Effect of Nd on Stacking Fault Energy in Pure Copper: A First-Principles and HRTEM Study

Abstract

Stacking fault energy (SFE) can significantly affect the plastic deformation mechanism of metal materials and then affect their mechanical properties. Changing the stacking fault energy by microalloying rare earth elements is an effective means to control the plastic deformation mechanism and optimize the mechanical properties of the metal materials. Based on first principles, the HRTEM technique and GPA method, the effects of Nd content on the SFE and microstructure of Cu alloys were studied. The results show that the Nd element can significantly reduce the SFE of pure copper. But the change in the Nd element content has little influence on the SFE of the alloy. In addition, with the increase in Nd content, the grain size and twin size are refined. The GPA results show that strong tensile strain is formed inside the twin, and alternating tensile strain and compressive strain structures are formed on the (-11-1) plane at the tip of the twin.

1. Introduction

Dislocation slip and twinning are the main deformation mechanisms of metal materials. The strength and plasticity of the metals can be improved by regulating the interaction between dislocation, the twin/grain boundary and the second-phase particle, such as strain hardening and twinning-induced plasticity (TWIP) [1,2,3]. Therefore, it is an important strengthening and toughening method to realize the simultaneous enhancement of strength and plasticity by adjusting the deformation substructure. Studies have confirmed [4,5,6] that stacking fault energy (SFE) is a key factor affecting the plastic deformation mechanism of the metals, and the value of the SFE determines the distance between two partial dislocations [4,5,6]. For the metal materials with high SFE or medium SFE, the cross-slip mechanism of the dislocation can be promoted due to the small distance between partial dislocations on the close-packed plane, while for the metals with low SFE, the distance between partial dislocations on the close-packed plane is large, resulting in the dislocation being difficult to coordinate the deformation through cross-slip. However, the decrease in the SFE promotes the occurrence of the twinning mechanism [4,5,6]. At present, the composition design of the alloy is the main method to control the SFE. In recent years, rare earth elements have attracted wide attention due to their active chemical properties [7]. Studies have shown that adding rare earth elements to the metals can not only enhance their high temperature strength properties but can also improve their oxidation resistance and corrosion resistance [8]. Therefore, the composition design of the alloys by regulating the content of the rare earth elements is an important method to develop a new generation of alloys.

Generally, the addition of rare earth elements in Cu alloys mainly has the following effects: (1) by changing the stacking fault energy of the Cu alloys, it regulates the deformation mechanism. Wang et al. studied the effects of different Y contents on the microstructure evolution and stacking fault energy of the 90Cu10Ni alloy. With the increase in Y content, the number of twins increases significantly, and the formation of the twins is related to the addition of Y element to reduce the SFE of the Cu alloy [9]. (2) Refining the grain size of Cu alloy improves the comprehensive mechanical properties. Wang et al. studied the effect of the Y element on the microstructure evolution and mechanical properties of the Cu-20Ag alloy [10]. The Y element mainly exists in the branches of the eutectic structure, resulting in an increase in the constitutional supercooling of the solidification process, thus refining the alloy grain structure and improving the tensile strength of the alloy [10]. Dalvand et al. studied the effect of Ce and La addition on the mechanical properties of the Cu alloys [11]. The addition of 0.04 wt.%Ce and La to Cu alloys can significantly refine the grain size, therefore improving the ductility of the alloys [11]. (3) The addition optimizes the microstructure of the Cu alloy to improve the mechanical properties. Yu et al. designed Cu-4.44Fe-0.26Cr-0.4Si-0.29Mg and Cu-4.73Fe-0.3Cr-0.38Si-0.28Mg-0.2Sc-0.24Y alloys to study the effects of rare earth alloying on the microstructure evolution and mechanical properties [12]. Compared with the Cu alloy without rare earth elements, the yield strength and tensile strength of rare earth-modified Cu alloys are increased by 124 MPa and 116 MPa, respectively, and the improvement of the mechanical properties of the alloy is mainly related to the suppression of the dislocation slip by rare earth atoms [12]. Zhao et al. studied the effect of Sc on the microstructure evolution and mechanical properties of the Cu-6Ag alloy during aging and cold drawing [13]. By adding Sc, the ultimate tensile strength of the Cu-6Ag alloy is increased by 15%. As the inclusion of Sc elements regulates the precipitation behavior of the Ag-containing second phase, the reduction in the size and spacing of the nanoscale Ag-containing precipitated phase effectively inhibits dislocation slip, thus improving the tensile strength [13]. Wang et al. systematically studied the effects of trace rare earths, such as Sc, Er and Y, on the microstructure and mechanical properties of the Cu-Cr-Zr alloys [14]. The addition of Y effectively inhibits the precipitation and growth of the Cr particles in the alloy. The high-temperature ultimate tensile strength of the peak-aged Cu-Cr-Zr-Y alloy is 381 MPa at 450 °C, and the high-temperature ultimate tensile strength of the over-aged alloy is 341 MPa, which is much higher than that of the Cu-Cr-Zr alloy [14]. The main strengthening mechanism of the Cu-Cr-Zr-Sc alloys is grain refinement strengthening, while the main strengthening mechanisms of the Cu-Cr-Zr, Cu-Cr-Zr-Y and Cu-Cr-Zr-er alloys are precipitation strengthening and dislocation strengthening [14]. At present, although the effects of rare earth elements on the microstructure, stacking fault energy and mechanical properties of Cu alloys have been extensively studied, the effects of rare earth Nd microalloying on the stacking fault energy and deformation mechanism of Cu alloys have been less investigated. Therefore, it is very important to study the effect of Nd microalloying on the microstructure evolution of the Cu alloy to further reveal the strengthening and toughening mechanism of the rare earth modified Cu alloy.

In this study, the effects of different Nd content on the SFE of the pure copper were studied based on first principles, and the microstructure and nanotwin structure of the Cu alloys with different SFE were characterized by the geometric phase analysis (GPA) method and high-resolution transmission electron microscopy (HRTEM) technique.

2. Materials and Methods

In this study, the Cu-0.005 wt.%Nd and Cu-0.028 wt.%Nd alloys (mass fraction, wt.%) were prepared using a vacuum medium-frequency induction furnace at 1220 °C. The model ZJMSHPB-16 split-Hopkinson pressure bar (SHPB) was selected for dynamic compression mechanical property testing. The pressure bar material is high-strength alloy steel, with an elastic modulus of 210 GPa, a density of 7800 kg/m³ and a wave velocity of 5044 m/s. The dynamic impact test specimens were sized at Φ6 mm × 4 mm, prepared using electrical discharge molybdenum wire cutting and polished with 600~1000 grit sandpaper to ensure the surface finish. SHPB experiments were conducted on Cu samples with different rare earth contents at strain rates of 800 s⁻¹. The dynamic impact properties of pure copper, Cu-0.005 wt.%Nd and Cu-0.028 wt.%Nd alloys are given in

Table 1. Dynamic impact properties of pure Cu and Cu-Nd alloys at a strain of 800 s⁻¹ [7].

Sample Number	Stress (MPa)	Strain (%)
Pure Copper	445	0.12
Cu-0.005 wt.%Nd	522	0.11
Cu-0.028 wt.%Nd	554	0.13

[7]. As shown in Table 1, the dynamic impact strength increased with the increase in Nd content. For the related strengthening–toughening mechanisms, please refer to the literature [7]. For the calculation of the SFE, a stacking fault model was constructed by cleaving along the {111} crystal plane to generate a 1 × 2 × 1 supercell and introducing a 20 Å vacuum layer to isolate adjacent layers. The model was constructed by shifting 0.5 lattice constants b along the <112> direction of Cu crystal structure, as shown in Figure 1.

The calculations were performed using the Vienna Ab Initio Simulation Package (VASP) with spin-polarized density functional theory (DFT), employing a plane-wave basis set and the projector augmented wave method [15,16,17]. The exchange-correlation potential was treated using the Perdew–Burke–Ernzerhof (PBE) parameterization in the form of the generalized gradient approximation (GGA) [18,19]. To account for van der Waals interactions, dispersion corrections were applied. The energy cutoff was set to 500 eV, and Brillouin zone integration was performed using a 5 × 7 × 1 Monkhorst–Pack grid centered at the Γ point [20]. The structures were fully relaxed until the maximum force on each atom was less than 0.02 eV/Å, with an energy convergence criterion set to 10⁻⁵ eV.

The SFE was calculated using Equation (1) [21]:

$$\gamma ={\displaystyle \frac{E_{SF}-\mathrm{E}}{\mathrm{A}}}$$

(1)

where $E_{SF}$ is the energy of the stacking fault, E is the energy of the perfect structure, and A is the area of the stacking fault in the simulation cell [21]. The strain of the alloy microstructure was calculated using the GPA method, and the microstructures of the different alloys were characterized by HRTEM with the model Tecnai G2 F30 S-TWIN. TEM samples were prepared by a twin-jet polishing instrument with the model TJ100-SE-TMS. The optical microstructure of the Cu alloys was observed using a Zeiss ObserverA1 microscope (Carl Zeiss AG, Oberkochen, Germany), with the etchant being a FeCl₃-HCl (30%) aqueous solution. Electron back-scatter diffraction (EBSD) results of the Cu alloys were acquired via the high-resolution and high-sensitivity surface analysis system (S9000X) with an acceleration voltage of 20 kV. EBSD specimens were prepared by electropolishing technique [7]. The strain field was calculated from GPA using the open source program Strain++ [22,23].

3. Results and Discussion

Figure 2 shows the SFE calculation results of the pure copper and the Cu-Nd alloys with different Nd content. Due to the limitation of the element content in the first-principles method, it is impossible to calculate the influence of trace Nd content on the SFE. Therefore, the effects of 8.33%, 20.83% and 29.17% of the Nd content (at.%) on the SFE were investigated in this study. As can be seen from Figure 2, the SFE of the pure copper is 0.00459 eV/Ų, and after adding the Nd element, the SFE is significantly reduced to 0.00259 eV/Ų (8.33%Nd). With the increase in Nd content, the SFE increases from 0.00259 eV/Ų to 0.00265 eV/Ų (29.17%Nd). Therefore, the addition of the Nd element can significantly reduce the SFE, but the change in Nd content has little effect on the SFE.

Figure 3 shows the optical microstructure of the pure copper and Cu-Nd alloys after dynamic impact. It can be seen from Figure 3 that the metallographic microstructure of the three samples is composed of equiaxed grains and twins. Compared with pure copper, the equiaxed grain size and twin size of the Cu-Nd alloys decrease significantly, indicating that adding the Nd element to pure copper can refine grain size. However, it is worth noting that with the increase in Nd content from 0.005 wt.% to 0.028 wt.%, the change in the grain size of the Cu-Nd alloys is not obvious.

Figure 4 shows the SEM images of the three samples after dynamic impact. It can be seen from Figure 4 that the SEM microstructures of the three samples are composed of white second-phase particles (green arrow and circle) and gray Cu matrix. Compared with Cu-Nd alloys, a small number of the second-phase particles are formed in pure copper. With the increase in Nd content, the second-phase particles in Cu-Nd alloys increase, and these white second-phase particles are copper oxide [7].

Figure 5 shows the texture of the three samples after dynamic impact. As can be seen from Figure 5, ID//[101] (impact direction, ID) fiber texture is formed in all three samples. With the increase in Nd content, the texture types in the three samples do not change, but the pole density intensity of the texture gradually increases from 2.212 to 3.084, indicating that the addition of the Nd element cannot change the crystal orientation of the grain but can affect the dislocation slip behavior, resulting in the increase in the pole density intensity of the ID//[101] fiber texture.

Figure 6 shows TEM images of the pure copper and the Cu-Nd alloys after dynamic impact at a strain rate of 800 s⁻¹. As can be seen from Figure 6a,d, a large number of dislocation tangle and coarse twins are formed in the pure copper, and dislocation slip presents a wavy slip feature. The dislocation tangle and twins are also formed in the Cu-0.005 wt.%Nd alloy after the addition of trace Nd element. However, it is worth noting that compared with the pure copper, the dislocation movement of the Cu-0.005 wt.%Nd alloy is restrained, which is mainly related to the addition of the Nd element, which significantly reduces the SFE and inhibits the cross-slip of the dislocation. With a further increase in Nd content, the twin size of the Cu-0.028 wt.%Nd alloy is significantly refined compared with the pure copper and Cu-0.005 wt.%Nd alloy. The authors observed the region of the entire sample during TEM characterization and found that smaller twins were indeed formed in the Cu-0.028 wt.%Nd alloy. As can be seen from Figure 2, with the increase in Nd content, the SFE of the alloy increases slightly. Although the change in Nd content has little effect on the deformation mechanism, our results show that the change in Nd content has a significant effect on the twin size, and the twin size is significantly refined with the increase in Nd content.

The HRTEM and GPA analysis of the twin in Figure 6f are shown in Figure 7. In Figure 7, the x-direction is parallel to the [-2-11] crystal direction of the sample, and the y-direction is parallel to the [-100] crystal direction of the sample. The twin plane is parallel to the x-direction and forms an angle of 54.74° with the y-direction. In Figure 7, E_xx represents the stress condition of the twin along the [-2-11] direction; for example, when the twin is subjected to tensile stress along this direction, it indicates that the length of the twin along the [-2-11] direction has increased under the action of external force. E_yy represents the stress condition of the twin along the [-100] direction, while E_xy describes the shear deformation that occurs between the x- and y-directions of the twin. As can be seen from Figure 7d–f, a strong tensile strain is formed within the twins. It is worth noting that the structures with alternating tension strain and compressive strain are formed at the twin tip on the (-11-1) plane of the twin (Figure 7g–i), which is mainly related to the lattice distortion caused by the deviation of the atom occupying the ideal position of the twin (-11-1) plane and the matrix (-11-1) plane.

It can be seen from the above experimental results that adding trace Nd element to pure copper has the following effects: (1) it reduces the stacking fault energy of the Cu alloy. It can be seen from Figure 2 that the SFE of Cu-Nd alloys can be significantly reduced by adding trace Nd element to the pure copper. A large number of twins are formed in Cu-Nd alloys compared to pure copper (Figure 3), and twins tend to form in the materials with the lower-level SFE, indicating that the addition of Nd elements does reduce the SFE of the pure copper. (2) The addition refines the grain size of the Cu-Nd alloys. As can be seen from Figure 3, the addition of the Nd element can significantly refine the grain size of the Cu alloys, and the refinement of the grain size is mainly related to the large amount of copper oxide formed in the matrix during the dynamic impact. As shown in Figure 4, compared with the pure copper, a large number of the copper oxide particles are formed in Cu-Nd alloys, and the formation of these particles is mainly related to the higher affinity between rare earth elements and O [24]. Zhang et al. studied the effect of Nd on the microstructure evolution and mechanical properties of the Cu alloy, and their results also showed that the addition of the Nd element can effectively refine the grain size of the alloy and improve its mechanical properties [25]. (3) It promotes the formation of the preferred orientation. As can be seen from Figure 5, with the increase in Nd content, the pole density intensity of the ID//[101] texture gradually increases, while the texture type does not change. The increase in the pole density intensity of the texture is mainly related to the formation of a large number of the fine oxides. During dynamic impact, a large number of dispersed oxide particles can effectively restrain the grain boundary movement, resulting in significant refinement of the grain size and inhibition of the grain rotation, thus increasing the volume fraction of grains with the same orientation and promoting the formation of the ID//[101] preferred orientation.

4. Conclusions

In this study, the SFE of the pure copper and the Cu-Nd alloys with different Nd content were calculated based on first principles, and the effects of the SFE on the dislocation and twin structure of the Cu alloys were studied by HRTEM technique. The strain distribution of the twin structure and twin tip was calculated by the GPA method. The results show that the Nd element can significantly reduce the SFE of pure copper. With the increase in Nd content, the grain size and twin size are refined. The structures with alternating tension strain and compressive strain are formed at the twin tip on the (-11-1) plane of the twin. In addition, the addition of Nd content can promote the formation of the ID//[101] preferred orientation.