Thermomechanical Analysis of Various Solid-oxide-fuel-cell Components Using Simple Analog Micrometer Measurements

The solid oxide fuel cell (SOFC) is a device that can convert the energy stored in gaseous chemicals such as hydrogen into electricity. Because SOFCs are operated at high temperatures, their structures must be stable and durable. The thermomechanical compatibility of SOFC components is the main issue, as negligence in regard to material compatibility leads to cell destruction. In this study, we investigated the thermal expansion coefficient (TEC) of SOFC components, which characterizes their thermomechanical properties. We measured the TEC value of various electrolyte and electrode materials [La9.33Si4O26 (LSO), Ce0.9Gd0.1O1.92 (CGO), La0.8Sr0.2Ga0.8Mg0.2O2.55 (LSGM), LSO-CGO, LSO-LSGM, and La0.7Ca0.3MnO3 (LCM)] using an analog micrometer at temperatures between 298 K and 1073 K. The obtained TEC values matched well with the theoretical references, with errors between 1.80% and 8.00% for LSO, CGO, LSGM, and LCM. The TEC of composite SOFC materials, LSO-LSGM and LSO-CGO, were 10.29 × 10 K and 10.10 × 10 K, respectively. Given the slight difference in their TEC values, these electrolytes would thermomechanically match an LCM cathode.


Introduction
The solid oxide fuel cell (SOFC) is a device that can convert gaseous hydrogen into electricity. SOFCs operate in temperatures ranging from 873 K to 1473 K (600°C-1200°C). Because SOFCs can be constructed using a multiple-cell stack design, they are a promising energy source for high-temperature-operation systems and have the potential to produce up to 10 MW of electricity [1]. To withstand such high operation temperatures, SOFCs must be built to ensure thermomechanical and physical durability. An SOFC contains three main components: an electrolyte, anode, and cathode. To maintain good performance, these three components must be compatible. The thermal expansion coefficient (TEC) is an important parameter used to characterize the thermomechanical compatibility of an SOFC. All SOFC components must have similar TEC values. Negligence regarding the mismatch of TECs will lead to performance degradation from delamination, cracks, and vigorous cell destruction [2]. The basic features of the SOFC components, i.e., their chemical properties and structure of the materials, affect their TEC values [3].
Based on fundamental principles for determining expansion coefficients, dilatometric analysis is usually performed using a dilatometer [4][5][6]. This instrument provides the best accuracy by measuring the in-situ expansion as the temperature increases. However, the simultaneous measurement of all the materials leads to a very costly analysis. Letilly et al. [7] analyzed the TEC of the BIT07 electrolyte using X-ray diffraction (XRD) analysis at room temperature, whereby each sample was sintered at different temperatures, with the underlying assumption that the chemical expansion could transform the TEC value. Blum [8] conducted TEC measurements using a standard F-design. Based on the fact that material expansion occurs simultaneously in all directions, this author combined the basic principles of linear expansion that can be observed with room temperature measurements after sintering at a certain temperature, which is similar to the assumptions made by Letilly et al. [7]. The TEC measurements by Blum [8] were simply made using an analogous micrometer.
As a common anode material, NiO was used as the anode in a comparison study with other SOFC component materials. In that study, the main electrolyte selected was La 9.33 Si 4 O 26 (LSO), which was further processed using the solid-state method to produce composite electrolytes with other electrolyte materials, Ce 0.9 Gd 0.1 O 1.92 (CGO) and La 0.8 Sr 0.2 Ga 0.8 Mg 0.2 O 2.55 (LSGM) [9]. LSO and CGO are considered to be intermediate-temperature SOFC electrolytes, whereas LSGM is a well-known good ionic conductor electrolyte in the low-to-mid temperature range [10]. To monitor the TEC values in low-and mid-range operation temperatures, the electrolytes were treated as variables. The cathode, La 0.7 Ca 0.3 MnO 3 (LCM), was synthesized using a solid-state method. This cathode was selected because it exhibits high electronic conductivity. Theoretically, all the possible combinations were predicted to be good SOFC single-stack constructions.
To determine the thermomechanical compatibility of all the components in practical terms, the experimental TEC values must be measured.
The main purpose of this study was to construct a SOFC prototype and explore its TEC values. To study the TEC behavior, both the electrolyte and electrode components were observed. TEC is traditionally measured using a dilatometer [11,12]. In this study, we used a new and simpler method to monitor the TEC value of the SOFC components. This method is based on dilatometric analysis but does not involve the use a dilatometer. Instead, we used a manual micrometer over the experimental temperature range (298 K to 1073 K).

Methods
CeO 2 (99.9%), Gd 2 O 3 (99.9%), MnO 2 (99.9%), CaCO 3 (99.9%), and NaOH (99.9%) were obtained from Merck Singapore. LSGM (99.99%), La 2 O 3 (99.99%), Na 2 SiO 3 · 5H 2 O (≤95%), and La 2 O 3 (99.99%) were obtained from Sigma-Aldrich. The desired materials were all produced using the methods reported in our previous study [13]. XRD analysis was performed using a Rigaku MiniFlex600 X-Ray Diffractometer (γA system, Cu Kα radiation, λ = 0.15418 nm, T = 298 K, v = 0.02°i n the 2θ range 20°-80°). Data fitting was conducted using PANalytical X'Pert Highscore Plus© software and the ICSD/ International Crystallographic Structure Database. Sample pellets (0.4-0.6 g) were uniaxially pressed to a diameter of~1 cm using a Graseby Specac and then sintered at 1473 K to obtain similar initial densification conditions. The dimensions of the sample pellets were then measured using an analog micrometer at 298 K to obtain the initial dimensions. Thereafter, the sample pellets were heated at a rate of 5 K min −1 to the desired temperature, which was maintained for 2 h. The pellet dimensions were measured every 100 K up to 1073 K. The measured dimensions of the pellets were then applied in the TEC calculations using Equation 1.

Results and Discussion
Figures 1 and 2 present the XRD patterns of the SOFC components that were successfully prepared in this study. All the patterns were analyzed using the Rietveld refinement technique to obtain their lattice parameters, reliability profiles (Rp), reliability weight profiles (Rwp), and goodness of fit. The XRD patterns conformed to the ICSD standards 98-015-5624 (LSO), 98-002-8795 (CGO), 98-009-8170 (LSGM), and 98-008-8389 (LCM). These materials were then used for TEC measurements. Table 1 lists the refinement parameters of the samples.
TEC is one of the most important parameters for evaluating the thermomechanical compatibility of SOFC components. In this study, we calculated the TEC values as follows: where ΔL is the change in length, L 0 is the initial length, T initial is the initial temperature, and T is the final temperature.
Except for LSO, for which a significant statistical error was found, the relative errors were less than 5%. To study the TEC behavior further, we examined the and volumes that the test range of 298 K to 1073 K. Figures 3 to 6 show plots of the results for each component. Each figure shows a trend of increasing length with increases in temperature [8]. The positive gradient value emphasizes this trend, however, the gradient of each component was slightly different due to the respective   Figure 3, we can also observe a gap between points that may have a similar order as those of LSO With increases in temperature, the sample lengths i creased linearly for LSO-LSGM and LCM. However, for LCM, we found that the linear length increased dr matically between 873 K and 1072 K, which is similar to the behavior of NiO-CGO, although that increase began at 773 K. This behavior significantly affected the TEC value. To examine the shift, we measured these changes carefully (Table 3). (not studied)

of TEC Values for Various
Relative error/% 2.35 8.00 ---1.92 In Figure 3, we can also observe a gap between points that may have a similar order as those of LSO-CGO. With increases in temperature, the sample lengths in-LSGM and LCM. However, for LCM, we found that the linear length increased dramatically between 873 K and 1072 K, which is similar CGO, although that increase began at 773 K. This behavior significantly affected the To examine the shift, we measured these

Expansion of LSO-LSGM
The positive gap shown in Table 4 indicates that the value of each point increased with increasing temper ture. A zero value indicates that no meaningful change occurred as the temperature increased, whereas a neg tive value indicates a slight decrease in linear length as the temperature increased. Negative changes have yet to be reported and may have been caused by the of the linear length obtained from the calculation. A ratio phenomenon was observed in this study due to dilatation of the material in every direction. A occurs when the ratio between the areas of a cylinder to its thickness at higher temperature is lower than the r tio at a lower temperature. The occurrence of this ph nomenon suggests that linear expansion, as obtained from the ratio, did not occur at certain temperature, whereas volume expansion did occur. Since the TEC values obtained in this experiment are linear expansion coefficients, the area of the cylinder had to be divided by its thickness. As such, a negative value indicates a late ratio, which means that no linear expansion o curred at certain temperature between 873 ther study to learn more about this phenomenon is r quired to better understand how the late ratio behaves.

March
The positive gap shown in Table 4 indicates that the value of each point increased with increasing temperature. A zero value indicates that no meaningful change occurred as the temperature increased, whereas a negandicates a slight decrease in linear length as the temperature increased. Negative changes have yet to be reported and may have been caused by the late ratio of the linear length obtained from the calculation. A late phenomenon was observed in this study due to dilatation of the material in every direction. A late ratio occurs when the ratio between the areas of a cylinder to its thickness at higher temperature is lower than the rarence of this phenomenon suggests that linear expansion, as obtained from the ratio, did not occur at certain temperature, whereas volume expansion did occur. Since the TEC values obtained in this experiment are linear expansion he cylinder had to be divided by its thickness. As such, a negative value indicates a , which means that no linear expansion oc-873-773 K. Further study to learn more about this phenomenon is rer understand how the late ratio behaves. Figure 7 shows the variation in ΔL/Lo for each sample. LSGM experienced a sudden shift at 800 K. LSO-CGO and LSO also underwent a sudden shift at temperatures above 800 K. The LSO-CGO composite showed a slight change in its curve above that of its original matrix material, LSO. On the other hand, the electrolyte composite LSO-LSGM experienced a much smaller change than its original material, LSO, or even LSGM. This difference verifies the conclusions that could be drawn based on the TEC values, as shown in Figure 8. Figure 8 shows the TEC values at every temperature point of all the above materials. Three materials (LSGM, LSO-CGO, and LSO) showed a negative gradient or decreasing TEC value with increases in temperature. This implies a tendency that increases in temperature could cause infinite expansion of the material until it reaches a point of maximum expansion in its linear length before becoming permanently deformed. At that time, a positive gradient implies a lower rate of linear length expansion to a finite point near and above 800 K. Until this point, the average TEC would reflect the overall TEC behavior, although the TEC might vary at different temperatures, as shown in Table 3. The TEC also might differ in ranges based on the materials used, with expansion occurring until a certain high temperature, after which deformation takes over. However, in this study, the temperature was set to 1073 K as a mid operational temperature. Figure 8. TEC Shifts of Various CGO composite showed a slight ge in its curve above that of its original matrix material, LSO. On the other hand, the electrolyte LSGM experienced a much smaller change than its original material, LSO, or even LSGM. This difference verifies the conclusions that could be rawn based on the TEC values, as shown in Figure 8. Figure 8 shows the TEC values at every temperature point of all the above materials. Three materials CGO, and LSO) showed a negative gradient or decreasing TEC value with increases in ure. This implies a tendency that increases in temperature could cause infinite expansion of the material until it reaches a point of maximum expansion in its linear length before becoming permanently deformed. At that time, a positive gradient implies a ower rate of linear length expansion to a finite point near and above 800 K. Until this point, the average TEC would reflect the overall TEC behavior, although the TEC might vary at different temperatures, as shown in Table 3. The TEC also might differ in some temperature ranges based on the materials used, with expansion occurring until a certain high temperature, after which deformation takes over. However, in this study, the temperature was set to 1073 K as a mid-range SOFC