## 1 Introduction  
Recent developments in advanced dental materials [1,2], solid-oxide fuel-cell design to oxygen detection [3], nuclear waste confinement [4], optics [5], medical prosthesis [6,7], and catalytic [8] technologies have drawn attention towards the remarkable structural properties of zirconia (ZrO\({}_{2}\))-based ceramics. In all the current technological applications, ZrO\({}_{2}\)-based ceramics are preferred due to their advanced mechanical properties such as high-fracture toughness and bulk modulus, corrosion resistance, chemical inertness, low chemical conductivity and biocompatibility [9]. It is well known that three polymorphic forms of pure ZrO\({}_{2}\) can be found: the monoclinic state, P2\({}_{1}\)/c, stable at temperatures below 1170 \({}^{\circ}\)C; the tetragonal phase, P4\({}_{2}\)/nmc stable in the temperature range between 1170 and 2370 \({}^{\circ}\)C; and the cubic, Fm-3m phase, appearing at a temperature above 2370 \({}^{\circ}\)C [10]. These ceramics have mechanical properties, promoting them to special applications. Under external stress, as grinding or impact, transition from the tetragonal (t) to monoclinic (m) phase can appear at normal temperatures, being followed by an increase of volume of at least 4%, causing compressive stress. This can cause material failure. Ceria (Ce\({}_{2}\)O\({}_{3}\)) or yttria (Y\({}_{2}\)O\({}_{3}\)) are used to stabilize these ceramics at room temperature and allowing t \(\rightarrow\) m transformation to prevent crack propagation.  
The main method used for the stabilization of the ZrO\({}_{2}\) tetragonal phase is the introduction of stabilization components in the zirconia lattice, such as Mg, Ce, Fe, Y, _etc._[11, 12, 13, 14]. At nanoscale level, the metastable phase formation in ZrO\({}_{2}\) can be induced by including in the oxide structure some vacancy defects [11]. Although, the stabilization effect of the oxygen vacancies in tetragonal ZrO\({}_{2}\) is not yet well understood (contrary to cubic ZrO\({}_{2}\)) [14], the concentration of oxygen vacancies in the lattice required to stabilize the tetragonal phase is found in phases like ZrO\({}_{1.97}\) and ZrO\({}_{1.98}\) for tetragonal zirconia doped by rare-earth elements, mainly cerium (Ce) and yttrium (Y).  
Our aim is to investigate the influence of the phase change of ZrO\({}_{2}\) ceramics following doping with Ce on the mechanical properties. We investigated the structure of these ceramics and the phase stabilization using X-ray and neutron diffraction, Scanning Electron Microscopy (SEM) as well as microstructure characterization methods, including micro-hardness measurements. Moreover, we employed Resonant Ultrasound Spectroscopy (RUS) as a non-destructive evaluation method in order to estimate the presence of low-density regions, state of sintering, and the presence and development of small cracks in the structure, by evaluating the complete elasticity matrix. RUS appears to be a feasible method for the inspection of zirconia ceramics based on the changes of the resonance frequencies, being easily applied for the quality control procedure of such ceramic samples; essentially monitoring of a single resonance peak within the frequency band included in experiment would be sufficient for this purpose. We emphasize the properties of zirconium-based ceramics for applications in the biomedical field, such as ceramic femoral heads used in hip implant procedures, which are very resistant to scratches resulting from debris caused by accumulation of bone parts, cement, or metal that occasionally fall between artificial joint surfaces, but are extremely fragile.