Acta Materialia 225 (2022) 117522 Contents lists available at ScienceDirect Acta Materialia journal homepage: www.elsevier.com/locate/actamat Quantitative analysis of grain boundary diffusion, segregation and precipitation at a sub-nanometer scale Zirong Peng a,b,∗, Thorsten Meiners a, Yifeng Lu c, Christian H. Liebscher a, Aleksander Kostka d, Dierk Raabe a, Baptiste Gault a,e,∗ a Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Straße 1, Düsseldorf 40237, Germany Chair of Materials Engineering of Additive Manufacturing, Department of Materials Engineering, TUM School of Engineering and Design, Technical University of Munich, Boltzmannstr. 15, Garching b. Munich 85748, Germany c Database Systems and Data Mining Group, Ludwig-Maximilians-Universität München, Oettingenstraße 67, München 80538, Germany d Zentrum für Grenzflächendominierte Höchstleistungswerkstoffe (ZGH), Ruhr-Universität Bochum, Bochum 44801, Germany e Department of Materials, Royal School of Mines, Imperial College, Prince Consort Road, London SW7 2BP, UK b a r t i c l e i n f o Article history: Received 22 June 2021 Revised 15 October 2021 Accepted 23 November 2021 Available online 8 December 2021 Keywords: Atom-probe tomography STEM Grain-boundary diffusion Grain-boundary segregation Grain-boundary segregation-induced phase transformation a b s t r a c t Grain boundaries are intrinsic and omnipresent microstructural imperfections in polycrystalline and nanocrystalline materials. They are short-circuit diffusion paths and preferential locations for alloying elements, dopants, and impurities segregation. They also facilitate heterogeneous nucleation and the growth of secondary phases. Therefore, grain boundaries strongly influence many materials’ properties and their stabilities during application. Here, we propose an approach to measure diffusion, segregation, and segregation-induced precipitation at grain boundaries at a sub-nanometer scale by combining atom probe tomography and scanning transmission electron microscopy. Nanocrystalline multilayer thin films with columnar grain structure were used as a model system as they offer a large area of random highangle grain boundaries and inherent short diffusion distance. Our results show that the fast diffusion flux proceeds primarily through the core region of the grain boundary, which is around 1 nm. While the spatial range that the segregated solute atoms occupied is larger: below the saturation level, it is 1,2 nm; as the segregation saturates, it is 2–3.4 nm in most grain boundary areas. Above 3.4 nm, secondary phase nuclei seem to form. The observed distributions of the solutes at the matrix grain boundaries evidence that even at a single grain boundary, different regions accommodate different amounts of solute atoms and promote secondary phase nuclei with different compositions, which is caused by its complex threedimensional topology. © 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. 1. Introduction Grain boundaries (GBs), i.e., the interface between crystals of different orientations, are among lattice imperfections that have the strongest influence on the strength, conductivity, mass transport, and damage, etc. of materials, owing to their large volume fraction and 5–20% reduced atomic density compared to the adjacent crystalline regions [1,2]. In conventional polycrystal bulk alloys, GBs can form up to several hundred square meters of internal interfaces even in small volumes of material. In nanocrystalline materials, the fraction of atoms at GBs and bulk Abbreviations: GB, Grain boundary; APT, Atom probe tomography; STEM, Scanning transmission electron microscopy. ∗ Corresponding authors at: Max-Planck-Institut für Eisenforschung GmbH, MaxPlanck-Straße 1, Düsseldorf 40237, Germany. E-mail addresses: zirong.peng@tum.de (Z. Peng), b.gault@mpie.de (B. Gault). https://doi.org/10.1016/j.actamat.2021.117522 1359-6454/© 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. are even comparable [3]. If, for instance, the grains are spherical, the volume fraction of GBs can be estimated as 1-(1-δ /d)3 , where δ and d represent the width of the GBs and the diameter of the grains respectively [4]. Assuming δ is 0.5 nm and d is 10 nm, the volume fraction of GBs will be 14.26%. If d is further reduced to 5 nm, the GBs volume fraction can reach 27.1%. The less-dense atomic packing and relatively weaker chemical bonds make diffusion along GBs several orders of magnitude faster than that through crystals, in particular at elevated temperatures. Fast mass transport along GBs governs the kinetics of many processes occurring during materials production, heat treatment, as well as over their lifetime. Typical examples are creep, sintering, recrystallization, grain growth, phase transformation, and discontinuous reaction. Short-circuit diffusion is also one of the most critical threats to the stability and reliability of joints, thin-film interconnections, and multilayers [5,6]. Thus, understanding and controlling diffusion-controlled changes and decay, particularly critical Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 the service life of the mold. Besides, PtIr also has numerous applications in other industrial fields, for example as catalysts in hydrogenation and dehydrogenation reactions [37], and as electrodes for electrochemical oil/water demulsification and purification of bilge water [38]. in nanocrystalline materials, is a great challenge for the safe design of such diverse parts as artery stents, microelectronic circuits, and protective coatings, etc. Besides rapid diffusion, solutes and impurities segregation to GBs leads to a decrease in interfacial energy, as Gibbs adsorption isotherm states [7]. As a result, the overall free energy of the system also decreases. Segregation can induce the formation of complexions or secondary phases, giving rise to different GB structural-chemical states that can lead to e.g. intergranular failure or changes in transport properties [8–11]. Recently, much attention was devoted to GB segregation engineering [12] and complexion engineering [13], whereby the manipulation of solute decoration at GB allows for controlling bulk properties of polycrystalline and nanocrystalline materials. Direct experimental observation of GBs at atomic scales is very challenging, especially for GBs that have complicated local structures and chemistries after solutes adsorption. Recent developments in atomic resolved (scanning) transmission electron microscopy ((S)TEM) provide a possibility [14–17], but there, normally only two-dimensional (2D) projections of GB were obtained. By atomic electron tomography (AET), it is possible to reveal the three-dimensional (3D) atomic structure of GB [18–20]. However, this approach is still not widely applied. Since many images are needed to be taken from the region of interest, studying electron-beam-sensitive materials is problematic. In this work, we show that by combining atom probe tomography (APT) with high-resolution scanning transmission electron microscopy (HRSTEM), we can directly analyze the GB diffusion, segregation, and precipitation phenomena at a sub-nanometer scale. APT provides three-dimensional elemental mapping with sub-nanometer resolution and a sensitivity in the range of tens to hundreds of parts per million. It has been successfully applied to study different materials including metals and alloys, semiconductors, glasses, ceramics, and biological materials, etc [21–24]. With site-specific sample preparation [25] and advanced data analysis [26,27], APT becomes one of the most powerful 3D techniques to investigate GB and interfaces [28,29]. HR-STEM uses a tightly focused electron beam (<0.1 nm) scanning the specimen and offers a spatial resolution sufficient to resolve individual atomic columns [30]. Energydispersive X-ray spectroscopy (EDS) and electron energy-loss spectroscopy (EELS) performed along with STEM allow obtaining local chemical information, which becomes an important supplement to APT as the examination volume here is typically ten thousand times larger than that of APT. This combination of techniques is ideal for the quantification of solute atoms segregated at complex 2D interfaces as well as precise structural characterization of the GB [31–33]. We also introduced a new APT data analysis method to determine the chemical width of GB and the distribution of solute atoms along the GB surface [34]. This information provides new insights into the structure of the GB and the nucleation of the secondary phase. In principle, the methodology introduced here can be employed to study any material system. Most diffusion studies are performed by using bulk diffusion couples or tracer diffusion. Here, we showcase an approach using sputter-deposited multilayer thin films. Using thin films is a straightforward way to obtain a nanostructured matrix with a high density of general, random high-angle GBs, which facilitates APT measurements, as almost every sharp, needle-shaped APT specimen will contain one or more GBs. Thin films also provide short diffusion distances [35]. The system of interest here is PtIr-Cr that finds application as surface protective coatings for molds employed in precision glass molding, a manufacturing process applied worldwide to produce high-quality lenses with complex geometries [36]. Since the degradation of this bimetallic layer coating is controlled by the interactions between Cr and GBs in the PtIr layer [5], a detailed investigation of the diffusion of Cr can help to better predict 2. Materials and methods 2.1. Sample preparation Nanocrystalline cemented tungsten carbide with around 2 wt.% Co binder (Ceratizit S.A) was used as substrate. Before sputtering, the surface of the substrate was ground, polished, and cleaned. PtIr and Cr metallic thin layers were deposited by using a magnetron sputtering unit (CemeCon CC800/9). Detailed information about the layer deposition process can be found in Ref [5]. Overall, the PtIr layer contains approx. 33 at. % of Pt and 67 at. % Ir. Although according to the Pt-Ir phase diagram, this composition is located within the miscibility gap, we did not observe a clear indication of phase decomposition, which is in good agreement with experimental results reported previously [39–41]. As Fig. 1(a–d) illustrates, we designed two types of samples, denoted as PtIr/Cr and Cr/PtIr/Cr respectively. The bilayer PtIr/Cr sample (Fig. 1(a,b)), consisting of a ~650 nm-thick PtIr top layer and a 20 nm-thick Cr middle layer, was used for GB diffusion investigation. While, for the GB segregation and precipitation study, an additional 1 μm-thick Cr layer was deposited on the surface of the PtIr layer (Fig. 1(c,d)). Fig. 1(e) shows a cross-sectional brightfield (BF) STEM image of the as-deposited PtIr/Cr bilayer sample. As expected, the PtIr layer exhibits a structure of nanometre-sized columnar grains with mostly random high angle GBs (HAGBs), roughly perpendicular to the interface between the PtIr and Cr layer. In the following, unless otherwise specified, only random high angle GBs are considered. 2.2. Heat treatment The annealing treatments were performed at 630 °C under a 90% N2 -10% H2 gas mixture for 336 h in a custom-built set-up [42]. The dew point of the gas mixture, which governs the water content in the gas, is controlled at -36 °C. The oxygen content is adjusted through the equilibrium between H2 O and H2 . Here, the oxygen partial pressure of the atmosphere is 4.76 × 10−29 bar, i.e., 3.57 × 10−26 Torr and 4.67 × 10−29 Atm. According to the Ellingham diagram [43], this oxygen partial pressure is higher than the critical partial pressure of Cr oxidation. However, as we discussed previously [5], no internal oxidation of Cr is expected. Furthermore, under such annealing conditions, Cr atoms diffuse fast along the GBs within the PtIr layer, but the diffusion through bulk appears to be limited, facilitating our GB diffusion study. In the Cr/PtIr/Cr trilayer sample, since Cr atoms diffuse into the PtIr layer from both the top and bottom Cr layers, after prolonged annealing, PtIr GBs will be saturated with the segregated Cr atoms. Afterward, nucleation and precipitation of Cr-rich intermetallic particles can be observed. 2.3. Sample characterization APT specimens were prepared by an in situ lift-out method using a focused ion beam-scanning electron beam (FIB-SEM) dualbeam instrument (FEI Helios Nanolab 600i) [44]. Commercial flattop Si MicrotipTM arrays (CAMECA Instruments) were used as support posts. After sharpening the specimen to a sharp needleshaped tip, a milling step with a low-energy ion beam (2 kV and 28 pA) is carried out to remove the surface areas that are strongly damaged by the high-energy Ga ion beams. As Fig. 1(b) and (d) 2 Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 Fig. 1. (a–d) Sketches of the multilayer thin film samples studied in this work with the illustration of the position and orientation of the APT and STEM specimens: (a) and (c) as-deposited PtIr/Cr bilayer and Cr/PtIr/Cr trilayer sample respectively; (b) and (d) PtIr/Cr and Cr/PtIr/Cr sample after 336 h annealing at 630 °C under an atmosphere with 4.76 × 10−29 bar oxygen partial pressure respectively. (e) Cross-sectional BF-STEM image of the as-deposited PtIr/Cr bilayer sample. PtIr layer. Fig. 2(b–e) are atom maps of the annealed PtIr/Cr sample obtained by APT: (b) shows an overall cross-sectional view; (c–e) are magnified top views of the regions marked by the rectangles in (b). Consistent with the STEM observations, Cr atoms, represented by red dots, are segregated to the GB of the PtIr layer. However, the segregation is not uniform but shows a steep gradient. The further away from the Cr layer, i.e. the longer the diffusion distance, the lower the Cr content. Although this was expected, quantifying the changes in Cr content as a function of the diffusion distance remains challenging. To quantify the Cr content, we divided the regions (c–e) into bins of 0.5 nm, and for each bin, we calculated the atomic percent of Cr, i.e., Ncr /Ntotal where Ncr and Ntotal represent the total amounts of Cr atoms and atoms of all components, respectively. As Fig. 2(f) shows, by connecting the data points of each region, we obtain a 1D profile showing the changes in Cr content across the PtIr GB, which we refer here as to 1D composition profile. We use the peak value of this 1D composition profile as the Cr content at that specific location of the PtIt GB (cGB Cr) and the full-width at half-maximum (FWHM) of the peak of the profile as the chemical width of the PtIr GB [46]. In Fig. 2(f), this FWHM is indicated by dashed lines. For the regions (c), (d), and (e), where the atomic fraction of Cr at the PtIr GB is 13.0, 5.1, and 1.8 at.% respectively, the chemical width of the GB is 2.3, 2.0, and 1.3 nm respectively. This decrease in the chemical width of the GB is associated with the changes in the amount of Cr that has diffused. However, such an analysis leads to a fragmented picture of the Cr distribution at the PtIr GB. Fig. 3(a) is a magnified atom map of a single GB of the annealed PtIr/Cr bilayer sample. The green and large red dots represent Pt and Cr atoms, respectively. To highlight the GB region, surfaces where the Cr content is 0.3 at.%, determined by the method introduced in [40], are shown in red. Fig. 3(b) is a 2D quantitative map describing the Cr content of the PtIr GB shown in (a), which we calculated using the protocol we introduced in ref. [34]. In short, we divided the dataset into subvolumes that are locally perpendicular to the GB. The composition and FWHM are now accessible for each subvolume, allowing us to draw a 2D colored map by interpolating the values measured locally. In addition, we can also define the position of the GB surface by using the center of mass, i.e., the mean position, of the Cr atoms demonstrate, all the APT specimens were prepared with an alignment perpendicular to the sample surface so that the GBs are generally along the analysis direction. APT measurements were conducted using a LEAPTM 50 0 0 XS (Cameca Instruments) instrument with a 60 pJ, 355 nm wavelength UV-laser pulsing. The pulse repetition rate and target detection rate were set at 250 kHz and 15 events per 10 0 0 pulses, respectively. During analysis, the specimen was maintained at a base temperature of 60 K. The reconstruction and analysis of the APT data sets were done using the commercial software IVASTM 3.8.2 (Cameca Instruments). The detailed GB analysis was performed using the in-house developed APT data analysis method, which has been described in Ref. [34]. STEM lamellas were fabricated by an in situ lift-out method [45] using the same instrument as that used for the APT specimen fabrication. As Fig. 1(b) and (d) illustrate, cross-sectional (along the GB direction) lamellae were prepared from the PtIr/Cr bimetallic layer sample, while top-view (perpendicular to the GB direction) lamellae were fabricated from the Cr/PtIr/Cr trimetallic layer sample. STEM observations were carried out on a probecorrected FEI Titan Themis 60–300 S/TEM equipped with a highbrightness field emission gun and a gun monochromator. The microscope was operated at an acceleration voltage of 300 kV with a semi-convergence angle of 23.8 mrad. Images were taken using a bright field (BF) and high angle annular dark-field (HAADF) detector (Fishione Instruments Model 300) with inner and outer semicollection angles of 73 and 200 mrad, respectively. An electron beam current between 70 and 100 pA was used for imaging and spectroscopy. A Super-X windowless EDS detector was employed to make STEM-EDS measurements and a Gatan high-resolution Quantum ERS energy filter was used for STEM-EELS analysis. 3. Results 3.1. Grain boundary diffusion Fig. 2(a) is a cross-sectional HAADF-STEM image overlaid with the corresponding EDS map of Cr, obtained from the annealed PtIr/Cr sample. Within the PtIr layer, Cr appears almost exclusively at the GB, indicating preferential Cr diffusion along the GBs of the 3 Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 Fig. 2. Representative STEM and APT characterization results obtained from a PtIr/Cr bilayer sample after 336 h annealing at 630 °C under an atmosphere with 4.76 × 10−29 bar oxygen partial pressure, revealing the diffusion of Cr along the random high angle GB of the PtIr layer. (a) HAADF-STEM image overlaid with the corresponding EDS map of Cr. (b) Cross-sectional view atom map. The rectangles mark the regions shown in (c–e). (c–e) Magnified top view atom maps from the regions marked by the rectangles in (b). In all atom maps, only Pt atoms (represented by the green dots) and Cr atoms (represented by the red dots) are shown. (f) 1D profile of the atomic fraction of Cr in the PtIr matrix across the GB region of (c–e). The peak value of this profile is used to represent the Cr content at the PtIr GB (cGB Cr). The full-width at half-maximum (FWHM) of the peaks of the profiles, plotted using the dotted lines, are taken as the chemical widths of the GB. Fig. 3. (a) Magnified atom map of a single GB of a PtIr/Cr bilayer sample after 336 h annealing at 630 °C under an atmosphere with 4.76 × 10−29 bar oxygen partial pressure. The green and large red dots represent Pt and Cr atoms, respectively. To highlight the GB region, surfaces where the Cr content is 0.3 at.%, determined by the method introduced in [53], are shown in red. (b) 2D quantitative map depicting the local content of Cr at the PtIr GB (cGB Cr). The black dots are the mesh vertices, i.e. data points, used to calculate the map. At each vertex, we acquired a local Cr content value. Then the 2D color map is drawn by interpolating the value between the vertices. (c) 1D diffusion profile plotted using the data points of (b). The red solid, blue dotted and green dashed lines were drawn using Eq. (1) with the GB diffusion coefficient DGB being 3.6 × 10−22 , 1.7 × 10−22 , and 7 × 10−23 m2 /s, respectively. The blue dotted and green dashed lines represent the estimated diffusion profile from the STEM-EELS measurements. that segregate at the PtIr GB. Compared to the traditional APT data analysis routine, our approach enables a more refined and accurate analysis of both the solute distribution on the GB surface and the local chemical width of the GB. Moreover, since the GB has been reconstructed numerically, detailed information about, e.g. its curvature or roughness can be quantified. These two aspects are essential to a nanoscale GB study [47]. Fig. 3(c) is the 1D diffusion profile (black dots) drawn using the data of the 2D composition map in Fig. 3(b), depicting the Cr content at the PtIr GB as a function of the distance to the Cr layer. Based on the tabulated values for pure species, the evaporation field of the PtIr layer is expected to be relatively high (44 and 45 Vnm−1 for Ir and Pt, respectively) compared to that of Cr (29 Vnm−1 ) [48]. This difference will lead to the specimen developing local curvatures that result in local magnification effects that are well documented for multilayer systems [49]. To avoid this ef- fect, here, the distance is calculated from a position approx. 40 nm above the physical interface. As the 1D composition profiles giving the atomic fraction of Cr in the PtIr matrix in Fig. 2(f) and Fig. S1 reveal, the diffusion of Cr proceeds almost exclusively along the GB. Inside the PtIr grains, there is no measurable amount of Cr, indicating that its bulk diffusive transport is negligible. Therefore our annealing condition falls within the type-C kinetic regime [50,51]. Furthermore, since the total diffusion amount is very limited, we can make the following assumptions: (1) the source of the diffusing species, i.e., the Cr layer, can be approximated as an infinite reservoir, and hence, at the position distance= 0 nm, the composition of Cr is maintained at 100 at.%; (2) the GB can be approximated as a semi-infinite planar defect, making the results amenable to an analytical diffusion analysis. 4 Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 Fig. 4. (a) HAADF-STEM image of a random HAGB of the PtIr layer. (b) EEL spectra of the Cr-L2,3 edge from various positions along the GB shown in (a). As a reference, the EEL spectrum obtained from the Cr layer (position 1, drawn in blue) is also shown. For clarity, the EEL spectra obtained from positions 2-5 are shifted. Fig. 5. (a) Cross-sectional SEM image of a Cr/PtIr/Cr trilayer sample after 336 h annealing at 630 °C under an atmosphere with 4.76 × 10−29 bar oxygen partial pressure. Interdiffusion zone (IDZ) and Kirkendall voids formed between the Cr and PtIr layer. (b) Top-view HAADF-STEM image obtained from the PtIr layer, as marked using the blue line in (a). Intermetallic compound (IMC) precipitates formed along grain boundaries. (c) STEM-EDS map showing the distribution of Pt (in green) and Cr (in red) within the PtIr layer. (d) HR-HAADF-STEM Fourier filtered images resolving the atomic structure of the IMC phase and a PtIr grain. The corresponding fast Fourier transforms (FFT) from these two regions and a unit-cell model of the IMC are also shown. PtIr/Cr interface to the position where Cr can be detected ranges from 25 to 40 nm. Assuming that if the Cr content at the GB is below 5 at.%, the Cr L2,3 -edges will be not reliably detected by EELS, then we can estimate the GB diffusion coefficient using Eq. (1), which is in the range of 7 × 10−23 to 1.7 × 10−22 m2 /s. For comparison, the diffusion profiles estimated based on the STEM-EELS results are also plotted in Fig. 3 (c). Despite the inaccuracies in APT data reconstruction, the variations of the diffusion coefficient obtained from the APT and the STEM measurements at different GBs could result from the differences in the GB structure and geometry. Besides, since the PtIr matrix is nanocrystalline, fast diffusions of Cr along the GB triple junctions (TJs) also contribute to the total transport flux, and there might be a leakage of Cr from the TJs to the GBs [46]. For different GBs, the leakage amount might also be different. Then, applying Fisher’s model [52], the solution of Fick’s second diffusion law is cGB (x, y, t ) = c0 er f c  y  2 DGB t  . (1) Fitting Eq. (1) to the diffusion profile, the 95% confidence interval of the GB diffusion coefficient is 3.5 × 10−22 to 3.7 × 10−22 m2 /s. The R-squared value of the fitting is 0.8766. The red line in Fig. 3(c) is the estimated diffusion profile. Since as mentioned previously, the APT measurements were suffered from the local magnification effect, we also did a detailed STEM analysis to check the diffusion of Cr along individual GBs. As Fig. 4 shows, to accurately locate the diffusion front, EELS in STEM was used to record the Cr L2,3 -edges from various positions along the GB of the PtIr layer. Along random HAGBs, the length from the 5 Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 3.2. Grain boundary segregation and precipitation Fig. 5(a) is a cross-sectional scanning electron microscopy (SEM) image of the annealed Cr/PtIr/Cr trilayer sample. Different from the case of the PtIr/Cr bilayer sample, here the bulk diffusion of Cr inside the PtIr grain is significant, leading to the formation of the interdiffusion zones (IDZs) and Kirkendall voids. This difference in the Cr diffusion behavior between the PtIr/Cr bilayer and Cr/PtIr/Cr trilayer samples arises from the differences in the chemical potentials of Cr in these two material systems [5]. Fig. 5(b) shows a HAADF-STEM image obtained from a top-view TEM lamella (parallel to the sample surface and perpendicular to the GB direction) from the PtIr layer of the annealed Cr/PtIr/Cr trilayer sample. Fig. 5(c) shows a representative STEM-EDS result obtained from this top-view TEM lamella, where the distribution of Pt and Cr are presented in green and red, respectively. As marked by the white arrows, Cr segregates along the PtIr GBs. Small Cr-rich intermetallic compounds (IMC) particles with the size in the range of 10– 50 nm also heterogeneously precipitated along GBs. These are the results of short-circuit diffusion of Cr along the PtIr GBs and triple junctions. To reveal the crystal structure of the IMC, high resolution (HR) HAADF-STEM images were taken, shown in Fig. 5(d), where individual atomic columns can be resolved. Here, contrast is roughly proportional to the square of the average atomic number within a column. Atomic columns with higher atomic numbers exhibit higher intensity. The lattice of the IMC is nearly identical to that of the face-centered-cubic (FCC) PtIr grain, and the periodicity of these darker columns indicates that the IMC exhibits an ordered L12 structure in which we expect Cr atoms to mostly occupy the corners and Pt or Ir atoms occupying the face centers of the unit cell. The expected stoichiometric ratio between PtIr and Cr is 3. Although the IMC (Pt,Ir)3 Cr precipitated along the GB, it grew primarily into one of the adjacent grains. The fast Fourier transformation (FFT) analysis confirmed that the orientation relationship between them is {001}PtIr grain || {001}(Pt,Ir)3Cr. The measured lattice parameter a for the PtIr grain and the (Pt,Ir)3 Cr precipitate is 4.02 ± .06 and 3.94 ± .05 Å respectively. The lattice misfit δ between them, calculated as 2(a(Pt,Ir)3Cr −aPtIr )/(a(Pt,Ir)3Cr +aPtIr ), is 2%. When the (Pt,Ir)3 Cr precipitate is small, such as the case shown in Fig. 5(d), the interface between the PtIr matrix and the (Pt,Ir)3 Cr precipitate is coherent to maintain small interfacial energy. The low misfit there leads to coherency strains. With the growth of the precipitate, the surface energy scales with the surface area of the precipitate, i.e., the square of the precipitate size, while the elastic energy caused by the coherency strains generally scales with the volume of the precipitate, i.e., the cube of the precipitate size [54]. At a certain critical size rcrit , the elastic strain energy becomes dominant, and the coherent interface becomes energetically unfavorable. Then the (Pt,Ir)3 Cr precipitate will lose its coherency with the matrix and a semicoherent interface with the misfit compensated by misfit dislocations will form. Based on the Brooks formula [55], i.e., λ=|b|/δ (|b| is the magnitude of the Burgers vector of the dislocation), the spacing λ between the misfit dislocations will be about 14 nm for the dislocation ½(110). Fig. 6(a) is a cross-sectional APT map obtained from the annealed Cr/PtIr/Cr trilayer sample. To highlight the enrichment of Cr atoms to the PtIr GBs and the (Pt,Ir)3 Cr regions, a set of isocomposition surfaces with the threshold of 20 at.% Cr, are drawn in red and superimposed over the point cloud. Fig. 6(b) is a magnified top-view atom map of the thin slice marked by the semitransparent disc in (a). Overall, the APT data agrees with the STEMEDS data. Fig. 6(c) is a magnified atom map of a single GB. This GB is undulatory and the distribution of Cr atoms along the GB surface seems inhomogeneous. To quantify the local Cr content and the chemical width of the GB, we closely examined it using the Fig. 6. (a) Cross-sectional atom map obtained from the PtIr layer of a Cr/PtIr/Cr trilayer sample after 336 h annealing at 630 °C under an atmosphere with 4.76 × 10−29 bar oxygen partial pressure. (b) Magnified top-view atom map of the thin slice marked by the semi-transparent disc in (a), revealing the segregation of Cr atoms and the heterogeneous precipitation of Cr-rich intermetallic compound (IMC) along GBs. (c) Magnified atom map of the GB region marked by the semitransparent block in (a), revealing the inhomogeneous distribution of Cr atoms along the GB. In all atom maps, only Cr and Pt atoms are included, represented by the red and green dots, respectively. To highlight the GB and IMC regions, 20 at.% Cr iso-composition surfaces, plotted using the method introduced in [53], are shown in red in (a). APT data analysis protocol mentioned previously [34]. The results are summarized in Fig. 7. Fig. 7(a–c) show the 2D quantitative maps depicting in (a) the topography of the GB, i.e. the differences in the z-axis value of the GB surface, in (b) the chemical width of the GB, i.e. the FWHM of the peak of 1D composition profile across the GB, and in (c) the content of Cr at the GB (cGB Cr), i.e. the peak value of the 1D composition profile across the GB. Here, the z-axis is roughly perpendicular to the GB. In (a), to better depict the non-smoothness of the GB, counter lines are also shown. From Fig. 7(b) and (c) we can see that different GB regions accommodate different amounts of Cr atoms. The chemical width of the GB is also not constant. In Fig. 7(d), the chemical width of the GB, extracted from (b), is plotted against the content of Cr at the GB, extracted from (c). Except for a few local regions, marked by colored triangles in Fig. 7(a), 6 Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 Fig. 7. Detailed examination of the GB shown in Fig. 6 (c). (a–c) 2D quantitative maps coloring with (a) z-axis value of the GB surface, (b) chemical width of the GB, and (c) the content of Cr of the GB (cGB Cr). Here, the z-axis is roughly perpendicular to the GB. In (a), to better depict the topography and non-smoothness of the GB, counter lines are also shown. (d) Scatter plot showing the relationship between the chemical width of the GB and the content of Cr of the PtIr GB (cGB Cr), drawn using the data shown in (b) and (c). (e) 1D composition profiles showing the changing of the Cr content across the PtIr GB of the data points marked using triangles in (a) and (d). The composition profiles of the data points marked using triangles that are pointing left, i.e., in purple, red, magenta, orange, and brown, show asymmetric tails on the left side, indicating more Cr atoms distributed on the left side of the GB, marked as G1 in Figs. 6 (c) and 7 (a). The composition profiles of the data points marked using triangles that are pointing right, i.e., in blue, cyan, and green, show asymmetric tails on the right side, indicating more Cr atoms distributed on the right side of the GB, marked as G2 in Figs. 6 (c) and 7 (a). The profile of the data point that is highlighted using a larger black dot (marked by the semi-transparent grey arrow) in (a) and (d) is also shown for comparison. most of the GB area exhibits a chemical width of 1.9–3.3 nm. The Cr content ranges from 10 to 18 at.%. There appears to be no clear relationship between the compositional GB width and the Cr content. Compared to the other sections of the GB, those marked by triangles exhibit wider chemical widths, although their Cr compositions are not necessarily higher. Fig. 7(e) shows the 1D composition profiles across these specific GB regions. For comparison, the profile corresponding to the larger black dot, marked by the semitransparent grey arrow, in Fig. 7(a) and (d) is also plotted, which is nearly symmetrical, and similar to the 1D composition profiles observed previously in the Cr/PtIr bilayer sample (Fig. 2(f)). This is also the case of the GB regions marked using small black dots in Fig. 7(a) and (d) (for clarity, these profiles are not shown in Fig. 7). As Fig. 7(e) shows, the composition profiles of the regions with a larger width, i.e. those marked by the triangles, are asymmetrical. The composition profiles corresponding to the data points marked using triangles that are pointing left, i.e., in purple, red, magenta, orange, and brown, show asymmetric tails on the left side, indicating more Cr atoms distributed on the left side of the GB, marked as G1 in Figs. 6 (c) and 7 (a). The composition profiles of the data points marked using triangles that are pointing right, i.e., in blue, cyan, and green, show asymmetric tails on the right side, indicating more Cr atoms distributed on the right side of the GB, marked as G2 in Figs. 6 (c) and 7 (a). From Fig. 7 (a) we can see that the regions marked using blue, cyan, and green triangles are close to 7 Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 width. As Fig. 2 shows, near the diffusion front, Cr atoms only occupy a narrow zone of around 1 nm, and this is likely the diffusion width of the GB. Consistent with the archival literature, we noticed that the chemical width of the GB is different from the diffusion width. Before the entire GB gets saturated with segregants, the GB chemical width is 1,2 nm, while after the saturation segregation is achieved, the chemical width becomes wider, mostly in the range of 2–3.4 nm. Geometrically, a static GB is characterized by eight degrees of freedom (DOFs), including five macroscopic and three microscopic ones. The five macroscopic DOFs can be represented by the orientation relationship between adjacent grains, specified by a rigid body rotation that aligns the two grains along their common rotation axis o = [ho ko lo ] (2 DOFs) with the rotation angle θ (1 DOFs), and the inclination of the GB plane, which can be defined by the normal of the GB n = (hnA knA lnA ) (2 DOFs). The three microscopic DOFs describe the rigid-body translation of one grain to the other, normally represented by a vector consisting of two components: one is parallel and the other one is perpendicular to the GB. All these eight DOFs influence the properties of the GB. Therefore, when studying the GB diffusion, width, and composition, etc., it is necessary to determine all the eight DOFs, but in practice, this target is very difficult to achieve. There are a few techniques available for measuring all the five macroscopic DOFs, including 3D x-ray diffraction microscopy (3DXRD) [70], differential-aperture X-ray microscopy (DAXM) [71], 3D electron backscatter diffraction (3D-EBSD) [72,73], and several diffraction and orientation mapping methods in TEM [74–76]. Evaluating the microscopic DOFs is much more challenging, requiring techniques with atomic resolution. Although it is possible to measure the translations parallel to the GB using a few HR-TEM techniques [77], there is no universal, wellestablished method to determine all three microscopic DOFs for such a wide field of view as required here for calculations of GB diffusion coefficients. For non-flat GBs, the microscopic DOFs may change from region to region, giving rise to more complexities. In our experiments, we were not able to measure all these eight DOFs of the GBs, but based on the evidence from the (S)TEM measurements, the GBs studied here are supposed to be random HAGBs, similar to previous observations [32]. The results in Fig. 7 indicate that sites on a single random HAGB are not identical. Different areas along the GB can accommodate different amounts of segregated solute atoms with different lateral distributions. For a curved GB, as the one studied here, the segregation anisotropy could be due to gradual variation of the GB plane and also of the microscopic DOFs along the GB, such as ledges and steps. Besides the macroscopic and microscopic DOFs, the atomiclevel geometry and the local atomic structure of the GB could also influence the segregation behavior of solutes and impurities. This site-to-site variation in segregation on an individual GB has also been noticed previously in experiments [31,78,79]. For instance, Swiatnicki et al. detected different solute content at different parts of a curved grain boundary with different GB planes [80]. A comprehensive experimental characterization of the GB geometry and structure at the different scales is challenging, especially for random HAGBs, thus, there are also simulations studies along these lines, specifically regarding a better understanding of the GB structure, energy, chemistry, and properties [79,80]. The recent simulations done by Malik and Schuh proved the existence of multiple site-type at the general GBs of a polycrystal and the spectral nature of the GB segregation behavior [81,82], which support our observations here. More recently, Garg, Pan, and co-authors noted from their atomistic simulations [59] that in a randomly textured polycrystal, there are significant variations in solute segregation along individual GBs as well as within the entire GB network, which also agree well with our observations. The very recent work from Barr et al. [58] demonstrated again there is a high variation in solute each other and located on the top part of the GB while the regions marked using purple, red, magenta, orange, and brown are also close to each other and from the rest part of the GB. Another interesting phenomenon is that these special regions are from the relatively flat area of the GB rather than the curved area. 4. Discussion GB diffusion coefficients are usually derived from depth profiling or surface accumulation. In both cases, diffusion couples with diffusing species in contact with the matrix are fabricated. Subsequent annealing treatments are then conducted to trigger diffusion. After that, diffusion coefficients are evaluated using the composition profile of the diffusing species along the depth [52] or the total amount of the diffusing species accumulated on the free surface of the matrix as a function of holding time at a given temperature [56]. Radioactive isotopes of the diffusing species of interest are normally used to increase detection sensitivity. Compared to the depth profiling method, the surface accumulation method is generally inferior. In this work, we precisely determined the diffusion coefficient of an individual GB within a type-C kinetic regime after Harrison’s classification [51]. For the short circuit diffusion of Cr along a random high angle grain boundary of the studied PtIr matrix, the diffusion coefficient is estimated in the range of 7 × 10−23 to 3.7 × 10−22 m2 /s at 630 °C under an atmosphere with 4.76 × 10−29 bar oxygen partial pressure. A majority of previous measurements reported were performed in the Harrison type-B kinetic regime [50,51] where GB diffusion is accompanied by volume diffusion. There is hence a substantial leakage of the diffusing species from the GB into the adjacent grains. Under such conditions, only the so-called double product δ •DGB or triple product s•δ •DGB can be obtained, in which δ is the width of the GB and s is the segregation factor, quantified as the ratio between the solute composition at the GB cGB and inside grain interior cG . To estimate the value of diffusion coefficient DGB , GBs are usually treated as a uniform slab with a width of 0.5 nm. However, this assumption is proved to be wrong by both experiments and simulations [31,46,57–61]. Our measurements also show that this assumption does not hold even for a single GB. It is necessary to differentiate different types of GB width, i.e., structural width, diffusion width, and chemical width. The structural width refers to the thickness of the zone where the longrange order in the periodic arrangement of atoms is disrupted, which is typically 1–2 atomic planes. The diffusion width is the width of the boundary region where the enhanced transport of the diffusing species is possible. While the chemical width is the spatial range of chemical changes (composition, bonding, etc.) associated with the GB. Experimentally, the GB structural width can be directly determined by high resolution (S)TEM observations [62,63], while the diffusion width is commonly obtained indirectly, by comparing the diffusion data from the type B- and C- kinetic regimes [60]. For quantifying the GB chemical width, the frequently applied method is to collect a compositional profile across the GB using spatially resolved chemical analysis techniques such as APT [46], EELS [64], and EDX [65], and using the FWHM (in the case of enrichment) or FWH minimum (in the case of depletion) of the line profile to represent the width. In the past, many reports (see, e.g., the summaries in [60,61,66]) have already made it clear that these three widths are not necessarily the same, and can even be considerably different [66,67]. For metals and alloys, generally, the reported values of the structural width and the diffusion width were close to the assumed value of 0.5 nm, but the chemical width shows a large variation, normally ranging from a fraction of nm to a few nm [68,69]. In this work, owing to the direct measurement of the diffusion profile along a single GB in the type-C kinetic regime, we can directly quantify the diffusion 8 Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 et al. [91]. The effective spatial resolution can be assumed to be in the range of 1 nm, so even if this led to a broadening of the composition peak, this could not account completely for the measured value and would not qualitatively change our interpretation [92]. enrichment within the random HAGBs, which highlighted the importance of the full macroscopic and microscopic DOFs defining the GB. In most GB regions, marked by the black dots in Fig. 7(a), we detected that the lateral distribution of Cr across the GB is symmetrical with respect to the GB plane. However, as Fig. 7(e) shows, there are also a few locations, highlighted by the triangles in Fig. 7(a), associated with asymmetric Cr profiles, which could also result from the influence of the GB microscopic DOFs and/or the local atomic structure. Previously, Liebscher et al. [31], Zhao et al, [78], and Tsai et al, [79] also found asymmetrical solute segregation at faceted  3,  5,  7,  9,  11,  13 coincidence site lattice (CSL) GBs, which are due to the preferential segregation of solute to the particular facets. Kuo et al. also observed an asymmetric solute profile across a  =5 CSL GB in their Monte Carlo simulation, which results from the different amounts of solute segregating to different types of lattice planes at the two sides of the GB [83]. From the simulation work of Barr et al. [58], we can see that such asymmetric segregation could also be possible at the dislocation cores of low-angle GBs (LAGBs). The structure of HAGBs can be described using the CSL-dislocation model, where, similar to LAGBs, dislocations, known as secondary grain boundary dislocations (SGBDs), are introduced to accommodate the deviation from a perfect CSL. SGBDs have already been observed a long time ago [84]. Besides asymmetric segregation, nucleation and precipitation of IMC at GB can also lead to unequal distributions of solutes between two sides of the GB. Here, at the position marked by the blue triangle (Fig. 7(a)), the asymmetric tail of the Cr profile is about 10 nm (Fig. 7(e)), reaching a comparable size of the (Pt,Ir)3 Cr IMC precipitates observed in the STEM experiments (Fig. 5). Therefore, we think it is highly possible to be a (Pt,Ir)3 Cr nucleus. In the classical nucleation theory, the free energy required for the heterogeneous nucleation of an IMC at GB is 5. Conclusion Most materials are polycrystalline with numerous grain boundaries (GBs). A robust understanding of interactions between alloying elements or dopants and GBs of the matrix is necessary for advanced polycrystal materials design. Here, we demonstrate a reliable quantification of GB diffusion, segregation, and precipitation, which allows an assessment of both the kinetic and thermodynamic properties of GB-solutes interactions. To overcome the challenges in the direct experimental observation of GBs with complicated local structures and chemistries after solutes adsorption, we coupled systematic high-resolution imaging with a new, machinelearning-enabled, data processing technique. The strength of our approach is showcased in the quantitative analysis of the diffusion of Cr through the GBs of a PtIr matrix. By detailed analyzing the distributions of Cr both along and perpendicular to the GBs surface of PtIr, we can determine the regimes of unsaturated, saturated segregation, and segregation-induced precipitation. Consistent with the previous observations, we also found that GBs are not planar and uniform defects, but with complex three-dimensional topologies and local atomic structures that confine the interactions with solutes and heterogeneous nucleation of secondary phases. Compare to the studies at larger scales with only two dimensions, we were able to reveal the relationship between the local segregation amount and chemical thickness of GBs in a finer manner. Although presented using a PtIr-Cr system, this approach is applicable to any other system. Declaration of Competing Interest G = gv · VIMC + γIMC · AIMC − γGB · AGB There are no conflicts to declare. where gv (<0) represents the free energy difference between the IMC and the matrix per unit volume, VIMC represents the volume of the IMC, γ GB and γ IMC represent GB energy and the specific energy of the IMC-matrix interface respectively, and AIMC and AGB represent the areas of newly formed IMC-matrix interface and the eliminated GB respectively [85]. For a non-flat GB, γ GB is influenced by its local curvature. Compared to the atoms in flat or concave regions, the atoms in convex regions have the highest chemical potential, as the Young-Laplace equation expresses [86]. That is to say, in principle, the nucleation process should start in the convex regions. However, in this study, we did not observe this trend. The convex regions of the GB (the area in brown color in Fig. 7 (a)) are free of the IMC nucleus. The IMC precipitated at the relatively flat area next to the convex region. This phenomenon is similar to what Zhao et al. reported recently (see Fig. 2 in [78]). The reason is that the heterogeneous precipitation of secondary phase at GBs strongly depends on the GB planes. Some GB facets are more favorable than others. Previously, segregation on a similar width measured by APT was reported for a specific interface [87]. Here, the values of the width are affected by artifact-induced trajectories resulting from the composition- and structure-dependent differences in the field evaporation behavior, which leads to deflections in the ion trajectories in the early stages of their flight during the APT analysis [88– 90]. As shown in supplementary Figs. S1 and S2, there is an increase in the atomic density within the reconstructed point cloud between the two PtIr grains and the segregated region, indicative of compression of the trajectory. Here, this indicates a lower evaporation field, where the effective spatial resolution of the technique appears to be less affected based on the recent work by De Geuser CRediT authorship contribution statement Zirong Peng: Conceptualization, Methodology, Investigation, Formal analysis, Software, Validation, Visualization, Writing – original draft, Writing – review & editing. Thorsten Meiners: Investigation, Formal analysis, Writing – review & editing. Yifeng Lu: Software, Formal analysis, Writing – review & editing. Christian H. Liebscher: Formal analysis, Writing – review & editing. Aleksander Kostka: Formal analysis, Writing – review & editing. Dierk Raabe: Supervision, Writing – review & editing. Baptiste Gault: Supervision, Writing – review & editing. Acknowledgments Z.P. acknowledges the support from the Big-Data-Driven Material Science (BDDMS) project (https://bigmax.iwww.mpg.de/), founded by the Max-Planck-Gesellschaft (MPG). The multilayer samples were fabricated by Marcel Friedrichs (Fraunhofer Institute for Production Technology IPT). We greatly appreciate his help. The authors are thankful to Dr. Michael Rohwerder, who provided the annealing facility, and to Alexandra Vogel, who conducted the annealing treatments. Uwe Tezins & Andreas Sturm are thanked for their support of the APT & FIB facilities at MPIE. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.actamat.2021.117522. 9 Z. Peng, T. Meiners, Y. Lu et al. Acta Materialia 225 (2022) 117522 References [26] P. Maugis, K. Hoummada, A methodology for the measurement of the interfacial excess of solute at a grain boundary, Scr. Mater. 120 (2016) 90–93, doi:10.1016/j.scriptamat.2016.04.005. [27] P. Felfer, B. Scherrer, J. Demeulemeester, W. Vandervorst, J.M. 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