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Dislocations play an important role in semiconductor devices made of crystalline silicon (Si). They are known to be strongly performance-limiting defects in solar cell applications, since they act as preferred segregation sites for metallic impurities. In this work we investigate the segregation of iron (Fe) to the cores of the 30° and 90° partial dislocations in Si using atomistic calculations based on first-principles density functional theory. Our simulations show that interstitial Fe impurities segregate readily to all investigated cores and the driving force for the segregation increases with impurity concentration. Moreover, our analysis of the electronic structure reveals the existence of deep defect levels within the band gap that can be related to experimental observations by deep-level transient spectroscopy.