**2. Materials and Methods**

Atomistic simulations, including molecular statics, molecular dynamics (MD), and hybrid Monte Carlo (MC)/MD, were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software (Sandia National Laboratories, Albuquerque, NM, USA) [25] with an embedded-atom method (EAM) potential parametrized to reproduce the binary Fe-Ni system used to model atomic interactions [26]. All MD simulations used a 1 fs integration timestep. Atomic snapshots were analyzed and visualized using the OVITO software (OVITO GmbH, Darmstadt, Germany) [27]. The crystalline structure and chemical ordering were analyzed using the Polyhedral Template Matching method [28], while the positions of dislocation lines were identified using the Dislocation Extraction Algorithm [29].

The Fe-Ni system and the given potential were chosen for several reasons. First, the Fe-Ni phase diagram is similar to the phase diagram of the Fe-Mn system in which linear complexions were first discovered experimentally. This is important because only two Fe-Mn potentials currently can be found in the literature, but neither is appropriate for the goals of this study. Bonny et al. [30] developed an Fe-Mn EAM potential while Kim et al. [31] developed an Fe-Mn modified embedded atom method (MEAM) potential but neither was rigorously fitted to reproduce the bulk phase diagram. Moreover, MEAM potentials are not currently compatible with the hybrid MC/MD code used here. Since it is critical to reproduce the relevant phases for the alloy system, the Fe-Ni potential from Bonny et al. [26] was chosen for this work since it was fitted based on the experimental phase diagram for Fe-Ni and was found to reproduce the stable intermetallic phases (L10-FeNi and L12-FeNi3). The main weakness of the potential is that the solubility limit of Ni in BCC Fe is overestimated, meaning that exact composition values for complexion transitions should not be compared with experiments. In addition, Domain and Becquart [32] performed density functional theory (DFT) calculations of segregation to self-interstitial atom clusters, finding that Ni may be able to segregate to sites under both local compressive and tensile stresses, while the EAM potential only predicted segregation to the tensile regions. This suggests that some segregation of Ni dopants to both sides of the dislocation may occur during the initial

segregation stages. However, the final linear complexion structure is not expected to be affected by this, and, in fact, the simulated linear complexions resemble those observed experimentally in Fe-Mn [5,6]. Strong variations of Ni composition along the dislocation line were observed at the compression side in the dislocation segregation zone with the composition near precipitates approaching ~50 at.% Ni while, in between precipitates, the composition was near the global composition in the system. Based on these observations, we conclude that the final form of the complexion and solute distribution around the dislocation core is controlled by the second-phase precipitation and growth, and not by the initial solute segregation. Next, we provide the simulation details for a representative computational cell containing linear complexions, prepared for mechanical testing.

First, an initial simulation cell with two edge dislocations was prepared, as shown in Figure 1a. The dislocations were inserted by removing one-half of the atomic plane in the middle of the sample and relaxing the atomic structure using the conjugate gradient descent method implemented in LAMMPS. Next, 2 at.% Ni atoms were randomly distributed within the sample by replacing Fe atoms, which was followed by MD equilibration with an NPT ensemble (constant number of atoms, constant pressure, and constant temperature) at zero pressure and 300 K temperature for 20 ps. Three thermodynamically-equivalent initial solid solution configurations with different random distributions of solutes were prepared with this procedure, providing a baseline for comparison against samples containing linear complexions. To induce linear complexion formation, the alloy samples were equilibrated at 500 K using the hybrid MC/MD method, which allows for both chemical segregation as well as local structural relaxations. The MC steps were performed after every 0.1 ps of MD relaxation time, using a variance-constrained semi-grand canonical ensemble that can stabilize alloy systems with coexisting phases [33,34]. This method has been used in a number of recent modeling studies to capture complexion transitions in metallic alloys [35–37]. The MC/MD procedure led to Ni segregation to the compressive side of the dislocations and then formation of linear complexions in the form of nanoscale precipitate arrays composed of metastable B2-FeNi and stable L10-FeNi phases, as shown in Figure 1. The presence of nanoscale precipitates reduces the compressive stresses on the side of the dislocation with the extra half-plane of atoms (see the zoomed view of the bottom dislocation in Figure 2). More details about the MC/MD procedure for linear complexions in the Fe-Ni system can be found in our previous studies of equilibrium complexion states [5,6]. The MC/MD simulations were determined to be in equilibrium once the rate of evolution of total simulation cell energy fell below 1 eV/ns, even though the procedure was continued for additional time to sample three distinct yet thermodynamically equivalent samples. These samples were then cooled to 300 K over 20 ps with MD for subsequent mechanical testing.

The solid solution specimens and the samples containing linear complexions were then deformed to promote dislocation slip by applying the XY shear deformation to the simulation cell. The deformation of the cell was performed with the non-equilibrium MD method [38,39], using an engineering strain rate of 10<sup>8</sup> s−<sup>1</sup> at 300 K. To test the effect of deformation rate, an additional simulation was performed at an engineering strain rate of 107 s−1. The deformation of the cell was stopped after 10% applied shear strain, and the stress-strain curves were extracted and analyzed in the context of atomic-scale deformation mechanisms and the local structure of the linear complexions.

**Figure 1.** (**a**) 3D perspective view of the simulation cells with the random distribution of solutes, and with linear complexions comprised of nanoscale precipitates containing B2 (red) and L10 (green) phases. Atoms are colored by their local atomic order and the matrix Fe atoms are deleted for visualization purposes. The dislocations are shown as black lines. (**b**) XY slices of the system with Z-position of 28 nm and a thickness of 0.26 nm. The atoms are colored as follows: magenta–Fe, yellow–Ni, light blue–BCC pure Fe, dark blue–BCC Fe-Ni solid solution, red–B2-FeNi, and green–L10-FeNi. The XX component of the atomic stresses are shown in a red-white-blue color scheme with red indicating tensile stresses and blue indicating compressive stresses.

**Figure 2.** Zoomed view of the bottom dislocation in the system with linear complexions that was previously shown in Figure 1b.
