  Segregation of impurities to grain boundaries plays an important role in both
the stability and macroscopic behavior of polycrystalline materials. The
research objective in this work is to better characterize the energetics and
length scales involved with the process of solute and impurity segregation to
grain boundaries. Molecular dynamics simulations are used to calculate the
segregation energies for carbon within multiple grain boundary sites over a
database of 125 symmetric tilt grain boundaries in Fe. The simulation results
show that the majority of atomic sites near the grain boundary have segregation
energies lower than in the bulk. Moreover, depending on the boundary, the
segregation energies approach the bulk value approximately 5-12 \AA\ away from
the center of the grain boundary, providing an energetic length scale for
carbon segregation. A subsequent data reduction and statistical representation
of this dataset provides critical information such as about the mean
segregation energy and the associated energy distributions for carbon atoms as
a function of distance from the grain boundary, which quantitatively informs
higher scale models with energetics and length scales necessary for capturing
the segregation behavior of impurities in Fe. The significance of this research
is the development of a methodology capable of ascertaining segregation
energies over a wide range of grain boundary character (typical of that
observed in polycrystalline materials), which herein has been applied to carbon
segregation in a specific class of grain boundaries in iron.
