A critical catalogue of SEM‐EDS multispectral maps analysis methods and their application to hydrated cementitious materials

Many methods have been proposed to analyse SEM‐EDS hypermaps of hydrated cementitious materials but none can fit all purposes. In this presentation, we review existing methods for phase identification, stoichiometry quantification, and microstructure quantification in cementitious materials and related materials. We first discuss the unique contribution of SEM‐EDS with respect to the outstanding scientific challenges towards sustainable construction materials. We then compare the SEM‐EDS and image analysis techniques which contribute to answering these challenges. Convergence and divergence in current methods and workflows, and knowledge gaps are highlighted in terms of the specificities of the material (phase assemblage complexity, grain sizes, mixtures, etc.). The discussion is weighted by the required expert knowledge for the sample preparation, microscope operation, and data analysis. We conclude by discussing how microscopy and image analysis integrate into the overall experimental toolkit to investigate and improve cementitious materials.

semiquantitative analysis to provide advanced knowledge on our materials. 6,10A few alternatives exist but they seem limited for routine application due to the required expert knowledge.
To overcome this barrier, the goal of this paper is to review the state-of-the-art knowledge by focusing on the outstanding scientific questions related to the cementitious materials microstructure and the adequacy of SEM-EDS image analysis methods.We aim is to catalogue of techniques that a scientist can choose from depending on their scientific goal.It is assumed that readers have a basic familiarity with SEM-EDS methods applied to cementitious materials.Otherwise, the reader is invited to read the previous pragmatic review of Scrivener et al. 12 and the references therein.In particular, the process of obtaining the best quantitative data (if required by the data analysis methods) should be carefully observed. 13his review approaches the problem with a focus on the investigations of the microstructure of hydrated cementitious materials.By microstructure, we understand both the spatial distributions of grains, but also their composition.As such we only review advancements in the analysis of SEM-EDS data and do not consider the studies only investigating BSE images.It is known that BSE images are limited to differentiate between most hydrate phases. 12Morphology and texture analysis could separate these phases more efficiently in the future, 14 but it will still be restricted to determine, for example, the phase composition of solid solutions, 3 and/or distinguish between similar phases such as phases from the AFm family (monosulfate, hemicarbonate, monocarbonate and straetlingite). 15

SEM-EDS LIMITATIONS FOR CEMENTITIOUS MATERIALS
SEM-EDS is not a magical method either.There are three related underpinning constraints that guide the development of methods for SEM-EDS analysis.The first constraint concerns the highly heterogeneous hydrated cement paste microstructure.This microstructure is formed from the dissolution of anhydrous phases (the cement phases) and precipitation of hydrated phases, among them the calcium-silicate-hydrates (C-S-H), portlandite, AFt, ettringite, etc.Some of these phases are crystalline phases such as the clinker phases or portlandite, while other, are amorphous or poorly crystalline phases, such as the C-S-H.In addition, many phases do not have a fixed composition but are solid solutions.This heterogeneity is increased by the development of new ecoefficient cements, 16 both in terms of composition and particle morphology.The dissolution and precipitation mechanisms lead to a large range of grain and particle sizes from a few hundred nanometres to a few tens of micrometres.
The second constraint is related to these sizes as EDS is intrinsically limited by the volume of interaction of the electron beam.In the typical conditions for SEM-EDS in cementitious materials, the interaction radius is a few microns, in width and depth. 12The large interaction volume is due to the high acceleration voltage (15 kV) needed to quantitatively measure the iron content.This is below the resolution needed to differentiate with certainties the phases in cement paste microstructures, as illustrated in Figure 1.It means that at the typical effective resolution of a SEM-EDS hypermap, a pixel always contains information about the neighbouring pixels, but also about the unseen phases below the plane of interest, due to the pearlike shape of the interaction volume.It means that analysis methods should also focus on mixes of phases, rather than just the phases themselves if an overall quantification of the microstructure is of interest.
To ease this challenge, an obvious choice is to obtain higher-quality maps.This can be achieved with optimised acquisition parameters, higher-quality detectors, 5 and/or an increased number of detectors (e.g., QEMSCAN 17 ), and/or long analysis time. 18However, the third constraint is that access to SEM-EDS is still often limited.In most academic institutions, the electron microscopes are shared in a central facility between many departments/faculties.It means that typically experiment time is constrained, especially for state-of-the-art equipment.In addition, the sample preparation is also challenging. 12It could be simplified with the development of ion beam polishing methods aiming to simplify the preparation steps in the future 19,20 but these methods are not yet well matured in the cement community.Therefore, to be useful to the majority of users, methods should be adapted to the average conditions (medium-to low-quality maps).However, specialised methods for high-quality maps should allow exist to answer the most challenging questions.
These limitations need to be kept in mind when discussing the main scientific challenges that SEM-EDS can answer, as presented in the next section.

Phase identification
For typical cementitious systems, most phases can be easily recognised from the backscatter electron (BSE) image from their brightness (e.g., to separate anhydrous vs. hydrates) or their morphology (e.g., to separate AFm from C-S-H). 12,21The identification can be made much easier for nonexperts by applying fake colouring based on SEM-EDS maps as described in Section 4.1.1 and shown in Figure 1 and Figure 3. Therefore, phase identification by SEM-EDS is largely for further automated analysis (e.g., volume fraction or composition quantification), minor phases detection in clinkers, 20 and/or the detection of phases subresolution such as ettringite 5 or the iron-bearing phases. 2225]8 An important application of phase identification is the analysis of the pozzolanic reaction, the reaction between silica-rich supplementary cementitious materials and the calcium-silicate-hydrate (C-S-H) phase. 26For F I G U R E 1 Details of a microstructure of a calcined clay limestone cement paste (LC 3 , w/c0.4).BSE image (left), and fake colours (right) on BSE image from the composite image (Si: red, Al: green, Ca: blue).Scale is in micrometre.][29] The future challenges regarding phase identification are mostly related to the increasing variety of supplementary cementitious materials.As reactive is often synonymous with amorphous, SEM-EDS is one of the only methods to probe the composition of these SCMs, especially if they are an agglomerate of several phases.This requires an advanced analysis of the composition and, thus will be discussed in the corresponding section.However, it is already important to note that the most successful application of phase identification in cementitious materials requires the input of expert knowledge to (pre-)define cluster centres, 5,18,20 that is, identify which phases are likely to be present in the sample.This assumes that a preliminary experimental investigation is carried out, for example, using X-ray fluorescence and X-ray diffraction analysis.

Morphology and microstructure descriptors
The first microstructure descriptor often used is the porosity.Although it is a crucial parameter for durability modelling, it is important to note that only the porosity higher than the BSE/EDS maps resolution (typically >1 μm in most low-to medium-quality maps) can be quantified reliably.In particular, it means that only the big capillary porosity can be quantified in cementitious materials, and the porosity where transport takes place in typical cement pastes cannot be observed (gel pores for liquid transport (< 10 nm) and interhydrates for gas diffusion(< 100 nm). 12,30herefore, for cementitious materials, the porosity measurement mostly provides an estimation of the overall 'density' of the system, that is, how well the initial pores due to the water content were filled up by hydrates phases during hydration.Although it could be argued that this porosity is still important for mechanical properties, standardised compressive strength, porosity measurement via drying, or proxy values such as the bound water 31 are much easier to obtain.
Another common average descriptor is the degree of hydration, that is, the ratio of volume fraction of unreacted clinker phases to their initial volume fraction.Although it is usually possible to obtain a good estimate from only the BSE image, 21 the EDS analysis can help the differentiation between the clinker phases, and reduce the impact of the varying brightness between SEM images. 12btaining the degree of hydration per phase is crucial for advanced microstructure characterisation such as applying a thermodynamic model, especially in the case of SCMs hindering some clinker phases reaction, 32 or studying the effect of minor elements on the hydration as their effect are different for each clinker phase. 33,34However, it should be noted that X-ray diffraction with quantitative Rietveld is usually more adapted in the case of crystalline phases 35,36 due to its easier access and simpler sample preparation, and better representativity.SEM-EDS is of higher interest for XRD-amorphous phases.The degree of reaction of SCMs is usually a case-by-case analysis.For example EDS and BSE segmentation is a recognised method for GBFS reaction quantification 37 or fly-ash, 9,38 and it can be used for natural pozzolans 2,38 and glasses, 39 while the very fine metakaolin is too challenging due to the presence of fine porosity, sometimes filled with hydrate phases. 5t is possible to measure the volume fraction of certain hydrate phases. 5However, the reproducibility is typically low, or challenging to achieve.In addition, it was shown that some differences can be observed with other technical methods such as TGA or XRD. 5 It is due to the intrinsic resolution limit of the EDS due to the interaction volume but also the presence of porosity/cracks in some grains such as the AFm phases.Due to the difficulty of sample preparation, the main phase of interest for quantification would be the XRD-amorphous phases such as C-S-H, hydrogarnet or hydrotalcite.However, these phases are also difficult to quantify by SEM-EDS due to the intrinsic resolution limitations. 3,5,22,40evertheless, it is important to note that SEM-EDS could be one of the only methods able to identify, and quantify the fraction of low-density (LD) and high-density (HD) C-S-H in complex microstructures 12,41,42 as the use of adsorption techniques is limited when other mesoporous SCMs are available (such as metakaolin).However, these C-S-H 'types' can be identified by EDS image analysis. 5,41he separation and quantification between these two C-S-H morphologies is important for the upscaling of mechanical and transport properties, as obtained with homogenisation models. 43,44nother application of SEM-EDS morphology quantification is the quantification of correlation functions such as the two-point correlation functions. 45,46These functions are necessary to validate virtual microstructure models of cementitious materials. 47As for most of the morphological descriptors, the precision of their quantification is related to the intrinsic resolution of SEM-EDS for grain segmentation, phase segmentation and phase identification.
Finally, important microstructure descriptors are the changes linked to durability issues such as carbonation or chloride ingress.Carbonation is usually easier observed by optical microscopy (due to the white colour of the calcite).However, SEM-EDS can be used to analyse the element segregation around the carbonation front as a proxy to measure the critical sizes of the transition zones. 7he interface steel-concrete and the apparition of the corrosion products can also be analysed. 48Cracks are also an important feature of cementitious materials.Although mechanical cracks can be easily identified by BSE if they have the sufficient size compared to the resolution, EDS still provides some benefits.First, it can analyse the products that formed in the cracks, for instance, self-healing products. 49,50Further, it can help to analyse the origin of cracks created by crystallisation pressure during sulfate attack or alkali-silica reactions. 17,51,52In particular, SEM-EDS can be used to match the precipitation of phases to the apparition of cracks and the overall expansion. 8

Quantification of the stoichiometry of solid phases
A key asset of quantitative SEM-EDS is to be able to obtain the composition of phases, as it is one of the only methods to measure it with a reasonable compromise between accu-racy and experimental complexity.As such, SEM-EDS is a key input for quantitative thermodynamic modelling.
The first data that can be obtained is the composition of the clinker phases, as they are typically solid solutions.For example, C 4 AF is generally better described as C 4 A 1.5 F 0.5 .Although for common European type cements, a good estimation of their composition can be obtained from the literature, 33 a better estimation can be obtained by SEM-EDS analysis, especially for nonstandard systems.This is also necessary when analysing the effect of minor components and/or the process conditions on the distribution of these minor elements. 53It should be noted that this investigation is limited to the detection limit of SEM-EDS, and trace elements (<0.1% wt) are typically not observed.
Many hydrate phases are also solid solutions, most importantly the C-A-S-H. 26Although huge progress has been made on thermodynamic models for C-A-S-H, 54,55 they are not able to reproduce the typical metastable composition found in cement pastes (Ca/Si >1.7).Similarly, the aluminium content is also important to correctly estimate the aluminium hydrates. 56Therefore, it needs to be measured.In addition, for alternative binders with different chemistries, analysing the C-S-H formation and composition is crucial to better understand the hydration of these systems, and their properties. 29,39lthough typically under less scrutiny, the aluminium hydrates are also of interest, in particular the AFm (Ca-LDH of the hydrocalumite family such as monosulfate, hemicarbonate or monocarbonate). 5,15This is important for the sulfate balance, 11 potential solid solutions with iron, 22 or for many new supplementary cementitious materials. 57Although, iron phases cannot be typically observed in typical microstructure, mixture analysis or the analysis of filtrate from selective dissolution can probe their composition. 29he binding of contaminants is also crucial for the investigation of chloride ingress.Chloride can bind both on the C-S-H 23,42 and the AFm, 58,59 and quantifying the binding is crucial to properly validate reactive transport models for chloride.Although other methods exist, none are very precise, and SEM-EDS can be used as a cross-validation.The incorporation of heavy metals in cement phases is also of critical importance for the valorisation of mine tailings. 60ven though progress has been made, the quantification of the elemental composition of phases is not a solved problem, particularly for 'fluffy' solid solution phases that are not present in bulk grains such as the C-S-H.The issue is related to the identification of end-members that are only present as mixtures due to the interaction volume.It means that each pixel contains two unknowns for each phase present: the amount of the phase in the interaction volume, and its stoichiometry.Since most pixels for these phases are a mixture of phases, it is not clear whether the centre of the cluster represents the average composition of the phase, and the definition of the stoichiometry of a phase can be subject to interpretation.For this reason, if high accuracy is needed, transmission electron microscopy 12 is often a preferred method, but the sample preparation (thin section) is more challenging.
2][63] It often involves a two-step process.First, the end-member signatures are extracted from the signal ('the stoichiometry').Then, these signatures are used to deconvolve the signal as a linear combination of the signature signals ('the amount').However, the straightforward application of these methods would require to reimplement the quantification algorithms included in the EDS detector software.
A similar concept was used by Münch et al., 18 but it was applied on the multispectral maps, that is, after element quantification.The phase signatures were found in two steps, where the initial signatures found by a clustering algorithm are refined by the user using the knowledge of expected phases.However, the application of this algorithm on noisier and more heterogeneous phases is not straightforward as the clusters are not well defined, as shown, for example, in Figure 4.

ANALYSIS STRATEGIES
This section describes some of the main methods to analyse SEM-EDS multispectral maps.

Methods for phase identification
Figure 2 presents the common clustering and identification strategies for analysing SEM-EDS hypermaps.These methods are classified by the number of inputs, as well as the complexity of the filters used for the clustering.It should be noted that some methods/software might use two or more strategies in combination.For example, edxia uses method a as a predenoising step, and method c for the actual clustering and phase identification, 5 or Münch et al. use method d iteratively to refine the answer to physically meaningful results. 18

Method a: composite image
Method a typically uses 3 or 4 inputs, and box filters on these same inputs.This method is based on the creation of a composite image by the superposition of coloured SEM-EDS hypermaps.Usually, 3 EDS maps are used coloured in red, green, and blue to form an RGB image with the maximum separation between elements.A common selection for cementitious materials is Ca, Al and Si as these are the main elements for cementitious materials.In addition, the composite image can be overlaid on top of the BSE map, to modulate the brightness, and sharpen the edges, as the BSE image has a higher resolution.This process creates a standard RGB colour image.Examples of these composite images are presented in Figure 3 for an ordinary Portland cement (OPC), and a limestone calcined clay cement (LC 3 ).The methods and materials are described by Georget et al. 5 .
These images can be analysed using algorithms for image analysis such as superpixel algorithms for segmentation.Each segment can then be identified visually using the colour as a proxy of the composition, or using an average over a region.As only three main inputs are present, it is possible to represent it in a ternary diagram as presented in Figure 4. Thresholds and clusters can be defined using this visualisation.
Although this approach seems very simple, it is sufficient in some applications, such as the identification and reaction of fly ashes. 9It can even be simplified to two inputs (Mg and BSE) in the case of slag cements. 37It is also a very good method for visualisation, 41 but also for denoising 5 as it allows one to quickly define regions of interest.The adequacy of the methods is shown in Figure 3, where the composite image provides a good false colouring for the BSE image.The simplicity of the method makes its implementation very easy in both graphical interfaces (e.g., ImageJ) or scripts.This method is limited if another element (e.g., Fe, Mg, S) becomes an important contributor to the microstructure, and it is necessary to use methods allowing a higher number of independent inputs.

Method b: decision tree
This method can use all inputs (BSE+EDS) and separate phases using binary threshold filters.
The decision tree was one of the first applied methods to analyse EDS hypermaps of cementitious materials 1 due to its simplicity of concept and implementation.This method is based on the creation of a decision tree where each node has an associated variable and threshold.The nodes are evaluated sequentially.Depending on the value of the variable with respect to the threshold, the corresponding child node is chosen.When the leaf node ( = terminal node) is reached, the pixel/region is associated with the corresponding phase.The theoretical foundation of this method is the Gibbs Phase Rule, which states that at equilibrium, and constant temperature and pressure, the number of phases that can form is equal to the number of elements.As such, in theory, only one filter is required to separate the hydrated phases.This is made more difficult by the presence of unreacted anhydrous and metastable phases, as such the BSE information is required in this analysis.
This method does not include a built-in segmentation strategy.Therefore, each pixel can be analysed one by one, 34 or regions can be defined with an adequate segmentation strategy. 20The simplicity of the method means that it can be easily implemented in graphical interfaces where the effect of the threshold values can be visualised graphically.
Although this method is usually used with the elements as the node variables, it would be possible to use more complex variables such as the ratio of elements as described in the next section.

Method c: Ratio plots and box filters
This method can use all inputs (BSE+EDS) and applies combined linear and nonlinear filters to define clusters and identify them.This method is inspired by the method used to interpret SEM-EDS points analysis: the ratio plot. 12,64In ratio plots, the axes are the ratio of elements (such as Si/Ca, or Al/Ca).This is at the core a denoising method that removes the influence of minor and light elements 64 which cannot be quantified accurately with a low-count EDS spectrum.For adequately selected views (such as Al/Ca vs. Si/Ca, S/Ca vs. Al/Ca), the EDS points cluster around mixing lines as shown in Figure 4. Filters can be defined in order to separate clusters.A single filter is often not enough for a successful clustering.For example, aluminium anhydrous and hydrate phases overlap in the Al/Ca versus Si/Ca view.However, an additional filter can be defined on the SoX (Sum of oxides) versus BSE view to identify the clinker phases, or even distinguish calcium carbonate from portlandite. 5For any combination of 3 elements, a ratio plot is roughly equivalent to a ternary diagram, as displayed in Figure 4, with the advantage of being easier to read, but with some value becoming ill-defined (such as the points associated with quartz).
This approach is very flexible to adjust the visualisation to the scientific problems at hand 5 similar to the decision tree approach.However, the filters that can be defined are more advanced and customisable.The compromise is that not every pixel or region is necessarily covered by a given set of filters, and some regions are not associated with a phase, or some phases could be doubly associated.Depending on the scientific goal, this might or might not be a desired feature.For example, this is not optimal to compute morphological descriptors, but this is important to compute phase compositions, to not consider outliers, and points that are mixtures of several phases. 5,42[67]

Method d: supervised clustering
This set of methods can use all inputs (BSE+EDS) and use complex, black-box algorithms to define and identify clusters.
Unlike previous methods which relied on filters that could be defined using analytical equations, this set of methods relies on more complex algorithms.The advantage is that they do not have to prioritise variables, or a set of variables over others, instead, they can analyse the whole set of input variables at once.An apparent advantage is the reduction of the user bias, and the possibility to more easily detect minor phases.
Many types of algorithms can be used, for example, K-means, 18 Gaussian Mixture Model 41,42 or Support Vector Machine. 2,38Unless very high-quality data maps are used, 18 the results need to be regularised taking into account the spatial information 2 as described in Section 4.2.For supervised algorithms, methods a, b, or c can be used to create the necessary labels. 14The composition of expected phases can also be used predefined the cluster centres, but the presence of solid solutions often means that an iterative process needs to be used. 18Constraining the clustering is important for typical hydrated microstructures, since as shown in Figure 4, the clusters are not well-defined visually.
Although clustering methods can be challenging to implement efficiently, they are available for most common programming languages such as Java for inclusion in ImageJ, 18,68 or the scikit-learn 69 and scikit-image 70 libraries for Python.Examples and illustrations of supervised clustering methods are available in the documentation of the scikit-learn library.

Pre-and posttreatment
The core strategies presented above define the abilities of a particular analysis method, but their applications to real cases are also defined by the constraints identified in Section 2. In particular, denoising methods are very important for low-quality maps, and the resolution limitation can be partially bypassed using the information from the BSE image.

Filter-based denoising
To reduce the experimental time and the damage to the sample, the total count per pixel for typical SEM-EDS hypermaps is low.It usually results in a high salt and pepper noise.As such denoising algorithms are crucial tools for any image analysis workflow.Although it is possible to obtain high-quality images, it often requires analysis time that is too restrictive for routine usage; even though, this could be a valid method for special investigations, especially given today's high-efficiency detectors. 5,18he usual reservations about common filters such as the median or Gaussian filter apply to the denoising of SEM-EDS maps, especially those with low signal-to-noise ratio.The use of these filters leads to a blurring effect, a loss of maximum magnitude, and the creation of a nonzero background (e.g., see Ref. 5

for visualisation).
For that reason, edge-preserving filters are often preferred, such as the total variation algorithm 71 or the bilateral filter. 72,73For edge-preserving filters that requires a reference image, the BSE image which is more resolved is often a good choice to detect the grain edges.
It should be noted that filtering the multispectral images can lead to artefact if each element is averaged separately.It would be better to average the spectra, and quantify the averaged spectra as demonstrated by Georget et al. 5 However, the lack of open quantification algorithms makes this process too tedious in practice to be useful in routine applications.
Morphological opening and closing can also be used to reduce the salt and pepper noise, and erase the features close to resolution. 9

Segmentation
Segmentation is the process by which an image is split into separate regions where pixels are grouped by their similarity for one or several features (colour, grey value, textures etc.).This process is important for grains, or phase identification.For visualisation of common segmentation algorithms, the reader is invited to consult the documentation of the scikit-image library. 70The superpixel family of algorithms is among the most used, 74,75 due to its simplicity.The watershed algorithm was found to better respect phase boundaries 20 but it requires the predefinition of markers.
The segmentation can be applied to all maps, or a combination of maps, although it is of particular interest to perform the segmentation on the BSE image as it allows including the higher resolution of the BSE image into the analysis of the EDS information.In particular, particle edge detection is more relevant to the BSE image.However, as often, combining information provides a better result. 20he segmentation can be used to extract representative points, to reduce the interference of the interaction volume, as the pixel size is often smaller than this interaction volume.It means that adjacent pixels are not independent, and do not provide as much information.It means that after an adequate segmentation (see next section), a unique composition (from a point, or an average of points) can be defined for each region of the segmentation.In addition, this step can also accelerate further data treatment.If an image with a resolution of 1024 × 768 pixels is reduced to 10,000 regions, it represents a division by 80 of the number of variables.This is crucial for interactive interfaces when using algorithms with a polynomial or exponential complexity.This subset of points can be used to interactively define/refine the clustering algorithm to be applied to the entire dataset (the full set of multispectral maps).Due to the interaction volume and the inherent map noise, this reduction of complexity is not necessarily associated with a loss of information. 5

4.2.3
Reducing the segmentation complexity Segmentation groups pixels of similar composition, but the algorithm can be arbitrary and difficult to control with pre-cision, especially with noisy data.A strategy to improve the granularity is to first use an over-detailed segmentation, and in a second step to use an algorithm to group the regions.The type of algorithms that have been used is based on graph theory, where each segment is represented by a node linked together with weighted links by an appropriate metric.The graph is then visited and pruned to group the nodes according to the metric.
The Markov random tree, 2 a binary tree 38 or the k-d-Tree algorithms 42 have been used to carry out this task in cementitious structures.In addition, these algorithms can be used to remove the regions corresponding to a mixture of phases, to remove the noise induced by the interaction volume. 42

Correlation with other measurements
Even though it is important to see the object we study, SEM-EDS analysis is not the end tool.It can be correlated to other measurements to better understand the properties of each phase.An important contribution is the coupling of SEM-EDS to Nanoindentation. 76,41It allows us to better interpret the individual contribution of each phase to the overall mechanical properties.Other imaging techniques such as optical microscopy, fluorescence, 77 EBSD 78 or Raman 79 can be combined to obtain complementary information.

CONCLUSION AND OUTLOOK
We presented how the unique features of scanning electron microscopy with energy dispersive spectroscopy can be leveraged to investigate the complex microstructure of hydrated cementitious materials.Image analysis methods allow the identification of phases seen on backscatter electron images.From this phase identification, further analysis allows quantifying morphology descriptors (grain size, spatial correlation) or the stoichiometric composition of these phases.
The visualisation and quantification of the microstructure are crucial to the development of mechanistic and predictive models.We reviewed some of the main novel applications of SEM-EDS for cementitious materials for both hydration and durability studies.
There are many methods to carry out the quantitative analysis but no method fits all purposes, and it is important to identify the type of scientific questions to answer, the quality of the raw data available, but also the desired interactivity of the methods and the required expert knowledge.For example, a method that needs to be applied routinely needs to work for average-quality maps in an interactive graphical interface.However, advanced scien-tific challenges can utilise the highest quality map with complex supervised workflows.
Continuous work in the field can improve the methodology and come to the best compromise.The constant advancement in image analysis and data science is promising to gain even more out of the EDS hypermaps and solve the remaining knowledge gaps.
The first obstacle concerns the adoption of these techniques by the general scientific community.As demonstrated by the Rietveld quantification for XRD, the adoption of advanced analytical methods is often slow in the cement community, due both to the complexity of the material and its practical use in our day-to-day life.This can be overcome with more user-friendly tools and training.However, unlike XRD, SEM-EDS analysis is limited by the general availability of the equipment.Therefore, analysis methods should also focus on nonoptimal conditions, by developing robust algorithms able to adapt to lower-quality maps, and to reduce the chance of mis-or over-interpretation.
Due to the well-defined chemistry of cementitious materials, phase identification is mostly a solved problem for traditional systems, but morphology descriptors and stoichiometries quantification are still an open problem.The issue with morphology descriptors is due to the intrinsic physical limitations of SEM-EDS compared to the multiscale heterogeneities of cementitious materials.This challenge can only be solved by using complementary analytical methods.This requires the development of combined workflows and frameworks.The quantification of the elemental composition of solid phases is hindered by the same limitations, in particular the interaction volume.Unmixing data from hyperspectral images has been studied over the last decades, but their successful application to SEM-EDS is still an open challenge.
Even though these limitations exist, even semiquantitative analyses, that is, analyses that provide the general trends, are better than nothing.As demonstrated through the literature cited in this review, SEM-EDS has a lot of potential to provide key pieces of information to unravel the complexity of cementitious materials.

A C K N O W L E D G E M E N T S
Open access funding enabled and organized by Projekt DEAL.

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I G U R E 2 4 common analysis strategies: (A) composite image, (B) decision tree (low values correspond to the down choice), (C) ratio plot and visual filters and (D) supervised clustering.F I G U R E 3 Composite images for (A) OPC and (B) LC 3 cement paste.Scale is in micrometre.

F I G U R E 4
Ternary diagrams (A, C) and ratio plots (B, D) for OPC (A, B) and LC 3 (C, D) microstructures.Colours are the corresponding colours from the composite image shown in Figure3.In subfigure c, red points corresponding to quartz (Si→1.0)are not visible in the chosen scale of the ratio plots, as these points become undefined (Ca→0.0).