Cite this Article
Liu Xiang-Yue, Zhang Hong, Cheng Xin-Lu. Effect of nickel segregation on CuΣ9 grain boundary undergone shear deformations. Chinese Physics B, 2018, 27(6): 063103  
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Effect of nickel segregation on CuΣ9 grain boundary undergone shear deformations
Liu Xiang-Yue1, Zhang Hong1, 2, 3, †, Cheng Xin-Lu1
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610065, China
College of Physical Science and Technology, Sichuan University, Chengdu 610065, China

 

† Corresponding author. E-mail: hongzhang@scu.edu.cn

Abstract

Impurity segregation at grain boundary (GB) can significantly affect the mechanical behaviors of polycrystalline metal. The effect of nickel impurity segregated at Cu GB on the deformation mechanism relating to loading direction is comprehensively studied by atomic simulation. The atomic structures and shear responses of Cu Σ9(114) ⟨110⟩ and Σ9(221) ⟨110⟩ symmetrical tilt grain boundary with different quantities of nickel segregation are analyzed. The results show that multiple accommodative evolutions involving GB gliding, GB shear-coupling migration, and dislocation gliding can be at play, where for the shear of Σ9(114) ⟨110⟩ the segregated GBs tend to maintain their initial configurations and a segregated GB with a higher impurity concentration is more inclined to be a dislocation emission source while maintaining the high mechanical strength undergone plastic deformation for the shear of Σ9(221) ⟨110⟩. It is found that the nickel segregated GB exerts a cohesion enhancement effect on Cu under deformation: strong nickel segregation increases the work of separation of GB, which is proved by the first-principles calculations.

PACS: 31.15.xv;62.20.-x;61.72.sd;74.62.Dh;
Keyword:grain boundary segregation;nickel impurity;first-principles calculations;cohesion effect;
1. Introduction

Understanding the function of grain boundary (GB) is of great importance for regulating the properties of polycrystalline materials on a nanoscale, which suggests that the change of grain size can significantly affect the plasticity of material according to the Hall-Petch relationships.[1–4] It is well established that the GB would act as a heterogeneous nucleation source for emitting dislocations or a barrier to dislocation sliding, which would facilitate multiple deformation behaviors during external loading such as GB sliding, GB migration, local dissociation, mechanical twins, etc.[5,6] The accumulation of various defects tend to maintain a high concentration in the disordered region in GB generally.[7] Embrittlement or cohesion enhancement induced by impurity segregation at GB has been extensively analyzed.[8–13] Experimentally, impurity segregation phenomenon can be commonly investigated by transmission electron microscopy (TEM), electron backscattered diffraction (EBSD), atom probe tomography (APT) and Anger electron spectroscopy techniques.[14–16] Meanwhile, atomic scale simulation is also an essential approach to the exploration of the mechanism of how the GB segregation affects the mechanical properties of materials from energetic and electronic aspects.[17–19] According to the first-principles calculations, Lozovoi et al.[20] have determined that the embrittlement of impurity segregation is attributed to either structure effect or electronic effect in a binary copper alloy. Zhang et al.[21] further analyzed the effect of dense impurity segregation at GB on the plastic evolution of aluminum alloy. The cohesion influences of Mg, S, P segregated at tilted GB have been investigated by Li et al.,[22] indicating that chemical contribution plays a major role in GB cohesion. In Ref. [23], Chen et al. have proposed a theoretical model regarding the quasi-thermodynamics and the kinetics of non-equilibrium GB segregation and predicted the P nonequilibrium segregation induced by high temperature deformation. The recent atomic-level study reported by Zhao et al.[24] clearly showed the effects of Mg, Cu impurity segregation at GB in Al from the aspects of GB structure, charge density evolution and tensile strain. Besides, Cai et al.[25] have proved that the segregated elements could stabilize the grain size and strengthen the mechanical properties of nano-crystals experimentally.

Cu–Ni alloys have wide applications due to their high electrical resistance and low temperature coefficient.[26] Normally, Ni segregated at Cu interface or surface can hardly be observed by experimental means on account of their completely mutual miscibility and no obvious impurity-induced embrittlement effect. Nevertheless, Divinski et al.[27] proved that Ni impurity can be moderately segregated in Cu–Ni alloy, measured by the radiotracer technique. For a better understanding of segregated GB deformation mode, such an external loading is necessary to bring about plastic and fracture process.[28] Consequently, the influence of nickel enrichment at GB is well worth exploring through the combination of density functional theory (DFT) and molecular dynamic (MD) simulations. In this paper, the shear responses of Σ9(114) and Σ9(221) GB with different impurity concentrations are investigated by the MD simulations where the deformation process can be visually displayed on a large atomic scale. The DFT method is adopted to realize the accurate energetic calculations. Attention is paid to the difference among GB coupling motions with various dopants. The rest of this study is organized as follows. In Section 2, we describe the modelling process and the computing method in detail, and the simulation results and analysis are presented in Section 3. And finally, some conclusions are drawn from the present study in Section 4.

2. Modelling and simulation approach

The original cells of CuΣ9(114)/[110] and Σ9(221)/[110] symmetric tilt GB were constructed by joining two separate (upper and lower) grains with the determinate lattice orientations. The details of models are listed in Table 1. The boundary is parallel with the xz plane that was repeated periodically in the X and Z dimensions to represent the extended GB structure, while nonperiodic boundary condition was imposed along the Y direction. We constrained several layers of atoms near the top/bottom surface of the upper/lower grain, and the rest of atoms were set to be dynamic. A conjugate-gradient algorithm was used to prepare the energy minimization of GB structure. To acquire the impurity enrichment at GB, a certain number of solute atoms around GB were replaced by Nickel randomly. The segregation models are illustrated in Fig. 1 and the model without impurity substitution is also shown here for reference, in which the doping quantities are 0.7 at.%, 1.6 at.%, 4.3 at.% correspondingly. Owing to similar atomic radius, the volume of simulation box might not be changed after nickel segregation. Prior to deformation loading, the initial equilibrium of the whole system had been achieved at 10 K and zero external stress state under constant pressure condition (NPT ensemble, where the NPT refers to constant-pressure and constant-temperature) for at least 15 ps. The effect of thermal stress could be ignored under the ambient temperature. Afterwards, the shear deformation was carried out by applying a homogeneous shear strain at a constant rate of 108 s−1 for about 2000 ps. Several shear directions of (114) GB and (221) GB models, which are aligned with , ; , respectively, were chosen to identify different mechanisms of responses. The common neighbor analysis (CNA) manner was used to detect the lattice imperfection during shear loading.[29] Throughout this work, all MD simulations are performed via adopting the LAMMPS package, unless otherwise stated,[30] and using the embedded-atom-method (EAM) potential to account for the interatomic interaction. The atomic motion of both the pure Cu model and Cu-Ni model are described by EAM-type potential fitted by Berk et al.[31] The visualization tool, Ovito, was employed to produce atomic configuration.[32] Besides, the coincidence site lattice (CSL) theory was used in our work to facilitate the analysis of the GB character changes under plastic deformation.

Fig. 1. (color online) Segregation models in MD simulations, showing impurity concentrations at high-angle GB in Cu displayed in projection, adding varying levels of nickel.
Table 1.

Orientation details of bicrystal cells.

.

Furthermore, to study how the concentration of GB segregated dopants affects the mechanical properties, the first-principles calculations were performed by employing VASP code.[33,34] The exchange correlation effects were described employing the generalized gradient approximation of Perdew–Burke–Ernzerhof functional (GGA-PBE).[35] A plane-wave cutoff energy of 500 eV and a suitable Gamma-centered k-point mesh were used for the geometry optimization. The global convergence criteria for electronic self-consistent cycles and interatomic force were set to be 1 × 10−5 eV and 0.01 eV/Å, respectively. Figure 2 shows the supercells containing Σ9(114) and Σ9(221) symmetric tilt GBs with different concentrations of Ni dopants which correspond to the segregation models in MD simulations approximately shown in Fig. 1. The Gibbs free energy can be assumed to be the total energy of system when the temperature tends towards zero.

Fig. 2. (color online) Supercells containing (a) Σ9(114) and (b) Σ9(221) symmetric tilt GB, with the black dotted lines marking the computationally repeated cells; ((c) and (d)) colored drawings of the various impurity concentrations denoting models A–C, in which the impurity atoms are segregated in GB region partially or segregated at GB totally or segregated at GB and grains partially through substituting solute atoms; (e) atom sites marked by numbers.
3. Results and discussion
3.1. Shear responses of Σ9(114) GB and Σ9(221) GB with various segregated Ni impurity concentrations

The deformation response and energy calculations concerning the segregated Σ9(114) and Σ9(221) symmetric tilt GB are discussed below.

3.1.1. Shear responses of Σ9(114) GB

(i) Considering the overall presentation of the shear process, the stress–strain curves of pure Cu (black), Cu-0.7 at.% Ni (red), Cu-1.6 at.% Ni (green), Cu-4.3 at.% Ni (blue) model with Σ9(114)/[110] GB are plotted in Fig. 3(a) at 10 K, loading in the direction. The first peak of shear stress of Cu-4.3 at.% Ni bicrystal is higher than those of other three systems, on account of its stable structure and high shear strength. The first sudden drop in each of shear stress curves corresponds to the GB migration coupling to GB sliding procedure. Subsequent trends of curves are irregular, which might manifest more complicated mechanical evolutions involving the intrinsic changes of GB structure and the plastic activities.

Fig. 3. (color online) Mechanical deformations of pure Σ9(114)/[110] Cu bicrystal and with different content values of Ni GB segregation, shearing along (a) and (b) at 10 K, respectively. Pure Cu structure was expressed as Cu (Cu–Ni base) because of the use of interatomic potential.

Some typical MD snapshots are selected to display the concrete deformation processes as shown in Figs. 5–8. For shear along , none of the features of Σ9(114)/[110] GB mechanical responses in four models is identical. For pure Cu, the structure units of GB are changed partially after migrating as shown in Fig. 5(a). During the GB migration coupling motion, the additional elements with the larger size remain in situ. The intrinsic stacking faults manifested by two adjacent hcp atom layers are generated during external loading, kept up with the leading Shockley partials (b = (1/6)⟨112⟩). The perfect lattice dislocations (b = (1/2)⟨110⟩) and Frank partial (b = (1/3)⟨111⟩) also nucleate in quantity to release the stress concentration undergone plastic deformation in Figs. 7(b) and 7(c). Meanwhile, GB dissociates into several pieces, all connected via twin boundary identified by one single hcp atom layer. The black arrow as shown in Fig. 5 indicates the degree and distance of the GB migration relative to the GB initial position.

Fig. 4. (color online) Coincident lattice site diagram of Σ9(114) GB in fcc crystal. Two different atomic radii do embody different {110} crystallographic planes. Orange balls are for upper grain, while blue for lower. Green spheres denote the coincident sites. Red solid line represents the unit structure of GB. Herein, T1b denotes a transitional form of T1a and T2 refers to another type different from the former two. T1a denotes original structure of Σ9(114) GB throughout the paper, which results from energy relaxation.
Fig. 5. (color online) Representative CNA snapshots of pure Cu (Cu–Ni base) configurations with Σ9(114) GB under shear deformation along direction at 10 K. In all CNA figures throughout this paper, atoms in yellow, blue and red refer to those in fcc, other, hcp structure, respectively. Purple line portrays the GB structure units in the enlarged view of z projection. Panels (a)–(c) show patterns at a shear strain of 0.093, 0.162, 0.248, respectively. The initial position of GB marked by black dotted line, and the black arrows demonstrate the migration direction of GB.
Fig. 6. (color online) Typical CNA snapshots of the Cu-0.7 at.% Ni bicrystal configuration with Σ9(114)/⟨110⟩ GB under the shear loaded along direction. Increasing the radii of impurity atoms to over 15 times those of solute atoms is for differentiating between those atoms easily in sequential figures. Purple arrow indicates the emitting partial dislocation, while the stair-rod dislocation and twin boundary are denoted by circle and dotted box. The applied strains in panels (a)–(c) are 0.071, 0.161, 0.263, respectively.
Fig. 7. (color online) Atomic configurations of the Cu-1.6 at.% Ni bi-crystal with Σ9(114) GB under the shear deformation along direction at strains of 0.071, 0.169, 0.264, respectively. SF1 represents extrinsic stacking fault caused by Frank leading dislocation.
Fig. 8. (color online) Representative CNA snapshots of Cu-4.3 at.% Ni bicrystal with Σ9(114) GB under the shear deformation along direction. SF2 exhibits the intrinsic stacking faults, accompanied with the leading partial dislocation motion. Under loading shear strain ε = 0.099, 0.192, 0.274 structures are changed as shown in panels (a)–(c) correspondingly.

The transformations of GB configuration in the four cases are approximately identical under the condition of small strain (T1a → T2, described in Fig. 4), in which the GB has migrated and both T1a and T2 types do coexist. However, with the further increase of applied loading, the GB tends to maintain its preliminary structure type (T1a) instead of dissociating locally in each of Cu-0.7 at.% Ni, Cu-1.6 at.% Ni, and Cu-4.3 at.% Ni bicrystals as presented in Figs. 6(b), 7(b), and 8(b), respectively. In this deformation stage, partial dislocations with both screw and edge characters emitting from GB may cross each other and form the stair-rod (Lomer–Cottrell lock b = (1/6)⟨110⟩), further migration process is accompanied with atomic shuffling, partial nucleation and dislocation activities. The GB structures may transform from the state of T1a and T2 coexistence into T1a type during GB coupling motion. Figures 6(c), 7(c), and 8(c) indicate that the degree of GB decomposition may be much smaller in the simulation model with the varying nickel segregation at a large strain, than in pure Cu model. The formation of GB step in Figs. 6(c) and 6(d) might be the consequence of the GB dislocation nucleation and motion. From Figs. 5–8 it follows that the activities of dislocations staying upper crystal in the Cu bicrystal with GB segregation are much negative than that in the case of pure Cu, which implies that the dislocation propagation could be pinned by adding the segregation elements effectively to impede the grain thickening or growing to some extent.

(ii) As shown in Fig. 3(b), curves shearing along the direction at 10 K display irregular fluctuations, which are not consistent with the former cases. The critical shear stress of Cu-1.6 at.% Ni bicrystal (σ = 2.42 GPa) is higher than the other ones. After sudden drop of stress reaching the first maximum stress point, another obvious strain-hardening stage identified by the second threshold stress point appears in each of pure Cu cell and Cu-0.7 at.% cell, while the model with higher-concentration GB segregation is inclined to experience the strain-softening stage. The four rough curves all present the disciplinary serration elatively after the shear strain ε > 0.15, which may result from the regular GB sliding and structure transformation.

Figures 9–12 show the deformation behaviors of Σ9(114) GB, shearing along [110] direction. For pure Cu model as illustrated in Fig. 9, the GB remains at its initial position without migration or dislocation activities. And the GB structure units have been portrayed in the enlarged view of figure in different stages, which go through the T1a → T2a → T2 transformation to relieve stress in system. Figure 10(a) indicates that, with 0.7 at.% substantial Ni added into GB surrounding, the initial structure units T1a might be transformed into T2 partially at a corresponding small strain, while the defects distributed in GB may increase with the increase of GB segregation concentration in this stage shown in Figs. 11(a) and 12(a). Note that the nucleation and radiation of Shockley partial and full dislocations, twins and stacking faults can be seen in Figs. 10–12, accompanied with atom shuffling and the GB structure units changing during GB coupling motion. In this case, the distribution of impurities around boundary is equivalent to the beforehand introduction of point defects, which may result in the decrease of dislocation generation energy. Under the same external force, the dislocations are generated in the model adding the substantial atoms, which could overcome the pinning resistance to realize the glide, while the outside force is insufficient to produce dislocation in the pure Cu model.

Fig. 9. (color online) Atomic structures of the Cu (Cu–Ni base) bicrystal with the Σ9(114) GB under the shear deformation along direction at shear strains of (a) 0, (b) 0.051, and (c) 0.169. Structure units of GB outlined by purple lines are shown in the enlarged view.
Fig. 10. (color online) Structural changes of the Cu-0.7 at.% Ni bi-crystal with the Σ9(114) GB under the shear deformation along direction at different shear stages (a) 0.028, (b) 0.805, (c) 0.169. Another enlarged view of the GB structure colored by particle type represents the GB segregation situation.
Fig. 11. (color online) CNA snapshots of the Cu-1.6 at.% Ni bi-crystal with the Σ9(114) GB under the shear deformation along direction, showing shear deformation evolutions at ε = (a) 0.036, (b) 0.080, and (c) 0.140, respectively.
Fig. 12. (color online) Representative CNA snapshots of the Cu-4.3 at.% Ni bi-crystal with the Σ9(114) GB under the shear deformation along direction at shear strains of (a) 0.0305, (b) 0.075, (c) 0.156.

We summarize the main mechanical behaviors of four model undergone and shear in this part as illustrated in Table 2.

Table 2.

Dominant deformation behaviors of four Σ9(114) bicrystal models.

.

The involved structural transformations of Σ9(114) GB in the aforementioned shear processes are shown in Fig. 13. The displacements remarked in Fig. 13 are probably not unique. The initial GB structural type of all models denotes as T1a. We can calculate the displacement vectors on the ground of coincident lattice site theory, , , , . The conversion modes of GB structure associated with shear direction are described in Table 3 in detail.

Fig. 13. (color online) Dichromatic diagrams of the shift of Σ9(114) structure units, showing (a) T1a, T1b and (b) T1a, T2 processes. Lines in pink and lines in yellow describe the primal and transformed structure units. Arrows in red depict the displacement vectors.
Table 3.

Transformation processes of Σ9(114) GB structures in four bicrystal models under loading.

.
3.1.2. Shear responses of Σ9(221) GB

i) The stress–strain curves of pure Cu, Cu-0.7 at.% Ni, Cu-1.6 at.% Ni, Cu-4.3 at.% Ni models with Σ9(221)/[110] GB are depicted in Fig. 14(a) with direction shearing at 10 K. The mechanical responses of GB in pure Cu, Cu-0.7 at.% Ni, Cu-1.6 at.% Ni models could be divided into elastic stage and plastic stage in light of similar features in the three profiles, where the shear critical stress value of GB with 1.6 at.% Ni segregation (σ = 0.79 GPa) is greater than those of other two models. Furthermore, in plastic stage, the stress curves display almost coincident profile with regular sawtooth configurations, which might be donated by the GB migration coupling shear loading. Distinguished from the curves of the former three models significantly, the Cu-4.3 at.% Ni bi-crystal stress curve exhibits the irregular fluctuations and the system maintains a high stress state.

Fig. 14. (color online) Mechanical deformations of pure Σ9(221)/[110] Cu bi-crystal with different levels of nickel GB segregation, shearing along (a) and (b) at 10 K respectively.

The detailed deformation behaviors are explained in Figs. 16–19. For the former three models, figures 16–18 indicate that a shear strain parallel to GB plane promotes the GB migration, without involving the lattice dislocation. Only a small portion of GB unit structure in pure Cu is transformed from R1 to R2 (identified in Fig. 15) at a large strain stage, while the segregated GBs keep those initial structures in the whole deformation. The lower enrichment of Ni in GB does not affect the primary deformation behavior, but the critical stress of Cu-1.6 at.% Ni (σ = 0.81 GPa) is significantly higher than that of pure Cu. For Cu-4.3 at.% Ni bicrystal model, lattice dislocations nucleate from GB with the formation of stacking faults. the GB becomes more disorderly and less flat, and may be dissociated into transformed GB and twinning boundaries during large loading. The disordered GB structure may restrain the GB sliding and migration so that the energy concentration is formed as depicted in the blue curve in Fig. 14(a). The GB configuration converts into the R1 and R2 coexistence and the point defects were generated in GB, which is attributed to the atom shuffling behavior and the break of the stable GB structure.

Fig. 15. (color online) Coincident lattice site diagram of Σ9(221) GB in fcc crystal. Characterization symbols are identical to those in Fig. 4. R1 and R2 are two different transformational types of GB structure during external loading, in which R1 is the equilibrium structure of Σ9(221) GB.
Fig. 16. (color online) Atomic structures showing shear evolutions of Σ9(221) GB in Cu (Cu–Ni base) bi-crystal loading along at strains of (a) 0, (b) 0.15, and (c) 0.246.
Fig. 17. (color online) Atomic structures showing shear evolutions of Σ9(221) GB in Cu (Cu–Ni base) bi-crystal loading along at strains of (a) 0, (b) 0.14, and (c) 0.241.
Fig. 18. (color online) Atomic structures showing shear evolutions of Σ9(221) GB in Cu-0.7 at.% Ni bi-crystal loading along at strains of (a) 0, (b) 0.146, and (c) 0.226.
Fig. 19. (color online) Atomic structures showing shear evolutions of Σ9(221) GB in Cu-4.3 at.% Ni bi-crystal loading along at strains of (a) 0, (b) 0.139, and (c) 0.233.

(ii) Figure 14(b) shows that the four shear stress–strain curves present similar tendencies and figures, which are associated with their analogous deformation mode. After reaching the yielding onset, each of the curves with the regular serrated shapes exhibits a shear-coupling behavior (sliding-migration). Critical stress increases with the quantity of segregated elements increasing. The elaborated shear processes corresponding to stress–strain curves are illustrated in Figs. 20–22. The deformation modes of pure Cu and Cu-0.7 at.% Ni are almost identical: the GB remains at its original position without migrating or structure transformation under straining, which is a pure GB sliding process attributed to the displacement vector . With segregated elements increasing, point defects are generated in GB and the unit configuration may change from R1 to R1 and R2 coexistence shown in Fig. 21. A deformation mode of sliding-migration coupling motion occurs in the case of Cu-4.3 at.% Ni. Due to the random distribution of Ni around GB in a wider region, the Gibbs free energy discrepancy between upper and lower grain facilitates the GB migration from middle to upper, accompanied with GB sliding, which is proved by DFT calculation results in Subsection 3.2.

Fig. 20. (color online) Representative CNA snapshots of (a) Cu, (b) Cu-Ni base bi-crystal, and (c) Cu-0.7 at.% Ni bi-crystal with the Σ9(221) GB under the shear deformation along direction at strains of (a) 0, (b) 0.1, and (c) 0.1.
Fig. 21. (color online) Representative CNA snapshots of Cu-1.6 at.% Ni bi-crystal with Σ9(221) GB under shear deformation along direction at strains of (a) 0, (b) 0.08, and (c) 0.15.
Fig. 22. (color online) CNA snapshots of Cu-4.3 at.% Ni bi-crystal with Σ9(221) GB under shear deformation along direction at strains of (a) 0, (b) 0.097, and (c) 0.174.

The deformation behaviors and the unit structure transformations in Subsection 3.1.2 are shown in Tables 4 and 5, respectively.

Table 4.

Dominant deformation behaviors of four Σ9(114) bicrystal models.

.
Table 5.

Transformation processes of Σ9(221) GB structure in four bicrystal models under loading.

.

Figure 23(a) shows the transformation mechanism of R1 and R2, where the main displacement vectors are . This mechanism shows that the GB migrates from middle to upper with a distance of two planes. The GB coupling motions of pure Cu and Cu-4.3 at.% Ni model shearing along , and of Cu-4.3 at.% Ni model shearing along are caused by this transformation mechanism. Another transformation mode displayed in Fig. 23(b) leads to the maintenance of configuration, the contributing displacement vectors are , acting on the Cu-0.7 at.% Ni and Cu-1.6 at.% Ni model shearing along . Meanwhile, the pure Cu and Cu-0.7 at.% Ni model shearing along present the pure GB sliding process without structure transformation or migration, which results from displacement vector . The above transformation mechanism may not be unique, hence we discuss only the dominant displacement modes.

Fig. 23. (color online) Dichromatic diagrams of the transformation of Σ9(221) structure units, showing (a) R1 and R2 and (b) R1 and R1 processes respectively. Pink line and yellow line describe the primal and transformed structure units, respectively, and red arrows depict displacement vectors.
3.2. Effect of segregated elements on GB fracture

Corresponding to Subsection 3.1, in this part, the work of separation within the same selected fracture path is calculated to determine the effect of Ni enrichment concentration on GB cohesion. The segregation of Ni does not lead to the size expansion due to the infinite miscibility of nickel and copper. The lattice parameter and the surface/GB configuration are fully relaxed to achieve equilibrium, where the k-point mesh of 3 × 3 × 3 is applied to both the Σ9(114) GB (72 atoms) bulk model and the Σ9(221) GB (104 atoms) bulk model, and the 3 × 3 × 1 k-point mesh is adopted for free surface models. The fracture behavior of GB is a complex deformation procedure through the growth of crack, involving the dislocation activities and defects nucleation. Here we can calculate the work of separation in light of Griffith’s theory:[36]Wsep = [Gfs1 (c) + Gfs2 (c) − GGB (c)]/A where c is the quantity of impurity; Gfs1 (c), Gfs2 (c) and GGB (c) are the total Gibbs free energies of the system illustrated in Fig. 24 containing free surfaces and GB; A is the area of GB plane.

Fig. 24. (color online) Diagrams of determined fracture paths for Σ9(114) and Σ9(221) GB models, where fs1 and fs2 represent the free surfaces caused by the fracture path.

The calculation results are listed in Table 6. The energy calculations are completed by substituting the solute atoms for impurities, which refer to models A, B, C as depicted in Figs. 2(c) and 2(d). For both Σ9(114) and Σ9(221) GB, the fracture energies of segregated models are all higher than that of clean Cu GB. The work of separation increases with the augment of impurity excess around GB. It is obvious that the substitutive segregation of Ni at GB in Cu exerts a significant effect of cohesion. The Model C can be recognized to be a homogeneous Cu–Ni alloying phase approximately, where the segregated atoms replace the atoms in grain and GB randomly.

Table 6.

Work of separation of Σ9(114) and Σ9(221) GB with varying segregated impurity.

.
4. Conclusions

Molecular dynamics simulations and first-principle energetic calculations have been carried out to investigate the effects of varying nickel segregation at GB on the mechanical behavior and structure configuration in copper. The deformation modes of Σ9(114) and Σ9(221) with varying segregation have been fully analyzed considering that two loading directions are parallel to GB plane. The results of this study can be summarized as follows.

The lattice dislocation activities can be motivated more commonly in models with relatively high concentration, which could improve the roughness under a high strength state. For the shear of Σ9(114) bicrystal along , GBs with segregated impurity retain relatively stable without fully local dissociation compared with the pure Cu GB; shearing along enables the dislocations to be activated and stacking faults to nucleate with a low spread speed. While for the shear of Σ9(221) bicrystal along and , a small quantity of segregation would not evidently affect the GB structure deformation behavior. More complicated deformation evolution tends to appear at Cu-4.3 at.% Ni bicrystal involving dislocation emission and GB migration. Moreover the GB configuration transformation manners have also been summarized according to CSL theory. Like the results of MD and DFT simulations, the dominant effect of nickel GB segregation is to enhance the cohesion of Σ9GB and impede the crack initiation and growth.

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