## 1 Introduction
Carrying out an intensive search in the SCOPUS database, filtering and classifying later, it was possible to construct Figure 2. As can be seen from Figure 2, despite the 1997 and 2008 economic recessions, a growing number of research articles were published from the year 1987 until the year 2020. According to refined data, China represents 32.07% of the total number of articles published, followed by USA (5.2%), Japan (4.9%), and India (3.9%). The gradual growth of publications on hydrothermal synthesis is due mainly to the fact that solvent used like reaction medium, distilled or millipore water in the majority of cases, is an easy-to-obtain solvent; it is environmentally friendly, harmless for human beings, non-flammable, and totally recyclable [13]. Another relevant feature is the reproducibility of the process and its capacity to generate pure particles with narrow size variations and a substantial variability of morphologies. As can be seen in Section 3.2, the industrial applications of the synthesized particles are numerous and include catalysis, energy storage, biomedicine, etc. The term \"hydrothermal\" has geological origin. It was used for the first time by the British Geological Sir [PERSON] (1792-1871) to describe the changes that water at high temperature and under high pressure caused on the Earth's crust, which leads to the formation of several rocks and minerals [17]. Hydrothermal or hydrothermal synthesis can be classified under the solvothermal synthesis category, that comprises any process by which particles are generated in the presence of a solvent while temperature is above ambient temperature and at pressure above 1 atm. Therefore, the hydrothermal reactions for the formation of particles are solvothermal reactions where water is used as a solvent. Authors such as Professors [PERSON] and [PERSON], from the Institute of Chemistry and the Condensed Matter (Bordeaux) and [PERSON] from the University of Nottingham (UK), completed numerous studies on the precipitation of nanoparticles using fluids such as acetone, hexane, or even a supercritical mixture in water; seeking a greater crystallization of the particles at lower temperatures, because the critical parameters of the mixtures are usually lower than those of pure water [18; 19]. Figure 1: Hydrothermal technology in the 21 st century. Figure 2: Evolution of the number of publications on hydrothermal synthesis from January 1987 until May 2020. For a better understanding and control of the hydrothermal process, it is necessary to be familiar with water properties according to temperature and pressure. Water supercritical point is of particular relevance, i.e., the point where water turns from subcritical into supercritical water; that is to say 221 bar and 374 \({}^{\circ}\)C.  
Figure 3 shows the phases diagram for pure water. Along the vaporization curve, as pressure and temperature increase, intermolecular interactions in the fluid decrease due to thermal expansion. On the other hand, the effect of compression prevails on the vapor phase against thermal expansion and intermolecular interactions increase. This makes the properties of the fluid and the vapor get closer until the critical point is reached, where water turns into supercritical state.