Simulation of XRD, Raman and IR spectrum for phase identification in doped HfO2 and ZrO2

Fluorite-structured hafnium and zirconia require different, complementary characterization methods to identify the numerous metastable phases. This is because of the many possible positions of the oxygen ions, which are difficult to observe directly. Ab initio simulations are useful to probe the corresponding XRD, Raman, and infrared spectra for fingerprints. However, the predictive power of theoretical methods is limited both by model errors and by boundary conditions such as defects, stresses, and morphology that are difficult to detect. We first consider the calculation of Raman and infrared spectra of the most interesting undoped phases of HfO2 and ZrO2, compare the results with known results, and discuss the uncertainties. Next, we consider the possibilities of classifying the phases using X-ray diffraction. To this end, we introduce the effects of doping, which increases the uncertainty due to structural disorder. For illustration, we examine a large data set of doped structures obtained with ab initio calculations. To make an unbiased assignment of phases, we use machine learning methods with clusters. The limits of X-ray diffraction spectroscopy are reached when phase mixtures are present. Resolution of single-phase polycrystalline samples may only be possible here if these three characterization methods are used.