*3.2.3. Boron impurity effect*

the GB. Our calculation corresponds to configuration 2P (Np = 2) corresponding to 0.5 atom/ ML at GB see [4], which is favorable from the energetic point of view of Liu (**Figure 6**). The largest segregation energy in Liu is −1.45 eV correspond to 4p concentration. This value is in agreement with ours about −1.77 eV for 1p concentration. The results of tensile strength are different from ours due to the different methods and approximation used for TTS calculation. Moreover, our results for segregation energy are much closer to Všianská et al. (Eseg = −1.6 eV). We found that P has embrittlement effect for this concentration, with positive RWEP, confirmed by the value of TTS (24.4 GPa) and with little decries of cohesive energy to 3.44 eV. For concentration 4P (Np = 4) (1atom/ML), we calculate the TTS, appear to be much lower than Liu value and correspond to 22 GPa with cohesive energy of 3.3 eV that confirm the increase of the embitterment effect with the increasing of the P concentration. Our results for two P concentrations show that there is no enhancing effect of phosphor impurities and acts always

**Figure 6.** The variation of TTS with function of concentration. The case of NP = 1 represents the GB with 1 P atom in layer 0 or 2, and the case of NP = 4 represents the GB with 4 P atoms in layer 0 or 2. In the range of NP = 5–7, layer 0 is fully

Oxygen and sulfur have very destructive effect on the Ni GBs. This is clear from tensile strength values presented in, which reduce TTS by 23%. Sulfur is always considered as the most damaging embrittler due to its inevitable existence sometimes in industrial processes. Many experimental and theoretical studies were carried out about its effect [10, 13]. In the other hand, oxygen didn't get that attention at least for theoretical calculation. Here we try to

Our results show that oxygen impurity present a clear embrittlement to the Ni GB, with the

value of 21.1 GPa and the largest RWEP (1.48 eV/atom). Všianská and Šob [10] explain that by the fact that isolated oxygen atom has a large magnetic energy, which is the reason for making

of Ni GB. The TTS presents a

focus more on the effect of oxygen and mention some literature reviews.

strongest reduction in the cohesive energy that reaches 3.08 J/m<sup>2</sup>

occupied by 4 P atoms and layer 2 is occupied by 1–3 P atoms, data from Ref. [4].

as embrittler.

10 Study of Grain Boundary Character

*3.2.2. Oxygen and sulfur impurity effect*

Masatake et al. [20] have calculated the embrittling potency energy of some light elements and show that boron has the best enhancing value for these impurities. This is also the case here. Later then, with 80 atom Ni FCC model, Kart and Cagin [18] investigated the effects of boron segregation at the Ni ∑5(210) GB in the four interstitial possible positions. They found that increment of the boron atom in the GB site 0 increases the value of the theoretical tensile strength for Ni. Using GGA approximation, they show that the stresses for the GB including one, two, three and four boron atoms are evaluated as 24, 26, 25.8 and 27 GPa, with 23 GPa for the pure GB. Our calculations are relatively in a good agreement, with 37.6 GPa for two boron atoms in GB and 27.6 GPa for the pure Ni GB. The difference in TTS results is due essentially to different TTS calculation methods, which is with GGA approximation known to give lower TTS value than our method approximation (LSDA). All these works agree together that boron is an enhancer to Ni GB. In our calculation, boron presents the highest tensile strength and also the highest RWEP of −0.94 eV. This makes him the best impurity type in the considered eight light elements.
