## 2 Structures, Synthesis, and Magnetic Properties of Fe\({}_{3}\)O\({}_{4}\) Nanoparticles
### Other Geometries
\begin{table}
\begin{tabular}{c c c c} \hline
**Morphologies** & **Size/Dimension (nm)** & **Magnetic Properties (at 300 K)** & **Ref.** \\ \hline Nanorods & 63 \(\times\) 6.5 & M\({}_{\text{S}}\) = 20.01, H\({}_{\text{C}}\) = 46.53 & [79] \\  & 140 \(\times\) 12 & & \\ \hline Nanorods & 41 \(\times\) 7 & M\({}_{\text{S}}\) = 86 emu/g & \\  & 65 \(\times\) 5.7 & M\({}_{\text{S}}\) = 84 emu/g & [40] \\  & 56 \(\times\) 10 & M\({}_{\text{S}}\) = 87 emu/g & \\ \hline Nanorods & 41 \(\times\) 7 & M\({}_{\text{S}}\) = 86 emu/g, H\({}_{\text{C}}\) = 50 (Oe) & \\ \hline Nanorods & 35 \(\times\) 5.5 & M\({}_{\text{S}}\) = 44 emu/g & \\  & 55 \(\times\) 8 & M\({}_{\text{S}}\) = 53 emu/g & \\ Nanorods & 75 \(\times\) 9 & M\({}_{\text{S}}\) = 59 emu/g & [80] \\  & 120 \(\times\) 8 & M\({}_{\text{S}}\) = 55 emu/g, H\({}_{\text{C}}\) = 1100 Oe (10K) & \\  & 180 \(\times\) 24 & H\({}_{\text{C}}\) = 850 Oe (10K) & \\ \hline Nanorods & 310 \(\times\) 135 & Superparamagnetic & [81] \\ \hline Nanoplates & Width (hexagonal): 120 & & \\ Side length (triangular): 90 & M\({}_{\text{S}}\) = 84.7 emu/g, H\({}_{\text{C}}\) = 117.72 Oe, M\({}_{\text{R}}\) = 13.36 emu/g & [82] \\  & Thickness: 7 & & \\ \hline Triangular nanoprisms & Edge: 113 & M\({}_{\text{S}}\) = 81.44 emu/g, H\({}_{\text{C}}\) = 126.29 Oe, M\({}_{\text{R}}\) = 11.29 emu/g & [83] \\  & Thickness: 25 & & \\ \hline Triangular nanoprisms & Edge: 22 & & \\  & Thickness: 10 & & \\ \hline Hexagonal nanoplates & Diameter: 200 & & \\ Thickness: 20–30 & M\({}_{\text{S}}\) = 51.4 emu/g, H\({}_{\text{C}}\) = 263 Oe, M\({}_{\text{R}}\) = 18.9 emu/g & [85] \\ \hline Multiarmed & Diameter of arms: 100–200 & & \\ (bipod, tripod, and tetrapod) & Length of arms: up to 2 & \\ \hline Hollow spheres & Diameter: 16 & & \\ Shell thickness: 3 & & \\ \hline Hollow spheres & Diameter: 120 nm & M\({}_{\text{S}}\) = 85.4 emu/g & [88] \\ \hline Hollow spheres & Diameter: 295 nm & M\({}_{\text{S}}\) = 76.7 emu/g & [89] \\ \hline \end{tabular}
\end{table} 
Table 4: Fe\({}_{3}\)O\({}_{4}\) nanoparticles with special geometries and their magnetic properties. magnetic anisotropy [90]. Nanorods of Fe\({}_{3}\)O\({}_{4}\) have also been synthesized using a two-step process starting with the preparation of \(\beta\)-FeOOH nanorods before refluxing in oleylamine to form the Fe\({}_{3}\)O\({}_{4}\) phase [80]. This method allows the preparation of nanorods with a wide range of controllable lengths from 35 to 180 nm, and the diameter can be tuned from 5.5 to 24 nm. Larger dextran-coated nanorods with average dimensions of L \(\times\) D 310 \(\times\) 135 nm were synthesized using a precipitation method [81]. Surprisingly, these large nanorods are retained in the superparamagnetic regime and have potential applications as spin-spin relaxation contrast agents and in monitoring peroxidase activity. Two-dimensional nanoplates of Fe\({}_{3}\)O\({}_{4}\) with hexagonal or triangular geometries have also been synthesized using various different methods. Single-crystalline Fe\({}_{3}\)O\({}_{4}\) nanoplates, consisting of triangular and hexagonal shapes, were synthesized with a facile template-free solvothermal method [82]. These nanoplates have an average thickness of \(\sim\)7 nm, a mean width of \(\sim\)120 nm for hexagonal shapes, and a \(\sim\)90 nm side length for triangular shapes. Interestingly, due to the shape anisotropy of nanoplates, the nanoplates exhibit an extremely high coercivity of 117.72 Oe, which is higher than the coercive fields observed for spheres, polyhedral, solid, or hollow spheres (usually less than 110 Oe). [PERSON] et al. also applied a simple hydrothermal method using 1,3-propanediamine to prepare single-crystalline Fe\({}_{3}\)O\({}_{4}\) triangular nanopisms with an average edge length of 113 nm and a mean thickness of \(\sim\)25 nm [83]. Triangular nanopisms have also been synthesized by the decomposition of Fe(acac)\({}_{3}\) in toluene using oleylamine as the surfactant and reducing agent [84].