## 2 Structures, Synthesis, and Magnetic Properties of Fe\({}_{3}\)O\({}_{4}\) Nanoparticles
### Other Geometries
In addition to wet syntheses, the supercritical fluid technique was also applied to synthesize Fe\({}_{3}\)O\({}_{4}\) hexagonal nanoplatelets. This method utilized ferrocene as a precursor and supercritical carbon dioxide (sc-CO\({}_{2}\)) as the solvent and oxygen sources [85]. As shown in Figure 6e,  
Figure 6: **(a,b)** TEM and HR-TEM images of Fe\({}_{3}\)O\({}_{4}\) nanorods. Reproduced with permission from ref. [79]. Copyright 2012 American Chemical Society. **(c,d)** TEM and HR-TEM images of porous hollow NPs. Reproduced with permission from ref. [87]. Copyright 2009 American Chemical Society. **(e)** TEM image of 2D hexagonal nanoplates. Reproduced with permission from ref. [85]. Copyright 2010 American Chemical Society. **(f,g)** TEM images of Fe\({}_{3}\)O\({}_{4}\) tripods and tetrapods. Reproduced with permission from ref. [86]. Copyright 2009 Elsevier. the obtained hexagonal plates are uniform with a mean diameter of 200 nm and thickness ranging from 20 to 30 nm. In addition to anisotropic shapes such as 1D nanorods and 2D nanoplates, a special geometry of multiarmed nanocrystals containing Y-shaped bipods, tripods, and tetrapods was successfully synthesized with a simple route using a mild hydrothermal protocol. This special geometry of multiarmed nanostructures exhibited an extremely high saturation magnetization of 106.6 emu/g, which is even higher than the maximum M\({}_{\text{S}}\) value of 92 emu/g for bulk magnetite [86]. TEM images of the tripod and tetrapod Fe\({}_{3}\)O\({}_{4}\) nanocrystals are shown in Figure 6f,g, respectively. Moreover, a special version of the isotropic morphology of SNPs with hollow nanostructures was also synthesized [87; 88]. Because they possess porous shells, these Fe\({}_{3}\)O\({}_{4}\) hollow nanostructures are potentially useful for drug delivery applications. Separately, 19 nm porous hollow Fe\({}_{3}\)O\({}_{4}\) nanoparticles were prepared through the controlled oxidation of Fe NPs, followed by an acid etching step [87]. The morphology and structure of these porous hollow NPs are presented in Figure 6c,d. Larger hollow Fe\({}_{3}\)O\({}_{4}\) NPs with a mean diameter of 120 or 295 nm were also prepared using a direct solvothermal method or a combination of a solvothermal route and etching, respectively [88; 89]. An atlas of synthetic strategies for synthesizing various geometries of magnetite nanoparticles, such as tetrahedrons, octahedrons, tetradecahedrons, cubes, and stars, was developed by [PERSON] and coworkers [76]. The authors proposed the growing mechanism of Fe\({}_{3}\)O\({}_{4}\) nanocubes during the synthesis process and provided controllable growth procedures to obtain different geometries, such as tetrahedrons, octahedrons, and star shapes (cubic with sharply extruded corners), as shown in Figure 7.  
Significant efforts have been made in the last 20 years to synthesize Fe\({}_{3}\)O\({}_{4}\) nanoparticles with highly pure compositions, controllable sizes in a wide range, good uniform geometry, and high degrees of crystallinity. Furthermore, the in-depth mechanism of  
Figure 7: Schematic illustration of the proposed growth model for MNCs. Reproduced with permission from ref. [76]. Copyright 2017 American Chemical Society. some synthetic protocols has been explained, which provides a better understanding of nanochemistry during synthesis processes and allows the tailoring of nanoparticle properties. In terms of synthesis, spherical Fe\({}_{3}\)O\({}_{4}\) nanoparticles are relatively easily prepared and available in a wide range of sizes for use in various applications. Compared to spherical NPs, cubic Fe\({}_{3}\)O\({}_{4}\) NPs show enhanced magnetic properties; however, the uniform growth of cubic crystals is more difficult to control. Although Fe\({}_{3}\)O\({}_{4}\) nanorods possess large surface contact areas, they exhibit moderate magnetic properties. Some special geometries have excellent magnetic properties, such as 2D nanoplates with high coercivity and multiarmed nanocrystals with high saturation magnetization.