Serial chemical crystallography for autonomous quantitative phase analysis in an electron microscope

Serial chemical crystallography for autonomous quantitative phase analysis in an electron microscope | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Serial chemical crystallography for autonomous quantitative phase analysis in an electron microscope Taimin Yang, David Waterman, Zheting Chu, James Beilsten-Edmands, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5300199/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Recent advancements in robotics and artificial intelligence have accelerated the development of autonomous workflows for material discovery. Powder X-ray diffraction (PXRD) remains the primary method for characterizing crystal structures in these workflows. However, its limitations become apparent when peak overlapping becomes severe. To address this, we present serial electron diffraction with tilt (t-SerialED), a method for fast autonomous phase and structural analysis of beam-sensitive, nano-sized polycrystalline materials. t-SerialED incorporates 3D reciprocal space information into SerialED, ensuring reliable quantitative phase analysis for complex mixtures that are difficult to analyze by traditional techniques. Conducted in a standard electron microscope without specialized hardware, t-SerialED enables high-throughput analysis of beam-sensitive, multi-phase mixtures across a wide range of materials, from nanoporous frameworks to pharmaceutical compounds. By resolving key challenges in serial crystallography such as indexing and preferred orientation, this method enables precise structure determination, including the visualization of disordered guest molecules and non-covalent interactions like hydrogen bonding network and proton charge transfer. t-SerialED expands the capabilities of serial chemical crystallography and it can become a complementary method to traditional crystallography methods, offering a robust solution for routine quantitative phase analysis and structure determination. Physical sciences/Nanoscience and technology/Techniques and instrumentation/Microscopy/Transmission electron microscopy Physical sciences/Chemistry/Analytical chemistry/X-ray diffraction Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Recent advancements in robotics and artificial intelligence have significantly propelled the development of autonomous synthesis and characterization workflows 1 , 2 . Powder X-ray diffraction (PXRD) is the dominant method for characterization in these workflows. Nevertheless, Challenges arise when a polycrystalline product contains multiple phases, phases with low contents (< 5%), phases with similar unit cell parameters and structures with peak overlaps in PXRD patterns. As autonomous synthesis can usually produce many samples within a short timeframe, there is a pressing demand for innovative techniques that can match the speed and obtain the compositions and atomic structures for complex mixtures simultaneously. The last ten years witnessed several emerging technologies to study crystals that traditional X-ray techniques cannot effectively analyze. X-ray free-electron lasers (XFELs) have been crucial in driving the advancement of serial femtosecond crystallography (SFX) 3 – 5 . This technique captures a single snapshot from each crystal, avoiding dose accumulation associated with rotation series. The method is widely used in macromolecular crystallography. However, when applied to chemical crystallography, the small unit cell leads to sparsity of reflections on each frame, hindering unit cell and orientation matrix determination 6 . Although attempts have been made to resolve this problem, the solution generally requires pure samples 4 – 6 and is difficult to apply to phase mixtures. Besides, the scarcity and costliness of XFEL beamtime limits this technique as a routine analysis method. Electron microscopes are a comparatively cost-effective alternative for measuring diffraction patterns from nanosized crystals. Recently, three-dimensional electron diffraction (3DED) has become an reliable method to determine beam-sensitive nanosized materials in TEMs 7 – 12 . Several attempts have been implemented to achieve automatic 13 – 16 or semi-automatic 17 , 18 structure analysis. However, the data collection speed is still not fast enough for phase analysis (fastest 1 min/crystal with speed of 1°/s) 14,17 . Therefore, serial electron diffraction (SerialED), a single-shot-per-crystal technique, has been applied to both small- 19 and macro-molecule crystals 20 . Nevertheless, the application of the method is limited by difficulties during data processing: (1) requires a known unit cell; (2) indexing is difficult, error-prone and time-consuming due to the nearly flat Ewald Sphere; (3) indexing ambiguity; (4) preferred orientation limits the completeness of the merged data; (5) unable to process an ED pattern from multiple crystals. Consequently, this method remains underutilized and has primarily been applied to crystals with relatively high symmetry and large unit cell parameters. Here we present SerialED with tilt (t-SerialED), a multi-shots-per-crystal approach aiming to perform autonomous quantitative analysis for complex mixtures. The full workflow can be conducted in a conventional TEM without customized hardware, making sure the accessibility of the method. This method addresses the challenges in small molecule SFX (smSFX) and SerialED by merging 3D reciprocal space information into the serial crystallography data acquisition and processing workflows. We conducted autonomous data collection and analysis of the compositions and crystal structures across a range of beam-sensitive and polycrystalline mixtures, spanning from nanoporous materials to pharmaceutical compounds. We demonstrate that t-SerialED can determine the positions of disordered guest molecules in the pore and visualize the interaction between the guest molecule and the framework. We also show that t-SerialED can accurately determine the positions of hydrogen atoms and study non-covalent interactions, such as hydrogen bonding and proton charge transfer. By resolving the challenges mentioned above, t-SerialED extends the analyzing scope of serial chemical crystallography from single phase to complex mixtures. We expect t-SerialED to become a general method for chemical crystallography and phase analysis of submicron or nano-sized mixtures, complementing PXRD for routine sample checking and phase analysis. Results Our t-SerialED approach is a combination of the conventional rotation method and SerialED. By exposing each crystal at multiple rotation angles, we mitigate the problem of indexing and preferred orientation. Our t-SerialED approach can autonomously work on crystals with large size distribution randomly with the following steps (Fig. 1 a-d). First, the eucentric height of the entire grid is determined using a hierarchical multi-resolution approach. A low-magnification overview image of the grid (LM 110) is captured, and the central positions of the grid squares are identified through automatic image analysis. The eucentric heights of the grid are then predicted from measurements of selected squares at medium magnification (LM 1150), as shown in Figure S 3. Second, a Ronchigram that shows the overview of a selected position (eq. SA 3300) is recorded in defocused diffraction mode with ~ 1% of the total dose, and the positions of the crystals are automatically identified. The algorithm detects isolated crystals, aggregated crystals, large bulks and tracks the edges of the larger crystals, as illustrated in Figure S 8. Once the stage reaches the target angle, still ED patterns are recorded for all crystals in the overview image at different angles. The stage will not advance to the next tilt angle until ED patterns have been collected for all crystals at the current angle. This workflow achieves a nearly 100% hit rate (crystals successfully hit by the electron beam) and a data collection rate of up to 180 t-SerialED datasets per hour (0.5 s/frame, 25 frames/dataset). When the target angle is reached, the stage is moved to a new area, repeating the above process until sufficient t-SerialED datasets have been gathered. The 3D reciprocal space (Fig. 1 d) for each crystal is visualized individually, and the unit cell and orientation matrix are calculated for each frame. At last, the reflections on each frame are integrated and merged. Structure determination for porous materials We chose MOF-235 as our test sample for structure determination from t-SerialED datasets. MOF-235 shares the same framework structure with MIL-88B. As shown in Fig. 2 a, some of the crystals are well-isolated and some of them tend to stick together. The crystal finding algorithm will identify both as targets and collect t-SerialED datasets. The ED pattern from aggregated crystals shows a typical multi-crystal ED pattern, which is successfully indexed and all three lattices with different orientations are resolved. As aggregated area is unavoidable for most of the TEM samples, inclusion for these areas will not only increase the data collection efficiency, but also reduce the bias and systematic error in quantitative phase analysis. We reached a complete dataset with high multiplicity by measuring 160 datasets within 1h, containing 159 indexable datasets. We applied both Crystfel and DIALS to process the dataset and obtained similar results (Table S 7). The 3D reciprocal space was visualized from an individual t-SerialED dataset and space groups (Figure S 13) was determined from the systematic absence conditions. As shown in Fig. 2 , the crystal structure can be determined ab-initio using direct methods in SHELXT in the space group of \(\:P\overline{6}2c\) and the structure can be refined anisotropically. The final R 1 reached around 15% and all of the symmetry-independent hydrogen atoms are resolved in the difference Fourier map. Moreover, disordered solvent molecules (DMF) in the channel are clearly visualized. The DMF molecules have two configurations to interact with the Fe atom. The results prove that t-SerialED is a high-accuracy structure determination method that allows investigation of guest molecules and their interactions with the framework. Phase analysis for complex mixtures Phase analysis of polycrystalline materials is crucial for various applications, including sample screening, synthesis optimization, and quality control. Traditionally, phase analysis is performed using PXRD. However, the result can be influenced by many factors, such as preferred orientation, reflection overlap from materials with low crystal symmetry or large unit cells, and the crystallinity of the samples. Next, we mixed 6 compounds with known percentage (16.7 w.t.%) to show that t-SerialED can automatically analyze the phase compositions with decent accuracy by clustering the unit cell parameters from each dataset. Figure 3. Dendrogram showing the compositional analysis results from t-SerialED and responding structure determined from each unit cell cluster. The y axis is the Euclidean distance between the unit cell parameters and is described in Methods (Eq. (1)). The horizontal axis is the index of the 3D ED datasets used for HCA. HCA showed six phases by setting the Euclidean distance cut threshold at 5.0. The branches under each phase/cluster are of the same color. As indicated by the number of branches (one branch represents one crystal) under each phase, the volume ratio of each compound can be calculated. “*” indicates the expected volume ratio for each compound. The expected volume percentage of the complex mixture can be calculated by dividing the weight percentage by the density of each compound (Table S8). We collected 902 datasets over 6.5 hours, with 495 of them successfully indexed (54.9%). The indexing of the rest of the datasets was obstructed by factors such as thick sample, amorphous content, or polycrystalline nature (Figure S12). The unit cells were clustered by applying a threshold to the dendrogram, resulting in six distinct clusters (Fig. 3). By counting the number of unit cells in each cluster, the relative volume ratio of each compound was calculated. The volume ratios from t-SerialED were as follows: 11.0% (glycine), 17.5% (L-ascorbic acid), 16.3% (zinc acetate), 27.7% (saccharin), 13.2% (magnesium acetate), and 14.3% (L-glutamic acid). Overall, the phase analysis results show trends consistent with the expected volume ratios, particularly for saccharin, which differed by only 0.2%. The absolute deviations for the other compounds ranged from 1.2–3.6%. Several factors could account for these deviations. One possibility is the loss of crystallinity during grinding, which may reduce the likelihood of indexing 17 . Another possibility is that some materials may have a higher affinity for the grid support during sample preparation, leading to selective adhesion of those materials. Since we count the number of indexed lattices rather than the actual volume, this could also introduce some error. Furthermore, the crystal shapes and sizes vary significantly (Figure S14), even after crushing. Some crystals are more resistant to being broken into smaller pieces and tend to aggregate. For aggregates larger than the beam size, we only collect datasets from the edges, as the inner parts of the particles are often impenetrable by electrons (Figure S 8). After phase analysis, we integrated and merged frames within each cluster using serial-crystallography based methods, determining the structures ab-initio for all compounds. These structures were refined anisotropically, with hydrogen atoms in four compounds identified from Q-peaks or difference Fourier maps. The clear identification of hydrogen atoms allows us to investigate charge transfer in glycine and L-glutamic acid, where hydrogen atoms in the carboxylic groups are transferred to neighboring amino groups, forming tetrahedral geometries, as shown in the electrostatic potential maps (Fig. 3). In saccharin, the hydrogen atom is positioned next to the nitrogen atom in the five-membered ring, confirming the dominant tautomeric form after crystallization 21 . All datasets achieve high completeness, with the lowest being 88.6% for Zn acetate (Table S10), which could explain the loss of hydrogen atoms in the difference Fourier map. The CC 1/2 plot (Figure S15) for Mg acetate shows low correlation, and we observed the resolutions of ED patterns for this compound are lower. Consequently, the number of merged frames for Mg acetate is limited to approximately 330, the lowest among the six compounds. The reduced resolution and frame count lead to incomplete high-resolution reflections and poor intensity estimations, resulting in the highest R 1 value (33.3%) among six. For the other compounds, R 1 values range from 16.1–22.6%, consistent with typical electron diffraction datasets. Phase analysis for pharmaceutical tablets and capsules As a further assessment of the general applicability of the method, we applied t-SerialED to one commercially available pharmaceutical tablet and one capsule (Figure S 14), in formulations of paracetamol and ferrous glycine complex (FGC), respectively. All of the drug formulations contain a variety of non-active agents such as binders, disintegrants and wax. According to the registration information (Table S 2), both drugs contain a tiny amount of talc in crystalline form but the percentage is unknown. Other non-active contents are unlikely to diffract to sufficient resolution. Paracetamol (one API polymorph) We collected 197 datasets in 1.7 hours, with 163 of them indexed to the unit cells of the API, indicating a volume ratio of 82.8% (Table S2). This deviates from the expected API volume ratio by just 1.4% (81.4%), demonstrating high accuracy considering the various influencing factors discussed above. Additionally, one dataset was indexed to the unit cell of talc, representing 0.6% of the crystalline contents in the tablet. Compared with the analysis from PXRD (Fig. 4 b), the result differs by 1.2% (1.8%). After phase analysis, we treated every frame from API as separate crystals and applied the serial crystallography approach to integrate and merge these datasets. From the HKL files, we solved the structure ab-initio and refined the structure anisotropically with final R 1 of 17.2% (Table S13). We also located all the H atoms in the structure and visualized the hydrogen bonding network (Figure S 17). Ferrous Glycine Complex (two API polymorphs) For Ferrous Glycine Complex (FGC) pellets, 497 datasets were collected within 3.8 hours and 215 of them were indexed to the API unit cells. The volume ratio of APIs in the pellet was determined to be 43.4%, which is 6.2% less than the expected ratio (49.6%). One possible explanation for this discrepancy is the low crystallinity of the API. As shown in Figure S21, more than 50% of the datasets have fewer than 150 indexed reflections, whereas for paracetamol, only 10% of the datasets have fewer than 150 reflections. Further evidence of the API's low crystallinity is the significantly longer time required for PXRD data collection − 28 hours for the FGC sample, compared to 5 hours for the paracetamol sample - to achieve sufficient counting statistics. From the clustering result (Fig. 4 c), we conclude that the FGC has two polymorphs, denoted as FGC form 1 and FGC form 2. They correspond to two polymorphs of FGC in CCDC: GLYCFE01 and UDOPIO01. Of the 215 datasets, 207 (95.4%) were indexed to the unit cell of form 1, while 8 (3.6%) were indexed to the unit cell of form 2. We use PXRD as a reference, since the ratio of different polymorphs is not provided in the drug registration files. However, even the strong peaks of FGC form 2 are submerged in the background (Figure S22). Consequently, content of FGC form 2 estimated from PXRD is very low (0.1%), which may not be reliable. For the highly crystalline content, talc, the strongest PXRD peak is clearly visible, indicating that talc constitutes 2.3% of the crystalline content. In contrast, t-SerialED identified only 2 datasets with the talc unit cell out of 217 indexed datasets (1%). Since both methods can exhibit significant variations when measuring trace amounts of minor phases, it is difficult to determine which result is more accurate. Nonetheless, we conclude that t-SerialED provides results consistent with PXRD for highly crystalline phases and can also detect minor phases with lower crystallinity. Given the shorter acquisition time (3.8 hours versus 28 hours) and the automated nature of t-SerialED, we expect this method to complement PXRD by enabling comprehensive analysis of all sample components, regardless of the crystallinity. Finally, we determined the structure of FGC form 1 ab-initio and assessed the impact of the number of datasets on data quality. By filtering datasets with fewer than 200 and 100 indexed reflections, we integrated and merged 39 and 93 datasets, respectively. The data processing statistics for both groups are similar, but the final R 1 value decreases by 4.33%, from 21.37–17.04%. This result demonstrates that including more datasets with sufficient indexing can significantly improve data quality. Discussion In the t-SerialED method, there is a tradeoff between the number of frames and accuracy. Acquiring more frames for a single target increases acquisition time but also captures more reflections, allowing the determination of additional sets of lattices from one dataset. Conversely, using fewer frames speeds up the acquisition process, but makes indexing more challenging. Table S 3 summarized the time and dose for different t-SerialED experimental setups. For the setting applied in our experiments, each dataset only needs 20.5s, including all the overhead time. Table S 4 compared t-SerialED with SerialED and SerialRED methods. The table shows that t-SerialED has the advantage of collecting datasets over large tilt angles within a short amount of time. Comparison with SFX Due to the sparsity of reflections, serial femtosecond crystallography (SFX) for small molecules identifies unit cells by aggregating spot-finding results into high-resolution powder diffractograms and generating candidate unit cells from the synthetic powder pattern 6 . However, this method struggles to provide accurate information when the sample contains a mixture of several phases. In contrast, t-SerialED can quantitatively analyze complex mixtures and accurately determine the structure of each phase. Moreover, images are acquired during t-SerialED data collection, providing valuable insights into particle size distribution, surface features, and internal morphology. t-SerialED can correlate real-space and reciprocal-space information, paving the way for future advanced studies. t-SerialED can be adaptable to various types of sample holders, such as the cryo-holders used in this study, and can be easily applied to other in-situ TEM holders, enabling the study of structural dynamics under different environmental conditions. Comparison with SerialED The bottleneck of SerialED is indexing. Due to the short de Broglie wavelength of electrons (0.0197 Å at 300 kV, as compared to several Å in the case of X-rays), the Ewald sphere is almost flat. Therefore, hardly any three-dimensional information can be extracted from a single pattern. Therefore, currently all indexing algorithms, such as TakeTwo 22 , FELIX 23 , problematic 19 , SPIND 24 , or PinkIndexer 25 , require prior unit-cell information as a restraint. Another challenge arises when an ED pattern contains reflections from multiple crystals, as current indexing algorithms are unlikely to provide a correct solution. The incorporation of 3D reciprocal information in t-SerialED datasets enables the use of indexing algorithms from traditional X-ray crystallography programs, improving the indexing rate to nearly 100% even for multi-crystal patterns. This enhances both the number of processable datasets obtained during a TEM session and the accuracy of phase analysis. By collecting ED patterns at various angles, preferred orientation can be mitigated, allowing for the acquisition of a complete dataset from fewer crystals. Notably, most of our samples have much lower symmetry compared with current SerialED examples. t-SerialED can obtain high completeness datasets from a small number of crystals. Additionally, t-SerialED do not require prior knowledge about unit cell, enabling phase analysis and structure determination for unknown phases. Comparison with SerialRED 3DED has become an effective method for structure determination for beam-sensitive materials 26 , 21 , 27 due to significant advancements in instrumentation and processing workflows 28 . SerialRED was developed as an automated workflow based on the continuous rotation geometry 16 . Depending on the level of automation, the SerialRED method has two types of implementations. One is a fully-automated workflow using an in-house program 16 . The other one is a semi-automated workflow for batch data collection based on commercially available software and the workflow requires manual crystal picking 18 . In both cases, the data acquisition speed is slower than t-SerialED due to longer overhead times and the method of data collection, which involves rotating each crystal individually. Additionally, if the stage rotation is unstable or the eucentric height is not properly adjusted, the crystal may move out of the beam during data acquisition, negatively impacting the quality of the dataset. Another limitation is the targets should be isolated, single crystals and the size of crystals should be smaller than the size of the beam. Consequently, SerialRED requires strict standards for grid preparation. If there are too many crystals on the grid, then most of the datasets will come from multi-crystals and are hard to be processed by the traditional 3DED workflow. If there are too few crystals on the grid, then the data collection efficiency will be very low because most of the time will be spent on searching the crystals instead of collecting datasets. On the other hand, manual crystal picking tends to select well-isolated single crystals while ignoring aggregated ones, introducing bias during data collection and making the phase analysis results less reliable. In contrast, t-SerialED does not require special grid preparation, allowing for high sample density and proper processing of ED patterns from multi-crystals. t-SerialED datasets can also be collected from the edges of large crystals, ensuring optimal data quality even for large and thick crystals. In SerialRED, however, these large crystals are often disregarded, leading to systematic errors in quantitative analysis. Conclusions In summary, by incorporating 3D information in the SerialED, t-SerialED resolves the major challenges faced by serial chemical crystallography. t-SerialED approach established in this study expands electron diffraction as a quantitative analytical method well beyond a structural determination approach. The data collection process requires minimum human intervention after initial setup, making it suitable to run during less busy microscope shifts. With the ability to collect and analyze vast amounts of data, t-SerialED can be used for compositional analysis, providing a fast, reliable and statistically significant quantitative analysis. We expect that t-SerialED will make a significant impact in the exploration of a wide range of materials, including minerals, zeolites, ceramics, MOFs and pharmaceutical compounds. Methods Grid Preparation The copper grids with continuous carbon support (300-mesh, ultra-thin carbon layer, EMS Inc.) are pretreated with glow-discharge plasma at 15 mA in negative mode using a PELCO easiGlow (Ted Pella Inc.). The glow discharge time is 60 seconds for all samples. Approximately 1 mg of sample is transferred to a 10 mL glass test tube and mixed with the grid. After shaking the tube, the grids are taken out and loaded onto the TEM holders, where the particles adhere to the carbon film through electrostatic forces. Data acquisition All datasets are collected on a Thermal Fisher Themis-Z microscope with an ASI Cheetah 3 detector. The microscope’s beam deflectors are synchronized with a high-frame-rate camera through program control. t-SerialED experiments are performed using Instamatic. Figure 5 is a schematic diagram to show the workflow. The experiment can be divided into two stages, preparation stage and collection stage. During the preparation stage, the microscope runs in LM mode to identify the grid holes and determine the eucentric height. This typically takes around 10 mins. During the collection stage, the size of C2 aperture is set to 50 µm and the microscope keeps running in diffraction mode, avoiding switching the microscope back-and-forth from different modes and saving time. The targets are shown in a Ronchigram by adjusting the diffraction defocus Through adjusting the beam diameter, the Ronchigram should cover the whole detector. When taking ED patterns, the electron beam diameter can be adjusted to match the typical size of the targets by adjusting the current of the C3 lens. An exposure time of 0.5 s was used for each diffraction pattern and 25 frames are recorded for each target. Details for automatic crystal finding, eucentric height prediction and crystal position prediction are discussed in SI. Data processing As shown in Figure S 23, t-SerialED can be processed by multiple workflows through combination of one of the programs in two groups: (1). For indexing and unit cell determination: DIALS 29 or PETS2.0 30 (2). Integration and merging: DIALS or CrystFEL 31 . The data processing workflows are implemented in edtools program 16 . Data Pre-processing: The raw detector datasets are saved by Instamatic 32 in MRC format with REDp 33 software input file (. ed3d format). REDp software can be used for 3D reciprocal space visualization During data acquisition, the center of diffraction pattern will move several pixels as the electron beam follows the crystal. The center beam drift in each t-SerialED dataset will be corrected by cross correlation. After the center beam drift correction, the MRC files are converted to SMV files for DIALS data processing or HDF5 files for CrystFEL data processing. If more accurate unit cell parameters are required, then the MRC files need to be converted into tiff files for PETS2.0 data processing. Indexing and Integration : Bragg reflections in diffraction patterns are identified using either the extended dispersion threshold algorithm in DIALS or a thresholding algorithm based on I / σ in PETS2.0 30 . Then the search for basis vectors in 3D reciprocal space is conducted using the 3D FFT algorithm in DIALS or the 3D difference space algorithm in PETS2.0 . Once identified, both programs provide the unit cell and the orientation matrix of the ED pattern at 0°. The orientation matrices for all frames in a tilt series are calculated by multiplying the initial orientation matrix by the rotation matrix, derived from the tilt angle and rotation axis direction. After obtaining the orientation matrix for each frame, the integrated image intensity at each predicted Bragg peak position is determined using either a background-subtracted summation algorithm in CrystFEL or a profile fitting algorithm combined with summation in DIALS . Clustering of unit cell parameters : Unit cell parameters are clustered by calculating the Euclidean distance, denoted as \(\:d\left(i,j\right)\) , between unit cells \(\:i\) and \(\:j\) . Datasets are grouped based on this distance metric, with each cluster comprising datasets that have similar unit cell parameters and are considered to represent the same phase. \(\:d\left(i,j\right)=\sqrt{\varDelta\:{a}^{2}\left(i,\:j\right)+\varDelta\:{b}^{2}\left(i,\:j\right)+\varDelta\:{c}^{2}\left(i,\:j\right)+k*\left[\varDelta\:{\alpha\:}^{2}\left(i,\:j\right)+\varDelta\:{\beta\:}^{2}\left(i,\:j\right)+\varDelta\:{\gamma\:}^{2}\left(i,\:j\right)\right]}\) Equation 1 In Eq. 1, k is a scaling parameter that is defined by the user to adjust the weighting between unit cell length and angle. By default, the value is set to 1. \(\:{a}_{i}\) , \(\:{b}_{i}\) , \(\:{c}_{i}\) , \(\:{\alpha\:}_{i}\) , \(\:{\beta\:}_{i}\) and \(\:{\gamma\:}_{i}\) correspond to the unit cell parameters from the ith dataset, where a, b, c are the unit cell lengths and α, β, γ are the unit cell angles. In order to resolve the angle ambiguities, angles larger than 90° will be transformed to the corresponding angle less than 90°. \(\:{a}_{j}\) , \(\:{b}_{j}\) , \(\:{c}_{j}\) , \(\:{\alpha\:}_{j}\) , \(\:{\beta\:}_{j}\) and \(\:{\gamma\:}_{j}\) are the parameters from the jth dataset. \(\:\varDelta\:{a}^{2}\left(i,\:j\right)\) is defined as ( \(\:{a}_{i}\) - \(\:{a}_{j}\) ) 2 . The same applies to \(\:\varDelta\:{b}^{2}\left(i,\:j\right)\) and \(\:\varDelta\:{c}^{2}\left(i,\:j\right)\) . The following are methods for calculating the distance between the newly formed cluster \(\:u\) and each \(\:v\) . \(\:v\) is the remaining cluster in the forest that is not \(\:u\) . The first one is called “average”. It uses the following formula to calculate distance: \(\:d\left(u,v\right)=\sum\:_{ij}\frac{d\left(u\left[i\right],\:v\left[j\right]\right)}{\left(\left|u\right|*\left|v\right|\right)}\) Equation 2 For all points \(\:i\) and \(\:j\) where \(\:\left|u\right|\:\) and \(\:\left|v\right|\) are the cardinalities of clusters u and v, respectively. The second method uses the Ward variance minimization algorithm. The new entry \(\:d\left(i,j\right)\) is computed as follows, \(\:d\left(u,v\right)=\sqrt{\frac{\left|v\right|+\left|s\right|}{T}{d\left(v,s\right)}^{2}+\frac{\left|v\right|+\left|t\right|}{T}{d\left(v,t\right)}^{2}-{\frac{\left|v\right|}{T}d\left(s,t\right)}^{2}}\) Equation 3 Where u is the newly joined cluster consisting of clusters s and t, v is an unused cluster in the forest, \(\:T=\left|v\right|+\left|s\right|+\left|t\right|\) . Merging and Structure determination : If the sample is a pure phase. Then all datasets can be merged directly. For mixtures, the unit cell is first clustered using the method described above. Then the datasets in each cluster are merged into an individual HKL file. We use partialator 34 or xia2.ssx_reduce 35 to merge the datasets, yielding a plain-text Shelx HKL file containing the full reduced data set. Next, ShelxT 36 was used for structure solution process. Structure refinement and visualization of the structure models were performed using ShelxL 37 , ShelXle 38 and VESTA 39 . Declarations Data availability Crystallography data for all the samples are available in the CCDC database (CCDC number: 2390619, 2390620, 2390621, 2390622, 2390623, 2390624, 2390854, 2390855, 2390856). These datasets can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif , or by emailing [email protected] , or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033. The raw t-SerialED datasets of this study are available in Zenodo: 10.5281/zenodo.13924322 . Code availability The source code of DIALS is available at https://github.com/dials/dials under the terms of BSD 3-Clause ‘New’ or ‘Revised’ License. The Instamatic Python package for t-SerialED experiments is available at https://github.com/instamatic-dev/instamatic under the terms of GNU General Public License v.3.0. The edtools Python package for t-SerialED data processing is available at https://github.com/instamatic-dev/edtools under the terms of BSD 3-Clause ‘New’ or ‘Revised’ License. All custom software for data acquisition and hardware control is available from the corresponding author upon reasonable request. Authorship contribution statement Taimin Yang : Conceptualization and planning for the whole project, Investigation, Implementation, Programming, Sample synthesis, Data acquisition, Data analysis, Manuscript writing and revision, Funding acquisition. David Geoffrey Waterman : Data analysis, Programming, Manuscript revision. Zheting Chu : Sample synthesis, Data analysis, Manuscript revision. James Beilsten-Edmands : Programming, Manuscript revision. Zhehao Huang : Funding acquisition, Manuscript revision. Xiaodong Zou : Funding acquisition, Manuscript revision. Conflicts of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We acknowledge financial support from Swedish Research Council Formas (T.Y. 2022–02778, Z.H. 2020 − 00831), European Union’s Horizon 2020 innovation program under the Marie Skłodowska-Curie grant agreement (T.Y. 101146059), The Royal Swedish Academy (T.Y. CH2022-0015, PH2022-0021), the Swedish Research Council (X.Z. 2019 − 00815, Z.H. 2022–02939), the Knut and Alice Wallenberg Foundation (X.Z. 2018.0237). We also acknowledge the Electron Microscopy Center at Stockholm University and the Knut and Alice Wallenberg Foundation for an equipment grant for the electron microscopy facilities at Stockholm University, Sweden. References Szymanski NJ et al (2023) An autonomous laboratory for the accelerated synthesis of novel materials. Nature 624:86–91 Lunt M (2024) Modular, multi-robot integration of laboratories: an autonomous workflow for solid-state chemistry. Chem Sci 15:2456–2463 Chapman HN et al (2011) Femtosecond X-ray protein nanocrystallography. Nature 470:73–77 Takaba K et al (2023) Structural resolution of a small organic molecule by serial X-ray free-electron laser and electron crystallography. Nat Chem 15:491–497 Takaba K et al (2024) Comprehensive Application of XFEL Microcrystallography for Challenging Targets in Various Organic Compounds. J Am Chem Soc 146:5872–5882 Schriber EA et al (2022) Chemical crystallography by serial femtosecond X-ray diffraction. Nature 601:360–365 Kolb U, Gorelik T, Kübel C, Otten MT, Hubert D (2007) Towards automated diffraction tomography: Part I—Data acquisition. Ultramicroscopy 107:507–513 Nederlof I, van Genderen E, Li Y-W, Abrahams JP (2013) A Medipix quantum area detector allows rotation electron diffraction data collection from submicrometre three-dimensional protein crystals. Acta Cryst D 69:1223–1230 Palatinus L et al (2017) Hydrogen positions in single nanocrystals revealed by electron diffraction. Science 355:166–169 Xu H et al (2018) A Rare Lysozyme Crystal Form Solved Using Highly Redundant Multiple Electron Diffraction Datasets from Micron-Sized Crystals. Structure 26:667–675e3 Gemmi M et al (2019) 3D Electron Diffraction: The Nanocrystallography Revolution. ACS Cent Sci 5:1315–1329 Kolb U, Krysiak Y, Plana-Ruiz S (2019) Automated electron diffraction tomography – development and applications. Acta Cryst B 75:463–474 Wang B, Zou X, Smeets S (2019) Automated serial rotation electron diffraction combined with cluster analysis: an efficient multi-crystal workflow for structure determination. IUCrJ 6:854–867 Takaba K, Maki-Yonekura S, Yonekura K (2020) Collecting large datasets of rotational electron diffraction with ParallEM and SerialEM. J Struct Biol 211:107549 Yonekura K, Maki-Yonekura S, Naitow H, Hamaguchi T, Takaba K (2021) Machine learning-based real-time object locator/evaluator for cryo-EM data collection. Commun Biol 4:1–8 Luo Y et al (2023) High-throughput phase elucidation of polycrystalline materials using serial rotation electron diffraction. Nat Chem 15:483–490 Unge J, Lin J, Weaver SJ, Her AS, Gonen T (2023) Autonomous MicroED data collection enables compositional analysis. 10.26434/chemrxiv-2023-8qvwg Lightowler M et al (2024) Phase Identification and Discovery of an Elusive Polymorph of Drug-Polymer Inclusion Complex Using Automated 3D Electron Diffraction. Angew Chem Int Ed 63:e202317695 Smeets S, Zou X, Wan W (2018) Serial electron crystallography for structure determination and phase analysis of nanocrystalline materials. J Appl Cryst 51:1262–1273 Bücker R et al (2020) Serial protein crystallography in an electron microscope. Nat Commun 11:996 Tang W et al (2023) Tautomerism unveils a self-inhibition mechanism of crystallization. Nat Commun 14:561 Ginn HM et al (2016) TakeTwo: an indexing algorithm suited to still images with known crystal parameters. Acta Cryst D 72:956–965 Beyerlein KR et al (2017) FELIX: an algorithm for indexing multiple crystallites in X-ray free-electron laser snapshot diffraction images. J Appl Cryst 50:1075–1083 Li C et al (2019) SPIND: a reference-based auto-indexing algorithm for sparse serial crystallography data. IUCrJ 6:72–84 Gevorkov Y et al (2020) pinkIndexer – a universal indexer for pink-beam X-ray and electron diffraction snapshots. Acta Cryst A 76:121–131 Wang S et al (2023) Thermodynamics and Kinetics in Anisotropic Growth of One-Dimensional Midentropy Nanoribbons. ACS Nano 17:15053–15064 Lv Z-P et al (2024) Visualizing Noncovalent Interactions and Property Prediction of Submicron-Sized Charge-Transfer Crystals from ab-initio Determined Structures. Small Methods n/a, 2301229 Yang T, Willhammar T, Xu H, Zou X, Huang Z (2022) Single-crystal structure determination of nanosized metal–organic frameworks by three-dimensional electron diffraction. Nat Protoc. 10.1038/s41596-022-00720-8 Waterman DG et al (2016) Diffraction-geometry refinement in the DIALS framework. Acta Cryst D 72:558–575 Palatinus L et al (2019) Specifics of the data processing of precession electron diffraction tomography data and their implementation in the program PETS2.0 . Acta Crystallogr B Struct Sci Cryst Eng Mater 75:512–522 Bücker R, Hogan-Lamarre P, Miller RJ (2021) D. Serial Electron Diffraction Data Processing With diffractem and CrystFEL. Front Mol Biosci 8 Cichocka MO, Ångström J, Wang B, Zou X, Smeets S (2018) High-throughput continuous rotation electron diffraction data acquisition via software automation. J Appl Cryst 51:1652–1661 Wan W, Sun J, Su J, Hovmöller S, Zou X (2013) Three-dimensional rotation electron diffraction: software RED for automated data collection and data processing. J Appl Cryst 46:1863–1873 White TA (2014) Post-refinement method for snapshot serial crystallography. Philosophical Trans Royal Soc B: Biol Sci 369:20130330 Winter G et al (2018) DIALS: implementation and evaluation of a new integration package. Acta Cryst D 74:85–97 Sheldrick GM (2015) SHELXT – Integrated space-group and crystal-structure determination. Acta Crystallogr Sect A: Found Adv 71:3–8 Sheldrick GM (2015) Crystal structure refinement with SHELXL. Acta Crystallogr Sect C: Struct Chem 71:3–8 Hübschle CB, Sheldrick GM, Dittrich B (2011) ShelXle: a Qt graphical user interface for SHELXL. J Appl Cryst 44:1281–1284 Momma K, Izumi F (2011) VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J Appl Cryst 44:1272–1276 Additional Declarations There is NO Competing Interest. Supplementary Files cifs.zip Crystallography structure files SI.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5300199","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":369697402,"identity":"9fedfd38-845a-444c-9876-e5f6634a5db8","order_by":0,"name":"Taimin Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIiWNgGAWjYFACxgaGBCjrAQOMiQ/wIGlhNiBSCwKwSRClxZ79cOuGhzsYEvtnt1+rupmTxiA/I4H5wwd8tvAktt1IPMOQOOPOmbLbudtyGAxuJLBJzsDrMJCWNobEhhs5aUAtFQwGEglszDz4tPA/hGiZD9RSDNICctjnP/i0SEBt2XAj/RgzyGEMNxIYpPF5n+cG2BYJ4403cpilc7el8Ricedgm2YNHC3t/+rObP9tsZOfdSH/4OXdbspx8e/LhDz/wWQMBEo4NDDwGYGvB6YEYYA+08AFRKkfBKBgFo2DkAQD4KVJQa/IOzQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-4318-8990","institution":"Stockholm University","correspondingAuthor":true,"prefix":"","firstName":"Taimin","middleName":"","lastName":"Yang","suffix":""},{"id":369697403,"identity":"409a31dc-58a1-48ec-871c-82c4545be44f","order_by":1,"name":"David Waterman","email":"","orcid":"https://orcid.org/0000-0002-2134-182X","institution":"UKRI Science and Technology Facilities Council","correspondingAuthor":false,"prefix":"","firstName":"David","middleName":"","lastName":"Waterman","suffix":""},{"id":369697404,"identity":"0414c0c4-1911-4722-811b-e15b3974b578","order_by":2,"name":"Zheting Chu","email":"","orcid":"","institution":"Stockholm University","correspondingAuthor":false,"prefix":"","firstName":"Zheting","middleName":"","lastName":"Chu","suffix":""},{"id":369697405,"identity":"44fc82f6-5182-40d0-83d4-a2bf6f6a4a75","order_by":3,"name":"James Beilsten-Edmands","email":"","orcid":"https://orcid.org/0000-0003-1565-5328","institution":"Diamond Light Source Ltd","correspondingAuthor":false,"prefix":"","firstName":"James","middleName":"","lastName":"Beilsten-Edmands","suffix":""},{"id":369697406,"identity":"bd2c63fa-3d24-4a6c-9808-059d1d9809a2","order_by":4,"name":"Zhehao Huang","email":"","orcid":"https://orcid.org/0000-0002-4575-7870","institution":"Stockholm University","correspondingAuthor":false,"prefix":"","firstName":"Zhehao","middleName":"","lastName":"Huang","suffix":""},{"id":369697407,"identity":"ac66df77-ce89-456d-be78-b5f81a64e66a","order_by":5,"name":"Xiaodong Zou","email":"","orcid":"https://orcid.org/0000-0001-6748-6656","institution":"Stockholm University","correspondingAuthor":false,"prefix":"","firstName":"Xiaodong","middleName":"","lastName":"Zou","suffix":""}],"badges":[],"createdAt":"2024-10-21 00:15:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5300199/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5300199/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68228339,"identity":"24455cfa-8271-473a-b3d8-19ab03fbbc5b","added_by":"auto","created_at":"2024-11-05 04:42:11","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1361316,"visible":true,"origin":"","legend":"\u003cp\u003eSchematics of t-SerialED data acquisition process: (a) In the preparation stage, grid holes are found and eucentric height is determined under low-mag mode. This usually takes around 10 mins. (b) At the center of each grid hole, a user-defined area is divided into multiple blocks and the stage will move to these blocks sequentially. Moving into the collection stage, crystals are first mapped in low-dose defocused diffraction mode (typically 10 um edge length) at 0 degrees. (c) Crystals show up as clear features and can be identified and ED patterns will be taken for each crystal automatically. After all ED patterns are taken at this angle, the stage will tilt to another angle and repeat the mapping and diffraction step. (d) At last, the ED patterns taken at different tilt angles for each crystal can form a 3D reciprocal space, in which unit cell and orientation matrix can be reliably identified. (e) Comparison of SerialED and t-SerialED. SerialED captures only one snapshot from one crystal while t-SerialED collects multiple shots from different angles.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-5300199/v1/366a06bd2e266123bfd0286e.jpeg"},{"id":68228340,"identity":"c320d500-ad60-4c93-ad6d-341be1764664","added_by":"auto","created_at":"2024-11-05 04:42:11","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1107557,"visible":true,"origin":"","legend":"\u003cp\u003eStructure determination of MOF-235 by t-SerialED: (a) the TEM image shows the morphology and distribution on the grid. The red dots indicate the positions for collecting datasets. Position I is a single crystal and (I) shows the ED pattern from this area. The green dots show the indexed spots by a single lattice. Position II reveals the aggregation of multiple nanocrystals and (II) displays the ED pattern from this area. The red, green and blue dots indicate that the ED pattern is indexed by three distinct sets of lattices. (b) Refined MOF-235 structure. Electrostatic potential map of (c) guest molecule attached to the Fe atom and (d) hydrogen atoms on the ligand.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-5300199/v1/162f9076db70c0da69efebca.jpeg"},{"id":68228344,"identity":"51e48417-7cc5-4ffc-ba78-2a2beecda7fd","added_by":"auto","created_at":"2024-11-05 04:42:11","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":514258,"visible":true,"origin":"","legend":"\u003cp\u003eDendrogram showing the compositional analysis results from t-SerialED and responding structure determined from each unit cell cluster. The y axis is the Euclidean distance between the unit cell parameters and is described in Methods (equation (1)). The horizontal axis is the index of the 3D ED datasets used for HCA. HCA showed six phases by setting the Euclidean distance cut threshold at 5.0. The branches under each phase/cluster are of the same color. As indicated by the number of branches (one branch represents one crystal) under each phase, the volume ratio of each compound can be calculated. “*” indicates the expected volume ratio for each compound.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5300199/v1/4f13e0448df3dc8297876d9f.png"},{"id":68228343,"identity":"a5e22c9a-5222-4270-abaa-b358017bdcda","added_by":"auto","created_at":"2024-11-05 04:42:11","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1033892,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of phase analysis results from t-SerialED and PXRD Rietveld refinement for (a, b) paracetamol tablet and (c, d) iron supplement capsule. The results from t-SerialED shows the relative volume ratio of paracetamol and talc is 99.4: 0.6, while the volume ratio of ferrous glycine complex (FGC) form 1, form 2 and talc is 95.4: 3.6: 1.0.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-5300199/v1/2d60d375925ab35149d25370.jpeg"},{"id":68228342,"identity":"d046949f-e1c9-4d9e-8177-9e314e81d59d","added_by":"auto","created_at":"2024-11-05 04:42:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":879161,"visible":true,"origin":"","legend":"\u003cp\u003eSchematics to show the autonomous workflow of t-SerialED for structure determination and quantitative phase analysis.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5300199/v1/8a3761e0c94c61a970ef5bcd.png"},{"id":81236617,"identity":"09cfaca6-c684-4705-b2c1-7282b9e66280","added_by":"auto","created_at":"2025-04-23 20:03:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5663027,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5300199/v1/e0360bca-0b51-4aaa-98e2-d4f98861df71.pdf"},{"id":68228472,"identity":"9eff499e-a5b4-4c19-9053-e678f7d68dce","added_by":"auto","created_at":"2024-11-05 04:50:11","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2336692,"visible":true,"origin":"","legend":"Crystallography structure files","description":"","filename":"cifs.zip","url":"https://assets-eu.researchsquare.com/files/rs-5300199/v1/2fa0e24e0bad4adbcfa0b6f5.zip"},{"id":68228345,"identity":"1249456b-7805-454b-bbf5-5c49274ef6ec","added_by":"auto","created_at":"2024-11-05 04:42:11","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":30805633,"visible":true,"origin":"","legend":"","description":"","filename":"SI.docx","url":"https://assets-eu.researchsquare.com/files/rs-5300199/v1/30315125738169b54aa88354.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Serial chemical crystallography for autonomous quantitative phase analysis in an electron microscope","fulltext":[{"header":"Introduction","content":"\u003cp\u003eRecent advancements in robotics and artificial intelligence have significantly propelled the development of autonomous synthesis and characterization workflows\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Powder X-ray diffraction (PXRD) is the dominant method for characterization in these workflows. Nevertheless, Challenges arise when a polycrystalline product contains multiple phases, phases with low contents (\u0026lt;\u0026thinsp;5%), phases with similar unit cell parameters and structures with peak overlaps in PXRD patterns. As autonomous synthesis can usually produce many samples within a short timeframe, there is a pressing demand for innovative techniques that can match the speed and obtain the compositions and atomic structures for complex mixtures simultaneously.\u003c/p\u003e \u003cp\u003eThe last ten years witnessed several emerging technologies to study crystals that traditional X-ray techniques cannot effectively analyze. X-ray free-electron lasers (XFELs) have been crucial in driving the advancement of serial femtosecond crystallography (SFX)\u003csup\u003e\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. This technique captures a single snapshot from each crystal, avoiding dose accumulation associated with rotation series. The method is widely used in macromolecular crystallography. However, when applied to chemical crystallography, the small unit cell leads to sparsity of reflections on each frame, hindering unit cell and orientation matrix determination\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Although attempts have been made to resolve this problem, the solution generally requires pure samples\u003csup\u003e\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e and is difficult to apply to phase mixtures. Besides, the scarcity and costliness of XFEL beamtime limits this technique as a routine analysis method. Electron microscopes are a comparatively cost-effective alternative for measuring diffraction patterns from nanosized crystals. Recently, three-dimensional electron diffraction (3DED) has become an reliable method to determine beam-sensitive nanosized materials in TEMs\u003csup\u003e\u003cspan additionalcitationids=\"CR8 CR9 CR10 CR11\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Several attempts have been implemented to achieve automatic\u003csup\u003e\u003cspan additionalcitationids=\"CR14 CR15\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e or semi-automatic\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e structure analysis. However, the data collection speed is still not fast enough for phase analysis (fastest 1 min/crystal with speed of 1\u0026deg;/s)\u003csup\u003e14,17\u003c/sup\u003e. Therefore, serial electron diffraction (SerialED), a single-shot-per-crystal technique, has been applied to both small-\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e and macro-molecule crystals\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Nevertheless, the application of the method is limited by difficulties during data processing: (1) requires a known unit cell; (2) indexing is difficult, error-prone and time-consuming due to the nearly flat Ewald Sphere; (3) indexing ambiguity; (4) preferred orientation limits the completeness of the merged data; (5) unable to process an ED pattern from multiple crystals. Consequently, this method remains underutilized and has primarily been applied to crystals with relatively high symmetry and large unit cell parameters.\u003c/p\u003e \u003cp\u003eHere we present SerialED with tilt (t-SerialED), a multi-shots-per-crystal approach aiming to perform autonomous quantitative analysis for complex mixtures. The full workflow can be conducted in a conventional TEM without customized hardware, making sure the accessibility of the method. This method addresses the challenges in small molecule SFX (smSFX) and SerialED by merging 3D reciprocal space information into the serial crystallography data acquisition and processing workflows. We conducted autonomous data collection and analysis of the compositions and crystal structures across a range of beam-sensitive and polycrystalline mixtures, spanning from nanoporous materials to pharmaceutical compounds. We demonstrate that t-SerialED can determine the positions of disordered guest molecules in the pore and visualize the interaction between the guest molecule and the framework. We also show that t-SerialED can accurately determine the positions of hydrogen atoms and study non-covalent interactions, such as hydrogen bonding and proton charge transfer. By resolving the challenges mentioned above, t-SerialED extends the analyzing scope of serial chemical crystallography from single phase to complex mixtures. We expect t-SerialED to become a general method for chemical crystallography and phase analysis of submicron or nano-sized mixtures, complementing PXRD for routine sample checking and phase analysis.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eOur \u003cem\u003et-SerialED\u003c/em\u003e approach is a combination of the conventional rotation method and SerialED. By exposing each crystal at multiple rotation angles, we mitigate the problem of indexing and preferred orientation. Our \u003cem\u003et-SerialED\u003c/em\u003e approach can autonomously work on crystals with large size distribution randomly with the following steps (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea-d).\u003c/p\u003e \u003cp\u003eFirst, the eucentric height of the entire grid is determined using a hierarchical multi-resolution approach. A low-magnification overview image of the grid (LM 110) is captured, and the central positions of the grid squares are identified through automatic image analysis. The eucentric heights of the grid are then predicted from measurements of selected squares at medium magnification (LM 1150), as shown in Figure S 3. Second, a Ronchigram that shows the overview of a selected position (eq.\u0026nbsp;SA 3300) is recorded in defocused diffraction mode with ~\u0026thinsp;1% of the total dose, and the positions of the crystals are automatically identified. The algorithm detects isolated crystals, aggregated crystals, large bulks and tracks the edges of the larger crystals, as illustrated in Figure S 8. Once the stage reaches the target angle, still ED patterns are recorded for all crystals in the overview image at different angles. The stage will not advance to the next tilt angle until ED patterns have been collected for all crystals at the current angle. This workflow achieves a nearly 100% hit rate (crystals successfully hit by the electron beam) and a data collection rate of up to 180 t-SerialED datasets per hour (0.5 s/frame, 25 frames/dataset). When the target angle is reached, the stage is moved to a new area, repeating the above process until sufficient t-SerialED datasets have been gathered. The 3D reciprocal space (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed) for each crystal is visualized individually, and the unit cell and orientation matrix are calculated for each frame. At last, the reflections on each frame are integrated and merged.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eStructure determination for porous materials\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe chose MOF-235 as our test sample for structure determination from t-SerialED datasets. MOF-235 shares the same framework structure with MIL-88B. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea, some of the crystals are well-isolated and some of them tend to stick together. The crystal finding algorithm will identify both as targets and collect t-SerialED datasets. The ED pattern from aggregated crystals shows a typical multi-crystal ED pattern, which is successfully indexed and all three lattices with different orientations are resolved. As aggregated area is unavoidable for most of the TEM samples, inclusion for these areas will not only increase the data collection efficiency, but also reduce the bias and systematic error in quantitative phase analysis. We reached a complete dataset with high multiplicity by measuring 160 datasets within 1h, containing 159 indexable datasets. We applied both Crystfel and DIALS to process the dataset and obtained similar results (Table S 7). The 3D reciprocal space was visualized from an individual t-SerialED dataset and space groups (Figure S 13) was determined from the systematic absence conditions. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the crystal structure can be determined \u003cem\u003eab-initio\u003c/em\u003e using direct methods in SHELXT in the space group of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:P\\overline{6}2c\\)\u003c/span\u003e\u003c/span\u003e and the structure can be refined anisotropically. The final \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e reached around 15% and all of the symmetry-independent hydrogen atoms are resolved in the difference Fourier map. Moreover, disordered solvent molecules (DMF) in the channel are clearly visualized. The DMF molecules have two configurations to interact with the Fe atom. The results prove that t-SerialED is a high-accuracy structure determination method that allows investigation of guest molecules and their interactions with the framework.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003ePhase analysis for complex mixtures\u003c/h3\u003e\n\u003cp\u003ePhase analysis of polycrystalline materials is crucial for various applications, including sample screening, synthesis optimization, and quality control. Traditionally, phase analysis is performed using PXRD. However, the result can be influenced by many factors, such as preferred orientation, reflection overlap from materials with low crystal symmetry or large unit cells, and the crystallinity of the samples. Next, we mixed 6 compounds with known percentage (16.7 w.t.%) to show that t-SerialED can automatically analyze the phase compositions with decent accuracy by clustering the unit cell parameters from each dataset. \u003c/p\u003e \u003cp\u003eFigure 3. Dendrogram showing the compositional analysis results from t-SerialED and responding structure determined from each unit cell cluster. The y axis is the Euclidean distance between the unit cell parameters and is described in Methods (Eq.\u0026nbsp;(1)). The horizontal axis is the index of the 3D ED datasets used for HCA. HCA showed six phases by setting the Euclidean distance cut threshold at 5.0. The branches under each phase/cluster are of the same color. As indicated by the number of branches (one branch represents one crystal) under each phase, the volume ratio of each compound can be calculated. \u0026ldquo;*\u0026rdquo; indicates the expected volume ratio for each compound.\u003c/p\u003e \u003cp\u003eThe expected volume percentage of the complex mixture can be calculated by dividing the weight percentage by the density of each compound (Table S8). We collected 902 datasets over 6.5 hours, with 495 of them successfully indexed (54.9%). The indexing of the rest of the datasets was obstructed by factors such as thick sample, amorphous content, or polycrystalline nature (Figure S12). The unit cells were clustered by applying a threshold to the dendrogram, resulting in six distinct clusters (Fig.\u0026nbsp;3). By counting the number of unit cells in each cluster, the relative volume ratio of each compound was calculated. The volume ratios from t-SerialED were as follows: 11.0% (glycine), 17.5% (L-ascorbic acid), 16.3% (zinc acetate), 27.7% (saccharin), 13.2% (magnesium acetate), and 14.3% (L-glutamic acid). Overall, the phase analysis results show trends consistent with the expected volume ratios, particularly for saccharin, which differed by only 0.2%. The absolute deviations for the other compounds ranged from 1.2\u0026ndash;3.6%. Several factors could account for these deviations. One possibility is the loss of crystallinity during grinding, which may reduce the likelihood of indexing\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Another possibility is that some materials may have a higher affinity for the grid support during sample preparation, leading to selective adhesion of those materials. Since we count the number of indexed lattices rather than the actual volume, this could also introduce some error. Furthermore, the crystal shapes and sizes vary significantly (Figure S14), even after crushing. Some crystals are more resistant to being broken into smaller pieces and tend to aggregate. For aggregates larger than the beam size, we only collect datasets from the edges, as the inner parts of the particles are often impenetrable by electrons (Figure S 8).\u003c/p\u003e \u003cp\u003eAfter phase analysis, we integrated and merged frames within each cluster using serial-crystallography based methods, determining the structures ab-initio for all compounds. These structures were refined anisotropically, with hydrogen atoms in four compounds identified from Q-peaks or difference Fourier maps. The clear identification of hydrogen atoms allows us to investigate charge transfer in glycine and L-glutamic acid, where hydrogen atoms in the carboxylic groups are transferred to neighboring amino groups, forming tetrahedral geometries, as shown in the electrostatic potential maps (Fig.\u0026nbsp;3). In saccharin, the hydrogen atom is positioned next to the nitrogen atom in the five-membered ring, confirming the dominant tautomeric form after crystallization\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. All datasets achieve high completeness, with the lowest being 88.6% for Zn acetate (Table S10), which could explain the loss of hydrogen atoms in the difference Fourier map. The CC\u003csub\u003e1/2\u003c/sub\u003e plot (Figure S15) for Mg acetate shows low correlation, and we observed the resolutions of ED patterns for this compound are lower. Consequently, the number of merged frames for Mg acetate is limited to approximately 330, the lowest among the six compounds. The reduced resolution and frame count lead to incomplete high-resolution reflections and poor intensity estimations, resulting in the highest \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e value (33.3%) among six. For the other compounds, \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e values range from 16.1\u0026ndash;22.6%, consistent with typical electron diffraction datasets.\u003c/p\u003e\n\u003ch3\u003ePhase analysis for pharmaceutical tablets and capsules\u003c/h3\u003e\n\u003cp\u003eAs a further assessment of the general applicability of the method, we applied t-SerialED to one commercially available pharmaceutical tablet and one capsule (Figure S 14), in formulations of paracetamol and ferrous glycine complex (FGC), respectively. All of the drug formulations contain a variety of non-active agents such as binders, disintegrants and wax. According to the registration information (Table S 2), both drugs contain a tiny amount of talc in crystalline form but the percentage is unknown. Other non-active contents are unlikely to diffract to sufficient resolution.\u003c/p\u003e\n\u003ch3\u003eParacetamol (one API polymorph)\u003c/h3\u003e\n\u003cp\u003eWe collected 197 datasets in 1.7 hours, with 163 of them indexed to the unit cells of the API, indicating a volume ratio of 82.8% (Table S2). This deviates from the expected API volume ratio by just 1.4% (81.4%), demonstrating high accuracy considering the various influencing factors discussed above. Additionally, one dataset was indexed to the unit cell of talc, representing 0.6% of the crystalline contents in the tablet. Compared with the analysis from PXRD (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003eb), the result differs by 1.2% (1.8%). After phase analysis, we treated every frame from API as separate crystals and applied the serial crystallography approach to integrate and merge these datasets. From the HKL files, we solved the structure \u003cem\u003eab-initio\u003c/em\u003e and refined the structure anisotropically with final \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e of 17.2% (Table S13). We also located all the H atoms in the structure and visualized the hydrogen bonding network (Figure S 17).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eFerrous Glycine Complex (two API polymorphs)\u003c/h3\u003e\n\u003cp\u003eFor Ferrous Glycine Complex (FGC) pellets, 497 datasets were collected within 3.8 hours and 215 of them were indexed to the API unit cells. The volume ratio of APIs in the pellet was determined to be 43.4%, which is 6.2% less than the expected ratio (49.6%). One possible explanation for this discrepancy is the low crystallinity of the API. As shown in Figure S21, more than 50% of the datasets have fewer than 150 indexed reflections, whereas for paracetamol, only 10% of the datasets have fewer than 150 reflections. Further evidence of the API's low crystallinity is the significantly longer time required for PXRD data collection \u0026minus;\u0026thinsp;28 hours for the FGC sample, compared to 5 hours for the paracetamol sample - to achieve sufficient counting statistics. From the clustering result (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003ec), we conclude that the FGC has two polymorphs, denoted as FGC form 1 and FGC form 2. They correspond to two polymorphs of FGC in CCDC: GLYCFE01 and UDOPIO01. Of the 215 datasets, 207 (95.4%) were indexed to the unit cell of form 1, while 8 (3.6%) were indexed to the unit cell of form 2. We use PXRD as a reference, since the ratio of different polymorphs is not provided in the drug registration files. However, even the strong peaks of FGC form 2 are submerged in the background (Figure S22). Consequently, content of FGC form 2 estimated from PXRD is very low (0.1%), which may not be reliable. For the highly crystalline content, talc, the strongest PXRD peak is clearly visible, indicating that talc constitutes 2.3% of the crystalline content. In contrast, t-SerialED identified only 2 datasets with the talc unit cell out of 217 indexed datasets (1%). Since both methods can exhibit significant variations when measuring trace amounts of minor phases, it is difficult to determine which result is more accurate. Nonetheless, we conclude that t-SerialED provides results consistent with PXRD for highly crystalline phases and can also detect minor phases with lower crystallinity. Given the shorter acquisition time (3.8 hours versus 28 hours) and the automated nature of t-SerialED, we expect this method to complement PXRD by enabling comprehensive analysis of all sample components, regardless of the crystallinity.\u003c/p\u003e \u003cp\u003eFinally, we determined the structure of FGC form 1 \u003cem\u003eab-initio\u003c/em\u003e and assessed the impact of the number of datasets on data quality. By filtering datasets with fewer than 200 and 100 indexed reflections, we integrated and merged 39 and 93 datasets, respectively. The data processing statistics for both groups are similar, but the final \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e value decreases by 4.33%, from 21.37\u0026ndash;17.04%. This result demonstrates that including more datasets with sufficient indexing can significantly improve data quality.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn the t-SerialED method, there is a tradeoff between the number of frames and accuracy. Acquiring more frames for a single target increases acquisition time but also captures more reflections, allowing the determination of additional sets of lattices from one dataset. Conversely, using fewer frames speeds up the acquisition process, but makes indexing more challenging. Table S 3 summarized the time and dose for different t-SerialED experimental setups. For the setting applied in our experiments, each dataset only needs 20.5s, including all the overhead time. Table S 4 compared t-SerialED with SerialED and SerialRED methods. The table shows that t-SerialED has the advantage of collecting datasets over large tilt angles within a short amount of time.\u003c/p\u003e\n\u003ch3\u003eComparison with SFX\u003c/h3\u003e\n\u003cp\u003eDue to the sparsity of reflections, serial femtosecond crystallography (SFX) for small molecules identifies unit cells by aggregating spot-finding results into high-resolution powder diffractograms and generating candidate unit cells from the synthetic powder pattern\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. However, this method struggles to provide accurate information when the sample contains a mixture of several phases. In contrast, t-SerialED can quantitatively analyze complex mixtures and accurately determine the structure of each phase. Moreover, images are acquired during t-SerialED data collection, providing valuable insights into particle size distribution, surface features, and internal morphology. t-SerialED can correlate real-space and reciprocal-space information, paving the way for future advanced studies. t-SerialED can be adaptable to various types of sample holders, such as the cryo-holders used in this study, and can be easily applied to other in-situ TEM holders, enabling the study of structural dynamics under different environmental conditions.\u003c/p\u003e\n\u003ch3\u003eComparison with SerialED\u003c/h3\u003e\n\u003cp\u003eThe bottleneck of SerialED is indexing. Due to the short de Broglie wavelength of electrons (0.0197 \u0026Aring; at 300 kV, as compared to several \u0026Aring; in the case of X-rays), the Ewald sphere is almost flat. Therefore, hardly any three-dimensional information can be extracted from a single pattern. Therefore, currently all indexing algorithms, such as TakeTwo\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e, FELIX\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, problematic\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, SPIND\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, or PinkIndexer\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, require prior unit-cell information as a restraint. Another challenge arises when an ED pattern contains reflections from multiple crystals, as current indexing algorithms are unlikely to provide a correct solution. The incorporation of 3D reciprocal information in \u003cem\u003et-SerialED\u003c/em\u003e datasets enables the use of indexing algorithms from traditional X-ray crystallography programs, improving the indexing rate to nearly 100% even for multi-crystal patterns. This enhances both the number of processable datasets obtained during a TEM session and the accuracy of phase analysis. By collecting ED patterns at various angles, preferred orientation can be mitigated, allowing for the acquisition of a complete dataset from fewer crystals. Notably, most of our samples have much lower symmetry compared with current SerialED examples. t-SerialED can obtain high completeness datasets from a small number of crystals. Additionally, t-SerialED do not require prior knowledge about unit cell, enabling phase analysis and structure determination for unknown phases.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eComparison with SerialRED\u003c/h2\u003e \u003cp\u003e3DED has become an effective method for structure determination for beam-sensitive materials\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e due to significant advancements in instrumentation and processing workflows\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. SerialRED was developed as an automated workflow based on the continuous rotation geometry\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Depending on the level of automation, the SerialRED method has two types of implementations. One is a fully-automated workflow using an in-house program\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. The other one is a semi-automated workflow for batch data collection based on commercially available software and the workflow requires manual crystal picking\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. In both cases, the data acquisition speed is slower than t-SerialED due to longer overhead times and the method of data collection, which involves rotating each crystal individually. Additionally, if the stage rotation is unstable or the eucentric height is not properly adjusted, the crystal may move out of the beam during data acquisition, negatively impacting the quality of the dataset. Another limitation is the targets should be isolated, single crystals and the size of crystals should be smaller than the size of the beam. Consequently, SerialRED requires strict standards for grid preparation. If there are too many crystals on the grid, then most of the datasets will come from multi-crystals and are hard to be processed by the traditional 3DED workflow. If there are too few crystals on the grid, then the data collection efficiency will be very low because most of the time will be spent on searching the crystals instead of collecting datasets. On the other hand, manual crystal picking tends to select well-isolated single crystals while ignoring aggregated ones, introducing bias during data collection and making the phase analysis results less reliable. In contrast, t-SerialED does not require special grid preparation, allowing for high sample density and proper processing of ED patterns from multi-crystals. t-SerialED datasets can also be collected from the edges of large crystals, ensuring optimal data quality even for large and thick crystals. In SerialRED, however, these large crystals are often disregarded, leading to systematic errors in quantitative analysis.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn summary, by incorporating 3D information in the SerialED, t-SerialED resolves the major challenges faced by serial chemical crystallography. t-SerialED approach established in this study expands electron diffraction as a quantitative analytical method well beyond a structural determination approach. The data collection process requires minimum human intervention after initial setup, making it suitable to run during less busy microscope shifts. With the ability to collect and analyze vast amounts of data, t-SerialED can be used for compositional analysis, providing a fast, reliable and statistically significant quantitative analysis. We expect that t-SerialED will make a significant impact in the exploration of a wide range of materials, including minerals, zeolites, ceramics, MOFs and pharmaceutical compounds.\u003c/p\u003e "},{"header":"Methods","content":"\u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003eGrid Preparation\u003c/h2\u003e \u003cp\u003eThe copper grids with continuous carbon support (300-mesh, ultra-thin carbon layer, EMS Inc.) are pretreated with glow-discharge plasma at 15 mA in negative mode using a PELCO easiGlow (Ted Pella Inc.). The glow discharge time is 60 seconds for all samples. Approximately 1 mg of sample is transferred to a 10 mL glass test tube and mixed with the grid. After shaking the tube, the grids are taken out and loaded onto the TEM holders, where the particles adhere to the carbon film through electrostatic forces.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eData acquisition\u003c/h2\u003e \u003cp\u003eAll datasets are collected on a Thermal Fisher Themis-Z microscope with an ASI Cheetah 3 detector. The microscope\u0026rsquo;s beam deflectors are synchronized with a high-frame-rate camera through program control. t-SerialED experiments are performed using Instamatic. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e is a schematic diagram to show the workflow. The experiment can be divided into two stages, preparation stage and collection stage. During the preparation stage, the microscope runs in LM mode to identify the grid holes and determine the eucentric height. This typically takes around 10 mins. During the collection stage, the size of C2 aperture is set to 50 \u0026micro;m and the microscope keeps running in diffraction mode, avoiding switching the microscope back-and-forth from different modes and saving time. The targets are shown in a Ronchigram by adjusting the diffraction defocus Through adjusting the beam diameter, the Ronchigram should cover the whole detector. When taking ED patterns, the electron beam diameter can be adjusted to match the typical size of the targets by adjusting the current of the C3 lens. An exposure time of 0.5 s was used for each diffraction pattern and 25 frames are recorded for each target. Details for automatic crystal finding, eucentric height prediction and crystal position prediction are discussed in SI.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eData processing\u003c/h2\u003e \u003cp\u003eAs shown in Figure S 23, \u003cem\u003et-SerialED\u003c/em\u003e can be processed by multiple workflows through combination of one of the programs in two groups: (1). For indexing and unit cell determination: \u003cem\u003eDIALS\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e or \u003cem\u003ePETS2.0\u003c/em\u003e\u003csup\u003e30\u003c/sup\u003e (2). Integration and merging: \u003cem\u003eDIALS\u003c/em\u003e or \u003cem\u003eCrystFEL\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. The data processing workflows are implemented in \u003cem\u003eedtools\u003c/em\u003e program\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eData Pre-processing:\u003c/h2\u003e \u003cp\u003eThe raw detector datasets are saved by \u003cem\u003eInstamatic\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e in \u003cem\u003eMRC\u003c/em\u003e format with \u003cem\u003eREDp\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e software input file (.\u003cem\u003eed3d\u003c/em\u003e format). \u003cem\u003eREDp\u003c/em\u003e software can be used for 3D reciprocal space visualization During data acquisition, the center of diffraction pattern will move several pixels as the electron beam follows the crystal. The center beam drift in each \u003cem\u003et-SerialED\u003c/em\u003e dataset will be corrected by cross correlation. After the center beam drift correction, the \u003cem\u003eMRC\u003c/em\u003e files are converted to \u003cem\u003eSMV\u003c/em\u003e files for \u003cem\u003eDIALS\u003c/em\u003e data processing or \u003cem\u003eHDF5\u003c/em\u003e files for \u003cem\u003eCrystFEL\u003c/em\u003e data processing. If more accurate unit cell parameters are required, then the \u003cem\u003eMRC\u003c/em\u003e files need to be converted into tiff files for \u003cem\u003ePETS2.0\u003c/em\u003e data processing.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e\u003cem\u003eIndexing and Integration\u003c/em\u003e:\u003c/h2\u003e \u003cp\u003eBragg reflections in diffraction patterns are identified using either the extended dispersion threshold algorithm in \u003cem\u003eDIALS\u003c/em\u003e or a thresholding algorithm based on \u003cem\u003eI\u003c/em\u003e/\u003cem\u003eσ\u003c/em\u003e in \u003cem\u003ePETS2.0\u003c/em\u003e\u003csup\u003e30\u003c/sup\u003e. Then the search for basis vectors in 3D reciprocal space is conducted using the 3D FFT algorithm in \u003cem\u003eDIALS\u003c/em\u003e or the 3D difference space algorithm in \u003cem\u003ePETS2.0\u003c/em\u003e. Once identified, both programs provide the unit cell and the orientation matrix of the ED pattern at 0\u0026deg;. The orientation matrices for all frames in a tilt series are calculated by multiplying the initial orientation matrix by the rotation matrix, derived from the tilt angle and rotation axis direction. After obtaining the orientation matrix for each frame, the integrated image intensity at each predicted Bragg peak position is determined using either a background-subtracted summation algorithm in \u003cem\u003eCrystFEL\u003c/em\u003e or a profile fitting algorithm combined with summation in \u003cem\u003eDIALS\u003c/em\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e\u003cem\u003eClustering of unit cell parameters\u003c/em\u003e:\u003c/h2\u003e \u003cp\u003eUnit cell parameters are clustered by calculating the Euclidean distance, denoted as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\left(i,j\\right)\\)\u003c/span\u003e\u003c/span\u003e, between unit cells \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e. Datasets are grouped based on this distance metric, with each cluster comprising datasets that have similar unit cell parameters and are considered to represent the same phase.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\left(i,j\\right)=\\sqrt{\\varDelta\\:{a}^{2}\\left(i,\\:j\\right)+\\varDelta\\:{b}^{2}\\left(i,\\:j\\right)+\\varDelta\\:{c}^{2}\\left(i,\\:j\\right)+k*\\left[\\varDelta\\:{\\alpha\\:}^{2}\\left(i,\\:j\\right)+\\varDelta\\:{\\beta\\:}^{2}\\left(i,\\:j\\right)+\\varDelta\\:{\\gamma\\:}^{2}\\left(i,\\:j\\right)\\right]}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEquation 1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn Eq.\u0026nbsp;1, k is a scaling parameter that is defined by the user to adjust the weighting between unit cell length and angle. By default, the value is set to 1. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\gamma\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e correspond to the unit cell parameters from the ith dataset, where a, b, c are the unit cell lengths and α, β, γ are the unit cell angles. In order to resolve the angle ambiguities, angles larger than 90\u0026deg; will be transformed to the corresponding angle less than 90\u0026deg;. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{j}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{j}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{c}_{j}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{j}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{j}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\gamma\\:}_{j}\\)\u003c/span\u003e\u003c/span\u003e are the parameters from the jth dataset. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{a}^{2}\\left(i,\\:j\\right)\\)\u003c/span\u003e\u003c/span\u003e is defined as (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{i}\\)\u003c/span\u003e\u003c/span\u003e - \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{j}\\)\u003c/span\u003e\u003c/span\u003e)\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. The same applies to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{b}^{2}\\left(i,\\:j\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:{c}^{2}\\left(i,\\:j\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe following are methods for calculating the distance between the newly formed cluster \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:u\\)\u003c/span\u003e\u003c/span\u003e and each \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:v\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:v\\)\u003c/span\u003e\u003c/span\u003e is the remaining cluster in the forest that is not \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:u\\)\u003c/span\u003e\u003c/span\u003e. The first one is called \u0026ldquo;average\u0026rdquo;. It uses the following formula to calculate distance:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\left(u,v\\right)=\\sum\\:_{ij}\\frac{d\\left(u\\left[i\\right],\\:v\\left[j\\right]\\right)}{\\left(\\left|u\\right|*\\left|v\\right|\\right)}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEquation 2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor all points \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|u\\right|\\:\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|v\\right|\\)\u003c/span\u003e\u003c/span\u003e are the cardinalities of clusters u and v, respectively.\u003c/p\u003e \u003cp\u003eThe second method uses the Ward variance minimization algorithm. The new entry \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\left(i,j\\right)\\)\u003c/span\u003e\u003c/span\u003e is computed as follows,\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\left(u,v\\right)=\\sqrt{\\frac{\\left|v\\right|+\\left|s\\right|}{T}{d\\left(v,s\\right)}^{2}+\\frac{\\left|v\\right|+\\left|t\\right|}{T}{d\\left(v,t\\right)}^{2}-{\\frac{\\left|v\\right|}{T}d\\left(s,t\\right)}^{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEquation 3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWhere u is the newly joined cluster consisting of clusters s and t, v is an unused cluster in the forest, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T=\\left|v\\right|+\\left|s\\right|+\\left|t\\right|\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e\u003cem\u003eMerging and Structure determination\u003c/em\u003e:\u003c/h2\u003e \u003cp\u003eIf the sample is a pure phase. Then all datasets can be merged directly. For mixtures, the unit cell is first clustered using the method described above. Then the datasets in each cluster are merged into an individual HKL file. We use partialator\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e or xia2.ssx_reduce\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e to merge the datasets, yielding a plain-text Shelx HKL file containing the full reduced data set. Next, \u003cem\u003eShelxT\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e was used for structure solution process. Structure refinement and visualization of the structure models were performed using \u003cem\u003eShelxL\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003eShelXle\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e and \u003cem\u003eVESTA\u003c/em\u003e\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\n\u003ch2\u003eData availability\u003c/h2\u003e\n\u003cp\u003eCrystallography data for all the samples are available in the CCDC database (CCDC number: 2390619, 2390620, 2390621, 2390622, 2390623, 2390624, 2390854, 2390855, 2390856). These datasets can be obtained free of charge via \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ewww.ccdc.cam.ac.uk/data_request/cif\u003c/span\u003e\u003c/span\u003e, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033. The raw t-SerialED datasets of this study are available in Zenodo: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.5281/zenodo.13924322\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\n\u003ch2\u003eCode availability\u003c/h2\u003e\n\u003cp\u003eThe source code of DIALS is available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/dials/dials\u003c/span\u003e\u003c/span\u003e under the terms of BSD 3-Clause \u0026lsquo;New\u0026rsquo; or \u0026lsquo;Revised\u0026rsquo; License. The Instamatic Python package for t-SerialED experiments is available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/instamatic-dev/instamatic\u003c/span\u003e\u003c/span\u003e under the terms of GNU General Public License v.3.0. The edtools Python package for t-SerialED data processing is available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/instamatic-dev/edtools\u003c/span\u003e\u003c/span\u003e under the terms of BSD 3-Clause \u0026lsquo;New\u0026rsquo; or \u0026lsquo;Revised\u0026rsquo; License. All custom software for data acquisition and hardware control is available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cdiv id=\"Sec23\" class=\"Section3\"\u003e\n\u003ch2\u003eAuthorship contribution statement\u003c/h2\u003e\n\u003cp\u003e\u003cstrong\u003eTaimin Yang\u003c/strong\u003e: Conceptualization and planning for the whole project, Investigation, Implementation, Programming, Sample synthesis, Data acquisition, Data analysis, Manuscript writing and revision, Funding acquisition. \u003cstrong\u003eDavid Geoffrey Waterman\u003c/strong\u003e: Data analysis, Programming, Manuscript revision. \u003cstrong\u003eZheting Chu\u003c/strong\u003e: Sample synthesis, Data analysis, Manuscript revision. \u003cstrong\u003eJames Beilsten-Edmands\u003c/strong\u003e: Programming, Manuscript revision. \u003cstrong\u003eZhehao Huang\u003c/strong\u003e: Funding acquisition, Manuscript revision. \u003cstrong\u003eXiaodong Zou\u003c/strong\u003e: Funding acquisition, Manuscript revision.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\u003cp\u003e \u003ch2\u003eConflicts of interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eWe acknowledge financial support from Swedish Research Council Formas (T.Y. 2022\u0026ndash;02778, Z.H. 2020\u0026thinsp;\u0026minus;\u0026thinsp;00831), European Union\u0026rsquo;s Horizon 2020 innovation program under the Marie Skłodowska-Curie grant agreement (T.Y. 101146059), The Royal Swedish Academy (T.Y. CH2022-0015, PH2022-0021), the Swedish Research Council (X.Z. 2019\u0026thinsp;\u0026minus;\u0026thinsp;00815, Z.H. 2022\u0026ndash;02939), the Knut and Alice Wallenberg Foundation (X.Z. 2018.0237). We also acknowledge the Electron Microscopy Center at Stockholm University and the Knut and Alice Wallenberg Foundation for an equipment grant for the electron microscopy facilities at Stockholm University, Sweden.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSzymanski NJ et al (2023) An autonomous laboratory for the accelerated synthesis of novel materials. Nature 624:86\u0026ndash;91\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLunt M (2024) Modular, multi-robot integration of laboratories: an autonomous workflow for solid-state chemistry. Chem Sci 15:2456\u0026ndash;2463\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChapman HN et al (2011) Femtosecond X-ray protein nanocrystallography. 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J Appl Cryst 44:1272\u0026ndash;1276\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5300199/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5300199/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRecent advancements in robotics and artificial intelligence have accelerated the development of autonomous workflows for material discovery. Powder X-ray diffraction (PXRD) remains the primary method for characterizing crystal structures in these workflows. However, its limitations become apparent when peak overlapping becomes severe. To address this, we present serial electron diffraction with tilt (t-SerialED), a method for fast autonomous phase and structural analysis of beam-sensitive, nano-sized polycrystalline materials. t-SerialED incorporates 3D reciprocal space information into SerialED, ensuring reliable quantitative phase analysis for complex mixtures that are difficult to analyze by traditional techniques. Conducted in a standard electron microscope without specialized hardware, t-SerialED enables high-throughput analysis of beam-sensitive, multi-phase mixtures across a wide range of materials, from nanoporous frameworks to pharmaceutical compounds. By resolving key challenges in serial crystallography such as indexing and preferred orientation, this method enables precise structure determination, including the visualization of disordered guest molecules and non-covalent interactions like hydrogen bonding network and proton charge transfer. t-SerialED expands the capabilities of serial chemical crystallography and it can become a complementary method to traditional crystallography methods, offering a robust solution for routine quantitative phase analysis and structure determination.\u003c/p\u003e","manuscriptTitle":"Serial chemical crystallography for autonomous quantitative phase analysis in an electron microscope","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-05 04:42:06","doi":"10.21203/rs.3.rs-5300199/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0fa5aad0-02ba-4da7-a180-8aaad5f460ba","owner":[],"postedDate":"November 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":39344656,"name":"Physical sciences/Nanoscience and technology/Techniques and instrumentation/Microscopy/Transmission electron microscopy"},{"id":39344657,"name":"Physical sciences/Chemistry/Analytical chemistry/X-ray diffraction"}],"tags":[],"updatedAt":"2025-04-23T19:55:46+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-05 04:42:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5300199","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5300199","identity":"rs-5300199","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}