**3. Results and Discussion**

Figure 3a shows the obtained stress-strain curves for the samples with linear complexions. We observe profound initial stress peaks for all the samples, indicated by black circles. The initial plastic events are followed by smaller peaks, indicated by black triangles, that represent the flow stress of the dislocations passing by the linear complexions. Similar stress-strain curves with a profound first peak have been previously reported in experimental work on linear complexions in an Fe-9 at. % Mn alloy [13]. The substantial strain aging is observed in both experimental Fe-Mn and modeled Fe-Ni systems with linear complexions. The average values for both the initial break-away stress and the flow stress for the simulated Fe-Ni samples with linear complexions are presented in Figure 3b. The mean initial break-away stress of 586 MPa is 45% higher than the mean flow stress of 404 MPa. We note that these values should not be directly compared to experimental measurements, as other aspects of alloy strengthening from defects, such as grain boundaries, are not present in the simulation cell, which isolates the dislocation pair.

**Figure 3.** (**a**) The stress-strain curves for three samples with linear complexions. The initial peak stresses and flow stresses are denoted by circle and triangle symbols, respectively. (**b**) Mean values and corresponding standard deviations for the initial peak stress and flow stress.

To understand how deformation differs between the solid solution and linear complexion states, Figure 4 presents the initial flow events for representative examples of each of the two sample types. Figure 4a shows the elastic loading and initial flow event, where it is clearly observed that the dislocation can move much more easily in the solid solution sample. Figure 4b shows the dislocation pair at three different simulation times (or, equivalently, applied strains since the strain rate is controlled). The two dislocations in the solid solution remain relatively straight during the motion, with the top dislocation shifting to the right and the bottom dislocation moving to the left. The solutes in the solution act as obstacles that must be locally overcome, leading to very little change in the dislocation shape. The bottom dislocation is shown from a top view in the lower half of Figure 4b, demonstrating the progressive migration that leads to a temporary stress drop as a set of local, solute obstacles are overcome. The local obstacles are easily overcome, which is why the initial peak stress for the solid solution specimens is relatively low. In general, the dislocation in the solid solution sample behaves in a "textbook" fashion, with few features of interest.

**Figure 4.** (**a**) Representative stress-strain curves showing the initial break-away event for a sample with solid solution (blue) and a sample with linear complexions (orange). 3D perspective views of the entire computational cell and 2D views of the bottom dislocation are shown for (**b**) the solid solution and (**c**) the sample with linear complexions. The position of the dislocations are shown as solid curves of different colors corresponding to different times, as shown in section (**a**).

The mechanism of the dislocation motion is drastically different for the specimen with linear complexions with dislocation bowing and unpinning from the nanoscale precipitates one by one, starting in the region with the largest distance between particles, controlling the yield event shown in Figure 4c. It is important to note that only one dislocation, which is the defect at the bottom of the cell, is moving in the linear complexion sample. The other dislocation at the top of the cell bows under increasing stress but remains pinned by the nanoparticle array linear complexion. One dislocation is favored to move over the other because the nanoparticle arrays, while similar, are not exactly identical. A bowing mechanism is easiest in the location where there is the largest spacing between obstacles, which occurs near the middle of the lower dislocation. While dislocation bowing is a common mechanism for overcoming precipitates in conventional alloys, an important distinction is found for the linear complexion state. The obstacle is not in the dislocation's slip plane. Traditional Orowan bowing occurs when an impenetrable obstacle (e.g., a precipitate with a different crystal structure than the matrix) impedes the dislocation's slip path, requiring bowing to move past the obstacle in a way that leaves dislocation loops around the obstacle. However, in the case of linear complexions, the nanoparticles are primarily above or below the dislocation slip plane (depending on whether one is looking at the top or bottom dislocation). Even the small portion of the B2-FeNi intermetallic phase that crosses the slip plane in Figure 1 has the same BCC crystal structure as the matrix phase and a lattice parameter that is similar. The linear complexion is not an impenetrable obstacle and, in fact, no new dislocation loops or segments are formed as the dislocation pulls away. The strong initial pinning can be explained from the same energetic perspective that is used to describe the complexion nucleation. Segregation of Ni occurs to the compressed region near the edge dislocation until the local composition is enriched enough that a complexion transition can occur [5,6]. Although the Gibbs free energy of the L10 phase is lower, which is why this structure appears on the bulk phase diagram, the restriction to a nanoscale region and the large energy cost for an incoherent BCC-L10 interface results in the formation of a "shell" of a metastable B2 phase surrounding the L10 core [6]. Fundamentally, the local stress field near the dislocation is relaxed by this transformation and the driving force for motion under shear stress (i.e., the Peach-Koehler force [40,41]) is, therefore, reduced. We do note that segregation of Ni to the dislocation is needed to create the linear complexion states, lowering the solute composition in the matrix solid solution and removing some weak obstacles. However, the net effect is still a notable strengthening increment, as the strong linear complexion obstacles more than make up for losing some amount of solid solution strengthening.

Since periodic boundary conditions are used here, the dislocation exits the cell after it breaks away from the linear complexion and then re-enters on the other side, where it eventually interacts with the complexion again. Therefore, subsequent dislocation-complexions can be observed by continuing the simulation and investigating the flow events at larger strains. A detailed look at multiple flow events is shown in Figure 5 for one of the linear complexion samples. In addition to the stress-strain curve shown in black, measurements of the dislocation length at any given time are also extracted and presented as the blue curve. Three separate events are labeled A-B, C-D, and E-F and isolated into separate parts of the figure. Similar to the initial yield event in Figure 4, only one dislocation (bottom) is moving while the other (top) remains pinned by the nanoscale precipitates. Figure 5 shows that there are cyclic undulations in the shear stress, which correlate with the observation of repeated bursts in the dislocation density associated with dislocation bowing. Furthermore, the shapes of the dislocation length bursts are extremely similar for each cycle, suggesting that the physical events are similar as well. Snapshots A-B show the final pinned segment of the dislocation, breaking away from a large particle in the complexion array, and then entering from the other side and actually being attracted to the particles, as shown by the fact that the dislocation is pulled closer to the precipitates first in frame B. Snapshots C-D show the first bowing event in a new cycle, which occurs at the location with the largest spacing between particles and is reminiscent of the events presented in Figure 4c. We do remind the reader that this bowing does occur at lower stresses than the initial yield event, suggesting that

something about the complexion has evolved. Finally, snapshots E-F show an intermediate bowing event, neither the first nor the last in a cycle.

**Figure 5.** The evolution of the simulation cell shear stress (top, black) and dislocation length (bottom, blue) for the sample with linear complexions, with (**A**–**F**) different atomic configurations sampled. The atomic configurations are grouped by different passes of the dislocation that happen due to the periodic boundary conditions of the simulation cell. Black arrows denote the direction of motion for mobile dislocation at the bottom of the cell.

To investigate the complexion structure during the deformation simulation, the number of B2 and L10 atoms in the simulation cell were tracked and are shown in Figure 6a. A cyclic pattern is again observed, suggesting a connection to the repetitive dislocation motion through the cell. Most notable is that reductions in L10 atoms are generally aligned with increases in the number of B2 atoms (and vice versa). Figure 6b–e show atomistic snapshots of important dislocation interactions with a linear complexion particle in an effort to understand this cyclic behavior. In Figure 6b, the dislocation is still pinned next to the L10 precipitate, so the complexion contains the expected L10 core and B2 shell. The dislocation started to pull away from the particle in Figure 6c, and close inspection of the complexion particle shows a reduction in the size of the green L10 region. However, the transition to the B2 structure does not happen immediately, as some time is apparently needed, although short, since it is captured on MD time scales. Figure 6d shows a later time when the dislocation has moved fully away from the particle, and the linear complexion is almost entirely composed of the B2 structure in this frame (a very small number of green L10 atoms remain, but the number is dramatically reduced). This observation provides further support for the concept that the two-phase complexion structure is caused by the dislocation's hydrostatic stress field. When that stress field is no longer present,

a diffusion-less and lattice distortive transformation from an FCC-like structure (L10) to a BCC-like structure (B2) occurs. Figure 6e shows that the L10 region of the precipitate starts to be recovered as the dislocation, and its stress field, arrives at the other side. We note that, while a cyclic behavior is observed in Figure 6a, the number of B2 atoms trend downward as the process continues. This could be a sign that the linear complexion particles are becoming smaller in subsequent cycles (or at least during the transitions from the first few cycles to the steady-state cycling), which would provide an explanation for why the initial yield event is more difficult than later dislocation flow. Figure 6 generally highlights the close connection between the structure of the linear complexion and its interactions with the dislocation. The complexions restrict the dislocation and make it harder to move, while the structure of the complexion relies on the local stress field from the dislocation to find a local equilibrium state. There is, hence, an interdependence of these two defect structures, which truly sets linear complexions apart from traditional obstacles to dislocation motion.

**Figure 6.** (**a**) The number of B2 (red) and L10 (green) atoms in the computational cell containing linear complexions, as the deformation simulation progresses. (**b**–**e**) A region perpendicular to the Y-direction from the dislocation slip plane to the middle of the precipitate. Yellow spheres represent Ni atoms, while violet, red, and green spheres represent Fe atoms in the matrix, B2, and L10 phases, respectively. The dashed line shows the position of the dislocation line. A diffusion-less and lattice distortive transformation is observed with the complexion structure being dependent on the dislocation position.

Finally, to show that this local transition within the complexion is not dependent on the deformation rate used here, an additional deformation simulation was run at one order of magnitude slower strain rate (107 s−1). The results of this simulation are presented in Figure 7, capturing all of the same important features described above. Loading is initially elastic until a high stress is reached, when the dislocation is able to bow out at the region with the largest spacing between linear complexion particles. The dislocation re-enters the simulation cell and becomes pinned, and subsequent dislocation unpinning and motion follows the same mechanism. A reduction of the number of L10 atoms in the system and a corresponding increase in the number of B2 atoms is observed each time the dislocation is able to break away. These trends agree with the L10-to-B2 lattice distortive transformation shown in Figure 6.

**Figure 7.** The evolution of the simulation cell shear stress (black), dislocation length (blue), the number of B2 (red), and L10 (green) atoms for the sample with linear complexions deformed at a strain rate of 107 s<sup>−</sup>1, with (**A**–**D**) different atomic configurations sampled on the right side of the figure for the initial break-away event of the dislocation.
