of the anomalous USAXS results to a treatment of the main lognormal size distribution component, as best representing the overall structural and accessible morphology of the SOFC system.

Anomalous USAXS measurements

As discussed elsewhere,^25,26 the physical principles of the USAXS instrument design strongly discriminate against Raman scattering and fluorescence contributions, making USAXS measurements particularly suited for anomalous SAXS studies. The only parasitic contribution in the data is a flat background due to air scattering between the analyzing crystals and the instrument's photodiode detector.

To interrogate the multiple phases present on the anode side of the SOFC system, the apparent volume fractions and derived surface areas of the main component lognormal size distribution were measured in two separate experiments in which the X-ray energy was tuned using a Si (111) monochromator to several energies just below the Ni K-absorption edge, specifically (8.000, 8.212, 8.278, 8.308 and 8.329) keV, and below the Zr K-absorption edge, (17.200, 17.828, 17.951, 17.985 and 17.994) keV. In order to obtain sufficient accuracy in the energy selection, the intensity of the monochromatic beam transmitted through the sample was measured as a function of photon energy using a photodiode detector placed after the sample. The ratio of this intensity to that of the incident beam, measured using an ionization chamber placed before the sample, provided a sample transmission spectrum versus X-ray energy. Inflections in the measured transmission spectrum close to the absorption edge were used to calibrate the energy scale of the monochromator by comparison with a standard reference curve for the pure element (Ni or Zr), previously calibrated against published tables of X-ray binding energies.⁴¹ Several inflection points were matched over a range of ≈20 eV to fix the energy calibration to within ±1 eV. The energy bandpass of the Si (111) monochromator optics, coupled with the USAXS instrument Si (220) collimating optics was ≈1.5 eV, with a repeatable X-ray energy accuracy of <1 eV.

Our objective in making measurements close to the two resonant absorption-edge X-ray energies (close to just the Zr edge on the cathode side) was to compare the energy dependence of the apparent surface area of the main feature population (assuming |Δρ|² = 2000 × 10²⁸ m⁻⁴) with the scattering contrast factor variation predicted for the solid/void and solid/solid interfaces potentially present at given locations in the SOFC system. With appropriate constraints applied (see below), the contributions to the total surface area could then be determined for the various component interfaces.

To predict the scattering contrast factor close to X-ray absorption edge energy, E₀, for one of the elements incorporated in a solid phase, we can write:^27,28

Contrast_Factor = |Δρ + f′ + if′′|² = |Δρ|² + 2Δρf′ + [f′² + f′′²] (1)

where f′ is related to the sample absorption and is usually much less than |Δρ|, while f′′(E) is not a strong function of the X-ray energy, E. For most interfaces of interest, both f′(E) and f′′(E) are much less than |Δρ|, making the 3rd term in eqn (1) small for E close to E₀. Although, in principle:where P denotes a principal integral, this integral has a singularity at E = E₀ and must be determined numerically over the region near E₀. In practice, for energies just below E₀, we can write:³⁰

Thus, the anomalous scattering contrast factor can be fitted by plotting |Δρ(E)|² versus ln{(E₀ − E)/E₀}, and fitting a straight line of the form:

to obtain |Δρ|₀² and |Δρ|_E². Table 2 lists predicted values of |Δρ|₀² and |Δρ|_E² applicable to relevant solid phases at X-ray energies just below the Ni K-absorption edge, and Table 3 does the same for the Zr K-absorption edge. Relevant |Δρ|₀² values are included for interfaces where no anomalous energy variation is predicted (|Δρ|_E² = 0). To predict the experimentally measured energy dependences, the terms |Δρ|₀² and |Δρ|_E² for the possible interfaces must be weighted according to the constraints discussed below.

Table 2 Scattering contrast factors for SOFC interfaces near Ni X-ray K-absorption edge^a

Interface:	Fixed contrast factor, |Δρ|0^2 (10^28 m^−4)	Anomalous contrast factor, |Δρ|E^2 in |Δρ|E^2 ln{(E0 − E)/E0} (10^28 m^−4) {E0 = 8.333 keV}
a Interfaces labeled a, b, c, etc. are discussed later in the text.
YSZ/void (f)	2096.3	0
YSZ/CGO	29.240	0
CGO/void (c)	2614.3	0
LSM/void (g)	2043.7	0
YSZ/LSM (h)	9.3060	0
Ni/void (a)	5062.4	302.94
Ni/YSZ	601.74	82.309
Ni/CGO (b)	373.31	61.161
Ni3S2/void (x)	2271.8	105.14

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Table 3 Scattering contrast factors for SOFC interfaces near Zr X-ray absorption edge^a

Interface:	Fixed contrast factor, |Δρ|O^2 (10^28 m^−4)	Anomalous contrast factor, |Δρ|E^2 in |Δρ|E^2 ln{(E0 − E)/E0} (10^28 m^−4) {E0 = 17.998 keV}
a Interfaces labeled a, b, c, etc. are discussed later in the text.
Ni/void (a)	5241.9	0
Ni/CGO (b)	413.35	0
CGO/void (c)	2711.5	0
LSM/void (g)	2075.0	0
Ni3S2/void (x)	2275.9	0
YSZ/void (f)	2111.8	61.44
YSZ/CGO	20.07	−14.45
Ni/YSZ	684.0	−43.53
YSZ/LSM (h)	−27.81 (corrected)	−7.05 (corrected)

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Fig. 4 shows the anomalous scattering contrast factor versus energy for the Ni/void and Zr/void interfaces close to the respective absorption edge energies, together with straight line fit plots of |Δρ(E)|² versus ln{(E₀ − E)/E₀} for E < E₀. Note that for positive |Δρ|_E², |Δρ(E)|² decreases as E increases towards E₀ from below. Also shown are equivalent plots for the YSZ/LSM interface close to the Zr absorption edge. For this interface on the cathode side of each SOFC, |Δρ(E)|² increases as E increases towards E₀ from below with both |Δρ|₀² and |Δρ|_E² negative (see Table 3). We call this a negative anomalous effect. Some significant loss of linearity is apparent in Fig. 4f closest to the absorption edge. This is due to |Δρ| being small so that the requirements for linearity are violated. A corrected fit is shown and corrected fit parameters are given in Table 3.

Fig. 4 Real part of the calculated scattering contrast factor, |Δρ|², versus X-ray energy for (a) the Ni/void interface near the Ni X-ray absorption edge; (b) the YSZ/void interface and (c) the YSZ/LSM interface near the Zr X-ray absorption edge; (d)–(f) corresponding straight line fits for (a), (b) and (c) of |Δρ|² versus ln{(E₀ − E)/E₀} for E < E₀. Here, the horizontal bars reflect the precision of the tabulated X-ray energies.

Despite the use of thin 30 μm sample sections, significant multiple scattering corrections were needed for data measured near the Ni K-absorption edge. As a precaution, in comparing the predicted |Δρ(E)|² with those measured experimentally, only relative comparisons were explored among the various phases for the Ni K-absorption edge measurements. Absolute comparisons were made using data measured near the Zr K-absorption edge, where little or no significant multiple scattering occurred.

Analysis and results

Fig. 5 presents the four representative diameters of the main lognormal feature size distribution versus position in each SOFC sample. The four diameters, D_MODE, D_MED, D_MEAN and D_SURF, were determined from the anomalous USAXS study at X-ray energies just below the Zr K-absorption edge. The results are consistent with those obtained in our earlier characterization of this SOFC system,¹¹ but show the variation through the anode/electrolyte and cathode/electrolyte interfaces in more detail. The separation in values of these four representative diameters is an indicator of the size-distribution width.

Fig. 5 Representative diameters versus position (a) through the anode side and (b) through the cathode side of sample A filter; sample B sulfur and sample C pristine fuel cells.

In moving from the outer anode to the inner anode of sample C pristine there is a clear narrowing of the size distribution, with the thin inner anode layer demarcating differences in size distribution characteristics between the outer anode and the electrolyte. Service life at 950 °C for 1000 h (A filter and B sulfur) results in a broadening of the size distribution in the outer anode. The mean feature diameter, D_MEAN, does not coarsen, but there is a decrease in all of the representative diameters except for D_MEAN. The increase in feature surface area within the anode during service life (discussed below) is significantly greater than can be accounted for by the reduction in D_SURF. This is due to a significant increase, previously reported,¹¹ in the apparent volume fraction of the main feature population, predominantly attributable to voids.

The feature size distribution varies more smoothly with position on the cathode side, and the representative diameters increase from the electrolyte, through the inner cathode layer, into the outer cathode. Service life at 950 °C for 1000 h causes marked narrowing of the size distribution, with some reduction in D_MEAN within the outer cathode. The increase in surface area during service life is more modest than in the anode, consistent with the modest decrease in diameter observed and the previously reported increase in main population apparent volume fraction¹¹ again mainly attributable to voids.

Spatial variation of anode interfaces and effects of sulfur exposure

Fig. 6 presents linear least-square fits based on eqn (4) to the experimentally measured apparent surface area variation (in m² cm⁻³, i.e., 10⁶ m⁻¹), multiplied by |Δρ|² = 2000 × 10²⁸ m⁻⁴, versus ln{((E₀ − E)/E₀)} for X-ray energies just below the Ni K-absorption edge (E₀ = 8.333 keV). The product of the apparent surface area, S_V, and this notional contrast factor is numerically equal to the product of the (unknown) true surface area and the true mean contrast factor (or the sum of such products for all contributing interfaces). Thus, y-axis values can be considered the sums of the contributing interfacial surface area components, each weighted by its associated contrast factor derived from Table 2 for the applicable X-ray energy. Note the highest energy (E closest to E₀) is on the left in these plots. Fits are given for positions 1 and 2 in the outer anode, position 3 in the inner anode, and position 4 in the electrolyte, for all three SOFC samples. In most cases the lowest energy, E = 8.000 keV, (right-most point in plots) significantly deviates from the linear dependence closer to E₀; so as a precaution these data points were excluded from the fits.

Fig. 6 Apparent surface area product (2000.S_V) versus ln{(E₀ − E)/E₀} with straight line fits for each of the 4 anode positions, 1 to 4 for (a) sample A filter; (b) sample B sulfur and (c) sample C pristine fuel cells. Lowest energy points (on right) excluded from fits.

For each straight line fit in Fig. 6 of form “U + V ln{((E₀ − E)/E₀)}”, U and V, respectively, are the sums of the component products of the various |Δρ|₀² or |Δρ|_E² values in Table 2 with their associated (initially unknown) interfacial surface areas. Every non-zero |Δρ|_E² value has a corresponding non-zero |Δρ|₀² value associated with the same surface area, but not every |Δρ|₀² value has a non-zero |Δρ|_E² value. If sulfur effects in sample B are initially ignored, then for anomalous measurements close to the Ni absorption edge at positions 1–3 in the anode, only the |Δρ|₀² values for the Ni/void, Ni/CGO and CGO/void interfaces in Table 2 need be considered, together with the |Δρ|_E² values for the Ni/void and Ni/CGO interfaces. Any interfacial surface area components within a Ni/CGO anode involving YSZ or LSM must be negligible relative to those involving Ni or CGO.

Table 2 was used to relate the fitted values of U and V to the known |Δρ|₀² and |Δρ|_E² values, and the unknown Ni/void, Ni/CGO and CGO/void interfacial surface areas. For example:

U = 5062.4a + 373.31b + 2614.3c (5)

V = 302.94a + 61.161b (6)

where the contrast factors (5062.4, etc.) are in units of 10²⁸ m⁻⁴, the interfacial surface areas, a, b and c are in m² cm⁻³, and a, b and c are, respectively, the surface areas for the Ni/void, Ni/CGO and CGO/void interfaces. Due to concerns regarding multiple scattering for anomalous USAXS measurements made near the Ni K-edge X-ray energy, eqn (5) and (6) are not used independently, but are combined to develop a relative expression for a, b and c. This is then used with an analogous expression, derived from Table 3 and the experimental fits for the measurements made near the Zr K-edge energy where multiple scattering is negligible, to give (following the example above):

W = 5241.9a + 413.35b + 2711.5c (7)

No significant anomalous scattering dependence on energy was observed for the anode positions near the Zr absorption edge, and W is simply an average obtained from the measurements at the five X-ray energies.

A further constraint is needed to obtain a, b and c. In most cases, that used is to require the ratio of the total Ni interface (a + b) to that for CGO (b + c) should equal the ratio of their volume fractions. Thus, (a + b)/(b + c) = 55/45 (or 1.2222) from Table 1 and:

45a − 10b − 55c = 0 (8)

This assumption is justified on the basis that previously obtained SEM images for these SOFC samples¹¹ indicate comparable feature sizes for Ni, CGO and voids within the anode, and no significant Ni coarsening during service life. The constraint is satisfied at many anode positions (1–4) in all three SOFC samples. Where it is not (i.e., it produces a negative value for one or more of a, b or c), the ratio, b/a, is constrained to take the same value as a neighbouring position. This is because (i) the ratio of internal Ni/CGO interface to external Ni/void interface is expected to vary smoothly throughout the anode region of the SOFC, even where the actual amount of Ni is depleted, and (ii) constraining b/a in this way results in values of (a + b)/(b + c) closer to the expected 1.2222 than do applications of similar constraints involving ratios such as a/c, c/b, etc.

In all three samples position 4 is nominally within the electrolyte layer where there is little porosity or interfacial surface area to give much scattering. The scattering observed is mainly from that part of the inner anode immediately adjacent to the electrolyte and included within the 20 μm sampling width centred on position 4. Given the anode and electrolyte compositions, we do not expect significant Ni/YSZ or CGO/YSZ interfacial surface areas to exist, and the surface area of the anode/electrolyte geometrical boundary is small compared to the interfacial surface areas within the microstructure. While some YSZ/void interface may exist within the electrolyte, its surface area measured at position 4 should be small compared to those of the Ni/void, Ni/CGO and CGO/void interfaces in the inner anode. Indeed, the anomalous USAXS measurements at the Zr X-ray absorption edge did not show significant anomalous intensity variation with energy at position 4. Nevertheless, to accommodate the small YSZ/void surface area present, denoted f to distinguish it from a, b and c, above, we modify eqn (5) and (7) to give:

U = 5062.4a + 373.31b + 2614.3c + 2096.3f (9)

W = 5241.9a + 413.35b + 2711.5c + 2111.8f (10)

In principle, the additional parameter, f, requires another constraint to provide unique values for a, b, c and f. In practice, eqn (6) requires that f is small and a, b and c take values within a narrow range.

For SOFC sample B, the sulfur in the fuel is expected to react with the Ni in the anode^42–44 to form a nickel sulfide compound of the form, Ni_XS_Y. The principal change in morphology within the anode is that the Ni/void interface is partially replaced with a Ni_XS_Y/void interface, which is an insulating barrier that degrades SOFC performance. Here, for analysis purposes, we assume the average composition to be Ni₃S₂, but we acknowledge that the true situation is more complex with a range of Ni/S content.⁶ In particular, there must be a gradation from most sulfur at the void surface to pure Ni deep within the Ni grains. Because of the diffuse nature of the interface between sulfide and Ni we do not assume a separate Ni₃S₂/Ni interface. To explore the effects of sulfur degradation, the results for sample B were re-analyzed by replacing a in the above equations with a Ni₃S₂/void interface that we denote x. Meanwhile, the other interfaces are assumed to remain as Ni/CGO and CGO/void, although the actual surface area values (b and c) found at each point change in the modified analysis. Using the contrast factor values in Tables 2and 3, eqn (5), (6) and (7) become:

U = 2271.8x + 373.31b + 2614c (11)

V = 105.14x + 61.16b (12)

W = 2275.9x + 413.35b + 2711.5c (13)

with similar modifications made to eqn (9) and (10) for position 4. The overall results for sample B sulfur were interpolated between those for the Ni/void and Ni₃S₂/void interface scenarios and then compared with the results for samples A filter and C pristine where no Ni₃S₂ interfaces are expected to occur.

The interfacial surface areas determined for all three samples are presented in Table 4, and in Fig. 7.

Table 4 Interfacial surface areas (in m² cm⁻³) on the anode side of each SOFC sample^a

Position: Ni or Ni3S2:	Sample A filter Ni/void (a)	Sample B sulfur Ni/void (a)	Sample B sulfur Ni3S2/void (x)	Sample C pristine Ni/void (a)
a a = Ni/void, x = Ni3S2/void, b = Ni/CGO, c = CGO/void, f = YSZ/void.
Position 1
a or x:	0.370 ± 0.003	0.756 ± 0.016	1.935 ± 0.046	0.209 ± 0.003
b:	0.893 ± 0.014	0.693 ± 0.076	1.183 ± 0.076	0.209 ± 0.013
c:	2.495 ± 0.019	1.605 ± 0.050	1.368 ± 0.046	0.314 ± 0.007
Position 2
a or x:	0.924 ± 0.013	1.463 ± 0.035	2.464 ± 0.091	0.299 ± 0.011
b:	2.230 ± 0.063	1.341 ± 0.168	4.263 ± 0.322	0.298 ± 0.051
c:	2.125 ± 0.034	0.953 ± 0.055	1.241 ± 0.054	0.190 ± 0.017
Position 3
a or x:	1.070 ± 0.026	0.865 ± 0.022	1.760 ± 0.065	0.168 ± 0.005
b:	2.583 ± 0.141	0.793 ± 0.106	2.115 ± 0.106	0.454 ± 0.031
c:	0.406 ± 0.031	1.063 ± 0.048	1.056 ± 0.045	0.055 ± 0.006
Position 4
a or x:	0.090 ± 0.006	0.072 ± 0005	0.100 ± 0.035	0.028 ± 0.003
b:	0.344 ± 0.032	0.051 ± 0.010	0.236 ± 0.060	0.122 ± 0.011
c:	0.011 ± 0.011	0.042 ± 0.003	0.039 ± 0.039	0.001 ± 0.004
f:	0.023 ± 0.023	0.030 ± 0.009	0.079 ± 0.079	0.076 ± 0.076
Electrolyte
f:	0.021 ± 0.002	0.026 ± 0.003	0.026 ± 0.003	0.024 ± 0.002

---

Fig. 7 Specific surface areas of the Ni/void, Ni/CGO, CGO/void and YSZ/void interfaces versus position through the anode side of (a) sample A filter, (b) sample B sulfur and (c) sample C pristine fuel cells.

The experimental uncertainties quoted are derived from those of the measurement parameters: U, V and W. For U and V, these are the standard deviation uncertainties (confidence interval = 1) from the straight-line fits shown in Fig. 6. For W, it is the computed standard deviation of the mean result from the five X-ray energies measured below the Zr absorption edge.

As the equations and constraints are combined to produce the interfacial surface areas (a, b, c, f, x), the uncertainties are promulgated through to the final values shown. While some co-variances exist among the surface area results, these have been neglected in the present analysis. More significantly, the uncertainties quoted do not take into account stochastic variations in the SOFC microstructures, or any errors in the constraints applied. We have minimized the former through radiography of each measurement position using the USAXS X-ray video camera, in order to ensure the microstructure sampled is representative of the region of interest. While changes in the applied constraints and fit criteria may change the detailed results by more than the indicated uncertainties, the interfacial surface area spatial variations, together with their comparison across the three SOFC samples, are preserved when the constraints and criteria are applied consistently.

Fig. 7 presents the spatial variations of the Ni/void, Ni/CGO, CGO/void and YSZ/void interfacial surface areas in all three samples – assuming no formation of Ni₃S₂. The additional position in the electrolyte (also included in Table 4 and Fig. 5) was derived from earlier anomalous USAXS measurements at X-ray energies near the Zr absorption edge on thicker sections of these same SOFC samples. Fig. 8 presents the spatial variations of the total boundary surface areas for three specific phases: voids, Ni and CGO. Fig. 9a and b present the corresponding spatial variations to Fig. 7 and 8 for sample B sulfur assuming the Ni/void interface is replaced with a Ni₃S₂/void interface.

Fig. 8 Total boundary surface areas for voids, Ni and CGO versus position through the anode side of (a) sample A filter; (b) sample B sulfur and (c) sample C pristine fuel cells.

Fig. 9 Specific surface areas of (a) the Ni₃S₂/void, Ni/CGO, CGO/void and YSZ/void interfaces versus position, and (b) the total boundary surface areas for voids, {Ni₃S₂ + Ni} and CGO versus position through the anode side of sample B sulfur assuming all the Ni/void interface has converted to Ni₃S₂/void; (c) inferred fraction of the Ni/void interface replaced by a Ni₃S₂/void interfaces using assumptions outlined in the text.

Several trends are apparent in Fig. 7, 8 and 9. Firstly, there is a significant increase in all of the interfacial surface areas during service life for both external solid/void interfaces and internal interfaces between the solid phases. Secondly, some migration of solid phases (especially Ni) occurs during service life. Thirdly, although a comparison between the two scenarios for sample B sulfur assuming Ni/void or Ni₃S₂/void interfaces is complicated, that assuming a Ni₃S₂/void interface more closely resembles the spatial variation for sample A filter, which has undergone the same service life. This indicates a significant fraction of the Ni/void interface has transformed to some form of Ni_XS_Y/void. Fig. 9c presents a possible scenario for the fraction of Ni/void surface area replaced by Ni₃S₂/void interface, based on interpolating between the sample B scenarios to reproduce the sample A spatial variation. The interpolation was applied separately to the Ni/CGO and total void surface area spatial variations, and then averaged.

Interfaces in the cathode

With no Ni present, the anomalous USAXS measurements at positions in the cathode of each sample (positions 5–7) were made only at X-ray energies near the Zr absorption edge. On the cathode side of the electrolyte, the spatial distributions of the YSZ/void, YSZ/LSM and LSM/void interfaces are of interest (Fig. 1 and Table 1). Straight line fits were applied to analogous plots to Fig. 6 of the experimentally measured apparent surface area variations, multiplied by |Δρ|² = 2000 × 10²⁸ m⁻⁴, versus ln{((E₀ − E)/E₀)} for X-ray energies just below the Zr K-absorption edge (E₀ = 17.998 keV). Straight line fits were of form “X + Y ln{((E₀ − E)/E₀)}”, where X and Y are the sums of the products of the respective |Δρ|₀² and |Δρ|_E² values in Table 3 with their associated interfacial surface areas, f, h and g. Following determination of X and Y, two analogous equations to eqn (5) and (6) could be applied:

X = 2111.8f − 27.81h + 2075.0g (14)

Y = 61.44f − 7.05h (15)

where f = YSZ/void, g = LSM/void and h = YSZ/LSM (using the corrected fit parameters shown in Table 3). As for the anodes a further constraint was required to determine f, g and h. For position 6, centred within the inner cathode layer of each sample, a similar rationale was applied as in the anode case, and it was assumed that the ratio of the total YSZ and LSM boundaries (solid/void + solid/solid) is the same as the ratio of their volume fractions. Thus, (f + h)/(h + g) = 51/49 (or 1.0408) from Table 1 and:

49f − 2h − 51g = 0 (16)

Application of this constraint allowed f, g and h to be determined at position 6 in each SOFC sample, but different constraints were needed for positions 5 and 7.

For position 5, centred in the electrolyte but with part of the inner cathode included within the sampling volume, a solution with all of f, g and h > 0 was found on assuming the same ratio, h/g, as for position 6. This is reasonable given that the LSM/void (g) and YSZ/LSM (h) interfaces within this sample volume should arise only in the inner cathode. However, it was found that g is close to zero. For position 7, centred in the outer cathode but again with part of the inner cathode included in the sampling volume, this assumption could not be made because the large contribution from the LSM/void interface in the outer cathode significantly reduces the h/g ratio from the value found in the inner cathode. Assuming the same ratio, h/f, as for position 6 did not provide a realistic solution for position 7 with all of f, g and h > 0. This is likely due to the strongly increasing porosity gradient on moving from the electrolyte, through the inner cathode, to the outer cathode. In fact, no solution was found for all of f, g and h > 0 where h was not much reduced from its position 6 value. Thus, a limiting case was assumed in which the internal YSZ/LSM interface (h) was assumed to go to zero on moving into the outer cathode.

The interfacial surface area spatial variations determined at positions 5–7 in all three samples are presented in Table 5 and Fig. 10. Again, an additional position in the electrolyte was derived from earlier anomalous USAXS measurements on thicker sections of these same SOFC samples. The experimental uncertainties quoted are derived from the standard deviation uncertainties (confidence interval = 1) of the straight-line fits used to determine the measurement parameters: X and Y, and are promulgated through to the calculated surface areas, f, g and h in similar fashion to the anode results.

Table 5 Interfacial surface areas (in m² cm⁻³) on the cathode side of each SOFC sample^a

Position:	Sample A filter	Sample B sulfur	Sample C pristine
a f = YSZ/void, g = LSM/void, h = YSZ/LSM.
Electrolyte
f:	0.039 ± 0.004	0.024 ± 0.002	0.021 ± 0.002
Position 5
f:	0.084 ± 0.020	0.056 ± 0.013	0.038 ± 0.002
g:	0.001 ± 0.016	0.000 ± 0.011	0.003 ± 0.002
h:	0.007 ± 0.156	0.004 ± 0.101	0.939 ± 0.216
Position 6
f:	0.296 ± 0.139	0.444 ± 0.015	0.353 ± 0.018
g:	0.197 ± 0.114	0.141 ± 0.014	0.016 ± 0.017
h:	1.468 ± 1.099	5.498 ± 1.834	5.439 ± 1.915
Position 7
f:	0.326 ± 0.284	0.081 ± 0.231	0.288 ± 0.108
g:	0.387 ± 0.226	0.729 ± 0.192	0.129 ± 0.089
h:	0	0	0

---

Fig. 10 Specific surface areas of the YSZ/void, LSM/void and total void interfaces versus position through the cathode side of (a) sample A filter, (b) sample B sulfur and (c) sample C pristine fuel cells. (Note significant uncertainties as indicated by large vertical bars.)

Clearly, many of the interfacial surface areas determined on the cathode side of each SOFC sample have greater uncertainties than on the anode side, but significant observations can be made. The YSZ/void and LSM/void interfaces are increased during service life, but the distinction between sample A filter and sample B sulfur is subtle.

The most striking result in Table 5 is the prominence in all 3 samples of the internal YSZ/LSM interface within the inner cathode – a point further illustrated in Fig. 11, which presents plots of the spatial variations of the YSZ/LSM interface in all 3 SOFC samples, based on the values of Table 5 derived from the corrected contrast factors of Table 3. The prominence of this interface can be associated with the negative (or near-negative) anomalous USAXS effect observed at position 6 (also Fig. 4 and Table 3). In sample A filter the YSZ/LSM interface is less prominent at this position than in sample B sulfur or sample C pristine, but this may be due to lack of precision in defining the measurement position. For the other samples, Fig. 10 and 11 suggest that the true maximum in the YSZ/LSM interfacial surface area occurs close to the inner cathode/electrolyte boundary.

Fig. 11 Specific surface areas of the YSZ/LSM interface versus position through the cathode sides of all 3 SOFC samples. (2 sets of vertical dashed lines are apparent because of the different relative position of the sample C pristine inner cathode layer on this plot.)

Discussion

A number of further findings can be deduced regarding the anode and cathode layers. As reported previously¹¹ service life did not significantly coarsen the microstructures of the SOFC samples studied here. Elsewhere^1,3,45,46 it has been found that the Ni phase in the SOFC anode can coarsen significantly through an Ostwald ripening mechanism, particularly for repeated reduction/oxidation cycling or sustained exposure to high temperatures in a moist environment. However, under some conditions, the CGO can have a constraining effect on the Ni grain size.² After operation at 950 °C for 1000 h under dry conditions, the Ni in the anode of SOFC systems similar to those studied here has been shown to coarsen by <10%.⁴⁶ The present measurements of the anode main feature population indicate D_MEAN decreases by a few percent from sample C pristine to sample A filter, and increases marginally from sample C pristine to sample B sulfur. All of the other finer characteristic diameters of the distribution, D_MED, D_SURF and D_MODE, decrease by successively greater amounts. A comparison of Fig. 3, 5, 7 and 8 indicates that service life increases the apparent volume fraction and surface area of the main feature population through the creation of additional fine features. In sample A filter and sample B sulfur, the anode main feature apparent volume fractions (Fig. 3) remain comparable to sample C pristine for feature sizes larger than 800 nm. The emergence of new features smaller than 800 nm increases the overall volume fraction and component surface areas during service life while decreasing the distribution mode value – but the original large features remain. This is not inconsistent with a modest coarsening in the Ni domain size given that much of the scattering comes from voids, particularly if thermal expansion mismatch between Ni and CGO causes some fracturing of the CGO structural backbone.^2,3,45,46

The smaller anode value of D_MODE for sample B sulfur, relative to sample A filter, is consistent with substitution of metallic Ni with less dense nickel sulfides, e.g., Ni₃S₂, and consequently smaller voids. The significant increase in the internal Ni/CGO interface during service life implies that the Ni migrates at least locally within the structure, which is not surprising given the high mobility of Ni at 950 °C. Comparison of Fig. 7–9 indicates that Ni, as measured by the Ni/CGO interfacial surface area, migrates outwards away from the anode/electrolyte interface during service life – both in sample A filter and, more significantly, in sample B sulfur – consistent with results reported elsewhere.³³ Both samples have seen the same service life, making it reasonable to relate the sample B spatial variations to sample A, and interpolate between the Ni/void and Ni₃S₂/void scenarios to determine the degree of sulfide surface coverage in sample B. Unfortunately, the different degrees of Ni migration, and absence or presence of Ni₃S₂ formation, complicate such comparison. However, the spatial variations of the Ni/CGO and total void interfaces were found to be suitable for interpolation; so Fig. 9c is based on these. The deduced fraction of Ni/void surface area coverage by sulfide is comparable to that found in other studies.⁴²

The cathode results show greater uncertainties than the anode results. The effects of service life are significant but less marked, and effects of sulfur in the fuel are subtle. The increases in apparent volume fraction and surface area in the cathode take place across the entire size range. This is evident in Fig. 5 in some narrowing of the size distribution through a significant decrease in D_MEAN and more modest decreases in D_MED, D_SURF and D_MODE. Fig. 10 shows little change in the spatial variation of the YSZ/void interface surface area. The principal change comes from a substantial increase during service life of the LSM/void surface area, which is sufficient to double the overall outer cathode void surface area. Meanwhile, as Fig. 11 indicates, the internal YSZ/LSM interface dominates within the inner cathode layer for all 3 samples.

One aspect common to the anode and cathode microstructures is that, while service life increases virtually all of the component interface surface areas, the solid/void interface shows the largest increase. Thus, there is a relative reduction in the proportion of internal Ni/CGO and YSZ/LSM surface areas (despite the latter dominating the inner cathode) compared to the external solid/void surface area. Fig. 12 presents simplified schematics illustrating several microstructure changes inferred to take place during service life. While these 2D schematics are over-simplified, they illustrate how the solid/void surfaces areas can increase during service life, even with some Ni coarsening in the anode. They show how the anode porosity can increase through the introduction of new fine voids to produce a broader size distribution. The anode schematic after service life illustrates a significant presence of sulfide at the Ni/void interface, as would occur in sample B sulfur. Meanwhile, the inner cathode schematic illustrates how the morphology can accommodate a disproportionately large fraction of YSZ/LSM interface, and a possible breakup of large voids to create a narrower distribution of finer features.

Fig. 12 Idealized schematics illustrating generic microstructural changes in (a) anode and (b) inner cathode layers during SOFC service life. In anode: Ni₃S₂ formation is highlighted by a glowing Ni/void interface; for boundaries: red = Ni/void, green = CGO/void, blue = Ni/CGO. In cathode: L = LSM, Y = YSZ, V = voids; for boundaries: orange = LSM/void, purple = YSZ/void, black = YSZ/LSM.

Summary and conclusions

Anomalous USAXS measurements made close to two well-separated absorption-edge X-ray energies have interrogated the evolution of SOFC microstructures during service life, and quantified the influence of sulfur in the fuel on anode microstructure degradation. These studies differ from other recent anomalous SAXS studies using multiple X-ray absorption edges,^47,48 which have characterized discrete scattering particles within a uniform matrix. By contrast, SOFC microstructures are complex and heterogeneous in nature, with each phase having boundaries with multiple other phases. Although void and grain volume fraction size distributions are of interest, the component surface areas quantify the degree to which one phase is intimately connected to another, providing constraints for defining the TPB morphology and deducing TPB length within the anode and cathode layers. Indeed, the ability of ions to diffuse along grain boundaries and other interfaces^21,22 makes quantifying the component surface areas, as a function of position, key to understanding many aspects of SOFC performance.

In this paper, we have demonstrated how, with application of suitable constraints, anomalous USAXS measurements can separate out the spatial variations of the Ni/void, Ni/CGO and CGO/void interfaces in a Ni/CGO SOFC anode, and the YSZ/void, YSZ/LSM and LSM/void interfaces in a YSZ/LSM SOFC cathode. We have shown how these interfaces change under service life conditions, and how the presence of sulfur in the fuel can modify the microstructure evolution in the anode by the significant formation of sulfides at the Ni/void interface. After allowing for some stochastic behaviour in individual SOFC cells, greater degradation is detected in the performance of SOFCs of the kind studied here when sulfur is present in the fuel (sample B), as compared to performance using a filtered fuel (sample A).^3,45,46,49 Meanwhile, the present study has detected a disproportionately large YSZ/LSM interfacial surface area within the inner cathode. Clearly, this interface could play a significant role in SOFC performance degradation given both the reported critical nature of the oxygen stoichiometry in both YSZ and LSM¹⁶ and the potential formation of an insulating layer at the YSZ/LSM interface due to sintering effects during service life.¹³ This study has also shown that service life significantly increases the solid/void surface area and introduces finer features (mainly pores) in both the anode and cathode. We assert that the resulting disruption in percolation paths to active TPB sites is the dominant mechanism for SOFC performance degradation, especially in the anode.

Future anomalous USAXS measurements could further quantify the electrochemically-active interface response to SOFC service life, especially for the anode in the presence or absence of sulfur within the fuel. Also, using the Cr and Sr K-edges instead of the Ni and Zr K-edges, the anomalous USAXS method could be applied to investigate Cr-spinel formation in SOFC cathodes. More generally, such studies could play a key role in improving our understanding of complex electrochemical interface gradients not only within SOFCs but also in other advanced energy material systems.

Acknowledgements

We thank J. Sfeir (Hexis AG) for discussions and providing SOFC test specimens; S. Claggett (NIST Metallurgy Division) for ceramographic USAXS sample preparation; R. Bachtold (Empa) for the optical micrographs; and P. Holtappels and T. Graule (Empa) for supporting this project. A.B. is grateful for financial support from the European Union (Real-SOFC project no. SES6-CT-2003-502612; Marie Curie Actions no. MIRG-CT-2006-042095, SOFC-LIFE project no. 256885), and from the Swiss Competence Center for Energy & Mobility, project no. CCEM-705. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract no. DE-AC02-06CH11357.

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