Predicting formation energies of crystals is a common but computationally expensive task. In this work, it is therefore investigated how a neural network can be used as a tool for predicting formation energies with less computational cost compared to conventional methods. The investigated model shows promising results in predicting formation energies, reaching below a mean absolute error of 0.05 eV/atom with less than 4000 training datapoints. The model also shows great transferability, being able to reach below an MAE of 0.1 eV/atom with less than 100 training points when transferring from a pre-trained model. A drawback of the model is however that it is relying on descriptions of the crystal structures that include interatomic distances. Since these are not always accurately known, it is investigated how inaccurate structure descriptions affect the performance of the model. The results show that the quality of the descriptions definitely worsen the accuracy. The less accurate descriptions can however be used to reduce the search space in the creation of phase diagrams, and the proposed workflow which combines conventional density functional theory and machine learning shows a reduction in time consumption of more than 50 \% compared to only using density functional theory for creating a ternary phase diagram.

Perovskite based materials have great potentials for various energy applications and the search for new materials for uses in SOFCs has largely been concentrated to this class of compounds. In this search, we have studied perovskite phases in the system La2Co1+z(Ti1-xMgx)1-zO6, with 0  x 0.9 and z = 0.0, 0.2, 0.4, 0.6. Crystal structures were characterized by XRD and, for selected compositions, also by NPD and SAED. They exhibit with increasing x, as well as increasing z, a progressive increase in symmetry from monoclinic to orthorhombic to rhombohedral. The main focus in this work has been on the investigation of structure-property relations for compositions with 0.0 x 0.5 and z = 0. The nominal oxidation state of Co increases for these with increasing x, from Co2+ for x = 0 to Co3+ for x = 0.5. Magnetic measurements and XANES studies showed that the average spin state of Co changes linearly with increasing x, up to x = 0.5, in accordance with varying proportions of Co with two fixed oxidation states, i.e. Co2+ and Co3+. The data suggests that the Co3+ ions have an IS spin state or a mixture of LS and HS spin states for all compositions with nominally only Co2+ and Co3+ ions, possibly with the exception of the composition with x = 0.1, 0.2 and z = 0, for which the data indicate that the spin state might be HS. The XANES data indicate furthermore that for the perovskite phases with z = 0 and x > 0.5, which in the absence of O atom vacancies contain formally Co4+, the highest oxidation state of Co is Co3+, implying that the substitution of Ti4+ by Mg2+ for x ³ 0.5 effects an oxidation of O2- ions rather than an oxidation of Co3+ ions. The thermal expansion was found to increase nearly linearly with increasing oxidation state of Co. This agrees well with findings in previous studies and is attributable to an increase in the ionic radius of Co3+ ions with increasing temperature, due to a thermal excitation from a LS to IS or LS/HS spin states. High temperature electronic conductivity measurements indicate that the electronic conductivity increases with an increase of both relative and absolute amount of Co3+. The latter can be attributed to an increase in the number of Co-O-Co connections. Additional high temperature magnetic measurements for selected samples, whose susceptibilities did not follow a Curie law behaviour up to room temperature, showed effective magnetic moments that did approach plateaus even at high temperatures (900 K). Interpretations of these data are, however, hindered by the samples losing oxygen during the applied heating-cooling cycle. The present study has shown that the investigated system is suitable for further studies, of more fundamental character, which could provide further insight of the structure-property relationships that depend on the oxidation state of Co. / Studies of cobalt based perovskites for cathode materials in solid oxide fuel cells.