## 1 Introduction  
Various bone graft materials, such as blocks and granules, are used for bone reconstruction [1; 2; 3]. In clinical dentistry, granule-type bone graft materials are frequently employed to promote new bone formation owing to their ease of moldability to fit irregularly shaped bone defects and extraction sockets [4; 5]. However, the efficacy of bone reconstruction with granules is often difficult to predict owing to the risk of granule migration from the bone defect during and after implantation [6; 7; 8; 9]. To prevent granule migration, a membrane is placed over the implanted granules and sutured to the gingiva, which is a complicated procedure. Additionally, improper positioning of the membrane can lead to exposure to the oral cavity, resulting in bacterial colonization, delayed wound healing, and a heightened risk of infection. These complications not only compromise the success of bone regeneration but also increase the likelihood of secondary interventions to manage the infection or remove the graft material [10; 11; 12; 13; 14; 15; 16]. Therefore, an approach that prevents granule migration without the use of membranes is required. Several synthetic bone grafts, such as \(\beta\)-tricalcium phosphate (\(\beta\)-TCP) and hydroxyapatite (HAp), have been developed with varying degradation rates and osteoconductivity [2; 4]. \(\beta\)-TCP degrades rapidly, making it suitable for cases where faster bone replacement is required. However, its rapid degradation may result in insufficient mechanical stability under load-bearing conditions or if bone formation does not keep pace. In contrast, HAp is more mechanically stable and degrades slowly, which can limit its ability to promote timely bone regeneration [2]. Carbonate apatite (CAP) is an analog of bone minerals that exhibits osteoconductive properties and is resorbed by osteoclasts [17; 18; 19]. Recently, CAP has been reported to resorb at an appropriate rate compared to \(\beta\)-TCP and HAp and is eventually replaced by new bone [20; 21]. Based on these properties, CAP granules have attracted considerable attention in dental surgical procedures for bone reconstruction and augmentation [22; 23; 24]. While CAP granules strike a balance between degradation rate and osteoconductivity, an effective solution to migration problems is still needed. The setting reactions of various cementitious materials, such as \(\alpha\)-tricalcium phosphate (\(\alpha\)-TCP) [25; 26] and brushite (dicalcium phosphate dihydrate (DCPD)) [27; 28], have been explored to address the issue of granule migration. Similarly, bassanite (calcium sulfate hemihydrate, CaSO\({}_{4}\cdot\)0.5H\({}_{2}\)O, CSH) is known to set when exposed to water by precipitating as interlocking needle-shaped gypsum (calcium sulfate dihydrate, CaSO\({}_{4}\cdot\)2H\({}_{2}\)O, CSD) [29; 30; 31]. The DCPD cement utilizes strong acids, which cause inflammation, whereas CSH sets with water, which causes no inflammation [32; 33]. In the \(\alpha\)-TCP cement, \(\alpha\)-TCP sets as poorly soluble HAp [33; 34], whereas CSD produced by set CSH is highly soluble [35]. However, CSD alone is significantly soluble and entirely disappears within two months; hence, it does not act as a scaffold for bone formation [36; 37; 38]. Consequently, fibrous tissues form within two months post treatment, and bone formation is poor even at six months post treatment [38]. According to the abovementioned background, utilizing the set properties of CSD may prevent CAP granule migration without causing inflammation. Furthermore, the CSD portion of the set CAP granules may dissolve early in vivo, while the remaining CAP granules may function as porous scaffolds for bone tissue regeneration. Based on this hypothesis, in this study, we attempted to set the CAP granules through crystal interlocking driven by the phase transition from CSH to CSD on the surface of the CAP granules at different CSH/CAP ratios.