**3.3. The effect of transition metal elements "Ti, V, Cr, Mn. Zr, Nb, Mo, Hf, Ta, W, Re" in NiΣ5 GB**

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 sig-

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

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

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

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.

 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

lowering of the RWEP), while phosphorus has little

), and boron offers appreciable strengthening (−0.54

nificant effect in Ni GB with RWEP −0.03.

12 Study of Grain Boundary Character

*3.2.5. Carbon and nitrogen impurity effect*

can give wrong values.

N is embrittler.

J/m<sup>2</sup>

*3.2.6. General tendency*

in other type of Ni GBs.

Helium is strongly embrittling (+1.07 J/m<sup>2</sup>

effect on the grain boundary (−0.05 J/m<sup>2</sup>

impurity to 28.2 GPa, and validate the RWEP values.

Light elements are, in general, known as embrittling agents for Nickel, whereas transition metal elements are known as the main enhancing alloying impurities. Even though these elements have been subject of intensive thermodynamic based studies for their effects on Nickel as impurities, there is a lot of discrepancy in results of different models [19]. Nevertheless, there are few works which treat it by quantum mechanical approaches [23, 24]. Razumovskiy et al. [5] calculated the segregation energy, partial cohesive energy and RWEP for W, Zr, Hf, Bi, S, B, Ta and Re. While writing this work, another work from Ref. [3] conducts a study of purpose to the design of Ni-base polycrystalline superalloys by studying the influence of a wider range of transition metal elements on grain boundary segregation and bulk cohesion in Ni ∑5(210) GB.

In this paragraph, we compare and discuss the results of segregation energy and tensile strength for some elements mentioned in other works. Hf impurity shows an important RWEP of −0.61 in agreement with Razumovskiy et al. value of −0.69 eV/atom. Sanyal et al. [23] found that Hf was favored at the GB by +0.8 eV/atom relative to that in the bulk. Hf is experimentally found to strengthen GBs [26]. In this work, we add more information about its effect by TTS calculation. We predict that Hf is not a good enhancer if available alone in the GB. Its existence in Ni GB with other embrittling elements such as sulfur further should be studied. The high segregation energy of Hf may compete S segregation to Ni GB and overcome its undesired effect.

Ta has the highest RWEP among transition metals with a large cohesive energy of +5.22 eV and second largest TTS after W. Ta is hence one of the best enhancer. We found a negative and large value of segregation energy at GB for Ta −0.91 eV. Similar conclusion was also drawn by [5].

If we referee to our calculated results about Cr additions, this element does not prefer to be at the GB region, but rather to the surface. Even though, it presents a positive RWEP. Its effect in the GB if existed is not harmful and doesn't affect considerably the cohesive energy and TTS calculations. The later result is confirmed by the small negative RWEP value of Cr in Young work [24].

W has the largest cohesive energy, the highest TTS and a very important RWEP. Based on these factors, we can say that W is the best enhancer among the 12 considered transition metals elements with small difference with Ta. Represents high cohesive energy, but it does not have the highest tensile strength, in accordance with Tahir's work [27] that cohesive energy does not give full presentation of enhancement/embrittlement.

Based on other first-principles method calculations (full-potential linearized augmented plane-wave method FLAPW). Geng et al. [19] calculated that the cohesive energy for all transition metals elements in order to, unambiguously, predicts the effect of a substitution alloying addition on grain boundary cohesion of metallic alloys. **Figure 7** presents a comparison between our calculated values for the cohesive energy and those obtained by Gang et al. [19]. We notice that even there is a similar trend in both results (e.g., W has the largest cohesive

**Figure 7.** The cohesive energy of Nickel Σ5 GB with impurity type in it, element in X axes represents the impurity type (one atom) generally located on Site1. Data 1 taken from Ref. [19].

energy followed by Re and Ta approximately with the same value and so on), and the cohesive energy values are quite different. **Figure 7** shows that the cohesive energy from our calculations varies in the range [+5.6 to +4.6 eV], while Geng results fluctuate largely from +8.66 to +2.98 eV. Geng results seem to be less accurate than ours. For example, Geng calculated cohesive energy for W impurity at Ni GB and found 8.66 eV, 2.4 time larger than our value and other known pure GB cohesive energies [19]. This value (8.66 eV) could lead to very high value of tensile strength equal to 65 GPa and vice versa 22 GPa for Mn (lower than sulfur), which are simply not reasonable for the magnitude range of Ni-TTS. We think that these fluctuations are first due to the number of atoms (22 atoms) in Geng model, which leads to highest segregation energies and therefore higher effect on the GB TTS. Also, the relaxation of atomic positions was only done in the normal direction to the GB plane and ignored in both lateral and the mirror symmetries in the normal direction to the GB plane (210).
