# Controlled-Atmosphere Sintering of KNbO\({}_{3}\)
## 4 Discussion
Once \(\Delta G\) became large enough, the growth rate should then increase very rapidly (the steeply sloping region of the blue curve). However, this did not appear to happen as the grain size distributions of the N\({}_{2}\)-sintered samples did not change significantly as sintering time increased. A longer sintering time was possibly needed to allow the abnormal grains to grow large enough to reach the region of the growth rate vs. \(\Delta G\) curve where the growth rate increases rapidly. For samples sintered in N\({}_{2}\)-5% H\({}_{2}\), the number of oxygen vacancies increased further. \(\varepsilon\) and \(\Delta G_{c}\) were further lowered (Figure 11). The number of grains with \(\Delta G\geq\Delta G_{c}\) increased, and their growth rate also increased compared to those in the N\({}_{2}\)-sintered samples. These grains underwent rapid growth and became abnormal grains (Figures 3 and 6), causing a rapid increase in the mean grain size (Figure 5). Extensive abnormal grain growth took place by 1 h. After impingement of the abnormal grains, their value of \(\Delta G\) decreased rapidly, and further grain growth was very limited. For the H\({}_{2}\)-sintered samples, \(\varepsilon\) and \(\Delta G_{c}\) were further lowered. The increased curvature at the corners and edges of the KNbO\({}_{3}\) powder annealed in H\({}_{2}\) is indicative of a reduced \(\varepsilon\) (Figure 7). The value of \(\Delta G_{c}\) became so low that many grains had \(\Delta G\geq\Delta G_{c}\) and could grow. Even grains with \(\Delta G\approx\Delta G_{max}\) could not now grow rapidly to form abnormal grains as they had to compete for material with many other growing grains. A shift from abnormal to pseudo-normal grain growth took place, with the grain size distribution becoming narrow and unimodal [56; 67; 77; 78]. For the O\({}_{2}\)-, air-, and N\({}_{2}\)-sintered samples, abnormal grain growth occurred at the edges of the samples. This was probably due to the increased evaporation of potassium at the sample edges, increasing the number of potassium vacancies. The concentration of oxygen vacancies at the sample edges was also likely to be larger than in the bulk. This caused \(\varepsilon\) and \(\Delta G_{c}\) to be lower at the sample edges than in the bulk. During prolonged sintering, some of the grains at the sample edges could grow sufficiently to have \(\Delta G\geq\Delta G_{c}\) and could then form abnormal grains. For the N\({}_{2}\)-5% H\({}_{2}\)-sintered samples, \(\varepsilon\) and \(\Delta G_{c}\) were also lower at the sample edges than in the bulk. The number of grains at the edges of the sample with \(\Delta G\geq\Delta G_{c}\) and therefore able to grow was larger than in the bulk, causing the grain growth behavior at the edges of the sample to transition towards pseudo-normal grain growth. Comparing the SEM micrographs (Figure 3) with the mean grain size measurements (Figure 5), it can be seen that there are many large grains over 10 \(\upmu\)m in radius in the samples sintered in N\({}_{2}\)-5% H\({}_{2}\); however, the mean grain radius is only 6-8 \(\upmu\)m. The measured mean grain radius will depend on the relative numbers of small matrix and large abnormal grains measured. Due to their large size, the abnormal grains were measured from micrographs taken at lower magnification, and their grain boundaries were not always clearly visible. It was easier to measure the size of the remaining small matrix grains, so the mean grain size and grain size distributions of the samples sintered in N\({}_{2}\)-5% H\({}_{2}\) were likely skewed towards smaller values. Nonetheless, it is still clear that sintering in N\({}_{2}\)-5% H\({}_{2}\) caused a large increase in mean grain size. The appearance of secondary phases in the samples sintered in H\({}_{2}\) indicates that KNbO\({}_{3}\) is unstable when sintered in strongly reducing atmospheres (Figure 8b). Such instability was not noticed in (K\({}_{0.5}\)Na\({}_{0.5}\))NbO\({}_{3}\) samples sintered in H\({}_{2}\)[45; 46; 47].