Hardness-Porosity-Grain Size Interrelationship in Conventionally Sintered 3 mol% Yttria Stabilized Zirconia

3.1. Green Compaction Behavior Defect-free, dense pressed pellets are crucial to obtain consistent, low-porosity fired ceramics. Figure 2 shows that increasing the PVA content and applying a higher forming pressure increase the green density, consistent with findings from other studies on YSZ [2]. This type of compaction study is often done in the industry whenever a new raw material supplier is used. This is because differences in the starting powder particle size, morphology or processing history can create major variations in the compaction behavior. It was observed that the green densities of pellets with 1%, 3%, 5%, 7%, and 9% PVA, pressed at 261 MPa, were 2.70, 2.76, 2.80, 2.92, and 2.95 g/cm³, respectively. The major phase in the YSZ powder was tetragonal zirconia, which had a theoretical density of 6.13 g/cm³ (ICDD PDF 00-050-1089). This implied that the green density increased from 44% to 48% upon pressing at 261 MPa when the PVA addition was raised from 1% to 9%. The powder containing 1% PVA was too dry, which is expected as zirconia lacks plasticity (unlike clays), and consequently, the pressed pellet delaminated beyond 261 MPa. This indicated that it had inadequate workability and insufficient green strength. From 5% PVA onwards, an additional trend of flattening of the green density curve with pressure was observed when 305–392 MPa was reached. Excessively high forming pressure provides better compaction but, to the detriment, undergoes more springback. This typically makes green bodies more susceptible to delamination, which becomes prominently visible after firing. Compared to 5% PVA added pellets, the green density with 7% PVA was significantly higher, but 9% PVA did not bring much improvement till 218 MPa forming pressure. Although the addition of green binder gradually enhanced compaction, its burnout during sintering could lead to excessive porosity, potentially reducing mechanical properties such as hardness [17,26,27]. As such, the moderate PVA addition level of 5% was selected, and the dwell time at a maximum pressure of 392 MPa was increased from 20 s to 1 min, which increased the green density from 2.84 g/cm³ to 2.89 g/cm³. The final pressing regime for preparing 15 mm diameter and 4 mm thick pellets was loading up to 110 MPa, dwelling for 10 s to de-air, increasing pressure up to 392 MPa and dwelling for 60 s, followed by release. 3.2. Densification YSZ is known to have high sinterability due to its high oxygen vacancy concentration caused by the substitution of Zr⁴⁺ ions by Y³⁺ ions, as oxygen is the slowest diffusing species in the crystal structure [21]. This is also observed when a low valency ion substitutes a high valency ion in other oxide ceramics, like MgO-rich MgAl₂O₄, where Mg²⁺ substitutes Al³⁺, producing oxygen vacancies that accelerate sintering [28]. A high % linear firing shrinkage (Figure 3a) of 22.2% was observed in 3YSZ when fired at 1500 °C with a 2 h dwell time. Shrinkage increased steadily to 24.4% after firing at 1650 °C for 2 h, indicating that densification was active throughout. Bulk density (Figure 3b) increased rapidly from 5.61 g/cm³ at 1500 °C to 5.98 g/cm³ at 1600 °C, following which it slowly increased to 6.08 g/cm³ upon heating at 1650 °C for 2 h, suggesting it had approached final stage sintering. Compared to the theoretical density of tetragonal ZrO₂ (6.13 g/cm³), this would mean a 99.2% density. Inversely related to bulk density, open porosity reduced from 5.9% after firing at 1500 °C to 0.8% after sintering at 1650 °C for 2 h. Closed porosity, obtained by 100 − (density %) − (open porosity %), was hardly present at that high temperature. These results are reasonably close to the 99.7% density reported for commercial 3YSZ conventionally sintered at 1600 °C for 2 h [29]. 3.3. Phase Evolution The secondary cubic ZrO₂ phase detected in the starting YSZ powder (Figure 1) was seen to disappear upon firing at 1500 °C for 2 h (Figure 4a), forming a desirable, single-phase tetragonal ZrO₂ product. TZP are prized for their high fracture toughness, hardness and strength [2,5,6,21]. The (011) peak of the tetragonal ZrO₂ phase in the sintered material was at a higher angle (30.48° 2θ) than the raw YSZ powder (30.28°) and the ICDD PDF (30.27°), indicating a contraction of the unit cell per Bragg’s law [30]. An unidentified peak of 4.3% relative intensity (after subtracting its immediate baseline noise) remained at 73.28°. It should be noted that grinding in an agate mortar for powder XRD sample preparation can partially reduce the stabilization of zirconia [31,32]. However, all four sintered samples were ground in the same manner. The phase composition of the sintered YSZ remained the same for firing temperatures up to 1650 °C (Figure 4b–d), but the relative intensities of the (112) peak at ~50.5° first increased from 1500 °C to 1550 °C (56.5% to 67.4%) and then gradually reduced after that at 1650 °C (58.8%). Moreover, the (020) peak at ~50.8° was only observed after sintering at 1550 °C and 1650 °C. These two observations suggest that changes in crystal structure may have occurred due to the different sintering temperatures, possibly induced by thermal strain. The monoclinic phase was confirmed to be absent as the 100% intensity peak at 28.175° was not detected in any of the sintered samples. The small unidentified peak at ~73.2° found in the 1500 °C sintered YSZ was also present at 1550 °C and 1600 °C. Apart from these, a small unindexed peak at 28.54° was found after firing at 1550 °C, an unknown peak at 31.6° was observed after heating at 1600 °C, and the 1650 °C sintered sample had two tiny unidentified peaks at 35.02° and 49.62°. Some of these unindexed peaks were close to cubic ZrO₂, but this could not be confirmed due to the absence of the major (111) peak at 30.12°. This may be because the conversion of the tetragonal phase was not fully completed. Finally, a steady shift of the (011) peak of the tetragonal phase was observed when the firing temperature was increased from 1500 °C, 1550 °C, 1600 °C and to 1650 °C (30.48°, 30.48°, 30.42° and 30.38°). This suggested an expansion of the unit cell, which may be caused by the incorporation of more yttria from the cubic phase in the starting material into the tetragonal phase at higher sintering temperatures as the ionic radii of Y³⁺ (0.90 Å) for an octahedral site is larger than Zr⁴⁺ (0.72 Å) [33]. 3.4. Microstructure Fracture surfaces are generally preferred over polished surfaces for grain size measurement. The secondary electron image of the fracture surface of YSZ sintered at 1500 °C shows uniformly sized, spherical grains with an average size of 0.44 µm (Figure 5a). This is nearly twice the size of the starting powder (0.25 µm). Some amount of porosity could also be seen. The extensively reported nano-sized [31,34], lenticular- shaped morphology [34] of tetragonal ZrO₂ grains was not observed in this work, possibly due to using a coarser starting powder. Increasing the sintering temperature produced a denser microstructure (Figure 5b–d) with an increase in grain size from 0.57 µm (1550 °C), 0.76 µm (1600 °C) to 0.96 µm (1650 °C). The grain growth in this article was not very high (not like tens of microns), and a similar grain size was reported by another study [35]. The dense microstructure of Figure 5d correlates well with the low open porosity of 0.8% in Figure 3b. 3.5. Hardness Figure 6a shows the steady grain growth of YSZ with increasing sintering temperature. Rockwell hardness expressed as scale A values was found to increase rapidly from 49 HRA upon firing at 1500 °C to 62 HRA at 1550 °C, then gradually rose to 69 HRA at 1600 °C and finally improved to 86 HRA at 1650 °C. Similarly, Vickers hardness has been reported to increase with rising sintering temperatures as long as densification continues, after which it tends to drop [36,37]. As higher sintering temperature increased both grain size and hardness simultaneously, it could be mistakenly inferred that hardness was directly proportional to the grain size. This would be in contradiction to the Hall-Petch relation [37,38] given in Equation (1), where H is the hardness, $$\mathrm{H}_0^\prime$$ is the hardness at zero porosity (fully dense material), k is a constant and d is the average grain size. The Hall-Petch regime, which means a material becomes harder when the grain size is smaller, has been observed not only in metals but also in oxide ceramics like Al₂O3, MgO and MgAl₂O₄ [39], especially below 1 µm grain size [40]. In fact, it has been observed that 3YSZ follows the Hall-Petch relation for grain sizes > 120 nm [37], but at finer sizes the inverse Hall-Petch relationship is observed, wherein the hardness linearly drops with (grain size)^−0.5. The breakdown of the Hall-Petch effect at very small grain sizes has been attributed to a change in the deformation mechanism, as reported for 10YSZ when the grain size dropped below 21 nm [40]. The pseudo-inverse Hall-Petch relationship observed in the 3YSZ samples in Figure 6b is unlikely to be real, as the grain sizes are much coarser (437–964 nm) than those reported in the literature. Moreover, the Hall-Petch relationship should be ascertained only for fully dense samples or at least specimens with the same density, although, this is rarely pointed out in publications. It is possible to draw misleading Hall-Petch equation related conclusions from just a plot of hardness and the inverse square root of grain size without delving deeper into the differences in the porosity of the samples. The main intention of this section is to point that out. The deficiency of the pseudo inverse Hall-Petch effect in this study can be seen in the slightly low fitting quality given by a coefficient of determination (COD) or R-squared value of 0.95. The hardness at zero porosity was found to be 153.1 HRA, while the constant, k, was −69.2 HRA$$\sqrt{µ\mathrm{m}}$$. It must be mentioned that care must be taken while comparing values of the Hall-Petch constants between literature due to the differences in the units of hardness (HRA vs. GPa) and grain size (µm vs. nm). The inverse Hall-Petch effect observed in Figure 6b is a false or pseudo-effect, as another crucial variable—porosity—is also changing alongside grain size. The dominant effect of porosity on hardness is presented in Figure 7, where the well-known exponential decay of hardness per Equation (2) is observed. Here H₀ is the hardness of fully dense material, b is a pre-exponential constant and P is the total pore fraction [27]. The higher quality of fitting of the exponential decay equation (R² of 0.99) as compared to the pseudo inverse Hall-Petch regime (R² of 0.95) indicates that porosity is stronger as a controlling parameter of hardness than grain size. Figure 7 indicates that the measured hardness varies as H = 92.9 exp(−11.1P). McColm [41] mentioned that compared to regular, phase-stable ceramics that exhibit a constant “b” of 7, partially stabilized zirconia, due to its transformation toughening behavior has a higher dependence of Vickers hardness on porosity, expressed by H = 12.27 exp(−8P). The H₀ and b constants are not necessarily very different between the current article and McColm’s work, as the Rockwell hardness scale A values are quite different than Vickers hardness values. Even with Vickers hardness data, Stevens and Luo [27] had observed different constants (especially the pre-exponential term b) than McColm [41] as H = 11.76 exp(−5.03P). Because the fitting quality (R²) of the pseudo inverse Hall-Petch analysis in this study was lower, and as the former had an inverse square root relation while the hardness and porosity are linked with an exponential decay equation, it can be deduced that porosity has a more dominant effect on hardness of 3YSZ than grain size.