Descriptors based on the density of states for efficient machine learning of grain-boundary segregation energies

The segregation of alloying elements to grain-boundaries (GB) has a significant impact on mechanical and functional properties of materials. The process is controlled by the segregation energies, that can accurately be computed using ab-initio methods. Over the last years, ab-initio computations have been combined with machine-learning (ML) approaches for a reduction of computational cost. Here, we show how information from the electronic structure can be incorporated in the ML. To obtain the electronic structure we use two methods, (i) density functional theory (DFT), and (ii) a recursive solution of a tight-binding (TB) Hamiltonian. With the derived descriptors we train a linear model and a Gaussian process on ab-initio segregation data from 15 coincident site lattice GBs with $\Sigma$-values up to 43, where the models are compared using cross-validation scores. Both the TB and DFT-derived descriptors are found to clearly outperform common structure-based features that have been used for ML segregation energies before. Furthermore, TB descriptors almost reach the same accuracy as DFT descriptors although their computational effort is significantly reduced. We test our approach on segregation of Ta and Re to GBs in a bcc-W matrix, which are materials of relevance for fusion-energy research.