An Operando calorimeter for high temperature electrochemical cells

The calorimeter's temperature, atmosphere, and electrochemistry capabilities presented here are designed to support operando studies of high temperature solid electrolytes. The target range of values for the key performance parameters are presented in table 1. The operating temperature range, from room temperature to 1000 °C, includes the typical temperature range of interest for solid oxide fuel cells (SOFCs). The electrical parameters allow for the application of electrochemistry and the use of temperature sensors for the calorimeter. With at least two temperature probes, each utilizing two connections, and a two-electrode setup to probe the electrochemical cell or device, a minimum of six electrical connections are needed. If additional capabilities are needed, such as three-electrode electrochemical cells or four-point-probe electrical measurements, up to 11 electrical connections may be required. Designing the calorimeter to enable the use of two different gases simultaneously is necessary for testing fuel cells under realistic operating conditions. The samples used have a diameter of approximately 20 mm, a common size format in literature [8, 10].

A typical target for electrical power density in fuel cells is 500–2000 mW cm⁻² [14]. Because currently fuel cells are approximately 50% efficient [15], a 500 mW cm⁻² thermal power density is assumed here, representing the low end of the above range. The goal of the present calorimeter design is to capture at least 10% of that power. Therefore, the minimum sensitivity is 50 mW, assuming a minimum active electrode area of 1 cm². Furthermore, estimates from solid oxide electrolyte side reactions in the literature [10] show heat effects of order 100 mW g⁻¹. Assuming that samples contain 1 g of material, typical for the sample dimensions used here, heat effects are expected to be on the order of 100 mW for these reactions, which is measurable at the target sensitivity.

The calorimeter presented here modifies a commercially available high temperature electrochemistry apparatus, the ProboStat^TM (figures 1 and A1), which provides the necessary temperature range, electrical connections to power the fuel cell samples and temperature sensors, and two-gas capability. The apparatus tubing is made from either alumina for high temperatures (>600 °C) or quartz for medium temperatures (<600 °C), and the section exposed to elevated temperatures uses electrical connections made from platinum. Both materials remain inert and structurally stable in high temperature H₂ and O₂ ambient. Here the ProboStat^TM is operated within a vertically mounted 18" tube furnace (Mellen) that can reach temperatures in excess of 1000 °C.

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Modifications to the ProboStat^TM are made through the addition and relocation of temperature sensors. An S-type thermocouple that is provided with the ProboStat^TM for monitoring the approximate sample temperature is relocated to the alumina support post below the sample and cemented (Cotronics Resbond 907GF, a high temperature cement) in place for better heat conduction. This thermocouple is used to measure the temperature proximal to the location of the sample (T_prox ). A small, thin film resistance temperature detector (RTD, Omega F3142 or US Sensor PPG102A1) is attached to the sample itself, using the same high temperature cement. In addition to the furnace thermocouple used by its proportional-integral-derivative (PID) temperature controller, a K-type thermocouple (T_fw ) is attached to the wall of the furnace near the sample. T_fw is used to acquire a more accurate temperature reading of the furnace temperature, picking up fluctuations in the wall temperature that are not recorded by the PID thermocouple. Finally the temperature of the room is monitored using a K-type thermocouple (T_room ) located in the vicinity of the ProboStat^TM base. All temperature data from thermocouples are recorded using an eight channel data acquisition module (Omega).

The electrical connection schematic is shown in figure 2(a). The ProboStat^TM is designed for a maximum of six electrical connections for power applications and up to six thermocouple connections. One pair of thermocouple connections is used for T_prox . All six power connections are used. Two of these electrical connections are used for operating the RTD, while four are connected to the sample. Two connections are made to opposite ends of the cathode to enable current flow across the cathode, as discussed in section 4.1, in order to simulate heat-generating reactions at the electrolyte-electrode interface. In addition, one connection is made to the anode, and another is made to the reference electrode of the sample. In certain cases, additional connections are needed for four-point measurements or other types of electrical stimulation or monitoring. In those situations, voltage measurements can be made using the unused thermocouple connections, while reserving the other electrical connections for running current. All electrical sourcing and measurement is performed using a commercial potentiostat (Bio-Logic).

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The calorimeter's fluidic infrastructure is designed for use of up to two gases with the option of running those gases dry or humidified (figure 2(b)). The sample, sealed to the inner tube of the ProboStat^TM, serves to isolate the gases and prevent mixing. A water bubbler is used to humidify gases at room temperature to about 3% (0.03 atm). The gases are flowed through the ProboStat^TM at flow rates typically between 5–20 ml min⁻¹.

The calorimeter can support samples between 10 and 30 mm in diameter and between 0.5 and 10 mm in thickness, which corresponds to a sample mass of up to approximately 10 g. These samples are mounted into the Probostat^TM with the appropriate electrical connections and can be sealed to the inner tube to allow for the simultaneous use of two gas atmospheres, each being exposed to one side of the sample.

In order to test the high temperature performance of the calorimeter, cells in the configuration of an electrochemical hydrogen pump using BZCY as the solid proton conductor were used. This cell is simpler than the corresponding high temperature fuel cell since H₂ is supplied to both sides of the sample; a fully operational fuel cell results if H₂ and O₂ are supplied to the anode and cathode respectively. Operating as a hydrogen pump, hydrogen gas is oxidized at the anode, supplying protons which diffuse through the solid electrolyte to the cathode whereupon they are reduced and evolve hydrogen gas. No net molecules of hydrogen are produced or consumed in this operation, but since ionic current does flow through the electrolyte, it mimics the electrochemical operation of a solid oxide fuel cell.

The sample was constructed using a 20 mm diameter and 1 mm thick BZCY ceramic plate (CoorsTek Membrane Sciences AS) as a platform (figure 3). Thin film Pt and Pd electrodes are used as catalysts to promote the H evolution and oxidation reactions at the surfaces of the BZCY disk. A cathode, anode, and reference electrode each between 20 and200 nm thick were sputtered on top of a 3–4 nm thick sputtered Cr adhesion layer, using Kapton tape to mask off areas between the electrodes. To monitor the local temperature an RTD (Omega F3142 or US Sensor PPG102A1) was cemented on top of the cathode side of the sample, making sure that the RTD leads do not short to the cathode surface. The RTDs used in this report have a maximum operating temperature of 600 °C. However, RTD's with higher maximum operating temperatures are available (US Sensor PPG201B3 and PPG201E7) for studies at higher temperatures.

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A nonlinear lumped-parameter model is used to describe the behaviour of heat transfer within the calorimeter, similar to the method of MacLeod et al [16]. The dynamics of this system are approximated using a grey-box approach. This entails developing an appropriate equivalent circuit model to describe the heat flow pathways through the calorimeter, and then experimentally obtaining the parameters of the model through a calibration process. The model is calibrated by measuring temperature changes at various temperature probes that result from input power of known quantities. The relationship between power and temperature in the model is thus established. The calibrated model allows the output power to be predicted knowing only the input power and temperatures of those temperature probes. Any mismatch between the input and output powers can then be attributed to thermal events in the cell, e.g. side reactions or degradation, which along with electrochemical data can be analyzed to gain insight on the performance of the cell and its components over time.

A one-state, nonlinear equivalent circuit diagram of the calorimeter is shown in figure 4(a). Numerous model candidates were analyzed, including two- and three-state models, but this one-state model with two nodes and three measured grounds was determined to be the model that provides the best calorimeter sensitivity.

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In this equivalent circuit model, the resistors represent heat conductances between different nodes. A capacitor represents a heat capacitance, while grounds represent thermal sources and sinks. Power inputs are modelled as current sources. The model has one measured node, T_RTD , and one unmeasured node, T_sample , although only one heat capacitance is needed to approximate both. Other than the absolute ground used to reference power inputs and heat capacitance, there are three grounds in this model: one source and two sinks.

Figure 4(b) shows the heat flow pathways in the system in relation to a schematic representation of the sample, supports, and temperature sensors. This diagram illustrates the physical origins of the heat flows within the system that are represented in the equivalent circuit diagram (figure 4(a)). Heat is generated in the furnace, represented by T_fw , and flows to the RTD node, which has a temperature T_RTD . Heat then continues to flow through the sample node, an unmeasured node that approximates the sample itself, before exiting out either through an intermediate ground T_prox or the room temperature ground T_room . The need for two sinks stems from the inability of T_prox to capture all of the heat flowing out from the sample node due to other heat flow pathways out to the surrounding environment.

The model includes three power sources that correspond to the different power inputs to the sample during either calibration or testing. P_RTD is a baseline power that is emitted by the RTD when in operation. Typically for a 1 kΩ RTD a sense current of 1 mA is used, generating between 1 and 5 mW of power, depending on the temperature of the system. P_ion is the power generated from operating the solid electrochemical cell. It is caused by both resistive heating of the solid electrolyte and reaction overpotential losses. Lastly, P_cat is used to study surface reactions or other surface phenomena related to the solid electrolyte. This power is approximated during calibration of the model by running current laterally across the cathode of the sample. Two nodes were modelled to appropriately capture system dynamics. The time constant for heat detection by the RTD for a heat source originating within the RTD (P_RTD ) is smaller than the time constant for heat detection when the source is nearby, but not within, the RTD itself (P_ion and P_cat ).

The dynamics of the system described by the equivalent circuit diagram can be distilled into the following system of equations, in which c_x are capacitances, k_xx are conductances, and α is a scale factor fitted to adjust P_cat based on the ratio of P_cat:P_ion detected by the temperature probes in the calorimeter:

$$\begin{equation}\frac{{d{T_{RTD}}}}{{dt}} = \frac{1}{{{c_{sys}}}}\left( {{P_{RTD}} + {k_{fR}}\left( {{T_{fw}} - {T_{RTD}}} \right) - {k_{Rs}}\left( {{T_{RTD}} - {T_{sample}}} \right)} \right),\end{equation} \tag{ 1 }$$

$$\begin{equation}_{ion} + \alpha {P_{cat}} + {k_{Rs}}({T_{sample}} - {T_{RTD}}) + {k_{sp}}\left( {{T_{sample}} - {T_{prox}}} \right) + {k_{sr}}\left( {{T_{sample}} - {T_{room}}} \right) = 0,\end{equation} \tag{ 2 }$$

where

$$\begin{equation}{c_{sys}} = {\text{ }}{c_{sys,0}} + {c_{sys,1}}{T_{RTD}} + {c_{sys,2}}T_{RTD}^2,\end{equation} \tag{ 3 }$$

$$\begin{equation}{k_{fR}} = {\text{ }}{k_{fR,0}} + {k_{fR,1}}{T_{RTD}} + {k_{fR,2}}T_{RTD}^2,\end{equation} \tag{ 4 }$$

$$\begin{equation}{k_{Rs}} = {\text{ }}{k_{Rs,0}} + {k_{Rs,1}}{T_{RTD}} + {k_{Rs,2}}T_{RTD}^2,\end{equation} \tag{ 5 }$$

$$\begin{equation}{k_{sp}} = {\text{ }}{k_{sp,0}} + {k_{sp,1}}{T_{sample}} + {k_{sp,2}}T_{sample}^2,\end{equation} \tag{ 6 }$$

$$\begin{equation}{k_{sr}} = {\text{ }}{k_{sr,0}} + {k_{sr,1}}{T_{sample}} + {k_{sr,2}}T_{sample}^2,\end{equation} \tag{ 7 }$$

$$\begin{equation}\alpha = {\text{ }}{\alpha _0} + {\alpha _1}{T_{sample}} + {\alpha _2}T_{sample}^2.\end{equation} \tag{ 8 }$$

Although equations (1) and (2) could be combined into one equation, thereby eliminating T_sample , they are split out to better represent the physical model. Each element in the model is split out to second order nonlinear parameters, which aggregates to 18 possible parameters to be fitted. For operation within a limited temperature range, the model typically does not need to be fit with second order nonlinear parameters, so just zeroth and sometimes first order parameters can be used.

The operation of the operando calorimeter in a test case where the sample is a thin disc of a BZCY proton conductor, coated with sputtered Pt electrodes on both faces, is now demonstrated. The instrument was first used to measure the conductivity of the BZCY solid electrolyte, and yielded expected results over the temperature range from 350 to 850 °C in 4% humidified H₂ in Ar (figure 5, and appendix C).

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Next, the calorimeter was calibrated by establishing a set of parameters for the model that produce an output matching experimental results. Three sources of input power, P_RTD, P_cat , and P_ion , representing three possible sources of heat generated during an experiment, were supplied. Each as a different temporal variation, as shown in figure 6(a). The largest temporal variation in input power was for P_ion , the power supplied to the solid electrolyte, as would be the case during actual operation of the device as an electrochemical cell. Three of the corresponding temperature measurements are shown in figure 6(b). T_fw, T_prox , and T_room (not shown) are the grounds in the model, see figure 4(a). T_RTD,meas is the measured temperature at the RTD node, T_RTD in the model in figure 4(a). The input power from figure 4(a) and temperatures in figure 4(b) were then analyzed with a MATLAB script utilizing the MATLAB System Identification Toolbox^TM nlgreyest procedure, similar to one described by MacLeod et al [16, 17]. The script takes the model described by equations (1)–(8), as well as the input power and ground temperatures, and estimates the vector of model parameters θ to create a modelled version of T_RTD , here referred to as T_RTD,mod . A search for fitted model parameters is initiated and iterated in order to minimize a cost function

$$\begin{equation}V\left( \theta \right) = \frac{1}{{{t_{max}}}}\mathop \sum \limits_{t = 0}^{{t_{max}}} {(\Delta {T_{meas}}\left( t \right) - \Delta {T_{mod}}\left( {t,\theta } \right))^2},\end{equation} \tag{ 9 }$$

$$\begin{equation}\Delta {T_{meas}}\left( t \right) = {T_{RTD,meas}}\left( t \right) - {T_{prox}}\left( t \right),\end{equation} \tag{ 10 }$$

$$\begin{equation}\Delta {T_{mod}}\left( {t,\theta } \right) = {T_{RTD,mod}}\left( {t,\theta } \right) - {T_{prox}}\left( t \right),\end{equation} \tag{ 11 }$$

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where t is the discretized time of each datapoint in the dataset ranging from 0 to t_max . A differential measurement between either the measured or the modelled temperature at the RTD node and a nearby temperature ground allows for fits to be made on smaller temperature ranges, and cancels out the majority of noise coming from the furnace, improving the goodness of fit. Typically only linear (zeroth order) terms for each element in the model are initially fitted, in order to scan for a global minimum in V(θ) with lower computational effort. Upon approaching a perceived cost function minimum, first order, nonlinear terms for each circuit element are then allowed to vary as well. It was found that second order, nonlinear terms are rarely necessary unless the experiment spans a temperature range of over several 100 °C.

After a suitable search and refinement of the model parameters θ that minimizes V(θ) below a certain cost tolerance, θ is considered to have reached at least a locally minimized value, θ_minimized . Upon reaching V(θ_minimized ), the measurement, ΔT_meas , is compared to the model, ΔT_mod , as illustrated in figure 4(c). An example of a parameter set for θ_minimized are shown in table A1 of appendix A. The goodness of fit for a set of parameters is obtained from the NRMSE between the ΔT_meas and ΔT_mod datasets. While the NRMSE is a good screening metric, one should be cautious about ascribing too much value to it since it is easily affected by the dynamic range of the temperature differential dataset. A dataset with a large dynamic range in temperature differential can lead to a better NRMSE score than an equivalent calorimeter with a lower dynamic range in the calibration dataset. A better quantification for the quality of the calorimeter-model system is the power sensitivity, which is described in the following section. Nonetheless, it is a useful feedback tool during parameter honing with a calibration dataset. Typically an acceptable result is above 60%, with the best calibrations exceeding 75% NRMSE. In the case shown in figure 6(c), the NRMSE is 79%. Poor sets of model parameters are easily identified with the NRMSE metric. Since NRMSE can range from negative infinity to 100%, negative NRMSE values (such as − 75%) are not uncommon in the early iterations of parameter searching, which indicates a fit worse than that of a straight line through the dataset.

To verify that the fitted model is applicable to a wide variety of datasets, and not just the one used for calibration, a second series of experiments was conducted. A set of input power signals utilizing different waveforms and magnitudes was used. The input powers from part of such a run are highlighted in figure 7(a), along with temperature in figure 7(b). Using the parameter set, θ_minimized , from the previous experiment, T_RTD,meas was used to in conjunction with the measured temperature grounds to recover a model of the input power. This modelled power can then be compared with the original input power to see how well the model reconstructs the power data (figure 7(c)). The residual power is calculated as the difference between these two powers (figure 7(d)). The standard deviation of the residual power is a measure of the calorimeter's lower limit of detection. However, an adjustment needs to be made to account for the fact that power is measured at the RTD node in the model while the input powers of interest (P_ion and P_cat ) originate at the sample node. Since only a fraction of the sample node's power flows into the RTD node, the power signal as well as the noise in the power are dampened. To correct for this effect, the standard deviation is multiplied by an adjustment factor from a node-to-node heat flow analysis described in appendix B. Doing so approximates the noise level in the sample node that is relevant to P_ion and P_cat . In the example presented in figure 7, the standard deviation is 1.7 mW and the adjustment factor is 2.6, giving an adjusted standard deviation of 4.4 mW. Power signals observed during experiments that exceed two times the adjusted standard deviation (i.e. 8.8 mW in the above example) can be taken, with 95% confidence, to be heat generated from cell reactions rather than instrumental factors. This metric is here defined as the calorimeter sensitivity. Following these two calibration experiments, the calorimeter is ready for use in measuring heat produced during electrochemical reactions.

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The above-described sequence of experiments was repeated seven times, once after each BZCY sample was loaded into the electrochemical cell and brought to operating temperature in H₂ atmosphere, and produced the results shown in figure 8. The calorimeter was found to have an average sensitivity of 16.1 ± 11.7 mW throughout these experiments, which exceeded the initial design objective of 50 mW sensitivity. The performance of the calorimeter did vary somewhat between the seven experiments, which could be due to some differences in sample preparation and mounting in the calorimeter.

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The average power residuals plotted in figure 8 are the time average of all the power residuals measured during a run such as in figure 7. The fact that these power residuals are well below the sensitivity of the calorimeter for each of the samples demonstrates that the parameter set θ_minimized determined during calibration is able to model the response of the system over the range of input power used and the corresponding temperature fluctuations. For the simple BZCY hydrogen pump tested here, no excess power was detected that could not be accounted for by the electrical inputs to the electrochemical cell, indicating that within the sensitivity of the operando calorimeter, no heat-producing degradation or side reactions were detected.