A macro-nano-atomic-scale high-throughput approach for material research.

Understanding the properties of materials requires structural characterization over large areas and different scales to link microstructure with performance. Here, we demonstrate a single-beam high-throughput scanning electron microscope allowing the collection of both secondary electron and backscattered electron signals over large areas. Combined with machine learning, a high efficiency in material research is achieved, illustrated here by a multiscale investigation of carbides in a second-generation nickel-base single-crystal superalloy. The resulting terabyte-sized panoramic atlas data, combined with conventional electron microscopy, enable a simultaneous multiscale analysis of carbide evolution during creep regarding specific type, location, composition, size, shape, and relationship with the matrix, providing sample-scale quantitative statistical data and giving a precise insight into the effect of carbides in the superalloy in a way not previously possible.

INTRODUCTION

The linkage between microstructure and properties forms a fundamental paradigm in materials science. A key challenge, however, is to characterize the microstructure at the appropriate length scale (or scales), which often requires information on the variation of nanoscale features over many length scales. One general approach to realizing such a scenario is through the use of a scanning electron microscope (SEM), a tool used for materials characterization that provides information about the surface, or near-surface, structure in materials (). Secondary electron (SE) signals and backscattered electron (BSE) signals are the two most important and widely used signals in an SEM system, where the image contrast mechanisms arising from these signals are known as topographic contrast and composition contrast, respectively ().

Scanning-based investigations over large areas are, however, impossible to realize in practice using conventional SEMs because these tools are inherently too slow (). Hence, assessments of macroscopic performance that rely on investigations only of microscale regions are likely to be fraught with errors because of limited microstructural sampling. Obtaining representative and comprehensive results requires, therefore, the collection of a massive amount of information over a large range of scale. To address this problem, multibeam high-throughput SEMs (mSEMs) (–) have been developed, where throughput is improved by increasing the number of primary beams. These microscopes have become popular in the area of biological research, allowing rapid investigation of millimeter- or centimeter-scale areas with nanoscale resolution, yielding achievable terabyte-sized datasets for analysis, far in excess of the data collection possible using a conventional SEM. In these mSEMs, however, the SE signal capability of each single beam remains similar to that in conventional SEMs, and, moreover, simultaneous additional collection of a BSE signal is not possible because of difficulties in separating each returning BSE beam and in avoiding cross-talk in the detection system. This places a major limitation on the use of mSEMs in the field of materials science, where, particularly in multiphase materials, both the SE and BSE signals provide important microstructural information for identifying and distinguishing different phases. Inspired by this limitation, here, we develop a single-beam high-throughput SEM method that can be used to collect both SE and BSE signals simultaneously at nanoscale resolution, with good signal-to-noise ratio and high imaging speed (minimum dwell time of 10 ns per pixel at 2 × 100 megapixels/s). The approach is based on a single-beam high-throughput SEM equipped with a specially designed electron optical system and detection system (), taking advantage of both direct electron detectors and an optimized deflection system (Fig. 1D). Combined with machine learning (Fig. 1H), this microscope can be used to identify and distinguish different phases, allowing postcollection analysis of experimental data over a wide range of length scale, thereby connecting experimental results from the centimeter scale to the nanoscale or even atomistic scale.

Fig. 1.

Schematic diagram illustrating the single-beam high-throughput SEM method.

(A) Master alloy of the superalloy. (B) Creep test bar of the superalloy. The blue arrows show the direction of the applied force, [001]. (C) Cold mounted [100] longitudinal section of the creep rupture sample. (D) Electron optical system of the single-beam high-throughput SEM. (E) The array scan area is shown in green. (F) Detailed view of the orange box in (E). (G) A single 15-nm native pixel resolution BSE image. (H) Panorama (right) and example details (left) after machine learning and automatic montaging from 1774 BSE images. MC and M23C6 carbides here are marked in red and green, respectively. The matrix in the panorama here is shown in black. (I) Electron optical paths of the TEM and STEM. (J and K) Schematic diagrams of the carbide microstructure. (L) Creep curve of the creep rupture sample. (M) Microstructure analysis acts as a link between large-scale high-throughput observation and macroscale performance.

We demonstrate here the powerful capability of our developed method to characterize the microstructure at different scales in large area using a model system of a second-generation nickel-base single-crystal superalloy. These alloys are generally used for turbine blades in aircraft aeroengines on account of their excellent creep properties, corrosion resistance, and fatigue properties (). A detailed understanding of the creep mechanisms that take place during high-temperature operation of second-generation nickel-base single-crystal superalloys is crucial to achieving improved performance by controlled alloy design. In recent years, the evolution of interfacial microstructure (–), the role played by alloying elements such as rhenium (–), and how elemental diffusion interacts with the interfacial structure (, ) have been characterized in a number of studies aimed at revealing creep mechanisms in second-generation nickel-base single-crystal superalloys. However, the forms in which minor elements such as carbon exist in nickel-base single-crystal superalloys and how this affects creep properties are still not well understood. Moreover, the effects of carbides in superalloys are controversial in that they can either enhance or degrade alloy properties, depending on their specific type, location, composition, size, shape, and relationship with the matrix (–), necessitating investigation from the macro- to microscale and even atomic scale. Unravelling the effects of carbides in superalloys therefore requires simultaneous analysis of several different influencing factors that may operate over different length scales and hence is well suited for our large-area macro-nano-atomic–scale high-throughput approach.

RESULTS

To achieve this goal, we combined the large-scale high-throughput observations with machine learning for structural analysis, as shown in Fig. 1, which illustrates the overall flow of the methodology used for study of the second-generation nickel-base single-crystal superalloy. Samples of the alloy were taken under five conditions: as-cast, heat-treated, creep-tested at 1038°C/155 MPa to 22.2 and 131.6 hours, and after creep rupture (denoted hereafter as SA1, SA2, SA3, SA4, and SA5, respectively). Preliminary investigation revealed, in addition to the two matrix phases (γ phase and γ′ phase), the presence of two types of carbide, namely, primary Ta/Hf-rich MC carbides and secondary Cr/Re-rich M23C6 carbides (as shown in fig. S6). Figure 1 uses the sample SA5 as an example (Fig. 1, A to C), where the direction of the applied force is [001]. Figure 1D shows the electron optical system of the single-beam high-throughput SEM, which allows simultaneous collection of SE and BSE signals. Figure 1E shows in green the array scan used for this sample, covering a total area of 12.96 mm by 4.33 mm and consisting of 1774 individual SEM images. The arrangement of the individual images is more clearly seen in Fig. 1F. The right-hand side of Fig. 1G shows the full BSE image (15-nm native pixel resolution) corresponding to the blue square in Fig. 1F, with a magnified view of part of this image shown on the left of Fig. 1G, where it can be seen that the two types of carbides have different grayscale levels in the BSE image as a result of their differing composition. Accordingly, a machine learning model was used to automatically identify the carbides in the entire array scan dataset of 1774 BSE images and postcollection of digital data for statistical analysis, with training data provided on the basis of manual inspection of carbide grayscale levels, allowing all carbides to be marked in each image, and the generation of a panoramic atlas of the rupture sample through automatic montaging (Fig. 1H). MC and M23C6 carbides here are marked in red and green, respectively, with the matrix in the panorama here colored in black to show the carbides in this reduced image-sized form with higher contrast. Additional microstructural analysis was also carried out (Fig. 1, I to K) to provide a link between the large-scale high-throughput observations and the material creep performance (Fig. 1, L and M). As will be discussed later, the selection of samples for this additional analysis, using the transmission electron microscope (TEM) and scanning TEM (STEM), was carried out on the basis of inspection of the high-throughput panoramic atlas data.

Establishment of high-throughput panoramic atlases

After automatically montaging thousands of BSE images, machine learning recognition was used to identify both the primary and secondary carbides and to determine their distribution over whole sample areas (Fig. 2), encompassing analysis of a total of 8449 images over the five samples. For training and testing of the automatic recognition model, 100 images were selected at random from the full dataset, with 80 assigned to the training dataset and 20 used for testing (Fig. 2A). Identification of the two types of carbides in the training and testing datasets was carried out by first applying a grayscale threshold-based algorithm combined with standard morphological feature detection operations. Each image was then inspected, and manual adjustments were made as necessary to obtain marked-up images identifying both sets of carbides for use as ground truth data for training and testing (Fig. 2B). To account for the diversity in both shape and size of the carbides and thereby achieve a more accurate and generic recognition model, we also carried out amplification of the original and marked-up training/testing datasets (Fig. 2C). In this process, many small image patches of fixed window size (512 pixels by 512 pixels in this case) were extracted at random from images in the training and testing subsets, and then each patch was transformed by extensive application of scaling, rotation, shearing, and mirroring operations. This process yields a much larger and more diverse library of image features for training and testing of the automatic recognition model, which was built on the basis of U-Net, a state-of-the-art segmentation network (). Training of the model was carried out in an iterative manner, with the model continuously tuned until the recognition accuracy for the testing dataset reached a predefined value, set here as a mean pixel accuracy (mAcc) of greater than 0.95 and a mean intersection over union (mIou) of greater than 0.85 (Fig. 2D). The automated recognition model was then applied using the same parameters to the remaining 8349 BSE images, resulting in a panoramic atlas for each sample showing the detailed distribution of the two carbides over a sample-scale area (Fig. 2E).

Fig. 2.

Schematic diagram illustrating the procedure for automated feature detection using machine learning based on an array scan.

(A) A large number of BSE images are acquired from an array scan, with 100 of these selected at random as training/testing images. (B) The left picture shows schematically one of the training/testing BSE images containing primary carbides (white), secondary carbides (light gray), and the matrix (dark gray). The middle and right pictures illustrate the images after semiautomated data labeling of the training/testing images, in which the primary and secondary carbides are marked by orange and blue, respectively. (C) Many image patches with fixed window size are extracted at random from the original and labeling training/testing images, illustrated here by the yellow dashed boxes (left), followed by application of scaling, rotation, shearing, mirroring, and operations (right) to build the final image dataset for model training and testing. (D) An automatic feature detection model is established using U-Net segmentation, and the training/testing images are used to tune the model parameters and check the accuracy of the model. (E) The model is used to automatically recognize features in the remaining array scan BSE images (left) with the primary carbides and secondary carbides in all images marked in red and green, respectively (middle), allowing a panoramic atlas with marked carbides to be created (right).

Panorama atlas images for all the five samples, after automatic montaging and carbide identification by machine learning, are shown in Fig. 3A. Both primary MC carbides (red) and secondary M23C6 carbides (green) are marked, from which the heterogeneity in spatial distribution of the two types of carbides can be directly seen. No M23C6 carbides are present in sample SA1. After heat treatment and during high-temperature low-stress creep, M23C6 carbides precipitate in the superalloy (SA2 to SA5). On the basis of the whole sample data, it is seen that all the MC carbides, as well as most of the M23C6 carbides, precipitate in interdendritic regions, with just a few M23C6 carbides precipitating in dendritic regions. Figure 3 (B and D) shows the examples of interdendritic and dendritic regions, corresponding to the areas marked by the orange and yellow wireframes in SA5 in Fig. 3A, respectively, in each case consisting of three automatically montaged 15-nm native pixel resolution BSE images, each covering a 184.3 μm–by–184.3 μm field of view. Figure 3C shows a magnified view of part of one high-resolution BSE image in Fig. 3B, from which details of the distribution of the MC and M23C6 carbides in an interdendritic region can be seen. Secondary carbides precipitate either around primary carbides or in interdendritic regions in locations independent from any primary carbides. All carbides are surrounded by the γ′ phase (the darker matrix in Fig. 3C) in the interdendritic region. Details of the carbide distribution in dendritic regions are shown in Fig. 3E. Several unconnected secondary carbides are distributed in different dendritic regions, surrounded in each case by locally distorted γ′ phase. Such a large-scale, high-resolution investigation highlights the heterogeneity in spatial distribution of the carbides and allows their evolution during creep to be established, revealing also no obvious difference in shape and size between dendritic M23C6 and interdendritic M23C6.

Fig. 3.

Heterogeneity in spatial distribution of MC and M23C6 carbides in the five samples.

(A) Panorama atlases for each of the five samples, showing the heterogeneity in spatial distribution of two types of carbides. MC and M23C6 carbides are marked in red and green, respectively. Note that the matrix here is shown in black to enhance visibility of the carbides in these reduced size images. The blue arrow indicates the heat treatment and creep timeline of the superalloy. Scale bars, 1 mm. (B and D) Example of 3 by 1 montaged areas showing interdendritic and dendritic regions, corresponding to areas marked by orange and yellow wireframes in (A). The matrix here is changed into black artificially to show the carbides with higher contrast. Scale bars, 50 μm. (C and E) Higher-magnification view showing the carbides and the γ/γ′ matrix. Scale bars, 5 μm.

Collection of digital data from panoramic atlases

The panoramic atlases resulting from high-throughput data collection and automated phase identification through a machine learning model can be readily converted into digital data for statistical analysis, from which the evolution in size and volume (area) fraction of the carbides can be quickly determined, on the basis of data collected over sample-scale areas. Figure 4 (A and B) shows the evolution in size of the two types of carbides during creep, where each sample column contains tens of thousands of data points, representing the size of individual carbides. The mean size of the MC carbides (Fig. 4A) decreases from 1.89 μm2 (SA1) to 1.03 μm2 (SA5), while the mean size of the M23C6 carbides (Fig. 4B) increases from 0.047 μm2 (SA3) to 0.135 μm2 (SA5), indicating growth of the secondary carbides during creep. Figure 4C shows the total array scan area for each sample (from SA1 to SA5, the areas are 18.86, 26.52, 26.33, 31.34, and 50.70 mm2, respectively) and the evolution in the number of M23C6 carbides per unit area from SA3 to SA5. The number of M23C6 carbides per unit area decreases from 37,601 mm−2 (SA3) to 20,001 mm−2 (SA5), indicating that the number of M23C6 carbides in the sample decreases during creep with growth of the carbides. Figure 4D shows the volume (area) fraction of the two types of carbides, whereas the volume (area) fraction of MC carbides decreases from 0.247% (SA1) to 0.148% (SA5), while the volume (area) fraction of M23C6 carbides increases from 0.178% (SA3) to 0.270% (SA5), indicating the decomposition of primary carbides. The data also show that after creep testing to 22.2 hours (sample SA3), the amount of M23C6 carbides exceeds that of MC carbides. Combined with the panorama atlas data, it can be inferred that the M23C6 carbide is very likely to play a key role during the creep process in this superalloy.

Fig. 4.

Statistical analysis of carbides based on sample scale data.

(A and B) Size distribution of all MC and M23C6 carbides in the five samples. A single MC/M23C6 carbide defined here is a single closed red/green area in each panorama atlas. Each colored point represents one carbide, and the horizontal spread shows the number of points for each value. Black circles are the mean values. (C) Total array scan areas for the five samples (bar chart, left ordinate) and number of M23C6 carbides per unit area for the creep samples (line chart, right ordinate using scientific notation). (D) Volume (area) fraction of MC (red fill) and M23C6 (green fill) carbides for the five samples. The reason for the absence of data for M23C6 carbides in SA1 and SA2 is that no M23C6 exists in sample SA1 and M23C6 cannot be adequately etched in SA2.

Additional microstructure characterization

As illustrated above, the single-beam high-throughput SEM method can realize fast multiscale identification and quantitative analysis at nanoscale resolution over large sample areas (tens of square millimeters), yielding comprehensive data on the spatial distribution, volume (area) fraction, and size of carbides and revealing their evolution during creep. However, determination of the microscopic structure of the carbides and their relationship with the matrix, both of which are important for understanding the effect of carbides on creep properties, still requires some additional microstructural analysis. The panorama atlas data greatly help here with the selection of these additional data, as illustrated by the TEM and STEM investigations summarized in Fig. 5.

Fig. 5.

Microstructure of M23C6 carbides and relationship to their surrounding matrix.

(A) Dendritic region of SA1, g = [020] and B = [100]. (B) Dendritic region of SA2, g = [] and B = [110]. The red arrows point to M23C6 carbides. (C) Dendritic region of SA3, g = [002] and B = [100]. (D) Dendritic region of SA4, g = [020] and B = [100]. (E) Dendritic region of SA5, g = [020] and B = [100]. The green triangles in (D) and (E) indicate dislocation networks at M23C6/γ′ interfaces. Scale bars, 0.5 μm (A to E). (F) Schematic diagram of the evolution of M23C6 carbides (from SA1 to SA5). The pink area represents the γ′ phase, and the white area represents the γ phase. (G) Schematic diagram of one type of polyhedral M23C6 carbide (in this case, with 26 faces). (H and I) Projection of (G) as viewed from the [100] and [110] zone axes, respectively. (J to O) HAADF-STEM images (a) and EDS mappings (b) of (J) M23C6 carbide, B = [100]; (K) (001) M23C6/γ′ interface, B = [100]; (L) () M23C6/γ′ interface, B = [100]; (M) () M23C6/γ′ interface, B = [110]; (N) (001) M23C6/γ′ interface, B = [110]; and (O) () M23C6/γ′ interface, B = [110]. Scale bars, 1 nm (J to O).

Detailed examination of the dislocation structures around carbides was carried out, taking care to examine carbides with size, shape, and location (dendritic region or interdendritic region) representative of the carbides identified in the high-throughput SEM observations. Figure 5 (A to E) shows the examples of dendritic region M23C6 carbides in this superalloy under 1038°C/155 MPa creep, and Fig. 5F illustrates schematically the evolution of M23C6 carbides in the dendritic region (a similar evolution of the M23C6 carbides is found for interdendritic regions—examples for this are shown in fig. S7). In SA1, no M23C6 carbides precipitate in this superalloy (Fig. 5A). In SA2, cluster-like M23C6 carbides precipitate along dislocations in the γ phase (Fig. 5B). The tendency for M23C6 carbides to nucleate at γ-phase dislocations can explain the heterogeneity in spatial distribution of the carbides seen in the high-throughput SEM data, accounted for by the more irregular structure, and therefore higher local dislocation density, in interdendritic regions. After creep testing to 22.2 hours (SA3), rafting structures (–) begin to form (0.58% creep strain). At the same time, M23C6 carbides consume the surrounding γ phase and occupy γ phase channels either parallel to or perpendicular to the stress direction (Fig. 5C). Carbides filling the γ channel can result in blocking of dislocation motion. Compared with SA2, the shapes of M23C6 carbides are more angular in SA3. In SA4 (see Fig. 5D), the M23C6 carbides are surrounded by the γ′ phase, as growth of the M23C6 carbides consumes all of the adjacent γ phase, with a corresponding outward discharge of γ′-forming elements. All M23C6 carbides at this stage are polyhedral with planar M23C6/γ′ interfaces. Dislocation networks are also developed at some of the M23C6/γ′ interfaces to release misfit stresses. In SA5 (see Fig. 5E), a large number of dislocations cut into the γ′ rafts, while the γ′ rafts undergo notable coarsening. Even at this stage, however, dislocations still cannot cut into the M23C6 carbides and remain blocked at M23C6/γ′ interfaces. Combining these observations with the high-throughput SEM data reveals that as the M23C6 carbides grow in size, their shape becomes faceted and connected to the matrix by M23C6/γ′ interfaces. During the entire creep period, these interfaces are important as they act as obstacles for the movement of dislocations.

On the basis of this insight, STEM experiments were also carried out to explain the relationship between M23C6 carbides and the matrix by analyzing the M23C6/γ′ interfaces at the atomistic scale. According to an additional set of high-throughput SEM observations on five deep-etched samples (see fig. S9, A to E) and STEM high-angle annular dark-field (STEM-HAADF) observation of the sample SA5, four typical types of polyhedral M23C6 carbides are found, defined by three types of coherent M23C6/γ′ interface, namely, those on {001}, {}, and {} planes (fig. S10). Here, we illustrate as an example one type of polyhedral secondary carbide in the SA5 sample. Figure 5 (G to I) shows a typical polyhedral M23C6 carbide, with 26 faces encompassing all three types of interfaces. Atomic-scale observations of the M23C6 carbide and its interfaces, as viewed along the [100] and [110] zone axes, respectively, are shown in Fig. 5 (J to O), demonstrating the coherency of all three types of M23C6/γ′ interface. Heavy atoms occupy special positions in the M23C6 carbide (Fig. 5J) and in (001) M23C6/γ′ interfaces (Fig. 5, K and N) and {} M23C6/γ′ interfaces (Fig. 5, L and O), as seen from the HAADF images, where the contrast is derived primarily from atomic number variations, such that atoms with larger atomic number (Z) appear brighter. Atomic-resolution energy-dispersive x-ray spectroscopy (EDS) results (Fig. 5, Jb to Ob) show that the heavy atoms in M23C6 carbides are Re, which agrees with the result of simulations by Xiang et al. ().

DISCUSSION

By the use of the single-beam high-throughput SEM, combined with a machine learning model, large-area multiscale analysis of several different influencing factors, such as the specific type, location, composition, and size of carbides, on superalloy creep behavior was achieved simultaneously. We successfully carried out a high-resolution multiscale characterization of microstructural evolution for a set of nickel-base superalloy creep samples, allowing the collection for each sample of a panorama atlas at nanoscale resolution identifying the primary (Ta, Hf) C carbides and secondary (Cr, Re)23C6 carbides. This large-scale investigation highlights the heterogeneity in spatial distribution of the carbides, where the carbides precipitate preferentially in interdendritic regions, with just a few M23C6 carbides precipitating in dendritic regions. Moreover, a quantitative analysis of the data over the entire sample-scale areas reveals trends in changes of the carbides during creep. Specifically, with the precipitation and growth of secondary carbides, the primary carbides gradually decompose. The single-beam high-throughput SEM data can also be used to guide more detailed targeted microstructural studies of carbide evolution during creep, with additional TEM and STEM microstructural examination acting as a bridge between length scales, e.g., the evolution in morphology of M23C6 carbides from irregular shape to regular polyhedral shape, and the change in coherency relationship between secondary carbides and the matrix during creep.

The ability to characterize a wide range of influencing factors helps to unravel the effect of carbides in superalloys. By linking the evolution of microscale MC carbides and nanoscale M23C6 carbides, as seen in the high-throughput observations, with the known blocking effect of M23C6 carbides on dislocation motion, combined both with identification of a cube-on-cube orientation relationship between M23C6 carbides and the matrix (fig. S8) and with observations that MC carbides act as crack sources (fig. S9F), it can be concluded that the changes in carbides occurring during creep have a positive effect on creep properties of the present superalloy. This can be further understood as the M23C6 carbides are connected to the matrix through three types of coherent interface, where the perfectly coherent relationship between M23C6 and γ′ ensures good strain compatibility between the secondary carbides and the matrix during creep. Although a decrease in the number of M23C6 carbides per unit area and the increase in M23C6 size, as seen from the high-throughput SEM studies, may lead to some decrease in strengthening during creep, the extent of any such effect is limited by the special occupation of Re atoms in M23C6 carbides, as the high activation energy for diffusion of Re (, –) places a limitation on the extent of carbide coarsening.

Our combined results presented here verify the feasibility and accuracy of this technique in identifying and distinguishing different phases at the micro- or nanoscale, allowing postcollection analysis of experimental data over a wide range of length scale and thereby connecting macro-nano-atomic experimental results to performance. We note that the ability, as demonstrated in this study for combined SE/BSE high-throughput data collection, can be expected to have widespread use for the analysis of structure-property relationships in multiphase materials. Furthermore, future applications could entail combination with tomographic techniques () to construct sample-scale three-dimensional (3D) models with full microstructural detail.

MATERIALS AND METHODS

Sample preparation

The material used in this study is a carbon containing second-generation nickel-base single-crystal superalloy. Its nominal composition is given in table S2. The single-crystal master alloy was prepared by the grain selection method. Then, samples of the as-cast alloy were heat treated according to the following schedule: 1300°C/2 hours, followed by air cooling (AC) + 1120°C/4 hours, AC + 1080°C/4 hours, AC + 900°C/4 hours, and AC. After heat treatment, samples of the alloy where the dendritic growth direction deviated by less than 10° from the [001] direction were made into creep test bars for the creep experiment. Creep testing was conducted along the [001] direction under a load of 155 MPa at 1038°C and was stopped after 22.2 and 131.6 hours and creep rupture. The creep curves of these three samples are shown in fig. S14.

Samples for high-throughput SEM, TEM, and STEM were cut from creep test bars along the [100] and [110] directions (as shown in fig. S15). Before single-beam high-throughput SEM examination, the samples were cold-mounted using resin and curing agent. Chemical etching with a solution containing 60 volume % hydrochloric acid, 20 volume % nitric acid, and 20 volume % glycerin, which only removes the γ′ phase, was used for the main investigation on MC and M23C6 carbides. Additional samples were also deep-etched in an electrolyte of 90 ml of methanol, 10 ml of hydrochloric acid, and 1 g of tartaric acid at 5 V for 5 min to obtain data on the 3D carbide morphology. All foils for TEM and STEM investigation were prepared by spark erosion and mechanical grinding, followed by twin jet polishing at 20 V and −25°C with a solution of 5 volume % perchloric acid, 35 volume % N-butanol, and 60 volume % methanol.

High-throughput SEM experiment

In this work, for the analysis of carbides in the superalloy, high-throughput BSE imaging, using materials information of atomic number (Z contrast) and morphology, was used instead of SE/BSE and EDS imaging in a conventional SEM with much lower throughput. A single-beam high-throughput SEM, Navigator-100 (Focus e-Beam Technology, Beijing), was used for data collection of carbides on whole centimeter-scale samples. The microscope is equipped with direct electron detectors and an optimized deflection system and can achieve practical high-speed dual simultaneous collection of SE and BSE images at speeds of up to 2 × 100 megapixels/s. In total, we collected thousands of BSE images from five samples for analysis at 5- to 8-keV landing energy, resulting in terabyte-sized datasets. The instrument parameters for data collection are shown in table S3.

Metric for evaluating model performance

The U-net, a state-of-the-art segmentation network, also known as an encoder-decoder network, is adopted in this study. The network is based on the fully convolutional network architecture, and its structure can be regarded as the association of the convolution layer in the encoding process and the deconvolution layer in the decoding process. The encoding process is a classic convolutional neural network architecture, which is composed of rectified linear units, pooling layers, and convolution layers. The decoding process consists of up-sampling feature maps, up-convolution layers, and convolution with rectified linear units. Concatenating of the feature maps from the encoding process with the corresponding layer in the decoding process (so-called skip connection) is also used, as this can effectively prevent the excessive loss of information in the decoding process.

In the model training phase, the image and its corresponding mask (ground truth) are taken as inputs, while in the testing phase, only the image is used as an input. The model will predict and generate its corresponding mask. The mask of ground truth is acquired first via a threshold-based algorithm and then rechecked concisely by expert manual supervision. Before training the model, the data were preprocessed as required. To adapt the image size to the input size of the network, we crop the images into 512 by 512 blocks and simply delete blocks without any regions of interest. Last, we enhance the image block sets by carrying out operations such as translation, shearing, rotation, and scaling, with the same operations performed on the ground truth.

To evaluate the performance of the network, we use both mAcc and mIou measures where the formulas are as followsandwhere k is the precipitation class number minus 1, TP is the number of true positives, TN is the number of true negatives, FP is the number of false positives, and FN is the number of false negatives.

Preliminary investigations were carried out using a Zeiss Merlin SEM. The voltage used for SE imaging was 5 to 15 kV; for EDS mapping, 15 kV was used. For EDS mapping, the K edge was used for C, Ni, Al, Cr, Co, and Mo. Because of the proximity of the M edges for Hf, Ta, and Re, the L edge was used for these three elements.

The TEM investigations were carried out using a FEI TECNAI G20 electron microscope, equipped with a tilt-rotation holder (±35°). A 100-nm aperture diameter was used for selected area electron diffraction imaging. Atomic structure investigations and element mapping characterization were carried out using STEM in a FEI Titan Cubed Themis 60-300 (operated at 300 kV), which is capable of recording high-resolution STEM images with a spatial resolution of ~0.059 nm. The microscope is equipped with a high-brightness electron gun (X-FEG with monochromator) and with Cs probe and image correctors. The energy resolution was <0.3 eV, and the collection angle of the HAADF detector was 48 to 200 mrad. For EDS mapping, the K edge was used for Ni, Al, Cr, Co, and Mo. Because of the proximity of the M edges for Hf, Ta, W, and Re, the L edge was used for these four elements. The thicknesses of samples used in our work were determined to range from 15 to 45 nm using the standard electron energy loss spectroscopy log ratio technique (). The Wiener filter was used for filtering of the STEM-HAADF images ().

Establishment of an interface atomic model was carried out using the Materials Studio 7.0 software.