Electron force-induced dislocations annihilation and regeneration of a superalloy through electrical in-situ transmission electron microscopy observations

1. Introduction

It had been proved that the electric current can not only significantly influence the macroscopic responses of materials such as flow stress and elongation [[1], [2], [3]], but also affect the microstructures [[4], [5], [6]]. Therefore, electrically-assisted manufacturing (EAM) had attracted increasing attentions in recent decades due to its convenience in setting up and efficiency during the manufacturing process [7]. However, the mechanism of electrically-assisted plastic deformation is still not fully understood because it is difficult to distinguish the electric effect and the Joule heating effect [8]. The Joule heating effect was the universally cognitive theory, which was caused by the materials’ resistance, and it was widely used in the experimental simulation of the hot working condition, such as Gleeble testing machine.

However, as more and more related experiments were conducted [9,10], it was found that the deformation ability was always improved more significant under electric current than that under the hot conditions even though the target temperatures are identical. This phenomenon was hard to be explained by the Joule heating theory. Simultaneously, the earlier occurrence of the second phase precipitation and recrystallization were observed during the electrically-assisted (EA) deformation than the time when the critical temperatures for such phenomena to occur reached [11,12]. More evidences [13] indicated that the improvement of material’s property was not only affected by the Joule heating effect and the electron force induced by the external applied electric field cannot be ignored during the EAM. The typical theory to explain the mechanism of electron force effect was the electron wind theory [14,15], in which the decrease in the flow stress of materials is considered as the momentum transfer from the electric field directly assists the dislocation movement within the metal’s lattice. However, until now, there is no direct evidence to prove the electron force effect and most of the previous work focus on theorical analysis [16]. Some researchers tried to eliminate the heating effect through some cooling equipment [17,18] during the EA experiment. In a similar manner, the pulse current experiments [[19], [20], [21]] were also designed to decrease the Joule heating effect by controlling the pulse width and pulse period parameters. All of these experiments suggested that the material’s property can be improved by electric current even when the temperature is not high. However, the aforementioned experiments still did not eliminate the heating effect completely. Especially the recent work on local Joule heating effect theory [8,12,22] indicated that the distribution of temperature is inhomogeneous in the materials: the Joule heating effect in the defect is more obvious than that in the perfect lattice because of the larger resistance in these defect areas (approximately six to eight times to the perfect lattice [23]), and thus the mechanical properties can also be affected even under the same surface temperature. Similar problems occur at the microscopic length scale, including the researches on the variation of dislocation [24], texture [25,26], grain size [27] and micro structure [28] during the EA deformation. Hereby, it is worth noticed that the initial microstructure is not exactly same in different samples, the variation difference under different conditions cannot be accurately reflected in this way.

To this end, the electrical in-situ transmission electron microscopy (TEM) experiment was conducted in this work, and the dislocation structure evolution was firstly observed at the same area under the electric current condition. By comparing with the in-situ high temperature deformation experiment, it was demonstrated that dislocation behaviour was indeed affected by the electron force.

2. Experimental

A Ni-based superalloy (Inconel 718) was used in this experiment. In order to observe the effect of electric current on the dislocation motion, it is necessary to use a pre-deformed sample to obtain enough dislocation density. The deformation test was conducted with a CMT4000 testing machine. The pre-deformed sample was cut using wire-cut machine and polished using a mechanical polishing machine, which then can be used for the in-situ TEM sample preparation, as shown in Fig. 1(a). The polished sample was stuck on an electrical E-chip, which was mounted on a special electrical holder from Protochips and inserted into the FEI Talos F200X TEM to conduct the electrical in-situ TEM experiment during which there was no external force applied. There were three important steps needed to be mentioned during the sample preparation. Firstly, a small region was extracted through focused ion beam (FIB) machining from the deformed sample, which should be suit for the space requirement of the electrode in the E-chip as shown in Fig. 1(b, c). Then, the selected foil was transferred to E-chip by micromanipulator and welded it on the electrode by platinum as in Fig. 1(d). Lastly, the target region for TEM characterization was further milled until the foil’s thickness is less than 100 nm. The final experimental condition is shown in Fig. 1(e, f).

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Fig. 1.   The steps of electrical in-situ TEM sample preparation: (a) the sample, (b) FIB process, (c) extracting foil by micromanipulator, (d) transferring foil to the E-chip, (e, f) the final experimental condition.

The electric current range of the electrical in-situ equipment is from 10 pA to 100 mA, and the resistance variation of the testing sample during the experiment can be measured accurately. During the experiment, the electric current value started with 0.1 mA and was kept for 30 s, if the dislocations didnot move, the electric current was set to be increased by a step of 0.1 mA. When dislocations began to move, the electric current value was kept as constant for dislocation motion observation. The heating in-situ TEM experiment was using the heating TEM holder and the sample was heated by radiation. The experimental procedure was identical to the electrical in-situ TEM experiment. The initial temperature started with 200 °C and was kept for 60 s, and the temperature increment was 20 °C in each step.

3. Results and discussion

Generally, the resistance of material is related to all defects, including grain boundaries, precipitates, solute atoms and dislocations. However, in this study, the experimental sample was a single crystal due to its small enough size. There were no grain boundaries, precipitates and solute atoms in this sample. Therefore, it needs to be declared firstly that the variation of resistance can only be affected by dislocation evolution. Fig. 2 shows the resistance evolution of the sample with the corresponding dislocation structures when the electric current is applied. Dislocations didnot move when the electric current value was below 2.1 mA, and the resistance of the sample had barely changed as shown in Fig. 2 (the blue curve). It was found that the dislocations start to move when the electric current value reaches 2.2 mA. Fig. 2(a-d) shows the development of the dislocation structure with the increase of the current applied time. There are two interesting regions in Fig. 2(a) needed to be noticed. In region 1, it could be observed that dislocations annihilated almost thoroughly when the current applied time reached 68 s, and the resistance of the sample is lowest. Interestingly, in the same region, new dislocations were generated again and the resistance of the sample increased simultaneously with the increase of the electric current holding time as shown in Fig. 2 (the red curve). When the current applied time reached 198 s, the new dislocation density in region 1 reached a large value. Consequently the resistance exceeded the initial value of the sample obviously, as shown in Fig. 2(d). However, the development of dislocation structure in region 2 is different from that in region 1. The dislocations density in region 2 kept increasing during the whole experimental process, but the rate was lower. In order to reveal this difference, the diffraction spot figure was analyzed, as shown in Fig. 2(e). The observed area was from the same grain, and the zone axis was [$\bar{1}$12] axis. The crystal indices of all lattice planes can be identified according to the orientation relationship between each diffraction spot. There were four slip planes can be confirmed and the crystal indices were (1$\bar{1}$1), (110), (13$\bar{1}$) and (311), respectively. The partial enlargement figure of Fig. 2(a) and (d) shows that the direction of the previous and regenerated dislocations was parallel to the (110) crystal plane, which indicated that the slip system in the (110) plane was activated.

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Fig. 2.   Resistance evolution of the sample with the corresponding dislocation structures with the electric current applied time: (a-d) the TEM images showing the evolution of dislocations captured from the electrical in-situ TEM experiment (Suppl. Vid. 1); (e) the diffraction spot of the observed plane.

In order to study whether the above phenomenon was just affected by the increased temperature due to the Joule heating effect, the heating in-situ TEM experiment was conducted, as shown in Fig. 3, for comparison. From Fig. 3, the dislocations annihilation began when the temperature reached 400 °C, and was almost complete when the temperature kept for 203 s. What is different, the dislocation didnot regenerate at the same region afterwards, which can be found in Fig. 3(c). It needs to be noted that the principle for determining parameters in the electrical/heating in-situ TEM experiment was that the same effect (i.e. dislocations starting to move) has been reached. That is to say when the current density rises to 2.2 mA or the temperature rises to 400 °C, dislocations moving were observed. So, the two conditions can be considered as equivalent. Because the Joule heat is the main factor for the dislocation annihilation during the electrical in-situ TEM experiment, the temperature in the electrical in-situ TEM experiment should be close to 400 °C. Therefore, the used annealing temperature in the heating in-situ TEM experiment is high enough.

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Fig. 3.   TEM images showing the evolution of dislocations captured from the heating in-situ TEM experiment (Suppl. Vid. 2): (a) 0 s, (b) 203 s, (c) 260 s.

The annihilation of dislocations always happened under the hot condition because the internal stress between dislocation were released, but it was hard to regenerate without changing the external environment. By contrast, the dislocation regeneration happened under the electric current condition, which was a surprising phenomenon. It means that there should be an extra force arising from the electric current, which is believed as electron force, apart from high temperature that could promote the dislocation movement.

Normally, the electron force F is the effect that these directionally fast-moving electrons strike lattice. It worth noting that the electron motion direction is contrary to the current direction. In the present work, the current direction was not vertical to the transmission electron beam direction because of the calibration of diffraction spots. The electrical in-situ holder rotated 7.8 ° around x axis during calibration, which means that the angle between the electron force (ydirection) and the observed plane was 7.8 ° in y1 direction, as shown in Fig. 4(a). Hence the electron force could be decomposed into the resolved force F₁, which was parallel to the observed plane and the resolved force F₂, which was vertical to the observed plane. According to the diffraction spot pattern in Fig. 2(e), the angle between the reciprocal vector of 110 plane and the resolved electron force F₁ was 57 ° in [$\bar{1}$12] axis direction, which means that the angle between the 110 plane and the resolved electron force F₁ was 33 °. Hence, the vector of electron force F in the cubic lattice can be determined as (-0.8059, 0.1536, -0.2007). The potentially activated slip systems under this electron force direction are (1$\bar{1}$1) <$\bar{1}$$\bar{1}$0>, (311) <01$\bar{1}$>, (13$\bar{1}$) <101> and (110) <$\bar{1}$10>. The Schmidt factor in each slip system then can be determined, according to the Schmid law m=cosφ∙cosγ, as 0.433, 0.261, 0.043 and 0.439, respectively, as shown in Fig. 4(b). The resolved shear stress from the electron force on the (1$\bar{1}$1) <$\bar{1} \bar{1}$0> slip system is similar to that on the (110) <$\bar{1}$10> slip system, but the slip resistance of (1$\bar{1}$1) <$\bar{1} \bar{1}$0> slip system is lower than (110) <$\bar{1}$10> slip system according to the calculation of interplanar spacing in each slip system. Therefore, the (1$\bar{1}$1) <$\bar{1}$$\bar{1}$0> slip system is easier to be activated under this electron force direction, which applied both to room-temperature and high temperature deformation. However, it was contrary that the (110) <$\bar{1}$10> slip system was activated during the experiment. The main reason is that the decreased slip resistance in the 110 plane since the Joule heat was more significant than that in the (1$\bar{1}$1) plane. The previous studies [12,22] had demonstrated the existence of local Joule heating effect in the Ni-based superalloy, and the local Joule heat in the region containing dislocations is much larger than other places. When the sample dimension was very small (the thickness of sample was less than 100 nm), the heat transfer within the sample wss not easy because the heat dissipation was extremely fast. Therefore, the elevated temperature induced by local Joule heating effect only occurred around dislocations during the electrical TEM experiment. The increasing temperature reduced the slip resistance of the （110）<$\bar{1}$10> slip system, and when the electron force exceeds the slip resistance of the slip system, dislocations start to move. At the same time, it could be observed that the initial density of dislocation along (110) plane direction in region 1 was larger than that in region 2, and hence, the dislocation evolution rate was faster in region 1 under the same electron force. What’s more, the electron force would not disappear under the continuous electric current, according to the phenomenon that the continuous multiplication of dislocation appeared in region 2 but the annihilation firstly and then regeneration of dislocation appeared in region 1, it could be concluded that the moving dislocation type induced by the electron force was same to the previous dislocation in region 2, but it was opposite to the previous dislocation in region 1. The dislocations in region 1 began annihilating at first and then the opposite type dislocations began regenerating in the same place after the completely disappeared of the previous dislocations, as shown in Fig. 4(c). Generally, When the slip direction is [uvw], the relationship between the shear stress τ and the Burgers vectors b as,

τ∝G∙b=G∙a/n(u²+v²+w²)^½ (1)

where G is the shear modulus, a is the lattice constant, and n represents the type of dislocation (full dislocation and partial dislocation, and the n of partial dislocation is larger than full dislocation). According to Eq. (1), the shear stress τ is inversely proportional to n, which means that the critical resolved shear stress of partial dislocation is lower than full dislocation under the same condition. Therefore, the partial dislocation can be regenerated more easily by the electron force under the same condition.

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Fig. 4.   (a) The relationship between the current direction and all lattice planes; (b) Schmidt factor under this electron force direction in each slip system; (c) the dislocation behaviour in (110) plane with the time.

To summarize, the electron force played an important role during the electric current condition. It can promote the movement of dislocation easier with the assistance of local Joule heat. Therefore, the dislocation structure evolution was always unusual during EAM. The findings in the present work can be used to explain some extraordinary observations during EAM. For example, when the Zn single crystal was subjected to an electron beam along different directions, the mechanical properties was obviously different [29].

4. Conclusion

This work directly proved the existence of electron force during the EAM, for the first time, by comparing the electrical in-situ TEM with the heating in-situ TEM experiment. It was found that the dislocation behaviour was affected by both the electron force and the local Joule heating effect. The electron force during the EAM could promote the dislocation movement, which was difficult to occur at the room temperature or conventional high temperature, and thus the mechanical properties and micro behavious during EAM were different to high temperature deformation. Furthermore, the experimental simulation which used high temperature condition through the Gleeble testing machine may not be accurate, especially when the electron force cannot be ignored when the electric current is larger during these experiments. This work presents a new method for the EA experiment designment, but it worth noting that the EA effect to materials can be different when the electric current applied time and current direction change, and hence how to use the understanding of local temperature, current direction and dislocation distribution is the key problems in designing the advanced EAM technology in the future.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Nos. U1737212 and U1637102) and the Natural Science Foundation for Distinguished Young Scholars of Shaanxi Province (No. 2019JC-09). The Analytical & Testing Center of Northwestern Polytechnical University is also acknowledged for the experiment support on this work.