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We propose a new statistical physics model to study equilibrium solutesegregation at grain boundaries and the resulting embrittlement effect. Thislow-temperature expansion model is general and efficient, and its parameterscan be obtained from atomistic calculations. It is possible to take intoaccount multiple species, multiple segregation sites with different segregationfree energies, account for configurational entropy, grain radius and sitecompetition between solutes. As an example, the model is then applied to thestudy of phosphorus and hydrogen co-segregation at $\Sigma3$$109.5\deg[0\bar{1}1]\{111\}$ twin boundaries in $\alpha$-Fe, using energeticparameters from density-functional theory calculations. We show that P--Hinteractions may lead to increased P segregation at grain boundaries and causeadditional embrittlement compared to the case where P and H are consideredseparately.

Ab Initio Investigation Of Phosphorus And Hydrogen Co-segregation And Embrittlement In {\alpha}-fe Twin Boundaries