Fuel Cell Preparation. The anode supported SOFC studied was Ni-YSZ/YSZ/LSM-

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1 Supplemental Information Fuel Cell Preparation. The anode supported SOFC studied was Ni-YSZ/YSZ/LSM- YSZ,LSM (YSZ = 8 mol% Y 2 O 3 -stabilized ZrO 2 and LSM = La 0.8 Sr 0.2 MnO 3 ). The anode substrates, consisting of NiO/YSZ (70/30wt%) with 10% starch filler, were bisque fired at C. Thin (10-20 µm) layers of NiO/YSZ (50/50wt%) and YSZ were deposited on the supports using a colloidal deposition technique similar to that described previously. 27 The anode and electrolyte were co-fired at C for 6h. LSM-YSZ cathode layers were applied and fired at C for 4 h. A second layer of pure LSM slurry was then applied and fired at C for 4 h. The colloidal NiO/YSZ layer adjacent to the YSZ electrolyte, which was the electrochemically active portion of the anode, was the region studied in detail here. Fuel Cell Testing. Single cells were tested using a standard testing geometry, similar to that reported previously. 19 At the beginning of each test, the Ni-based anode was fully reduced in humidified H 2 at C. The cells were tested with air at the cathode, while the fuel was humidified hydrogen. Image Collection. The present images were collected using a Zeiss 1540XB FIB-SEM. The configuration, illustrated schematically in Figure 1, allows simultaneous collection of a series of 2D cross-sectional SEM images as the specimen is sectioned by the FIB along the third axis. The fuel cell was first cut and polished, leaving a cross-sectional surface with the anode, electrolyte, and cathode exposed. The focused ion beam (FIB) was then used to mill a rectangular trench into this surface in the vicinity of the anode, as shown in Figure 1. The electron beam was used to image one of the trench side walls at an angle of 36 from normal to the side wall. As the FIB shaved away material from this surface, tilt-corrected SEM images were continuously acquired, with scan- and frame-grab rates synchronized with milling rate for

2 high quality imaging. In this manner, a series of 2D images was obtained. A few typical 2D images are shown in supplemental figure S2. A spacing v = 44nm between consecutive images was calculated from the fixed FIB milling rate and the milling time per image. Two independent milling rate calibrations were used. First, a calibration sample was milled using the same FIB scan rate and a fixed mill time, and the milled depth was measured by FIB imaging. The second method employed fiducial marks, milled on the top surface of the specimen prior to sectioning (Fig. 1A), to measure the milled depth. The two methods yielded results that agreed within 1% in measuring a milled depth of approximately 1 µm. Image Stacking. Accurate stacking of the images requires that the reconstruction account for any resolution differences in all directions and that the individual sections be aligned properly. Alignment of the images was accomplished by using the fiducial marks as points of reference. An FFT-based algorithm was subsequently implemented to verify the alignment. 28 A total of 82 images were used in the reconstruction to produce a total analyzed volume of µm 3. The above process was done manually for the present data, taking a few weeks, much more than that needed for image acquisition and 3D calculations (a few hours each). Advances in automating this procedure are being made, such that future timescales for full reconstruction will be on the order of days. Due to the different resolutions in different directions 10 nm in the image plane and 50 nm between images in the 3D data sets, the desired approximately cube-shaped voxels were obtained by reducing the resolution to 41.7 nm in the images. This loss of resolution was not a serious problem for the present anodes, which were typical of state-ofthe-art SOFC anodes, where the feature sizes ranged from ~ 200 nm to 1 µm (see Figure 2). In one case, we adjusted the image resolution to check for potential errors. We calculated the total interfacial areas on 2D images with the original resolution (13.9 nm) and with the reduced

3 resolution (41.7 nm) that was normally used to obtain nearly cube-shaped voxels. The reduction in the interfacial areas in the 2D images due to resolution reduction was found to be 5% on the average, providing an estimate for the errors in the surface area associated with the resolution used. In the future, it should be possible to reduce the spacing between images in the FIB-SEM measurements, perhaps as low as 10 nm, thereby improving the resolution.

4 Supplemental Figures. Figure S1. Measured voltage and power density versus current density for the SOFC utilized in the present study. Figure S2. Four representative SEM image sections of the Ni-YSZ anode separated by 150 nm, illustrating the change in the microstructure with depth along the milling direction.

5 27 Zhan, Z. & Barnett, S.A. Solid oxide fuel cells operated by internal partial oxidation reforming of iso-octane. J. Power Sources, in press. 28 Xie, H., Hicks, N., Keller, G.R., Huang, H. & Kreinovich, V. An IDL/ENVI implementation of the FFT-based algorithm for automatic image registration. Computers and Geosciences 29(8), (2003).