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Iron impurities have a negative effect on the efficiency of silicon-based solar cells because they act as trapping centers for charge carriers. Various processing techniques have been applied to improve the efficiency by passivating the Fe contaminants. For instance, internal gettering exploits the attractive interaction between interfaces and the diffusing Fe atoms. Therefore, it is interesting and important to develop a fundamental understanding of mechanisms for this interaction. In this work, we employ density functional theory to study the electronic structure and the segregation behavior of impurity atoms at grain boundaries (GBs). The investigated set of symmetrical tilt or twist GBs in Si provides a variety of interface orientations and structures at the atomic scale. Our results suggest that segregation of interstitial Fe occurs only at specific sites at some of these GBs, e.g., the Sigma 3 (112) GBs and Sigma 3 (110) GBs. However, there seems to be no obvious relation between the computed segregation energies and the local coordination and electronic structure at the segregation sites. Hence, the thermodynamics of interstitial Fe at GBs in Si is determined by rather subtle features of structure and bonding.