**4. Discussion**

While grain boundaries in nanocrystalline metals improve mechanical strength, they provide a strong driving force for grain coarsening [9]. Grain coarsening of NG metals involves GB migration at a certain velocity (ν), which can be expressed as [47,48]:

$$\mathbf{v} = M\_{\mathbb{S}^b} \cdot \boldsymbol{\gamma}\_{\mathbb{S}^b} \cdot \mathbf{k} \tag{1}$$

where *Mgb* represents the GB mobility, *γgb* is the GB energy and *κ* is the local grain boundary curvature. This equation implies that at least two approaches can be applied to alleviate grain coarsening: the kinetics-driven stabilization approach, in which grain coarsening is suppressed by pinning grain boundaries with second-phase Zener drag or by solute drag, and a thermodynamics approach, where lowering grain boundary energy can effectively reduce the driving force for grain coarsening [49–51]. Specifically, the driving force for grain coarsening of NG metals is the excess energy stored at the grain boundaries. Zhou et al. [25] reported that the grain boundary energy of NG Cu fabricated by SMGT declined from 0.52 to 0.25 J/m<sup>2</sup> when the average grain size decreased from 125 to 50 nm and showed a thermally stable NG layer when the average grain size is smaller than 70 nm. The grain boundary energy reduction was partially attributed to the formation of low-energy grain boundaries, consisting of nanotwins and stacking faults (SFs), and partially ascribed to the grain boundary relaxation [25].

In this study, a gradient NG surface layer was introduced into IN718 alloy by SMGT. The topmost area of the NG region with smaller grain size exhibited better thermal stability than the deeper area with larger grain size at high temperatures (Figure 3), similar to the reported thermally stable NG Cu [25]. Zhang et al. [52] reported that the grain boundaries of Cu evolved from low-energy twin boundaries (TBs) possess lower grain boundaries energy than conventional HAGBs. In this study, the grain boundary map in Figure 2d reveals that the majority of grain boundaries of nanograins are HAGBs. Our previous work on the microstructure evolution of gradient structured C-22HS Ni-based alloy indicates that these HAGB-dominated NG structures may derive from deformation-induced twin structures [23]. Such transformation led to the formation of grain boundaries in low-energy configuration. Slow grain boundary migration velocity is therefore expected according to Equation (1), indicating the improvement of thermal stability.

The high resolution TEM (HRTEM) image of the nanograins in the topmost NG region in Figure 4a reveals plenty of SFs and nanotwins formed inside the nanograins. The magnified HRTEM image of area b in Figure 4a is shown in Figure 4b. Nanotwins with an average twin thickness of 2 nm were observed. These nanotwins formed inside nanograins are too thin to be detected by ASTAR due to the limited spatial resolution of the technique (4 nm), which indicates that the proportion of CSL boundaries in the NG region is higher than what was revealed in Figure 2d. These CSL boundaries are also beneficial for improving the thermal stability of GBs [52]. The {111} planes forming a twinning relationship and TBs are labeled by solid and dashed lines in Figure 4b, respectively. These observations also imply that partial dislocations rather than full dislocation activities dominated the grain refinement process at the nanoscale. The partial dislocations-dominated grain refinement process led to the formation of a thermally stable topmost NG layer because the generation of SFs or nanotwins from grain boundaries plays a critical role in grain boundary relaxation, which impacts the migration of the boundary [26]. Based on the Orowan relation [25], the resolved shear stress (*τRSS*) required for the expansion of a dislocation loop derived from a Frank–Reed source with a diameter of *D* can be expressed as:

$$
\pi\_{RSS} = \mu b/D \tag{2}
$$

where *μ* represents the shear modulus and *b* is the Burgers vector. Hence, the minimum grain size (*D\**) required for the multiplication of full dislocations at a given yield strength (*σy*) can be calculated by:

$$D^\* = \frac{\mu bM}{\sigma\_y(D^\*)}\tag{3}$$

where *M* is the Taylor factor (3.0 for polycrystalline metals). The shear modulus and Burgers vector for Ni are 76 GPa and 0.25 nm, respectively. The yield strength *σy*(*D*∗) can be calculated by the classic Hall–Petch equation as [53,54]:

$$
\sigma\_y(D^\*) = \sigma\_0 + K(D^\*)^{-1/2} \tag{4}
$$

where *σ<sup>0</sup>* is the friction stress and *K* represents the Hall–Petch slope. Zhou et al. [25] estimated the *D\** for (full dislocation multiplication mechanism to operate) pure Ni by using Equation (2) and obtained *D\** = 43 nm, similar to what was calculated by Legros et al. (38 nm) [55]. Considering that the value of *K* for Ni alloys is higher than that for pure Ni, the calculated *D\** for IN718 alloys is expected to be smaller than that of pure Ni. Hence, an average *D\** value (40 nm) between those reported by Zhao et al. and Legros et al. is adopted in this story. As the grain size of IN718 is smaller than 40 nm, full dislocation activities are superseded by partial dislocation activities, leading to grain boundary relaxation. The experimental observation is consistent with the calculated results. As shown in Figure 3, the average grain size of the relative coarse-grained structures in the thermally stable area is 37 nm after annealing (700 ◦C/24 h), whereas prominent grain coarsening occurs in the grain coarsened area with an initial grain size greater than 40 nm.

**Figure 4.** (**a**) HRTEM image of nanograins containing high-density stacking faults (SFs) and nanotwins (as labeled by orange and white arrows, respectively) formed after SMGT. (**b**) An atomic-resolution TEM image of the area b in (**a**) showing the formation of nanotwin structures with an average twin thickness of 2 nm. (**c**) An atomic-resolution TEM image of the area c in (**a**) showing the faceted grain boundary. (**d**) HRTEM image showing the dissociated HAGBs formed between two adjacent nanograins. (**e**) An atomic-resolution TEM image of the area e in (**d**) showing an array of SFs (as labeled by orange arrows) decorated along the dissociated grain boundary.

We also observed that grain boundaries associated with nanotwins or SFs became faceted frequently, as shown in Figure 4c, where the steps of (111) planes along the grain boundaries are labeled. A previous study reported that the emission of nanoscale twins or SFs from grain boundaries reduces the excess energy of grain boundaries [56], leading to reduced atomic diffusion along the grain boundaries. The emission of SFs and nanotwins in this study led to the formation of faceted grain boundaries. Similar grain boundaries with zig-zag configurations have been reported in nanostructured Cu with good thermal stability [57]. Generally, a given grain boundary has five crystallographic degrees of freedom (three for the misorientation of the crystallographic axes of one grain and two for the inclination of the boundary between the two adjacent grains) [58]. Grain boundaries naturally find a low-energy configuration that fixes these degrees of freedom, i.e., minimize the free energy of the system pertaining to atomic coordinates or composition by specifying the five degrees of freedom [58,59]. For a system where its boundary free energy is anisotropic with respect to the inclination of the grain boundary, the corresponding boundary may lower its free energy by forming faceted planes [58]. Faceting is the process of decomposing the grain boundary into sections with low-energy inclination. Generally, the system with low grain boundary free energy possesses geometric characteristics of low reciprocal volume density of coincidence sites, large interplanar spacing and high planar density of coincidence site, etc. [60]. The twin boundaries in Figure 4b and the most densely packed (111) plane of the zig-zagged grain boundaries in Figure 4c are examples of such low-energy grain boundaries. However, the low grain boundary free energy system is not limited to these criteria as there is no direct connection between coincidence and grain boundary energy [60]. The non-CSL 9R structure was found to minimize the grain boundary energy by forming a body-centered-cubic structured grain boundary in the face-centered-cubic matrix [60,61]. Faceting has been observed at both micrometer and nanometer scales in several cases [57,62]. These faceted grain boundaries have low-energy states and, therefore, are more thermally stable than conventional grain boundaries according to Equation (1).

Grain boundary structure may also transform to a lower-energy state (grain boundary relaxation) through the dissociation of grain boundaries during deformation. The TEM image in Figure 4d shows a dissociated HAGB in the NG IN718 specimen after SMGT. As denoted by dotted lines, broad grain boundaries decorated with plenty of SF-like structures formed. The HRTEM image (of the area e in Figure 4d) in Figure 4e reveals an array of SFs (as noted by orange arrows) emitted from the grain boundary, leading to the broad/dissociated grain boundary with 1 nm in width. The formation of these SF-decorated broad grain boundaries indicates that grain boundary dissociation may have taken place in the topmost NG region during SMGT, leading to grain boundary relaxation to low-energy states and grain boundary stabilization. Rittner et al. found that grain boundary dissociation generally occurs via the emission of SFs from one boundary and termination at a second boundary [63]. Zhou et al. [25] reported that the formation of both SFs and nanotwins from grain boundaries involves emission of partial dislocations, leading to grain boundary relaxation and stable structures. The dissociation of grain boundaries usually leads to the formation of a wider grain boundary (or three-dimensional boundaries) of up to 1 nm or more in width, similar to the structures formed in this study.

The grain size evolution of the FNG and CNG structures of the thermally stable area and the grain coarsened area with annealing time is presented in Figure 5a. The calculated minimum grain size (40 nm) is labeled by the horizontal dotted line. It is evident that the coarsening rate of grains smaller than 40 nm is lower than that with grain sizes larger than 40 nm. The grain growth kinetic, correlating the grain size (*d*) to the annealing time (*t*), can be expressed as [64]:

$$d^n - d\_0^n = kt \tag{5}$$

where *d*<sup>0</sup> is the initial grain size, *n* represents grain growth exponent and *k* is a rate constant. The evolution of grain size (ln(*d*)) and annealing time (ln(*t*)) in different areas of the specimen is shown in Figure 5b. The *n* value can be determined by the slope of linear fit lines. It reveals that the average *n* value of the thermally stable area with initial grain size

smaller than 40 nm is 0.15, whereas the *n* value for the grain coarsened area is much greater, 0.59, confirming a much more sluggish grain growth behavior in the thermally stable NG structure when the initial grain size is smaller than the *D\**.

**Figure 5.** (**a**) Grain size evolution of FNG and CNG layers in the thermally stable area and the grain coarsened area of IN718 specimens with increasing annealing time. (**b**) The corresponding plot of ln (*d*) vs. ln (*t*) at several regions, where *d* and *t* are grain size and annealing time, respectively.
