*3.2.4. Aluminum and silicon impurity effect*

These two elements are juxtaposed on the same colon, that is, they have the same electron number in valence band. These elements take the less attention in the computational side due to their indecisive effect and controllability of their existence in experiments [22].

Geng et al. [19] have expect that aluminum and silicon, which have similar atomic size and bonding as phosphorus, would be embrittler for Nickel ∑5(210) GB. Later on, Všianská and Šob [10] have calculated the segregation energy and embrittlement potency and show that, contrary to the Geng prediction, Si acts as enhancer with Rice WEP −0.41, and Al has no significant effect in Ni GB with RWEP −0.03.

For Silicon, our results confirm Šob findings, but they go more to Geng prediction for Al which presents more embrittlement character with RWEP +0.16. Beside Geng and Šob approaches, our results expected to be more accurate with the calculation of the cohesive energy and the TTS, which show embrittlement of Al impurities to 24.6 GPa, and a little enhancement of Si impurity to 28.2 GPa, and validate the RWEP values.

### *3.2.5. Carbon and nitrogen impurity effect*

Siegel and Hamilton [31] have studied carbon segregation and diffusion within a Nickel ∑3 grain boundary and show that interstitial site is preferred for the magnetic and nonmagnetic cases. But the author did not calculate the strengthen effect. In 2008, Sanyal et al. [23] have talked about the strengthen effect of carbon impurity in Nickel ∑5(210) GB using the cohesive energy values. They founds decries of the cohesive energy from 3.60 to 3.54 eV, in which they concluded that C acts as embrittler. Using a 20 atoms model, Masatake et al. [20] have found negative RWEP which means that C acts as cohesive enhancer. Contrarily, Young et al. [24] find positive RWEP with 40 atom models which confirm that C is an embrittler impurity. This result is in agreement with our 2 × 2 64 atoms model, in which we found enhancement in cohesive energy, TTS and negative RWEP. This controversy in results is mainly due to the model number of atoms, and thus, we confirm the remark of [25] that low segregation energy can give wrong values.

For the Nitrogen case, we found that N impurity atom results a positive RWEP and a lower cohesive energy, but with a small enhancement in the TTS. This value of TTS is not in agreement with the RWEP and cohesive energy. RWEP results in [20] agree well with our RWEP finding for the non-spin calculation, taking into account the loose in cohesive energy of a GB with N impurity. Taking in to account the result of Masatake and as mention above that the total energy and forces of some elements mainly for N do not converge to the required criteria for some fracture cases, we can conclude based only on the two factors (RWEP en Ecoh) that N is embrittler.

#### *3.2.6. General tendency*

Young et al. [24] have put the order of the impurities effect from most embrittling to most strengthening, the impurity elements are ranked as He, Li, S, H, C, P, Fe, Mn, Nb, Cr, and B. Helium is strongly embrittling (+1.07 J/m<sup>2</sup> lowering of the RWEP), while phosphorus has little effect on the grain boundary (−0.05 J/m<sup>2</sup> ), and boron offers appreciable strengthening (−0.54 J/m<sup>2</sup> increase in RWEP). These findings are consistent with experimental observations (e.g., He, S and H are known embrittling agents and boron is a known strengthener in nickel-base alloys). This classification is in excellent agreement with our tensile strength results even the paper was conducted on ∑5 twist Ni GB along, which give us more confidence that the study of the effect of impurity in one type of GB could lead us to general result about its behavior in other type of Ni GBs.
