A practical analysis to predict sample overheating in flashexperiments using the current ramp methodology

Received: 19 February 2024 Revised: 12 September 2024 Accepted: 13 October 2024 DOI: 10.1111/jace.20248 RESEARCH ARTICLE A practical analysis to predict sample overheating in flash experiments using the current ramp methodology Alejandro F. Manchón-Gordón1Sandra Molina-Molina1Antonio Perejón1,2 Pedro Sánchez-Jiménez1Luis A. Pérez-Maqueda1 1Instituto de Ciencia de Materiales de Sevilla, ICMSE CSIC-Universidad de Sevilla, Sevilla, Spain 2Departamento de Química Inorgánica, Facultad de Química, Universidad de Sevilla, Sevilla, Spain Correspondence A.F. Manchón-Gordón and A. Perejón, Instituto de Ciencia de Materiales de Sevilla, ICMSE CSIC-Universidad de Sevilla, C. Américo Vespucio 49, Sevilla 41092, Spain. Email: alejandro[email protected] and [email protected] Funding information Junta de Andalucía-Consejería de Universidad, Investigación e Innovación, Grant/Award Number: ProyExcel_00360; Spanish Ministry of Science and Innovation, Grant/Award Number: PID2022-140815OB-C22 Abstract This work presents a straightforward strategy for achieving specific overheating during flash experiments by adjusting the initial electrical parameters. To do that, an extensive experimental analysis was performed to evaluate the temperature evolution of dense ZnO specimens during controlled-current ramping at different furnace temperatures, which in turn modified the initial electrical resistance of the sample. A detailed electrical explanation of controlled-current ramp flash processes is provided and, for the first time, a practical equivalence between current-ramp and temperature-ramp flash methodologies is established. By parameterizing the experiments in terms of an effective power density, a consistent heating pattern following the blackbody radiation trend was identified, despite the different electrical characteristics of each experiment. Finally, a “flash heating map” is introduced, which can be used to determine the starting electrical parameters necessary to achieve a specific temperature increase, whether employing current or temperature ramps. KEYWORDS blackbody radiation, controlled-current ramping, Flash sintering, overheating, zinc oxide 1 INTRODUCTION Flash sintering, FS, is an advanced ceramic sintering techniqueproposedin2010, 1in which an electric field is applied to a specimen, typically a ceramic, so that the current flows through the material. The technique is characterized by a dramatic drop in the electrical resistance of the specimen at a certain temperature, leading to a sudden surge in the electrical current density passing through it. This nonlinear increase in electrical current results in, typically, rapid densification at furnace temperatures significantly lower than those required in This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2024 The Author(s). Journal of the American Ceramic Society published by Wiley Periodicals LLC on behalf of American Ceramic Society. conventional sintering techniques.2Since its inception, FS has been employed to prepare a wide variety of materials, each featuring different conduction mechanisms, including dielectric, semiconductor, electronic, and ionic conducting materials.3–7 The flash phenomenon extends beyond green bodies and has been investigated in dense ceramics to eliminate the impact of densification on electrical conductivity.8Moreover, FS has been extended to the reactive flash sintering technique, aimed at producing dense and single-phase complex oxides in a single step9 and recently employed in the preparation of a wide range of materials.10–15 Furthermore, in a recent development, J Am Ceram Soc. 2025;108:e20248. wileyonlinelibrary.com/journal/jace 1of9 https://doi.org/10.1111/jace.20248 2of9 MANCHÓN-GORDÓN et al. it has been demonstrated that both flash16 and reactive flash17 processes can be initiated without the need for electrodes. In conventional FS experiments, the applied electric field remains constant while the furnace temperature is increased as a linear ramp. As the conductivity of the sample increases, the current density passing through the specimen rises until it reaches a maximum preset value. At this point, the power supply switches from controlledvoltage to controlled-current mode. In this approach, the management of thermal conditions during the flash process may result in various types of heterogeneities.18 This is attributed to the creation of preferential current paths that promote the development of thermal gradients, which are further intensified by cooling flows at the sample surface, ultimately giving rise to the formation of hot spots.19 Alternatively, furnace temperature can be kept constant as well. In this scenario, the incubation time, which corresponds to the time needed for the flash event to occur, plays a major role.20 FS can also be performed using a current ramping methodology, where the current density passing through the material increases linearly with time while the applied voltage is automatically adjusted and the furnace temperature is constant.21 Through this approach, despite maintaining a consistent furnace temperature, the temperature of the specimen undergoes a continuous rise as a result of the escalating current density flowing through it. This method efficiently reduces temperature gradients and the formation of hot spots typically found in conventional flash experiments.22–24 Accurately estimating the actual temperature of the specimen during flash experiments is crucial for a correct interpretation of the flash phenomenon, whose driving mechanisms are still under debate.1,25–27 For example, this is essential in elucidating whether Joule heating is the only reason for the electrical resistivity drop and rapid densification, or if there are also athermal, dielectric effects playing an important role in flash processes.28 Certainly, the flash community has dedicated substantial efforts to precisely assess thermal evolution during flash processes through multiple experimental approaches, including in situ impedance spectroscopy,29 pyrometers,30,31 thermocouples placed within the sample,4infrared cameras, thermal expansion measurements,32 and in situ X-ray diffraction.33–35 The latter technique, while likely the most accurate one, can be inaccessible to much of the scientific community due to its complexity and resource requirements. Furthermore, the community has explored a theoretical approach to estimate temperature changes during FS, employing both the blackbody radiation model,36,37 and finite element method simulations that consider conductive and convective heat transfer as well.38,39 The present work aims to provide a more extensive portrayal of the thermal evolution exhibited by dense samples undergoing flash processes in terms of their electrical parameters. Sample temperature estimations obtained from the blackbody radiation model were compared with IR thermal measurements for a broad set of experiments. The use of already dense specimens is intended to prevent microstructural changes associated with sintering, which can alter the electrical conductivity and complicate the study of thermal evolution. While the use of an infrared camera to determine the surface temperature of the sample may not be the most accurate technique, as the existence of temperature gradients between core and surface is dismissed,40 it is readily accessible in many flash laboratories. Zinc oxide is a n-type semiconductor with a bandgap of ∼3.3 eV at room temperature.41 As it has been extensively analyzed both inside and outside FS literature,33,42–46 it serves as a suitable standard to investigate flash phenomenology. To the best of our knowledge, establishing a practicalequivalence between different flash methodologies, which is the primary goal of this study, has not been previously reported. 2EXPERIMENTAL Commercially available zinc oxide nanopowders (<100 nm) from Sigma-Aldrich (product number 544906) were mixed with a 3 wt % polyvinyl alcohol binder solution in distilled water and uniaxially pressed into dogboneshaped pellets under a pressure of 500 MPa for 3 min. Subsequently, the specimens were heated at a rate of 3◦C/min up to 500◦C for 0.5 h in air to remove the binder. Following this, they underwent sintering at 1000◦Cfor 2 h, resulting in a relative density of 95 % as obtained using Archimedes’ principle. The dense dogbones were suspended by hooks at the ends of two platinum wires, which were hung together inside a tubular furnace. During the controlled-current ramping,thefurnace temperaturewaskeptconstant, while the current was gradually increased at 8 mA s−1.This rate represents the lowest increment achievable with the 1500 W DC power supply (EA-PSI 9760-06 DT) used for the experiments. Flash experiments were conducted at varying furnace temperatures (300–700◦C) and maximum current limits (10–500 mA). Conventional flash experiments were conducted at a heating rate of 10◦C/min under several combinations of applied electric field and current limit to modify the maximum electric power. In both methodologies, electrical parameters were recorded using a power analyzer (PPA1500 Newtons 4th Ltd). The two-dimensional temperature evolution of the specimens during the flash experiments was monitored using an infrared camera 15512916, 2025, 3, Downloaded from https://ceramics.onlinelibrary.wiley.com/doi/10.1111/jace.20248 by Readcube (Labtiva Inc.), Wiley Online Library on [12/05/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License MANCHÓN-GORDÓN et al. 3of9 (P1 1 M, Optris GmbH). The accuracy of the temperature measurements was ±10◦C in the temperature range 150−1500◦C. The camera was used after a precise calibration, which involved comparing the temperatures recorded by a thermocouple placed near the sample with those offered by the thermal camera. The videos recorded by the thermal camera were analyzed using the Optris PIX Connect software. Note that selecting a proper emissivity value is particularly challenging since it can vary with factors such as density, surface roughness, wavelength, and temperature. In this study, we chose an emissivity value of 0.9, which is typical of ZnO ceramics.39 For the purpose of comparison, the behavior of dogboneshaped pellets made from 8 mol% Yttria-stabilized zirconia (8YSZ, Tosoh Corporation, TZ-8Y, 40 nm) was analyzed. These pellets were also densified at 1400◦C for 1 h, achieving a relative density of 95% after sintering, as obtained using Archimedes’ principle. In that case, a surface emissivity value of 0.7 was used.47 Microstructural analysis of the samples was carried out by scanning electron microscopy (SEM) in secondary electron mode using a Hitachi S-4800 (Hitachi, Ltd.) operated at 2 kV. Average grain sizes were estimated from SEM images by measuring the dimensions of at least 100 grains. 3RESULTS AND DISCUSSION Figure 1shows several examples of typical data sets from controlled-current ramping experiments, plotted as a function of current density. The choice of using current density as the x-axis allows for direct data comparison. The panels show the applied electric field (a), dissipated power density (b), and resistance evolution (c) for experiments conducted at the indicated furnace temperatures, that is, corresponding to different initial resistance values of the material, 𝑅start, but the same value of maximum current density, 𝐽max=91 mA mm−2. The microstructure of the specimen before and after exposure to more extreme flash experimental conditions, i.e. at a furnace temperature of 700◦C and a maximum current density of 91 mA mm−2,isshown in Figure S1. No significant differences can be observed in the micrographs, confirming that the flash process did not affect the microstructure of the analyzed samples, at least under the explored conditions. The microstructure of the sample corresponds to a well-sintered material with a relatively uniform distribution of micrometric grains. The average grain sizes were estimated by measuring the dimensions of 100 grains, resulting in values of 90 ±20 µm for the sample before and 86 ±16 µm for the sample after flash. In controlled-current ramping experiments, unlike conventional flash experiments, the current density is regu- (A) (B) (C) FIGURE 1 (A) Applied electric field, (B) dissipated power density, and (C) resistance as a function of current density during controlled-current ramping for experiments conducted up to the same value of 𝐽𝑚𝑎𝑥 but at different furnace temperatures with the objective of changing the initial resistance of the material. lated right from the outset. In our case, the power supply adjusted the voltage to maintain the programmed linear ramp of 8 mA s−1up to the preset current density limit. Thus, depending on 𝑅start, three different regimes within the evolution of the applied electric field were found (see 15512916, 2025, 3, Downloaded from https://ceramics.onlinelibrary.wiley.com/doi/10.1111/jace.20248 by Readcube (Labtiva Inc.), Wiley Online Library on [12/05/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 4of9 MANCHÓN-GORDÓN et al. TABLE 1 Qualitative categorization of current ramp flash experiments based on the behavior of the main electrical parameters. Initial resistivity Electric field peak Power density peak Low No No Medium Yes No High Yes Yes Table 1). In the case of a high value of 𝑅start, such as for the experiment carried out at a furnace temperature of 300◦C, at low current values, a sharp increase in the applied field was clearly observed, which was essential to follow the prescribed current density ramp. Afterward, the electric field experienced a swift initial reduction followed by a gradual decline, even as the current density continued to elevate due to the diminishing resistance of the specimen, asshowninpanelc. A similar trend was observed for the dissipated power density, calculated as the product of the current density through the sample, 𝐽, and the applied electric field, 𝐸, resulting in 𝑃=𝐽𝐸. Consequently, a discernible peak in power density was evident at lower values of current density. Conversely, when the initial resistance value was low, as exemplified in experiments conducted at a furnace temperature of 700◦C, a gradual rise in 𝐸was evident, plateauing at approximately 𝐽= 30 mA mm−2with no observable peaks in 𝐸or 𝑃. In instances of intermediate 𝑅start values, such as experiments carried out at a furnace temperature of 500◦C, an intermediate behavior was apparent. A minor peak was observed in 𝐸, which was high enough to be reflected in the behavior of 𝑃.For 𝐽>30 mA mm−2,𝑃exhibited a similar behavior across all experiments, where increased 𝐽led to higher 𝑃. The continuous increase in electrical power density, a characteristic of controlled-current ramp FS experiments, also results in a continuous rise in the sample temperature during the flash process, despite keeping the furnace temperature constant. The temperature of the specimen, 𝑇𝑆, obtained using an infrared camera, is plotted as a function of time in Figure 2for the indicated furnace temperatures and 𝐽max=91 mA mm−2. The estimated temperature of the specimen is approximate due to uncertainties in emissivity and the assumption of uniform temperature, which may not be fully valid during the flash event. Additional factors include the imperfect geometry of the specimens and the contact resistance between the sample and the electrodes. Poor contact introduces high resistance in the electrode region, causing power dissipation and potential temperature asymmetry between electrodes of over 200◦C.27 This overheating can lead to excessive grain growth at both the anode and cathFIGURE 2 (A) Evolution of sample temperature with time for various current ramp experiments conducted on dense ZnO at different furnace temperatures, all using a current rate of 8 mA s−1, and the same value of 𝐽max=91 mA mm−2The increment in sample temperature, Δ𝑇, is indicated for the sample at a furnace temperature of 300◦C. (B) Infrared thermographic images showing the evolution of sample temperature during the flash experiment performed at a furnace temperature of 700◦C. ode for direct and alternating currents.48 Conversely, good thermal contact allows heat to sink from the sample to the cooler electrodes.49 A comprehensive analysis of the various thermal gradients typically found in FS experiments can be found in reference.50 Therefore, the herein estimated values should be interpreted as a temperature distribution rather than the exact sample temperature. Although the use of IR cameras for temperature estimation has some limitations in precision, they are widely employed by the FS community due to their capacity to provide real-time temperature visualization of relatively large areas, unlike other more precise instruments such as pyrometers. Figure S2 shows representative SEM images of the cross-sectional fracture of the flashed specimen, obtained using the specified current ramp at a furnace temperature of 700◦C and a maximum current density of 91 mA mm−2. The micrographs were taken at the center of the dogbone and near the electrode. No significant differences can be observed between the two micrographs, indicating good electrical contact between the sample and the electrodes. This is in agreement with the IR thermographic images shown in Figure 2B, where no temperature gradients were observed within the specimen. The temperature difference between the furnace temperature, as indicated by the furnace controller, and the sample temperature, determined by the IR camera, highlights the challenges in temperature measurement. 15512916, 2025, 3, Downloaded from https://ceramics.onlinelibrary.wiley.com/doi/10.1111/jace.20248 by Readcube (Labtiva Inc.), Wiley Online Library on [12/05/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License MANCHÓN-GORDÓN et al. 5of9 This underscores the importance of clearly defining the method employed for temperature measurement. The data obtained indicated that 𝑇𝑆increased at a nearly constant rate following a small incubation period after the power supply was turned on. During this incubation time, the application of an electric field to the specimen did not imply its significant heating, which suggests that the electrical behavior of the material can be changed without significant power dissipation, as recently reported.28 The determined heating rate was consistently registered at 360◦Cmin −1across all examined scenarios. In fact, it is established that the heating rate is influenced by the current rate; a higher current rate gives rise to a higher heating rate.21 It is noteworthy that this heating rate is significantly low when juxtaposed with rates achieved in conventional flash experiments, where the flash event induces rapid sample heating at a rate of approximately 103–105◦Cmin−1.51 Additionally, it is apparentthat at lower furnace temperatures (associated with higher 𝑅start values), there is a more pronounced variation in the sample temperature, Δ𝑇, during the experiment. For comparative analysis, a series of conventional voltage-controlled flash experiments were conducted using dense ZnO dogbones. As illustrated in Figure S3, as an example, the evolution of the electrical parameters during a temperature ramp at 10◦Cmin −1, an applied electric field of 167 V cm−1, and a current density limit of 43 mA mm−2, follows the three classical stages of FS.20 After an incubation time, in stage II, there is a sharp increase in conductivity up to the preset maximum limit of current density, accompanied by a decrease in the applied electric field when the power supply transitions to the current control mode. This rise in conductivity is correlated with an increase in the temperature of the sample (see Figure S4). Subsequently, the sample is maintained in a flash-activated state under a controlled current for a specific duration, representing stage III. The sample temperature can be also assessed using the blackbody radiation (BBR) model, according to the following Equation (1)25: 𝑇𝑆=(𝑇4 𝑓+𝑊𝑒 𝜀𝐴𝜎)1∕4 ,(1) where 𝑇𝑆and 𝑇𝑓represent the sample and furnace temperatures, respectively, 𝑊𝑒denotes power dissipation, 𝐴 represents the surface area of the sample, 𝜀is the emissivity and 𝜎corresponds to the Stefan-Boltzmann constant. It is worth noting two important factors when utilizing the BBR model for temperature estimation during FS. First, the assumption of a constant emissivity value of 1 for all materials may not be accurate as emissivity tends to vary (always <1) for ceramics depending on factors such as temperature and wavelength.37 Second, the omission of the fact that the model is valid for Δ𝑇∕𝑇 ≪ 1.52 Nevertheless, the BBR is commonly used by the FS community as an approach to obtain reasonably accurate estimations. The BBR model has proven most effective during Stage III, characterized by a steady-state power density. This allows the equating of the input rate of electrical energy to the rate of energy dissipated through blackbody radiation. Per Equation (1), the rise in the specimen temperature is correlated with the electrical power density. However, the characteristic behavior of dissipated power density in conventional flash experiments, 𝑃CF, differs markedly from that observed in the current ramp methodology. In conventional flash experiments, 𝑃CF exhibits an initial almost zero value that experiences a sudden surge during the flash event. Therefore, the theoretical maximum power density, associated with the peak temperature reached in the sample, can be expressed as Equation (2): 𝑃CF max =𝐸 CF max 𝐽CF max,(2) where 𝐸CF max represents the initially set applied electric field, and 𝐽CF max denotes the predetermined density current limit. The subscript 𝐶𝐹 indicates that these parameters are associated with conventional flash experiments. As demonstrated earlier, this situation does not apply to the controlled-current ramp methodology, where power density undergoes continuous changes with current density. This behavior provokes that, in the case of controlledcurrent ramps, the maximum power does not necessarily have to correspond to the moment when the maximum current value is reached, that is, at the end of the ramp. It can be clearly observed in Figure 1, in the case of higher 𝑅𝑠𝑡𝑎𝑟𝑡 and low current density values. For example, at a furnace temperature of 300◦Cand𝐽<40mA mm−2, the maximum power density corresponded to the peak observed around ∼15 mA mm−2. Given the divergent characteristics of power density in conventional and current ramp flash experiments, we employed an effective power density, 𝑃eff ,toenablea direct comparison of sample overheating in both flash methodologies. 𝑃eff is calculated as the product of the maximum applied electric field, 𝐸max, and the final predetermined density current limit, 𝐽max, that is, 𝑃eff = 𝐸max 𝐽max. In contrast to conventional flash experiments, where 𝐸CF max is initially fixed, 𝐸max isafreeparameter.Note that, while 𝑃max is an experimental value, 𝑃eff is not an actual power density experienced by the sample at any time, but rather a mathematical construct introduced to translateoverheating during controlled-currentrampsinto overheating during conventional voltage-controlled flash experiments. 15512916, 2025, 3, Downloaded from https://ceramics.onlinelibrary.wiley.com/doi/10.1111/jace.20248 by Readcube (Labtiva Inc.), Wiley Online Library on [12/05/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 6of9 MANCHÓN-GORDÓN et al. FIGURE 3 Relationship between 𝑃max vs. 𝑃eff . Each symbol represents a different flash experiment carried out at different furnace temperatures and different values of 𝐽max.Theredlineis just a guide to the eyes to show the deviation between both parameters. The log–log relationship between both parameters, 𝑃eff and 𝑃max, is evidenced in Figure 3for current ramp experiments carried out at different values of furnace temperature and 𝐽max (each point in the figure correspond to a different experiment). For values of 𝑃eff <200 mW mm−3, there is a strong correlation between both parameters, following a linear trend. However, for higher values of 𝑃eff , it can be observed that 𝑃max almost approaches a saturation point at ∼200 mW mm−3. This can be understood by examining the behavior of the applied electric field as a function of current density (see Figure 1A). At low current density values, power density is highly influenced by the electric field peak, but this contribution diminishes as current density increases. On the other hand, the height of the field peak is directly related to the initial resistance of the sample, which makes it crucial for understanding the evolution of the rest of the electrical parameters during the flash process. The apparent saturation of 𝑃max is an artifact related to the fact that the current density in our current ramp experiments was limited to 91 mA/mm2. As observed in Figure 1, this value of 𝐽max implies a 𝑃max of about 200–300 mW/mm3, which corresponds to the obtained saturation value. The existence of these two power density regimes aligns with the latest findings about the dielectric nature of the flash phenomenon. Very recently, it has been reported that power dissipation and temperature increase only become relevant once the sample is conductive enough to allow for significant current flow. Before this point, field-induced effects such as electric arc formation between the electrodes53,54 or athermal resistance degradation of the sample28 dominate over Joule heating. (A) (B) FIGURE 4 Sample temperature increment as a function of (A) 𝑃max and (B) 𝑃𝑒𝑓𝑓 for a series of controlled-current ramp experiments conducted on dense ZnO samples at different furnace temperatures and different values of 𝐽max . The continuous line represents the estimation of the overheating using the blackbody model. Figure 4shows the obtained values of Δ𝑇 for the series of controlled-current ramp experiments conducted with various current density limits and furnace temperatures, where each point corresponds to a different combination of furnace temperature and 𝐽max. The data are shown as a function of (A) 𝑃max and (B) 𝑃eff , regardless of the furnace temperature. For comparison purposes, we included the values of Δ𝑇 obtained for conventional flash experiments (i.e., ramping temperature with a constant value of applied voltage and a preset maximum current) conducted with dense ZnO samples. We also included the estimation of Δ𝑇 using Equation (1), represented by the continuous line (BBR model). In addition, the Δ𝑇 vs. 𝑃eff data corresponding to controlled-current ramp experiments conducted on dense 8YSZ dogbones are shown in Figure 5.Asanticipated from the correlation shown in Figure 3,notable 15512916, 2025, 3, Downloaded from https://ceramics.onlinelibrary.wiley.com/doi/10.1111/jace.20248 by Readcube (Labtiva Inc.), Wiley Online Library on [12/05/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License MANCHÓN-GORDÓN et al. 7of9 FIGURE 5 Sample temperature increment as a function of 𝑃eff for a series of controlled-current ramp experiments conducted on dense ZnO samples at different furnace temperatures and different values of 𝐽max. The continuous line represents the estimation of the overheating using the blackbody model. Star symbols correspond to current ramp flash experiments performed on dense 8YSZ dogbones. discrepancies in sample overheating are evident when comparing overheating in current and temperature ramp experiments for 𝑃max>200 mW mm−3. On the other hand, although the BBR model follows the same trend as the experimental data obtained from temperature ramp experiments, it clearly overestimates Δ𝑇, which is expected due to the limitations of the model described above. In fact, it was found that the temperatures estimated using the BBR model were significantly higher than the measured temperatures (when considering a lattice parameter expansion) due to flaws in the theoretical model, which dismisses non-radiative heat losses and strongly depends on the stage of the flash in which the power is considered.32 The discrepancies observed in both current and temperature ramp experiments are eliminated when plotting the overheating Δ𝑇 against the effective power density 𝑃eff (Figure 4B). For values of 𝑃eff <200 mW mm−3 (indicating low maximum current density and/or a low voltage peak), Δ𝑇 remains close to 0◦C. This range of dissipated power density corresponds to those in which 𝑃eff ∼𝑃 max (see Figure 3). As previously mentioned, the contribution of the electric field to the flash process is more prominent in this range, as it is evident that Joule heating does not occur instantly when the power supply is turned on. Conversely, for 𝑃eff >200 mW mm−3 (indicating a large maximum current density and/or a high voltage peak), Δ𝑇 becomes progressively more significant, and Δ𝑇 increases as 𝑃eff increases. The experimental results regarding the overheating of 8YSZ dogbones using a current-ramp methodology are shown in Figure 5.A similar trend was found across the complete studied range, despite the notable differences in electrical behavior between ZnO and 8YSZ, which is a model ionic conductor. Electrode effects leading to thermal heterogeneity when performing flash experiments in 8YSZ under DC fields have been amply reported and discussed.4,27 Even so, the overheating profile for 8YSZ controlled-current ramps remarkably resembles those obtained for ZnO and the BBR model. This suggests a common behavior primarily influenced by electrical power dissipation, consistent with the principle of Joule heating. Considering the common behavior described in Figures 4B and 5, this plot could be utilized to estimate the electrical parameters required for attaining a certain temperature increase during a flash experiment, regardless of the chosen methodology (current or temperature ramp). It is particularly valuable in the case of current ramp experiments where the furnace temperature remains constant. For instance, at a given furnace temperature, if the sample needs to be overheated by 300◦C, it would be necessary to dissipate a 𝑃eff of approximately 300 mW mm−3. While the parameters obtained may not be definitive, as finding the optimum combination of electrical field and current density limit leading to a successful experiment isacomplextask, 55 they can serve as a starting point for experimentation. This way, once the desired overheating value is known, the number of possible (𝐸,𝐽) combinations can be considerably reduced, hence optimizing the trial-and-error process most often employed to determine the experimental flash conditions. 4 CONCLUSION In this work, we analyzed the evolution of the sample temperature during controlled-current ramping flash sintering experiments of dense ZnO dogbones at different furnace temperatures, thus effectively changing the initial resistance of the specimen. Based on the obtained results, the following conclusions can be made: - The initial resistivity of the specimen determines the evolution of the various electrical parameters involved in the flash process, as well as the thermal evolution of the sample. - When introducing a simple equivalent electric power density, a common overheating behavior is found for controlled-current ramps and voltage-controlled in ZnO specimens, which is also found for controlled-current ramps in 8YSZ dogbones. A practical strategy to estimate the electrical parameters required to achieve a specific 15512916, 2025, 3, Downloaded from https://ceramics.onlinelibrary.wiley.com/doi/10.1111/jace.20248 by Readcube (Labtiva Inc.), Wiley Online Library on [12/05/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 8of9 MANCHÓN-GORDÓN et al. temperature increase under flash conditions has been defined. Future studies are welcomed to test the validity of the proposed strategy through a systematic analysis on different materials and geometries subjected to varying flash conditions. Moreover, the establishment of a practical equivalence between the two flash methodologies analyzed in this work and isothermal flash processes under constant voltage should be also explored in future studies. ACKNOWLEDGMENTS This work has been funded by Junta de AndalucíaConsejería de Universidad, Investigación e Innovación (proyect ProyExcel_00360). Financial support is also acknowledged from the grant PID2022-140815OB-C22 funded by the Spanish Ministry of Science and Innovation. ORCID AlejandroF. Manchón-Gordón https://orcid.org/00000002-8320-5575 SandraMolina-Molina https://orcid.org/0000-00019318-6585 AntonioPerejón https://orcid.org/0000-0002-5525-2227 Pedro Sánchez-Jiménez https://orcid.org/0000-00016982-1411 REFERENCES 1. Cologna M, Rashkova B, Raj R. Flash sintering of nanograin zirconia in <5sat850 ◦C. J Am CeramSoc. 2010;93(11):3556–9. 2. Yu M, Grasso S, Mckinnon R, Saunders T, Reece MJ. Review of flash sintering: materials, mechanisms and modelling. Adv Appl Ceram. 2017;116(1):24–60. 3. Perez-Maqueda LA, Gil-Gonzalez E, Perejon A, Lebrun J-M, Sanchez-Jimenez PE, Raj R. Flash sintering of highly insulating nanostructured phase-pure BiFeO3. J Am Ceram Soc. 2017;100(8):3365–9. 4. 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A practical analysis to predict sample overheating in flash experiments using the current ramp methodology. J Am Ceram Soc. 2025;108:e20248. https://doi.org/10.1111/jace.20248 15512916, 2025, 3, Downloaded from https://ceramics.onlinelibrary.wiley.com/doi/10.1111/jace.20248 by Readcube (Labtiva Inc.), Wiley Online Library on [12/05/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License