2023 Volume 64 Issue 9 Pages 2315-2320
The apparent activation energy of sintering for 8-mol%-Y2O3-doped ZrO2 during shrinkage-rate-controlled flash sintering was determined using a master sintering curve. The activation energy during SCF sintering was found to decrease from approximately 700 to 430 kJ/mol with density. The activation energy in a high-density region is approximately similar value of lattice diffusion, 460 kJ/mol. The relative density range over which the decrease in activation energy occurred during SCF sintering was smaller than during thermal sintering and further moved to a lower temperature range. The increase in shrinkage rate at lower temperatures that occurs during SCF sintering could be considered to be related to this decrease in activation energy.
Since shrinkage behavior during sintering is closely related to mass diffusion, the knowledge regarding sintering activation energies is valuable to understand sintering mechanisms. The use of a master sintering curve (MSC), as originally developed by Su and Johnson,1) is often used for this kind of analysis. MSC describes the sintering process using a simplified kinetic model,2) allowing a sintering curve to be produced regardless of heating history during sintering under the single-dominating-diffusion mechanism. Analysis of sintering processes using MSCs has been performed for various kinds of ceramics.3–7) Furthermore, MSC analysis has also been applied to sintering processes using external fields to increase shrinkage rates.8–10) However, it has rarely been applied to flash sintering, which is a sintering method that use an external electric field to complete shrinkage in a very short period of time.11–13) The flash sintering process is characterized by a power spike (a flash event) that occurs when the temperature of the ceramic green compact is increased as an electric field is applied. The instantons shrinkage during flash sintering is mainly caused by the joule heat supplied by the power sike. The limited application of MSC to flash sintering is possibly due to the fact that the very steep shrinkage rate makes it difficult to obtain reliable data on the time dependence of the shrinkage process, which is necessary when applying an MSC. Therefore, at least some time-dependent shrinkage profile is necessary to apply MSCs to flash sintering.
Ingraci et al. reported an MSC analysis of uranium dioxides using current-rate flash sintering,14) where the electric current during flash sintering is increased at a constant rate to avoid an overly steep power spike during the flash event.15) Compared to conventional flash sintering, this provides reliable time-dependent data on the shrinkage, to which MSC analysis can be applied. According to their results, the activation energy decreased to from 308 kJ/mol by thermal sintering without any electric field to 108 kJ/mol by current-rate flash sintering with an electric field.
A diffusion-related decrease in activation energy under an electric field has also been observed for grain growth during flash sintering. Specifically, the grain growth rate was reported to increase by two orders of magnitude compared with that for thermal annealing, and the activation energy decreased to 266 ± 26 kJ/mol from 517 ± 72 kJ/mol.16) The authors concluded that oxygen vacancies caused by the direct-current electric field were closely related to the kinetic decrease, in which this phenomenon has also been reported for zirconia.17,18) Changes in point-defect configuration during flash sintering upon the application of an electric field have been reported.19–23) Such point-defect formations may be responsible for the changes in activation energy described above. However, few studies on this phenomenon and how it relates to MSC analysis have been reported.
Accordingly, in the present study, we performed MSC analysis on the shrinkage-rate controlled flash (SCF) sintering of 8-mol%-Y2O3–ZrO2. SCF sintering is a modified flash-sintering technique that allows the gradual emergence of flash phenomena.24–26) In this technique, shrinkage progresses at a constant rate under a controlled specimen electric current, providing a shrinkage curve to which MSC analysis can be applied. By these means, the apparent sintering activation energy for 8-mol%-Y2O3–ZrO2 was estimated.
Commercially available 8 mol% Y2O3 doped ZrO2 powder (8YSZ; TZ-8Y, Tosoh Corp., Japan) with a specific surface area and average particle size of 13.4 m2/g and 22 nm, respectively, was used as the raw material. Green compacts with a cross-sectional area of 3.5 × 3.5 mm2 and a length of 15 mm were prepared by a conventional compacting procedure involving uniaxial pressing at 75 MPa and cold isostatic pressing at 100 MPa.
In this study, we applied two kinds of sintering methods, thermal sintering without an electric field and SCF sintering with an electric field. For thermal sintering, the green compacts were furnace-heated at heating rates of 5–25°C/min up to 1400°C in air. When the furnace temperature reached 1400°C, the furnace was switched off and the sintered compacts were furnace cooled to room temperature. For SCF sintering, an alternative current (AC) electric field was applied during sintering, as reported previously.24–26) Pt sheets were used as electrode materials and adhered with Pt paste to both longitudinal faces of the compact. A high-temperature dilatometer (EVO2 TMA8311, Rigaku, Japan) modified to apply an electric field was used for sintering in a controlled electric field.27) The power supply (Asterion AST-751, AMETEK.com) was initially set at a voltage control mode at 50 V/cm as a root mean square value and 1000 Hz until the current reached an initial current limit of 100 mA during the furnace-heating regime. When the current reached the initial current limit, the power supply was switched to a current control mode and the furnace ramp was stopped, maintaining that temperature. Then, the SCF regime was started by controlling the current limit value to keep the shrinkage rate constant. During the SCF regime, the shrinkage rate was checked at ∼3 s intervals, and the current limit of the power supply was increased manually at intervals of ∼3–30 s, depending on assumed shrinkage rates of 60–600 µm/min. When the current reached a maximum value of 1200 mA, current ramping was stopped and the current was maintained for 5 min under current control mode. Then, the power supply and furnace were switched off. The densities of the sintered compacts were measured using a conventional Archimedes method. The theoretical density used was 5.99 g/cm3.28)
2.2 Estimation of apparent sintering activation energy using the MSCIn this study, the sintering activation energies for thermal and SCF sintering were estimated using the MSC method originally developed by Su and Johnson.1) According to Hansen’s model,2) the rate equation for sintering can be expressed as
| \begin{equation} -\frac{dL}{Ldt} = \frac{d\rho}{3\rho dt} = \frac{\gamma\Omega}{kT}\left(\frac{\Gamma_{\text{V}}D_{\text{V}}}{G^{3}} + \frac{\Gamma_{\text{gb}}\delta D_{\text{gb}}}{G^{4}}\right) \end{equation} | (1) |
| \begin{equation} \frac{d\rho}{3\rho dt} = \frac{\gamma\Omega}{kT} \cdot \frac{\Gamma \text{D}_{0}}{G^{n}}\exp \left(-\frac{Q}{RT}\right) \end{equation} | (2) |
| \begin{equation} \frac{k}{3\rho \gamma \Omega \text{D}_{0}} \cdot \frac{(G(\rho))^{n}}{\Gamma(\rho)}d\rho = \frac{1}{T}\exp \left(-\frac{Q}{RT}\right)dt \end{equation} | (3) |
| \begin{equation} \frac{k}{3\rho \gamma\Omega \text{D}_{0}}\int_{\rho_{0}}^{\rho}\frac{(G(\rho))^{n}}{\Gamma(\rho)}d\rho = \int_{0}^{t}\frac{1}{T}\exp\left(-\frac{Q}{RT}\right)dt \end{equation} | (4) |
| \begin{equation} \Theta(T,t) = \int\nolimits_{0}^{t}\frac{1}{T}\exp \left(-\frac{Q}{RT}\right)dt \end{equation} | (5) |
| \begin{equation} \frac{k}{3\rho\gamma\Omega \text{D}_{0}}\int_{\rho_{0}}^{\rho}\frac{(G(\rho))^{n}}{\Gamma(\rho)}d\rho = \Theta(T,t) \end{equation} | (6) |
The apparent sintering activation energy can be estimated to make the respective density curves against Θ(T, t) coincident using the apparent sintering activation energy as a variable. During MSC fitting, to eliminate arbitrariness, the value of Q was determined when the mean residual square (MRS) value defined by the following equation becomes minimal:30)
| \begin{equation} \sqrt{\frac{1}{\rho_{s} - \rho_{0}}\int_{\rho_{0}}^{\rho_{s}}\sum\nolimits_{i = 1}^{N}\cfrac{\biggl(\cfrac{\Theta_{i}}{\Theta_{\textit{avg}}} - 1\biggr)^{2}}{N}d\rho} \end{equation} | (7) |
The compact temperature during SCF sintering was estimated by the heat balance between Joule heat and black body radiation,31) as follows:
| \begin{equation} \int_{t}^{t + \Delta t}P_{W}\text{d}t = \int_{t}^{t + \Delta t}(A\sigma \varepsilon(T^{4} - T_{\text{furnace}}^{4}))dt + mC_{p}\text{d}t \end{equation} | (8) |
Figure 1 shows the variation in relative density as a function of time for heating rates in the range 5–25°C/min during thermal sintering. Due to the equipment used in this study, the maximum sintering temperature was limited to 1400°C. In the range up to this sintering temperature, the attained density decreased as the heating rate increased.
Plots of shrinkage curves during thermal sintering at the heating rates of 5–25°C/min as a function of furnace temperature.
Figure 2 shows the results of MSC analysis performed for the thermal sintering curves presented in Fig. 1. MSC analysis was performed up to the relative density of about 83% in a thermal sintered compact at a heating rate of 25°C/min, which is the lowest attained density among the respective compacts shown in Fig. 1. Curve fitting to obtain MSC was yielded in a range of relative densities from 48% to 80%. The inset plot presents MRS values estimated from eq. (7) as a function of Q, which was used as a variable parameter for fitting the respective shrinkage curves. The minimum MRS value is ∼0.1 at ∼790 kJ/mol. The respective MSCs using 790 kJ/mol trace similarly against Θ, which means the curve fitting is accurate. The activation energy of 790 kJ/mol is near those previously reported for cubic zirconia, i.e., 620 kJ/mol,32) 770 kJ/mol,33) and 730 kJ/mol,34) where the latter two values are for the low-density region as discussed later.
Plots of MSCs during thermal sintering at the heating rates of 5–25°C/min as a function of ln(Θ(T, t)). The colors of respective curves correspond to those presented in Fig. 1. The inset presents MRS as a function of apparent sintering activation energy, Q. Respective MSCs were plotted with Q = 790 kJ/mol obtained MRS of 0.1.
Figure 3 shows (a) linear shrinkage and (b) volumetric power dissipation behaviors as a function of time during SCF sintering. In both plots, the horizontal axis is plotted from the onset of the SCF regime, in which the furnace temperature was ∼870°C. As can be seen in Fig. 3(a), the shrinkages occur almost linearly under SCF control, and the shrinkages are maintained at near-constant rates using the current-control mode of the power supply. The shrinkages achieved at all shrinkage rates are ∼24%, and the relative density is ∼99%. The volumetric power dissipation curves presented in Fig. 3(b) exhibit inversed S-like behavior to keep the shrinkage rate constant, which is similar to that of furnace ramping during rate-controlled sintering.35,36) The compact temperatures as presented later were estimated using these volumetric power dissipation behaviors.
Plots of (a) linear shrinkage curves and (b) volumetric power dissipation behaviors during SCF sintering as a function of time, where linear shrinkage rates are varied with 60 µm/min (red lines), 120 µm/min (violet lines), 300 µm/min (blue lines), and 600 µm/min (green lines), respectively. Time in the horizontal axis is plotted from the onset of SCF regime.
Figure 4 shows typical current density and electric field behaviors during SCF regime at a shrinkage rate of 300 µm/min. As described above, the current from the power supply was increased periodically during SCF regime to keep the shrinkage rate constant. The electric field (blue line) spikes when the current density (red line) increases, and then gradually decreases, which corresponds to the stage II–III behavior as defined in Ref. 37). An instantaneous small flash events are repeated during SCF regime.
Typical behaviors of current density (red line) and electric field (blue line) during SCF regime at a shrinkage rate of 300 µm/min. The time of horizontal axis is plotted from the onset of SCF regime.
Figure 5 shows a comparison of relative density variation against temperature for SCF and thermal sintering, in which compact temperature for SCF were calculated value obtained using eq. (8) and power dissipation curves presented in Fig. 3(b). In the case of thermal sintering, shrinkage starts at approximately 1200°C, followed by a large increase in relative density up to 1400°C. In contrast, in the case of SCF sintering, shrinkage starts at about 1000°C, where SCF control was started, and then increases slowly from about 1200°C. The shrinkage behavior differs greatly, with the temperature variation of relative density being convex downward for thermal sintering and convex upward for SCF. In other words, the temperature at which the shrinkage rate becomes pronounced is approximately 200°C lower for SCF sintering, indicating that shrinkage is promoted by the use of SCF sintering.
Figure 6 shows the results of MSC analysis performed for the SCF sintering data shown in Fig. 3(a), and the inset shows the MRS values. MSC analysis was performed for respective shrinkage curves up to relative density of 90%. A minimum MRS value of 0.31 is obtained at Q = ∼440 kJ/mol. The apparent sintering activation energy during SCF sintering is lower than that obtained from thermal sintering, as presented in Fig. 2. As described before, however, the apparent sintering activation energy was reported to decrease under the effect of an electric field.14,16) If the activation energy depends on electric field, it will change as shrinkage progresses during SCF sintering because electric field conditions were varied during SCF regime as presented in Fig. 4. Thus, the apparent sintering activation energies were re-estimated by MSC fitting with relative density stepping of about 10% from 48% to 90%. The obtained results are presented in Table 1. The activation energy of SCF sintering is close to that of thermal sintering in the early stages of shrinkage, however, it decreases significantly when the relative density is over 70%.
Plots of MSCs during SCF sintering at shrinkage rates of 60–600 µm/min as a function of ln(Θ(T, t)). The inset presents MRS as a function of activation energy, Q. Respective MSCs were plotted with Q = 440 kJ/mol obtained at MRS of 0.31. The colors of the respective MSCs correspond to those as presented in Fig. 3. A red arrow indicates MSC at 60 µm/min showing a deviation from MSCs of other shrinkage rates.
Figure 7 shows SEM images of respective compacts when SCF sintering was terminated to let the respective relative densities approximately at 90%. An average grain size becomes smaller slightly with increase in shrinkage rates during SCF sintering. This difference in a grain size can be considered to be responsible for the small deviation observed in MSCs as shown in Fig. 6.
SEM images of thermally etched sections in SCF sintered compacts at heating rates of (a) 60 µm/min, (b) 120 µm/min, (c) 300 µm/min, and (d) 600 µm/min. The average grain sizes estimated by a linear intercept method is about (a) 0.96 µm, (b) 0.88 µm, (c) 0.80 µm, and (d) 0.76 µm, respectively.
The apparent sintering activation energy during thermal sintering has been reported to decrease in a range of higher relative density. This variation has been investigated by Pouchly et al. for 8YSZ, with MSC analysis providing activation energy of 750 kJ/mol (relative density at 60%–93%) and 460 kJ/mol (relative density at 93%–99%), and with Wang and Raj analysis provided values of 762 kJ/mol (relative density at 60%–70%) and 645 kJ/mol (relative density at 90%–95%).38) Similarly, density dependence of apparent sintering activation energy has also been reported for 3YSZ.39) This density dependence of apparent sintering activation energy is discussed in terms of point defect formation.39) At lower densities (at lower sintering temperature), the formation energy of point defects is superimposed on the apparent activation energy of sintering because the concentration of point-defect is not sufficient, resulting in a higher activation energy. In contrast, at higher densities (at higher sintering temperature), since sufficient point defects are formed, the contribution to apparent sintering activation energy related to defect formation is reduced, and it decreases. The value will eventually approach the activation energy at diffusion-mechanism-dominated sintering at higher density (higher temperature). As for the reduced activation energy for thermal sintering, the diffusion mechanism that dominates sintering is rated by volume diffusion,34) considering the activation energy of 309–373 kJ/mol34,40) for grain boundary diffusion and approximately 460 kJ/mol34,41) for volume diffusion. The apparent sintering activation energy for thermal sintering in this study remains around 790 kJ/mol in a relative density up to about 83% as described in Fig. 2. Since the sintered density range in this study was limited up to 83%, as shown in Fig. 2, the activation energy would probably decrease to a similar level as that previously reported when density is further increased.
Conversely, even in SCF sintering, the activation energy decreases with increasing density and is about 430 kJ/mol at 80–90%, which is approximately similar value to that of volume diffusion (460 kJ/mol).34,41) As mentioned before, the application of MSC is predicated primarily on the assumption that there are no histological differences, including grain size. Even in the 70–80% relative density range, where grain growth is not significant, a decrease in apparent sintering activation energy is already observed, as presented in Table 1. These facts suggest that the reduction in apparent activation energy obtained from MSC analysis for SCF is worth discussing.
This reduced activation energy is similar to the activation energy in the high-density region during thermal sintering. In the case of SCF sintering, however, the temperature range where the activation energy decreases exhibits a shift to a lower density range as shown in Fig. 8. Figure 8 presents the activation energy in SCF sintering and previously reported values as a function of relative density. SCF sintering (red lines) shows a decrease in activation energy at lower relative density. This decrease in activation energy, which is transitioned to the lower relative density region, is considered to be responsible for the increase in shrinkage rate in the lower temperature region in SCF sintering shown in Fig. 5.
Similar decreases in activation energy under electric fields have been reported for current-rate flash sintering of UO214) and 3YSZ.15) Ren et al. reported that grain growth rate increases significantly during flash sintering, and the activation energy decreases to 266 ± 26 kJ/mol.16) Under an applied electric field, the activation energy associated with diffusion tend to become smaller than the decreased activation energy that appears in the higher temperature region under no electric field. There have been several studies that indicate the possibility of variation of point-defect configuration during flash sintering,9) such as luminescence,42,43) photoluminescence44–46) phase transitions,47,48) microstructure observation,49) and anelasticity,50) among others. More recently, enhanced diffusion has been observed in flash healing.51,52) It is reasonable to assume that the variation of point defect configuration was induced by applied electric fields, and this effect can be speculated to lead to a reduction in apparent sintering activation energy, in which the final activation energy is closer to the value for volume diffusion mechanism.
MSC analysis was performed for thermal sintering and SCF sintering in 8 mol% Y2O3-doped ZrO2. The conclusions drawn are as follows:
This work was supported financially by CREST (JPMJCR1996) from the Japan Science and Technology Agency (JST) and JSPS KAKENHI (Grant Number JP19H05788).
