In today’s digitized world, large amounts of data are becoming available at rates never seen before. This holds true also for materials science where high-throughput simulations and experiments continuously produce new data. Data driven methods are required which can make best use of the information stored in large data repositories. In the present article, two of such data driven methods are presented. First, we apply machine learning to generalize and extend the results obtained from computationally intense density functional theory (DFT) simulations. We show how grain boundary segregation energies can be trained with gradient boosting regression and extended to many more positions in the grain boundary for a complete description. The second method relies on Bayesian inference, which can be used to calibrate models to give data and quantification of the model uncertainty. The method is applied to calibrate parameters in thermodynamic models of the Gibbs energy of Ti-W alloys. The uncertainty of the model parameters is quantified and propagated to the phase boundaries of the Ti-W system.

In BiFeO 3 (BFO), Bi 2 O 3 (BO) is a known secondary phase, which can appear under certain growth conditions. However, BO is not just an unwanted parasitic phase but can be used to create the super-tetragonal BFO phase in films on substrates, which would otherwise grow in the regular rhombohedral phase (R-phase). The super-tetragonal BFO phase has the advantage of a much larger ferroelectric polarization of 130–150 μC/cm 2 , which is around 1.5 times the value of the rhombohedral phase with 80–100 μC/cm 2 . Here, we report that the solubility of Ca, which is a common dopant of bismuth ferrite materials to tune their properties, is significantly lower in the secondary BO phase than in the observed R-phase BFO. Starting from the film growth, this leads to completely different Ca concentrations in the two phases. We show this with advanced analytical transmission electron microscopy techniques and confirm the experimental results with density functional theory (DFT) calculations. At the film’s fabrication temperature, caused by different solubilities, about 50 times higher Ca concentration is expected in the BFO phase than in the secondary one. Depending on the cooling rate after fabrication, this can further increase since a larger Ca concentration difference is expected at lower temperatures. When fabricating functional devices using Ca doping and the secondary BO phase, the difference in solubility must be considered because, depending on the ratio of the BO phase, the Ca concentration in the BFO phase can become much higher than intended. This can be critical for the intended device functionality because the Ca concentration strongly influences and modifies the BFO properties.