**3.2 Sphericity mechanism of the AlN particle shape**

According to the comprehensive investigations in Section 2, it can be concluded that the amount and distribution of liquid aluminates were important for the formation of the spherical AlN morphology. Based on the crystal growth theory [41], crystals preferred to grow into the lowest energy state. When there were no liquids in the system, the AlN morphology was mainly determined by the internal intrinsic structure. Thus, AlN particles tended to grow in the angular morphology to achieve the most stable state of energy. However, when additives were used in the CRN process, AlN was nucleated in the liquid aluminates, and thus its morphology was consequentially influenced by the external liquid phase environment. The solid AlN and liquid phase constituted a common system, and hence the lowest solid-liquid interface energy became the main driving force for the growth of AlN. Compared with the angular morphology, spherical particles showed the least specific surface area and the corresponding lowest solid-liquid interface energy. Therefore, AlN tended to grow into the spherical morphology with the aid of liquid Ca-aluminates.

Based on the above inference, only when the AlN particles were completely wrapped in the liquids during the growth stage, the spherical morphology could be obtained. Thus, both the low liquid content and the fast AlN growth rate could lead to the disappearance of the solid-liquid interface and the difficulty to form the spherical shape. For example, when a low N2 pressure was used, the AlN growth rate was significantly increased so that the AlN particles could not be completely wrapped by the liquids, resulting in the poor sphericity. In addition, the low reaction temperature and the little additive content both led to the small liquid content, thus the spherical AlN particles could not be obtained as well. It can be concluded that the elevated N2 pressure, suitable additives, and relatively high reaction temperature greatly favored for carbothermally synthesizing AlN particles with a smooth spherical morphology.
