In metallic materials, where grain boundaries(GB) are of crucial importance, impurities and alloying elements play an important role in determining their physical and mechanical properties because the behavior of a grain boundary may change drastically with the presence of impurities and alloying elements. For example, in iron and its alloys, including industrially important steels, the intergranular embrittlement is usually associated with segregation of impurities, like P and S, toward the GBs. On the other hand, alloying elements, like Mo and Pd, are helpful for intergranular cohesion in iron, due to either direct cohesion effect or effect upon embrittling potency of other impurities. Understanding the mechanisms of impurity-promoted embrittlement and the consequent cohesion(decohesion) effects is becoming more and more important and remains as a challenge for materials scientists. There have been intensive investigations on these mechanisms for a long time and with the progress in computing techniques in recent years, calculations on more realistic representations of impurity-doped grain boundaries have become possible[1–4].