Role of disordered bipolar complexions on the sulfur embrittlement of nickel general grain boundaries

Minor impurities can cause catastrophic fracture of normally ductile metals. Here, a classic example is represented by the sulfur embrittlement of nickel, whose atomic-level mechanism has puzzled researchers for nearly a century. In this study, coupled aberration-corrected electron microscopy and semi-grand-canonical-ensemble atomistic simulation reveal, unexpectedly, the universal formation of amorphous-like and bilayer-like facets at the same general grain boundaries. Challenging the traditional view, the orientation of the lower-Miller-index grain surface, instead of the misorientation, dictates the interfacial structure. We also find partial bipolar structural orders in both amorphous-like and bilayer-like complexions (a.k.a. thermodynamically two-dimensional interfacial phases), which cause brittle intergranular fracture. Such bipolar, yet largely disordered, complexions can exist in and affect the properties of various other materials. Beyond the embrittlement mechanism, this study provides deeper insight to better understand abnormal grain growth in sulfur-doped Ni, and generally enriches our fundamental understanding of performance-limiting and more disordered interfaces.


Supplementary Note 1: Summary of the key experimental observations
In this study, we examined 34 independent GB facets in 10 randomly-selected boundaries in seven samples annealed at four different conditions, where: (A) Eighteen independent GB facets all have one lower-index terminal grain surface of the (100) plane with another higher-index matching grain surface: all 18 facets are Type A (amorphous-like).
The results are summarized in Table 1  A representative Type A amorphous-like intergranular film (IGF) with a uniform nanometer thickness is shown in Supplementary Figs. 2 and 3 further illustrates that the amorphous-like IGFs formed on a parallel set of Type A facets exhibit a nanoscale thermodynamically-determined or "equilibrium" thickness of little variation from facet-to-facet (instead of an arbitrary thickness for a wetting film), as shown in Supplementary Fig. 3B (with additional images in Supplementary Fig.  17). See further elaboration in Supplementary Note 12.
Moreover, the interfacial energy of a nanometer-thick, liquid-like IGF is less than that of two crystal-liquid interfaces (gb  IGF < 2cl), because the dihedral angle at the groove, where the liquid-like IGF meets the bulk liquid phase, is non-zero (Supplementary Figs. 3C and 3D).
Thus, they are a true interfacial phase that are thermodynamically two-dimensional, which are also termed as "complexion" to differentiate them from the thin layers of the wetting bulk (3-D) phases at the interfaces [1][2][3] .
The stabilization of the Type A amorphous-like (liquid-like) IGFs on the (100) facets can be explained by the low liquid-Ni (100) interfacial energy, which was confirmed experimentally by the Wulff shape of the Ni crystals in contact with the S-rich liquid ( Supplementary Fig. 4). Supplementary Figure 2. Atomic resolution STEM ABF image of a Type A GB facet, which is a nanometer-thick, amorphous-like, intergranular film (IGF, yet exhibiting partial structural order). This specific GB was randomly selected from a sample quenched from 675 ºC. (A) STEM ABF image showing a Type A GB facet. The mean width (± one standard deviation from multiple measurements along the GB) of this interfacial phase (i.e., equilibrium-thickness intergranular film) was measured to be 0.98 ± 0. 15  8 on cross sections should be identical to the mean of the true dihedral angles in 3-D (since the cross sections are random). These narrow thickness distributions, as well as the non-zero average dihedral angle, demonstrated that these IGFs exhibits a nanoscale thermodynamically-determined or "equilibrium" thickness (instead of an arbitrary thickness for a wetting film) and its interfacial energy is less than that of two crystal-liquid interfaces (gb  IGF < 2cl); thus, they are a true interfacial phase that are thermodynamically two-dimensional, which is also termed as "complexion" to differentiate it from a thin layer of a bulk (thermodynamically three-dimensional) phase at an interface. . These results suggest that surface adsorption of S stabilizes (100) facets of Ni. Moreover, the interface between Ni (100) crystalline facets and the equilibrium S-enriched liquid should have the lowest interfacial energy, thereby promoting the formation of Type A GB complexions on (100) facets, i.e., stabilizing S-enriched, nanometer-thick, liquid-like (amorphous-like), interfacial phases on (100) facets both above and below the bulk eutectic temperature.

Supplementary Note 2: Summary of the key simulation results
We simulated the equilibrium interfacial structures of the Type A, B, and C GB facets in semigrand canonical ensembles. The simulated GB interfacial structures are critically compared to the experimental results in terms of the excess adsorptions of S, interfacial width, the level of structural disorder, and the simulated STEM images ( Fig. 3 and Fig. 4 Fig. 5 illustrates a comparison of the GB interfacial structures obtained from the simulation and the experiments for one Type A GB and two Type B GBs. Additional modelingexperimental comparisons are presented in Fig. 3 and Fig. 4 in the main article and in Supplementary Fig. 42 and 43. The critical modeling-experimental comparisons are summarized in Supplementary Table 3. From the simulation results, we identified polar S-Ni clusters (defined in "Methods" and further discussed in Supplementary Note 16), as illustrated in Supplementary Fig. 6. We also discovered the bipolar distributions of the polar S-Ni clusters (Supplementary Figs. 6D and 8).
We further conducted an MD tensile simulation on the pure and S-doped Ni GBs of Type A and B (Supplementary Fig. 7; elaboration in Supplementary Note 17). We found that the S-doped Ni GBs exhibit a brittle fracture, whereas the dislocations initiate and propagate in the pure Ni GBs.
Supplementary Fig. 8 shows the evolution of the atomistic structures of a Type A and B GB during the tensile simulation. The evolutions of the polar S-Ni clusters indicate that the fractures of the S-doped Ni GBs are caused by the separation among those polar clusters that disorderly aligned in opposite directions (S-to-S) (i.e., with bipolar distributions of the ⃗ → vectors defined in Supplementary Fig. 6). The polar S-Ni clusters remain mostly intact after the fracture in the Type A and B GBs, as shown in Supplementary Fig. 8 and Fig. 5 in the main article. Further illustrations and discussion about the polar Ni-S clusters and their bipolar distributions can be found in Supplementary Note 16.
By changing the chemical potential of S in the semi-grand canonical ensemble atomistic simulations, we modeled the equilibrium GB interfacial structures with different amounts of S adsorption at Ni GBs. Supplementary Figs. 9A and 9B show a comparison of GB adsorption and the structural disorder of the GB structures obtained at different chemical potential differences for the (100)//(926) Type A GB and the (110)//(345) Type B GB.
Moreover, the tensile simulations showed that the computed tensile toughness (see Supplementary Note 17 for definition and discussion) decreases with the increasing bipolar index  (defined in "Methods") in both Type A and B GBs (Supplementary Figs. 9C and 9D). Thus, the formation of bipolar interfacial structures induced by the S adsorption causes brittle intergranular fractures between the polar S-Ni structures disorderly aligned in opposite directions, through a GB embrittlement (GBE) mechanism that is also displayed visually in Supplementary Fig. 8, as well as

Supplementary Note 3: Indexing grain boundary (GB) terminal planes
To determine the crystal orientation of the two terminal planes of a grain boundary (GB), we used a lattice imaging method. Once the grain was tilted into the low-index zone axis, the terminal planes could be unambiguously indexed.
For example, to index the two terminal planes of the long faceting plane as shown in Supplementary Fig. 10, Grain 1 was first tilted into [110] zone axis (and set to an edge-on condition). An atomic resolution lattice image was thus obtained. Based on the fast Fourier transformation (FFT) pattern shown in the inset of Supplementary Fig. 10B, three lattice planes were indexed to be (111 ), (11 1) and (200), respectively. Thus, the terminal plane for Grain 1 was exactly the (200) plane. Similarly, we tilted Grain 2 (on the other side of the same GB) into [114 ] zone axis. The atomic resolution lattice image and corresponding FFT pattern were obtained and are shown in Supplementary Fig. 10C. Three planes corresponding to the diffraction spots could thus be determined as (311 ), (13 1 ) and (2 20), respectively. The terminal plane of Grain 2 was then calculated based on three vectors to be close to (532) with 1° off. The two parallel terminal planes of this facet were determined to be (200) and (532). Therefore, the orientation relationship for this GB was (200)//~(532). This orientation relationship is labeled as (100)//~(532) ~1° off, which means that the actual plane on the right side is 1° off the exact (532) plane; noting that (200) lattice fringes in TEM represent the crystalline (100) planes of the FCC crystal. To maintain consistency, we always kept the lower Miller index, e.g., (100) and (110), on the left. Step 1, we tilted Grain 1 to its [110] zone axis, which was also an edge-on condition. An atomic-resolution lattice image was obtained and is shown in panel (b). The inset is the FFT pattern obtained from the selected area highlighted by the yellow frame. The FFT pattern was indexed as the standard diffraction pattern for the FCC structure in its [011] zone axis and the terminal plane of Grain 1 on the GB was determined to be (200). (C) In Step 2, we tilted Grain 2 to its [114 ] zone axis. An atomic resolution lattice image was then obtained and is shown in panel (c). The inset is the FFT pattern obtained from the selected area highlighted by the yellow frame. The FFT pattern was indexed as the standard diffraction pattern for the FCC structure in [114 ]. The terminal plane for Grain 2 was determined to be approximately ~1° off the (532) plane. Therefore, the GB orientation relationship is , approximately 1° off, which is also denoted as "(100)//~(532) ~ 1° off". Here we use (100) to label the grain surface, instead of (200), which is typically used to label lattice fringes or a diffraction pattern; noting that (100)  As shown in Supplementary Fig. 11, the amorphous-like and bilayer-like GB structures observed in this study cannot be clearly discerned in phase-contrast lattice imaging using conventional HRTEM imaging. Supplementary Figs. 11A1 and 11A2 are synchronized STEM ABF and STEM HAADF images of an amorphous-like GB facet. The conventional HRTEM image of the same GB is shown in Supplementary Fig. 11A3.
A similar pair of STEM ABF and HAADF images of a Type B GB facet, as well as the conventional HRTEM image of this Type B GB facet, were also taken and are shown in Supplementary Figs. 11B1, 11B2 and 11B3 for comparison. The application of STEM ABF enabled us to better visualize the interfacial structure composed of the light element sulfur, which is not clearly distinguished by conventional HRTEM and STEM HAADF. The adsorbed sulfur atoms on the GB facet, which was further confirmed by EELS and EDXS, gives the bright contrast in ABF images. In contrast, HAADF contrast is based on scattering amplitude and is known as atomic number Z contrast, whose sensitivity depends on the scattering power of the relevant atoms 4 . Thus, for detection of lighter atoms with extremely weak scattering, ABF phase-contrast imaging based on wave interference is preferred in the present case. This produces clearer atomic-resolution images because it requires that the atoms only alter the phase of a wave 5,6 .
Supplementary Figure 11. Comparison of aberration-corrected STEM ABF, STEM HAADF and conventional HRTEM images of Type A and Type B GB structures. (A1-A3) A Type A GB facet or a nanometer-thick amorphous-like intergranular film (that was observed in a S-doped Ni sample treated at 675 ºC in this specific case). (B1-B3) A Type B GB facet (that was observed in a S-doped Ni sample pretreated at 675 ºC and subsequently annealed at 575 ºC in this specific case). Here, (A1) and (A2), as well as (B1) and (B2), are a pair of synchronized STEM ABF and STEM HAADF images, respectively, while (A3), as well as (B3), is the conventional HRTEM image of the same GB facet. In both cases, STEM ABF images give better contrast and show the GB structures with the segregation of the light element S.

Supplementary Note 5: EDXS measurements of the GB adsorption of S
We used the energy dispersion X-ray spectroscopy (EDXS) based box scanning method (in STEM, JEOL ARM200F) to quantify GB excess adsorption of sulfur in the GBs. This was done by measuring the solute concentration in a well-defined volume containing GB, from which the excess concentration per unit area relative to the grain interior (as the reference) was determined. The details of this box scanning method can be found in Ref. 7 and is briefly explained with an example, as follows.
As illustrated in Supplementary Fig. 12A, the three identical rectangles represent the electron beam scanning area with a fixed size of 90.4 Å × 15.3 Å. The distance between the scanning area in the grain interior to the GB was fixed at 60 Å. Thus, the average thickness (scanned volume) of the scanned area in the grain interior should be similar to that of the GB. Each selected area was scanned by an electron beam with a spot size of 8C (the JEOL spot size number) for 70 seconds. The parameters of EDXS analysis were kept consistent for all the GBs in this study. Supplementary  Fig. 12D shows the typical spectra collected from a Ni GB and adjacent grains.
The Cliff-Lorimer method was used to obtain relative concentrations of the elements. 8 Normalized to nickel, the sulfur concentrations are given by: where kSNi is a calibration factor, and IS and INi are the integrated peak intensities for element sulfur and nickel, respectively. The database of calibration factors for this specific EDS detector in ARM200F was provided by the JEOL company. Taking the Si as a reference, the calibration factor is 1.783 for the Ni K line and 1.137 for the S K line. Thus, the calibration factor for the sulfur to the nickel is 0.64 and Eq. (1) can be rewritten as: By intergrading the peak intensities for the lines of interests (SKα, NiKα) after background stripping, the S concentration can be obtained. The S concentration in the Ni grain interior is negligibly small because of the low solubility of S in Ni, which cannot be detected by EDXS. Therefore, the excess of S on the GB per unit area can be expressed as: where ГS is the GB excess of S per unit area, N is the atomic density of the S (0.065 mol/cm 3 ), V is the analyzed volume, A is the GB area, w is the width of the scanned area (15.3 Å in this study), and Vm is the molar volume (9.63 cm 3 /mol). The corresponding EDX spectra obtained from the GB and the two adjacent crystalline grains in (c). The pink belt indicated the Skα peak that is significant in the EDX spectrum obtained on the GB, while the EDX spectra from the two adjacent grain interiors have no detectable Skα peak. The Cuk peaks were from the TEM Cu grid. No detectable Ga peaks appeared, indicating that the FIB milling did not result in chemical contamination. The same EDXS analysis method and parameters were used for analyzing all the GBs in this study for consistency.

Supplementary Note 6: EELS mapping
Electron energy loss spectrum (EELS) was recorded using a Gatan Enfinium spectrometer (equipped on the ARM-200F STEM) with an energy resolution of (full-width at half maximum) ~0.5 eV. The S segregation at a Type A GB facet was analyzed by EELS mapping as shown in Supplementary Fig. 13. A nanometer-thick S-enriched region was evident in the EELS map, consistent with STEM and EDXS observations. The energy-loss range near the S L2,3 edge shows the segregation of S at the GB. The energy-loss range near the Ni L2 edge shows no significant change at the GB.

Supplementary Note 7: GB edge-on conditions and verification with a throughfocus series of ABF images
An "edge-on" condition for GBs is a requirement to clearly image the GBs in TEM/STEM. When a GB was set to an "edge-on" condition, the GB is parallel to the electron beam in the microscope. To ensure that the GB was set on an "edge-on" condition, we used a through-focus series of ABF micrographs to examine through the thickness of the TEM specimen.
An example is shown in Supplementary Fig. 14, where there was no significant change in thickness and the morphology for the amorphous-like GB when the focus varied from −6 nm to +6 nm, implying that the GB is edge-on. Another example is shown in Supplementary Fig. 15 for a bilayer-like GB, where the position of the GB did not shift when the defocus varies, indicating an "edge-on" condition.
The through-focus series of ABF micrographs also indicated that the GB structures are uniform in the through-thickness direction, and as such the STEM images truthfully represent the interfacial widths and structures in the projections.
Supplementary Figure 14. A through-focus series of STEM ABF micrographs of a Type A (amorphous-like) GB facet. The defocus values are labeled. There is no significant change of the apparent interfacial width, indicating the uniformity of this nanometer-thick, amorphous-like, intergranular film throughout the specimen thickness direction.
Supplementary Figure 15. A through-focus series of STEM ABF micrographs of a Type B GB facet.
The defocus values were labeled. There is no significant change of the GB position and interface width/morphology, indicating that this GB facet is edge-on and it possesses the same character throughout the thickness direction.
Supplementary Note 8: FFT filtering of pair STEM HAADF/AFB images (for Fig. 3f & Fig. 3g in the main article only) FFT filtering of STEM HAADF/ABF images ( Fig. 3f and Fig. 3g in the main article) was implemented by performing FFT of the entire raw STEM image. The FFT pattern showed the periodic information of the lattice in the frequency domain. A concentric mask was applied to exclude the central spot and high frequency spots (while only first order spots were uncovered). The masked frequency information was then used to obtain the inverse FFT image.
FFT filtering was used to remove the background contrast to clearly show the partial structural orders in the amorphous-like GB structures.
We note that Fig. 3f and Fig. 3g in the main article are the only FFT filtered images reported (for the purpose of making the partial structural orders in the amorphous-like GB structures clearly visible); all other STEM and HRTEM images in the main article and the Supplementary Information are un-filtered images.
Supplementary Note 9: Testing and calibration of the first-principles derived reactive force field (ReaxFF) potential for Ni-S The first-principles derived reactive force field (ReaxFF) 9 for Ni and S used in this work has been validated against experimental data and first-principles quantum-mechanical calculations based on the density functional theory at 0 K. In order to calibrate the ReaxFF for simulating Sdoped Ni at high temperature, we first computed the melting temperature Tm of pure Ni using this ReaxFF. Pure molecular dynamics (MD) simulation (at a zero-pressure condition) was conducted on a supercell of pure Ni containing a solid-liquid interface. By calculating the volume of the supercell at various simulation temperatures, Tm was predicted to be 2227.5 K with an accuracy of ±5 K (Supplementary Fig. 16A). Therefore, all the simulated temperatures in this work were scaled based on the simulated melting temperature.
Subsequently, we used a hybrid Monte Carlo and molecular dynamics (hybrid MC/MD) method to determine the chemical potential difference that corresponds to the equilibrium condition (at each temperature), which should result in no motion of a solid-liquid interface. In hybrid MC/MD simulations, the total number of atoms and the chemical potential difference between Ni and S Δµ (µS − µNi) were fixed while the number of S atoms was randomly varied. The direction of the solid-liquid interface motion was monitored by computing the rate of the volume change of the system as the chemical potential difference Δµ was varied in small increments at a fixed temperature. When Δµ was set to −0.474 eV, there was no motion of the solid-liquid interface observed at T = 1222.12 K (corresponding to a scaled temperature of 675 °C in the experiments), as shown in Supplementary Fig. 16B. At the liquid front, the equilibrium between solid and liquid. Subsequently, the same Δµ obtained from the solid-liquid equilibrium was used in simulating the equilibrium structure in S-doped Ni GBs.
Supplementary Figure 16. Calculations of the melting temperature and equilibrium compositions of the Ni-S binary system using a first-principles derived reactive force field ReaxFF potential 9 . (A) The volume change of a supercell of pure Ni with increasing temperature, shows the melting of pure Ni at 2227.5±5 K with the ReaxFF potential. (B) A supercell with a solid-liquid interface that does not move at 1222.12 K; this and similar calculations were used to calculate liquidus composition to calibrate the ReaxFF potential.

Supplementary Note 10: Selection of model GBs for hybrid MC/MD simulation
Five GB models with different orientation relationships were created and simulated with hybrid MC/MD simulations to mimic the observed GBs in experiments. The sizes of the models must be significantly smaller than those in experiments to allow simulations in realistic timeframes. Periodic boundary conditions were used; thus, it is infeasible to exactly match the orientations of both the left and right grains observed experimentally nor adopt GBs of very large  values. We have further verified that the asymmetric GBs we selected have GB energies (GB's) that are comparable with those of general GBs.
 To confirm this, pure Ni GB models were created and relaxed at T = 300 K using MD simulations. The GB energies of these three models were obtained by first quenching them to T = 1 K and then calculating with the equation: EGB= (Eall -Ebulk * NNi) / A, where Eall is the potential energy for the model including the GB, Ebulk is the potential energy for a Ni atom in the bulk, NNi is the number of Ni atoms, and A is the GB area. In order to compare the GB energy with results from the literature, 10 we used the same EAM potential 10

Supplementary Note 11: Solubilities of S in Ni based FCC phase and alloy compositions
We used isothermal annealing and quenching to preserve high-temperature interfacial structures in the Ni specimens in equilibria with S-enriched secondary phases. Similar thermal treatments in a prior study 11 resulted in sulfur bulk concentrations lower than 100 ppm, which are below the detection limits of EDXS and EELS. Our TEM characterization for all the GBs studied in this work did not observe any precipitates at the GBs.
In this study, the alloy compositions of our specimens should be on the solidus/solvus line at the corresponding final equilibrium temperatures. The solubility limits of sulfur in nickel were estimated to be 20 ppm at 625 C 11 and 50 ppm at 700 C 12 in two separate studies. We estimated that the bulk compositions of the Ni-based FCC phase should be within a range of 10-100 ppm. More accurate data on the temperature-dependent solubility limits, which should represent our alloy compositions, are not available.

Supplementary Note 12: An exemplar to verify the thermodynamic equilibrium of Type A (amorphous-like) IGFs
To unequivocally demonstrate that the Type A GB complexions (i.e., amorphous-like IGFs) are indeed in a thermodynamic equilibrium state, Supplementary Fig. 17 shows the character and thickness of the amorphous-like intergranular films (IGFs) at four different Type A facets at different locations in one GB (in a specimen equilibrated and quenched from 675 C) as an exemplar.
As shown in Supplementary Fig. 17, all four parallel Type A facets of the (100)//~(532)~1° off orientation exhibited an amorphous-like IGF; furthermore, the measured means ( standard deviations) of the thicknesses of amorphous-like complexions on the four independent facets are 1.12  0.13 nm, 0.98  0.15 nm, 0.76  0.06 nm, and 0.92  0.17 nm, respectively. The narrow distributions of measured thicknesses throughout this long GB suggest the amorphous-like complexion represents a thermodynamic equilibrium state of this GB at this equilibrium temperature.

Supplementary Note 13: Analyses of partial structural orders in STEM images of Type A (amorphous-like) IGFs
To reveal the partial structural (crystalline) orders in the Type A (amorphous-like) IGFs, we used the "line-by-line FFT" analysis of the (partial) crystalline order (see "Methods") and Periodically-averaged STEM images following the method proposed by Ref. 13. Selected results are shown in Supplementary Fig. 18-20 as well as Fig. 3d in the main article.

Supplementary Note 14: Intergranular fracture of S-doped Ni specimens
S-doped Ni specimens were subjected to a bending test. As shown in Supplementary Fig. 21, the fracture surfaces of S-doped Ni specimens exhibited characteristic intergranular fracture features. The intergranular fracture occurred through the entire cross-section of the specimens. Faceting was observed on fractured surfaces for all specimens. Denser (and finer) facets were observed in specimens equilibrated (annealed) at higher temperatures.
We used SEM to image all fractured GB planes throughout the entire cross-section to count the fraction of the fractured GB planes without facets and the results are displayed in Supplementary Table 1. Higher fractions of fractured GB planes are faceted in specimens equilibrated (annealed) at higher temperatures. As the equilibration (annealing) temperature decreased, dimples on the fractured GB planes, which are indications of the occurrence of ductile fractures inside some pits of the bulk specimens, were observed in some regions, as shown in Supplementary Figs. 21C and 21D. Table 1, higher equilibration (annealing) temperatures result in more brittle fractures (in contrast to normal cases where materials are typically more brittle, which is presumably related to the fact that these specimens were S-saturated Ni specimens, in equilibria with S-rich secondary phases, so that S content is higher at higher equilibrium temperatures) with higher fractions of facets. Some dimples indicated that more ductility was observed in specimens equilibrated (annealed) at lower temperatures.  Noting that we often call the modeled GBs as "GB facets," since they correspond to the Type A and Type B facets observed in experiments, even if they are stand-alone GBs in bicrystals with periodic boundary conditions, instead of faceted GBs in simulations.
It is interesting to point out that a bilayer-like complexion also forms at the (100)//(926) GB facet at a low S chemical potential when Δµs is around −0.393 eV ( Supplementary Fig. 22A), which transforms to an amorphous-like structure with substantial interfacial disordering when the Δµs increases further to Δµs ~ 0 ( Supplementary Fig. 22B). In other words, the amorphous-like GB complexions at high S chemical potentials (corresponding to our experimental conditions, where the specimens were saturated with S) would also likely transform to bilayer-like complexions at lower S chemical potentials, and eventually to "clean" GBs, with reducing S chemical potential (or bulk S content).
Our MC/MD simulations suggest that interfacial phase-like transformations at these two facets -from a "clean" GB to bilayer-like complexion in both cases and from a bilayer-like complexion to an amorphous-like complexion at the (100)//(926) GB facet -are likely continuous (instead of first-order), which is indicated by the continuous changes in both adsorption and excess GB disorder in both cases ( Supplementary Figs. 9A and 9B).

Supplementary Note 16: Bond analysis, polar Ni-S structures, and bipolar interfacial structures
A Ni-S bond is considered to form between a S atom and a Ni atom if the distance between them is smaller than a certain cutoff. This cutoff is selected as 2.4 Å, which is larger than the bulk compound bond lengths of 2.05, 2.28, 2.38, and 2.34 Å for α-S, Ni3S2, NiS and NiS2, respectively.
It was observed that S atoms do not in general sit on the lattice positions of Ni in the GBs.
It was found that a large portion of Ni-S structures are polar, where Ni atoms are concentrated at one side of the S atom. Two typical polar Ni-S structures are shown in Supplementary Fig. 6. The polar Ni-S structures exist in both bilayer-like and amorphous-like GBs. The distributions of Ni-S bond angles and bond lengths are similar, as shown in Supplementary Fig. 24(A)-(D).
Furthermore, as shown in Supplementary Fig. 24, the polar Ni-S structures observed in Sdoped Ni GBs are different from all known Ni-S compounds, such as those in Ni3S2, NiS, NiS2, and Ni3S4. Although the bond angles (i.e., 60~70 and around 120) and bond lengths (i.e., around 2.25Å and 2.35Å) found in GBs correspond to the peaks in compounds, their distributions are different. Supplementary Note 17: Tensile properties from MD testing MD simulations of tensile testing were conducted on the GB structures obtained at different chemical potential differences for both the (100)//(926) GB facet (Supplementary Fig. 25) and the (110)//(345) GB facet (Supplementary Fig. 26). A constant strain rate was applied by deforming the simulation cell during the MD simulations. The periodic boundary condition was used in the direction perpendicular to the grain boundary. Due to the periodic boundary condition, there were two GBs in each simulation cell. Due to the constraint of computational time and resource, the strain rate in MD simulations is typically much higher than those used in experiments, which is an intrinsic limitation of all MD simulations. The same strain rate of 10 9 s -1 was applied to the pure and S-doped Ni models for a valid comparison. It is clearly shown that these GBs undergo a ductile-to-brittle transition as the GB excess in S increases. For the (110)//(345) GB facet ( Supplementary Fig. 26), this transition occurred when the GB excess in S reached 4.33 nm -2 . The toughness of these GB models was obtained by computing the area under the stress-strain curves for an applied strain of up to 0. GB embrittlement is defined as segregation-induced intergranular brittleness of normally ductile polycrystals following Rice and Wang 14 and others. The GB embrittlement is correlated with (but not identical to) the ideal work of interfacial separation (2γint in the Rice-Wang model, 14 as discussed below), which can be assessed by theories and DFT calculations. Experimentally, prior studies assessed the GB embrittlement from counting the fraction of intergranular fractures 15,16 or examining the effect of the embrittling element segregation in changing the ductileto-brittle transition temperature (DBTT) 17 . Yamaguchi and Kameda also showed that the GB embrittlement can be induced by a small amount of solute segregation, if the embrittlement is defined as the reduction of local fracture stress in notched-bar bending tests or fracture toughness in compact tension tests. 18 In this study, we used a "computed tensile toughness" from MD simulations, which was determined by integrating the stress-strain curve: where ε is strain, εf is the strain upon failure, and σ is the stress. This computed tensile toughness is a fracture stress defined in computation (the MD simulation), which is not the fracture toughness. This computed tensile toughness measures the ability of the testing material to absorb energy before fracturing in the MD simulation, including the energies for intragranular defects formation and movement (including dislocations, if they do initiate as in the case of pure Ni) and cracking (the formation of crack tips and subsequent decohesion).
We again emphasize that this computed tensile toughness (that is the energy of mechanical deformation per unit volume prior to fracture in the MD simulation, with a unit of J/m 2 or Pa) is not the "fracture toughness" defined in fracture mechanics (that has a unit of Pa√ ). The fracture toughness measures a material's ability resist fracture and it is a materials property (independent of the length and sharpness of the existing crack); however, it is difficult to compute the fracture toughness directly for the current case.
In general, the experimentally-measured tensile toughness is not an intrinsic material property for a brittle material since it depends on the size and shape of any preexisting cracks and defects; however, this "computed tensile toughness" can be well defined in computation (for a crack-free material) and conveniently calculated from the MD simulation to represent (at least) the (relative) extent of embrittlement of the testing material.
In a realistic situation, the fracture stress (or an experimentally-measured tensile toughness of a real material) depends on the length and sharpness of the existing crack(s). However, the current simulations do not include preexisting cracks (so that the computed tensile toughness measures the intrinsic material property, including the nucleation of any cracks). More importantly, this computed tensile toughness can be conveniently computed from the MD tensile simulation for a fair relative comparison of pure and doped specimens to (at least qualitatively) assess the GB embrittlement.
The tensile toughness should be correlated with (but not identical to) the work of separation: For a (completely) brittle intergranular fracture, the ideal work of interfacial separation (2γint, as denoted by Rice and Wang 14 ) without any energy dissipation from plastic deformation or other defects generation, also known as the work of adhesion in the wetting community, can be expressed for a GB as: where γS is the surface energy (after the fracture) and γGB is the GB energy (before the fracture). This ideal work of interfacial separation (2γint) is used to characterize the extent of GB embrittlement in the Rice-Wang model 14 and many DFT calculations.
We should further note that MD simulations can also provide further insights of failure modes, e.g., dislocations did initiate in pure Ni with ductile fractures, whereas the brittle intergranular fractures occurred in S-doped Ni, as shown in Supplementary Fig. 7.

Supplementary Note 19: Kikuchi patterns and measured GB disorientation angles
The misorientation of a GB is the rotation required to bring one set of crystal axis (of one of the two abutting grains) into coincidence with the other 19 . One can define a "disorientation angle" as the (smallest) rotation angle to bring two sets of crystal axes (of the two abutting grains) into coincidence within the fundamental zone for cubic symmetries, which should be in the range of 0° to ~62.8° due to the cubic symmetry.
The crystal axes of the adjacent grains were determined from Kikuchi patterns, which were obtained via Ronchigrams in STEM. The GBs were set to the "edge-on" condition, in which the electron beam is parallel to the GB planes. The two abutting grains were set on the same tilting angle. Tilting was eliminated during the Kikuchi patterns acquisition. Supplementary Table 2 listed the disorientation angles of selected GBs determined from Kikuchi patterns. The assembly of simulated results of five GB facets (Supplementary Table 3) and experimental observations of 29 independent GB facets ( Table 1 in the main article) clearly suggest that the formation of Type A vs. Type B facet is dictated by the orientation of the lower-index grain terminal plane, instead of misorientation as commonly believed.
On one hand, we have observed the following ( Table 1 in Table 3). In addition to the types of complexions formed, the simulated GB adsorption amounts of S also agree with experimental observations (the computed vs. measured 's, when comparisons are made for GB facets with the same dictating grain terminal planes, e.g., Here, it is worth noting that the asymmetric 3 (310)//(457) GB facet behaves more like a general GB (despite being a 3 GB) with a GB energy that is significantly higher than that of the special 3 (111)//(111) twin boundary, but more comparable with other more general GBs (Supplementary Table 3).
Furthermore, five normally "clean" or Type C GBs were found ( Table 1 in Table 1 and Fig. 39) and the other is a low-angle GB ( Supplementary Fig. 40), and all are low-energy GBs with little driving force for S adsorption. The absence of S adsorption on these GBs is due to the small free volume and low fraction of "broken bonds" at these lowenergy GBs, which is a well understood and established phenomenon; e.g., a similar phenomenon is observed in the Ni-Bi system. 21 Our simulation ( Supplementary Fig. 44) further supports that the 3 (111)//(111) twin boundary is normally "clean" or Type C; although we initially set the GB dividing plane of this 3 to be (100)//(21 2), nanoscale faceting occurred, producing "clean" (111)//(111) symmetric twin boundary facets (Supplementary Fig. 44).
Supplementary Table 3. Summary of the complexion formation of simulated GBs of different grain terminating plane orientations. The results clearly suggest the formation of complexions correlated with the orientation of the lower-index grain terminating plane, instead of the misorientation. The simulation results agree well with experimental observations and our hypothesis. The GB energies (GB's) listed in the following table were calculated for pure Ni using an EAM potential that was used by Olmsted et al., 10 who calculated the GB's for general GBs to be in the range of 1-1.5 J/m 2 ; these results suggest that most of these asymmetric GBs behave more like general GBs with comparable GB's, except for 3 (111)//(111) twin boundary, which has a substantially lower GB. Beyond the GB embrittlement, the current study also provided a significant new insight about the origin of abnormal grain growth in S-doped Ni (including electrodeposited nanocrystalline Ni with S contamination). [22][23][24] On one hand, a series of prior studies have demonstrated that the abnormal grains in S-doped Ni are often cubic with (001) terminal surface planes. [22][23][24] On the other hand, this current study showed that GB facets with one lower index terminal grain surface of the (100) plane and another high-index matching surface all exhibit Type A amorphous-like IGFs that are more disordered with higher levels of S absorption (than all other GBs examined); in contrast, all other types of GB facets (at least all those that have been examined in this study) are less disordered with lower levels of S adsorption (being Type B bilayer-like or Type C "clean" GBs). See, e.g., Table 1 in the main text and Supplementary Notes 1, 2, and 20 for summaries of relevant experimental observations and modeling results.
Combining the two above observations, we propose/conclude that abnormal grain growth in S-doped Ni, including that in electrodeposited nanocrystalline Ni with S contamination, [22][23][24] is likely a result of enhanced GB mobility of the more disordered Type A amorphous-like GBs, in comparison with other type of more ordered GBs.
Here, our proposed mechanism is consistent with Dillon et al.'s theory of abnormal grain growth mechanisms for doped Al2O3 and other systems; 3,25,26 they observed that the abnormal grain boundaries exhibit complexions with higher levels of impurity adsorption and structural disorder than the "normal" boundaries in the same specimens, thereby attributing abnormal grain growth to complexion transitions. 3,25,26 Yet, there may be a difference. The abnormal grain growth in S-doped Ni can (in principle) be resulted from the highly-anisotropic nature of complexion formation in this system (and may depend less on the occurrence of a complexion transition). Supplementary Figure 40. Another Type C or "clean" GB with no significant S segregation. This specific GB was observed in the S-doped Ni specimen annealed at 575 °C for 10 hours and subsequently water-quenched. Its orientation relationship was determined to be ~(111)~2° off//~(233)~1° off; the disorientation angle is about 10° so that it is a low-angle GB with low segregation driving force. The EDX spectra obtained from the GB and the two adjacent crystals are shown at the left side of the figure, and indicate no significant (detectable) S segregation.