**3. Results and discussion**

#### **3.1. Nickel Σ5 STGB**

In order to verify whether the present GGA norm-conserving pseudopotentials (NCP) basis sets are suitable to our Ni GB model, we calculated surface and grain boundary energies presented in Eq. (1) of Nickel GB and compare them with known results of previous experimental and theoretical works (**Table 2**). Indeed, our result agrees well with both experimental results and previous theoretical calculations (see **Table 2**). Thus, we have a strong confidence in the constructed GB configuration of this work.

The calculated total DOS (TDOS) for the grain boundary model (**Figure 5**) appears to have similar characteristics to that of the bulk, that is, the trend of the plot and the density of electrons values are close to each other, and also that the d-bonds are the responsible for bonding, which means that there is no major change in the metallic bonding.

Now we study the difference between Ni atom in perfect bulk and Ni atom in the GB region. From **Figure 5**, we take site 1 as example, because it represents well the different in environments, and we remark that there is a DOS shape compression of the Ni at GB. The difference is much remarkable for the d states that vary from −5 to +3 eV for Ni in the bulk and narrowed for the site1 from −5 to +0.5 eV (**Figure 5**). This compression happened more in the conduction which mean that the GB region reduces electric conduction (barriers) because we know that the electric conduction depends on the electron density around Fermi level [15].

Chen et al. [16] calculate partial DOS (PDOS) for different layers and show that the GB has a significant effect on the shape of d-DOS, and show that at layer 4 the d-DOS became indistinguishable from that calculated for the bulk atom; we could conclude that the effect of the grain boundary in Ni binding disappears totally in the 4th layer.


**Table 2**. Calculated grain boundary (GB) energy and free surface (FS) energy of Ni Σ5(210) GB (in J m−<sup>2</sup> ) [28]. The Effect of Impurities in Nickel Grain Boundary: Density Functional Theory Study http://dx.doi.org/10.5772/66427 9

**Figure 5.** Total and partial density of stated for Ni atom in bulk and in site 1 of the grain boundary.

In both cases, the magnetic moments of Ni increase when we move from GB until it reach the bulk value from the 6th layer on [10], which is also remarked here.

#### **3.2. The effect of light elements "B, P, O, N, Al, Si, S, C" in NiΣ5 GB**

In this part, we discuss our results of tensile strength which is uncovered topic for these eight light elements except B and S which is already calculated [17, 18]. We compare our results of segregation and binding energy with the available experimental and theoretical calculations.

#### *3.2.1. Phosphor impurity effect*

The maximum of *f*′(*x*) is at *x* = *λ* and corresponds to the maximum theoretical tensile stress or

′

The **Figure 4** represents a calculated example that shows the variation of total energy in Fe Σ3(111) GB with boron impurity segregate in site 0, and the value of the 2*γ* is 5.41 J m−2; thus, the cohesive energy *γ* is 2.70 J m−2. The tensile strength is plotted by evaluating the derivative

In order to verify whether the present GGA norm-conserving pseudopotentials (NCP) basis sets are suitable to our Ni GB model, we calculated surface and grain boundary energies presented in Eq. (1) of Nickel GB and compare them with known results of previous experimental and theoretical works (**Table 2**). Indeed, our result agrees well with both experimental results and previous theoretical calculations (see **Table 2**). Thus, we have a strong confidence

The calculated total DOS (TDOS) for the grain boundary model (**Figure 5**) appears to have similar characteristics to that of the bulk, that is, the trend of the plot and the density of electrons values are close to each other, and also that the d-bonds are the responsible for bonding,

Now we study the difference between Ni atom in perfect bulk and Ni atom in the GB region. From **Figure 5**, we take site 1 as example, because it represents well the different in environments, and we remark that there is a DOS shape compression of the Ni at GB. The difference is much remarkable for the d states that vary from −5 to +3 eV for Ni in the bulk and narrowed for the site1 from −5 to +0.5 eV (**Figure 5**). This compression happened more in the conduction which mean that the GB region reduces electric conduction (barriers) because we know that the electric conduction depends on the electron density around Fermi level [15]. Chen et al. [16] calculate partial DOS (PDOS) for different layers and show that the GB has a significant effect on the shape of d-DOS, and show that at layer 4 the d-DOS became indistinguishable from that calculated for the bulk atom; we could conclude that the effect of the grain

**J.m−2 Our NCP PP-PAW US-GGA Exp. (polycrystal)**

, 1.33<sup>c</sup> 1.41<sup>e</sup> 0.93<sup>d</sup>, 1.24<sup>f</sup>

. 2.40<sup>e</sup> 2.59<sup>d</sup>, 2.02<sup>f</sup>

) [28].

, 1.43b

, 2.65b , 2.29<sup>c</sup>

**Table 2**. Calculated grain boundary (GB) energy and free surface (FS) energy of Ni Σ5(210) GB (in J m−<sup>2</sup>

(*<sup>λ</sup>* ) <sup>=</sup> *<sup>e</sup>* −1 <sup>2</sup>*γ*\_\_\_

*<sup>λ</sup>* (6)

tensile strength *σMax*; therefore,

8 Study of Grain Boundary Character

**3. Results and discussion**

**3.1. Nickel Σ5 STGB**

*σMax* = *f*

in the constructed GB configuration of this work.

which means that there is no major change in the metallic bonding.

boundary in Ni binding disappears totally in the 4th layer.

GB energy 1.23 1.23<sup>a</sup>

FS energy 2.53 2.34<sup>a</sup>

a Ref. [18]. b Ref. [20]. c Ref. [13]. d Ref. [5]. e Ref. [29]. f Ref. [30].

of Rose function *f*′(*x*) with function of separation distance x.

Controversy regarding the role of P in the Ni GB, Geng et al. [19] proved that P is an embrittler to Ni GB by means of atomic distances, electronic structures and the RWEP. In contrast, Masatake et al. [20] declared that P has a beneficial effect on the Ni GB cohesion, which is in contradiction with previous calculations. While Všianská et al. showed that interstitially segregated P has none or negligible strengthening effect on Ni GB by studying the RWEP. Liu et al. [4] decide to reach a more profound conclusion by calculation of phosphor effect with function of concentration. They found that when the concentration of P is relatively low (0.25–0.5 monolayer, i.e., Np = 1–4; **Figure 6**), P tends to bond strongly with the neighboring Ni atoms, which is beneficial to the GB cohesion.

In the meanwhile, P draws charge from these Ni atoms and removes electrical charges from the Ni–Ni bonds to weaken them. As the P concentration increases (Np = 5–7), P atoms get close and exert a repulsive interaction on each other, thus result in a thin and fragile zone in

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

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 as embrittler.

#### *3.2.2. Oxygen and sulfur impurity effect*

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

Our results show that oxygen impurity present a clear embrittlement to the Ni GB, with the strongest reduction in the cohesive energy that reaches 3.08 J/m<sup>2</sup> of Ni GB. The TTS presents a 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 the binding energy of oxygen very large and cause a GB expansion which leads to embrittlement. Furthermore, some experimental observations about the effect of oxygen in NBS by Bricknell and Woodford [21] describe some results and observations on air embrittlement of a commercially pure nickel (Ni200) and show that oxygen was the damaging species and that nitrogen was innocuous. They mention that "*the high concentration of sulfur at the boundaries made oxygen detection by Auger analysis extremely difficult. However, direct evidence for grain boundary oxygen penetration was provided by the formation of various oxygen containing compounds, which were readily observed using scanning electron microscopy"* [21].

Yamaguchi et al. [13] perform comparison between calculated tensile strength for different sulfur impurity concentrations and compare them with experimental ultimate tensile strength with the same concentration of FCC Ni GB [13]. One can see that the order of the tensile strength largely differs between experiment and calculation, and both of strengths are reduced by one order of magnitude with increasing sulfur concentration [13]. The discrepancies in values are due to many reasons. The most plausible of them is the fact that DFT simulations are done for a small model of one symmetrical tilt grain boundary without taking in account the dislocations, while experimental fracture occurs at various kinds of grain boundaries (random grain boundaries, etc.) associated with dislocation emitting. Considering these facts, the agreement between behavior of TTS calculations and experiments seems to be reasonable.
