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The binary oxides HfO2, ZrO2 and their solid solutions have been an interesting research topic lately because of their large dielectric permittivities. Surprisingly, the mixture Hf0.5Zr0.5O2 (HZO) has shown ferroelectric behavior when created in thin film form and under certain conditions. The ferroelectricity of HZO is believed to result from the formation of a non-centrosymmetric orthorhombic Pbc21 phase. So far, all the research was conducted only in the thin films, because the ferroelectric properties typically disappear in thick films or bulk samples. Recently, the possible influencing factors on the ferroelectric phase stability, like temperature, doping and other defects, stress or strain and surface energy have been theoretically investigated. Based on this information, we aimed to investigate the effect of particle size in the HfO2-ZrO2 solid solution and the possible stability of the ferroelectric phase in fine powders. Mechanical alloying method was chosen as a way to reduce the particle size either by using dry or wet milling with variation of milling duration. The dry milling treatment gives us ~100nm particles size with sufficient homogeneity while wet milling gives smaller particles size (~70nm) with very good homogeneity. XRD measurements were performed to observe the phase of our material. Mainly monoclinic and tetragonal-monoclinic mixture phases are observed in dry milled and wet milled samples, respectively. Interesting results were obtained by performing heat treatment above 10000C, after which HZO shows very distinguishing pattern at room temperature. This pattern has been found to correspond to Hf1-xZrxSiO4, with tetragonal I41/amd space group, which is formed by Silicon contamination during the milling process. Low temperature dielectric measurements showed a clear transition at temperature around 255K, and the origin of this transition has yet to be analyzed, while ferroelectric measurement in this material show promising ferroelectric signatures. Eventually, these results give us notable information about the HfO2-ZrO2 compounds.