Keywords

1 Introduction

In the last two decades, nanowires (NWs) importance in nanoscale electronic and mechanical systems is increasing drastically due to their application as interconnectors [1]. Nanowire one-dimensional structure and enthralling properties have made the researchers go much depth into their mechanical and physical properties for new findings during different loading conditions. Scientific interest among researchers on nanowires is mainly due to their unique performance in numerous applications [2]. Majorly in the modern functional systems like NW transistors of high mobility and strain-controlled logic gates, supercapacitors, conductors, and other magnetic field devices [3]. Nickel (Ni) NW is essential and widely used in electromagnetic systems, owing to its broad applications [4]. The NW applications in modern nanodevices are increasing gradually. For better functionality of these devices, it is necessary to understand the influence of crystallographic orientation, sample size, and shape on the NW deformation mechanisms and their mechanical properties.

In the last two decades, many researchers have worked experimentally and computationally in the investigation of understanding the deformation behavior of metal NWs. Many researchers have reported the size, shape, and orientation influence on the deformation mechanism of NWs [5,6,7,8,9,10,11]. The deformation mechanism in FCC metal NW is either by slip through partial dislocations or by twinning. NW crystallographic orientation and its loading direction mainly determine the deformation mechanism. Hence the crystallographic orientation plays a vital role, followed by loading direction in the deformation behavior of metal NWs. For instance, using molecular dynamics (MD) simulation, Park et al. [5] investigated the tensile and compressive behavior of FCC NWs (Copper, Nickel, and Gold) of <100> and <110> orientations. They said that the NW deformation mechanism depends on material intrinsic properties, crystallographic orientation, applied stress field, and exposed transverse surfaces. Wen et al. [6] studied NW orientation influence on Au NW mechanical properties under tensile and compressive loading. The studied crystallographic orientations of Au NWs are [100], [110], and [111] and reported that there is a strong influence of orientations on the NW mechanical properties. Sainath et al. [7], using MD simulations studied tensile and compressive behavior of BCC Fe NWs of <100>, <110>, <111>, <112> and <102> orientations. Later Rohit et al. [8] studied the NW orientation and loading direction effect on the deformation mechanism of Cu NW. They reported that under tensile loading, all the NWs deform by twinning. Under compression, the NW of orientation <100> deform by twinning, and NW with all other orientations deform by slip. In [9], the author studied the strain rate and orientation dependence on the single-crystal titanium NW under tensile loading. The studied orientations are [11–20], [−1100], [0001] and they reported on the influence of orientation in the deformation of titanium NW at various srain rates.

In the literature, it is noticed that there are no studies on the compressive and tensile studies of NW at different orientations on a large scale. To understand the orientation influence on the tensile deformation of Ni NW in a large scale, we considered a Ni NW of dimension 100 Å × 1000 Å × 100 Å. Hence in this study, we performed the uniaxial tensile test using MD simulations on NW of four different orientations. The considered crystallographic orientation are [1–10], [20–1], [111] and [1–1–2]. The deformation mechanism and the dislocations are responsible for yield and the generated dislocation during the plastic deformation are well analyzed.

2 Simulation Details

MD simulation is used to construct and test the Ni NW of four different orientations using EAM (embedded atomic method) potential [12]. Previously, many researchers have conducted the tensile test and observed metals deformation behavior using the EAM potential. For example, Pei et al. [13] investigated Ni ductile versus brittle fracture at different temperatures. Razaei et al. [14] used the above potential in the study of Ni graphene and reported a twinning behavior. Large scale atomic/molecular massively parallel simulator (LAMMPS) [15] is used in running the MD code for studying the tensile behavior of nanocrystalline materials [5, 16,17,18].

The NW is created by filling a simulation box with FCC crystalline Ni atoms (a0 = 3.518 Å) with periodic boundary conditions along the y-axis [19]. In the other two directions (x and z) non-periodic boundary conditions are applied. All the NWs have a square cross-section with a box dimension of 100 Å (x-axis) × 1000 Å (y-axis) × 100 Å (z-axis). To study the orientation effect, four highly symmetry lattice orientated Ni NWs of [1–10], [20–1], [111], and [1–1–2] are constructed as shown in Fig. 1. After the NW preparation, it is relaxed by the conjugate gradient method [19, 20] and then equilibrated at 10 K temperature using the Nose–Hoover thermostat [21]. The equilibrated NW is then deformed along the y-axis at 108 s−1 strain rate and 10 K temperature. During the tensile test, the thermodynamic ensemble NVT is used. The tensile stress is calculated by using the virial stress at a time step of 1 fs [22]. During the tensile test of NW, the defect analysis is carried by using the centrosymmetric parameter (CSP) [23] and dislocation extraction algorithm (DXA) [24] of OVITO software [25].

Fig. 1
figure 1

Schematic view of Ni NW showing their orientations and surface structures and in the present investigation a [1–10], b [20–1], c [111] and d [1–1–2] orientations are considered

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3 Results and Discussions

3.1 Stress–Strain Behavior

Figure 2 represents the true stress vs true strain curves of Ni NW of [1–10], [20–1], [111] and [1–1–2] orientations under tensile loading at 108 s−1 strain rate and 10 K temperature. All the NWs strained elastically up to yield load, followed by a sudden fall in stress. Straining the NW beyond the yield has caused plastic deformation followed by fracture at different NW regions based on their orientations. In the stress–strain curves, the slope of the initial linear region gives Young’s modulus. All the mechanical properties, yield and fracture strain values are shown in Table 1. From the elastic region, it is noticed that FCC Ni NW has shown different stress–strain behavior depending on their orientation. A maximum elastic modulus of 232 GPa is observed in [111] orientation followed by [1–10] (172 GPa), [1–1–2] (120 GPa) and [20–1] (90 GPa) orientations. The elastic modulus of [111] NW is more than that of nickel bulk sample ~199 GPa [26], but for [1–10] NW, it is almost close. From Fig. 2, it is noticed that the [111] orientation has recorded the highest stress ~17.2 GPa, and [1–10] orientation has the lowest stress (~9.5 GPa). The reported yield stress in [20–1] and [1–1–2] oriented NW are 11.7 and 10.5 GPa. The reported mechanical properties from the literature are based on the size, shape, temperature and at different loading conditions of NW [19, 27,28,29]. On a small scale, Park et al. [5] studied the tensile properties of Ni NW of <100> and <110> orientations and the reported yield stress is 8 GPa in <110> oriented NW.

Fig. 2
figure 2

True stress vs true strain curves of Ni NW of [1–10], [20–1], [111] and [1–1–2] orientations

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Table 1 Mechanical properties of [1–10], [20–1], [111] and [1–1–2] Ni NW
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3.2 Deformation Mechanisms

3.2.1 [1–10] and [20–1] oriented Ni NW

To observe the deformation mechanism during tensile loading, CSP analysis has been carried out on all NWs. In identifying the type of dislocation, we carried out DXA analysis and represented the dislocations in different colored lines. To identify the type of stacking faults, we deleted the fcc, bcc and other atoms from the sample and showed only the hcp atoms with dislocations along with stacking faults. Figure 3 represents the CSP (a) and DXA analysis (b) images at various strains during tensile loading of [1–10] (A) and [20–1] (B) oriented Ni NW. In the figure it can be observed that both the [1–10] (e = 0.053) and [20–1] (e = 0.112) NW yield by Shockley partial dislocation. The partial surrounds an intrinsic stacking fault with a burger vector of 1/6 <121>. In the process of nucleation and propagation of a Shockley partial in an FCC crystal structure, we can observe two adjacent close pack HCP atoms in-between the partials [6]. Straining the NW further, nucleation of twin partials forming twin boundaries can be observed in both [1–10] (e = 0.057) and [20–1] (e = 0.118) oriented NWs. After the yield strain (e = 0.057) the NW of [1–10] orientation has reoriented to [100] orientation due to twinning. At 14% strain, we can notice a second reorientation at the end of the [1–10] oriented NW. Straining the NW further, the twin region grows along the NW axis and hence there is an increase in the volume percentage of the reoriented region and no fracture is observed in [1–10] orientation up to 30% strain. Rohit et al. [8] have conducted tensile studies on FCC Cu NW using MD simulations and reported that there is a complete reorientation in <101>, <103>, <212>, and <214> oriented samples. In the present tensile studies, [20–1], [111] and [1–1–2] oriented NWs have been deformed up to their fracture strain but reorientation is not observed. This is due to the slip activation in more twin system which causes twin-twin interactions that results in the disruption of twin growth and reorientation [30].

Fig. 3
figure 3

Ni NW deformation behavior showing the CSP (a) and DXA analysis (b) at different strains during tensile loading in (A) [1–10] and (B) [20–1] orientations

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3.2.2 [111] and [1–1–2] Oriented Ni NW

Figure 4 shows the CSP (a) and DXA analysis, (b) images at various strains during tensile loading of [111] (A) and [1–1–2] (B) oriented Ni NW. For [111] and [1–1–2] orientations, the plastic behavior is observed at the NW edge, corresponding to a strain, e = 0.075 and e = 0.076 with intrinsic stacking faults surrounded by Shockley partial dislocations. Similar deformation behavior is already shown by Zhan et al. [31] and Huang et al. [32] in their tensile deformation studies of Cu and Fe, Ni NWs using MD simulations. There is an increase in dislocation with strain in both [111] and [1–1–2] orientations after yield strain. This is because of slip activation on multiple slip systems and at strains e = 0.078 ([111]) and e = 0.08 ([1–1–2]), we can observe multiple intrinsic and extrinsic stacking faults. Dislocation densities of all oriented Ni NWs at yield strains is reported and explained in Sect. 3.3. The partials at the activated slip system start slipping on the close-packed {111} planes and their interaction results in the generation of Lomer-Cottrell (L-C) barriers [33] as shown in Fig. 4. Generally, these locks generate by the interaction of Shockley partials in different slip planes, which gives sessile stair rod dislocations as:

$${\text{1}}/{\text{6 }}\left[ { - {\text{21}} - {\text{1}}} \right] + {\text{1}}/{\text{6 }}\left[ {{\text{1}} - {\text{21}}} \right] \to {\text{1}}/{\text{6 }}\left[ {{\text{11}}0} \right]$$
(1)
Fig. 4
figure 4

Ni NW deformation behavior showing the CSP (a) and DXA analysis (b) at different strains during tensile loading in (A) [111] and (B) [1–1–2] orientations

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The successive emission of partial dislocations after yield strain has transformed to a nano twin which is due to the twinning partial propagation along the initial stacking fault planes. The highlighted regions in the inset image (Fig. 4A(a) (e = 0.078)) are <1> intrinsic stacking fault; <2> extrinsic stacking fault; <3> twin formation and <4> widely separated twins. Straining the NW further, much wider twins can be observed in both [111] (e = 0.184) and [1–1–2] (e = 0.15) orientation and failed by 45° shear fracture.

3.3 Dislocation Density

Figure 5 display the dislocation densities (total and Shockley partial) of [1–10], [20–1], [111] and [1–1–2] orientated Ni NW at respective yield strains. Almost in all samples, the nucleated dislocations are Shockley partials, and they initiate the plastic deformation by slip followed by twinning. A minimum dislocation density (total) of 0.5 × 1015 m−2 observed in  [111] and a maximum recorded in [1–10] orientation. In [34] the author studied the effect of void density on the dislocation and deformation behavior of a defective (voids) single crystal Ni of [100] orientation. The reported Shockley partial dislocation density is 50 × 1017 m−2 (single void), which is much higher than the present study is due to the different strain rate, orientation, sample defects, loading, and boundary conditions. In the present study dislocation density increase with strain is observed in all NWs, with a significant percentage of Shockley partials.

Fig. 5
figure 5

Total and Shockley partial dislocation density of [1–10], [20–1], [111] and [1–1–2] oriented Ni NW at respective yield strains

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4 Conclusions

The crystallographic orientation effect on the mechanical properties and deformation behavior of NW is studied. The tensile studies of Ni nanowires of [11–0], [20–1], [111], and [1–1–2] crystallographic orientations is carried out at 10 K temperature and deformation rate of 108 s−1. The simulated results show that the orientation has a notable influence on NW deformation. It is noticed from the results that the NW of various orientations yields by Shockley partial dislocation with intrinsic stacking faults followed by twinning partials. The yield stress of [11–0], [20–1], [111], and [1–1–2] orientation are 9.5 GPa, 11.7 GPa, 17.2 GPa and 10.5 GPa respectively. During tensile loading, reorientation of Ni NW is noticed only in [1–10]. At yield strains, a minimum and maximum dislocation density (total) of 0.5 × 1015 m−2 and 2.65 × 1015 m−2 are observed in [111] and [1–10] oriented Ni NWs.