**1. Introduction**

The theoretical investigation of mechanical properties of materials, by means of first-principle calculation and molecular dynamics, has known remarkable advances over the past 15 years [1]. These investigations relate directly to the intergranular behavior, which together with dislocation-based mechanisms determine mechanical response of materials with granular structures. Molecular dynamics calculations can give fundamental understanding of the effects of impurity segregation at GBs in order to predict the mechanical response of materials and their tenability as a function of alloying additions. On the other hand, first-principles calculations

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can be quite effective in developing this understanding. We can assess whether an impurity is a cohesion enhancer and causes the strengthening of the GB or is an embrittler and induces the weakening of the GB, while experimental techniques are difficult to investigate one impurity alone without the influence of other impurities.

First-principle calculations are widely used for metals and alloys. Grain boundaries of iron make a large part of these investigations. Impurity segregation to the GB in iron is described and understood relatively well, both theoretically and experimentally. In contrast, this is not the case of GB in nickel. The experimental information is quite rare [2]. In recent years, many efforts have been devoted to theoretically determine the effect of impurities on nickel grain boundaries, motivated by the industrial challenges facing fabrication and aging of nickel-base superalloys [3].

It is already well known, both experimentally and theoretically, that sulfur acts as an embrittling element in nickel grain boundary and boron acts as enhancing element [3]. Some other elements like phosphorus are not that clear from first-principle calculations and became a subject of debate between strengthen and embrittling [4]. In contrast to light elements, influence over Ni grain boundaries of alloying elements took less attention [5]. The main elements for this purpose are transition metals, and the most important of them are elements of columns IV–VII and periods 4–6 of the periodic table.

Even though some of these element impurities effects have been studied theoretically, it is remarkable that there are still no comparisons between the effects of theses element in the GB. This is because it is hard to make comparison between results of different works due to the differences in impurity concentrations, GB models, number of atoms per unit cell, methods of calculations and type approximations used. We think that it is important now to have a systematic study to find the most enhancing and the most embrittling elements on Ni GBs. This knowledge can be used also to optimize the material properties as we are trying to understand the mechanisms and effects of different impurity atoms.

This chapter is divided in two parts. Part I is about the methodology of our calculations. Part II describes and discusses the obtained results, and it is organized as follows. First, details of calculation of the effect of Vanadium and Niobium in Nickel GB are exhibited. The effect of light elements "B, P, O, N, Al, Si, S, C" in NiΣ5 GB and surface and also of transition metal elements "Ti, V, Cr, Mn. Zr, Nb, Mo, Hf, Ta, W, Re" in NiΣ5 GB and surface are presented and discussed. Finally, a main conclusion is drawn.
