**Author details**

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

**Figure 7.** The cohesive energy of Nickel Σ5 GB with impurity type in it, element in X axes represents the impurity type

In this work, we conduct analyses about the influence of segregated impurities on the properties of nickel grain boundaries. The problematics and controversy of results posed here have a dual character: fundamental and industrial. The selected impurities are eight light elements and eleven transition metals elements of the periodic table. The adopted methodology for this study was based on density functional theory widely used in recent years to predict the mechanical response of materials and their tenability as a function of alloying

After optimization study, we have shown that the norm-conserving approach together with local density approximation is best suited to solve convergence problems as well as to give accurate results in the case of metallic systems. Furthermore, different GB models have been

and the mirror symmetries in the normal direction to the GB plane (210).

(one atom) generally located on Site1. Data 1 taken from Ref. [19].

used in order to fulfill the required calculated property.

**4. Conclusion**

14 Study of Grain Boundary Character

additions.

Ibne Khaldoun Lefkaier1 and El Tayeb Bentria<sup>2</sup> \*

\*Address all correspondence to: ik.lefkaier@lagh-univ.dz

1 Materials Physics Laboratory, University of Laghouat, Laghouat, Algeria

2 Qatar Environment and Energy Research Institute (QEERI), Hamad Bin Khalifa University, Doha, Qatar
