C Naber

Julio Rößler

F Da Silva

Bellmann

J Neubauer
email: juergen.neubauer@fau.de

T Sowoidnich

L Valentini

C Schulbert

C Rößler

J Dasilva

F Bellmann

Evolution of the particle size distribution of tricalcium silicate during hydration by synchrotron X-ray nano-tomography

Keywords: Tricalcium silicate (D), hydration (A), synchrotron nano-tomography (B), near-field ptychography

whether they are published or not. The documents may come

Evolution of the particle size distribution of tricalcium silicate during hydration by synchrotron X-ray nano-tomography

Introduction

The hydration of tricalcium silicate (Ca3SiO5, C3S in cement notation) has been investigated in a large number of studies to understand the complex reactions that occur during the hydration of ordinary Portland cement [START_REF] Taylor | Cement Chemistry[END_REF]. The products of reaction between C3S and water (hydration) are C-S-H and portlandite (Ca(OH)2, CH) [START_REF] Taylor | Cement Chemistry[END_REF].

The mechanism of C3S hydration is consistently described as a dissolution-precipitation process with precipitation of C-S-H on the surface of C3S [START_REF] Ouzia | The needle model: A new model for the main hydration peak of alite[END_REF][START_REF] Rößler | Characterization of C-S-H and C-A-S-H phases by electron microscopy imaging, diffraction, and energy dispersive X-ray spectroscopy[END_REF]. Portlandite, in contrast, is formed in the pore space between C3S particles [START_REF] Möser | A New Model Of Ordinary Portland Cement Hydration Derived By Means Of ESEM-FEG[END_REF]. Hydration proceeds in stages with different reaction rates called (pre)induction, main hydration period (consisting of acceleration and deceleration) as well as the steady-state period [START_REF] Gartner | Hydration of Portland Cement. Structure and Performance of Cements[END_REF]. Beyond this definition, there is no general consensus on the mechanisms governing the kinetics. The present work attempts to provide experimental data for these discussions, particularly on the causes of the deceleration period.

A general discussion of C3S hydration kinetics is not within the scope of this paper but can be found in [START_REF] Ouzia | The needle model: A new model for the main hydration peak of alite[END_REF]. To explain the onset of the deceleration period, a limited diffusion of ions from the C3S surface into the aqueous phase due to covering of the interface by growth of C-S-H [START_REF] Gartner | Hydration of Portland Cement. Structure and Performance of Cements[END_REF][START_REF] Garrault | Study of C-S-H growth on C3S surface during its early hydration[END_REF] has been proposed. In addition, a reduction of the C3S dissolution rate by consumption of small C3S grains [START_REF] Taylor | Cement Chemistry[END_REF][START_REF] Kjellsen | Revisiting the microstructure of hydrated tricalcium silicate--a comparison to Portland cement[END_REF][START_REF] Masoero | A Reaction Zone Hypothesis for the Effects of Particle Size and Water-to-Cement Ratio on the Early Hydration Kinetics of C3S[END_REF][START_REF] Bergold | Mechanically activated alite: New insights into alite hydration[END_REF] that reduces the overall C3S reaction rate is discussed as a ratedetermining factor during the deceleration period. The main difficulty is the direct experimental observation of C3S particles during hydration that are overgrown by C-S-H in the presence of portlandite.

Gas adsorption measurements are state-of-the-art for the experimental determination of the specific surface area of anhydrous cementitious materials. Alternatively, the surface area of C3S can be calculated from the particle size distribution, usually under the assumption that the particles are spheres without consideration of the particle roughness. Laser scattering is commonly applied to determine the particle size distribution of anhydrous cement/C3S. Because gas adsorption and laser scattering are not phase selective, neither method can be used to measure the C3S specific surface area of hydrated samples because these contain anhydrous and hydrous phases (C3S, C-S-H and portlandite).

Imaging techniques such as electron and X-ray microscopy have high potential in the experimental determination of the particle size distribution and thus the specific surface area of C3S during hydration. This is due to the ability of these methods to identify individual particles in the microstructure. High resolution of scanning electron microscopy (SEM) can be used to record 3D images of cementitious materials using focussed ion beam serial sectioning [START_REF] Song | Pore network of cement hydrates in a High Performance Concrete by 3D FIB/SEM -Implications for macroscopic fluid transport[END_REF]. The limiting factor is the small size of the analysed volume in the SEM, that is often too small to deduce statistical relevant data for a variety of particle sizes [START_REF] Zingg | The microstructure of dispersed and non-dispersed fresh cement pastes --New insight by cryo-microscopy[END_REF][START_REF] Holzer | Cryo-FIBnanotomography for quantitative analysis of particle structures in cement suspensions[END_REF][START_REF] Kleiner | Reconstruction of calcium silicate hydrates using multiple 2D and 3D imaging techniques: Light Microscopy, µ-CT, SEM, FIB-nT combined with EDX[END_REF]. For X-ray microscopy, one can obtain the absorption and phase-contrast images of the sample for larger volumes. The X-rays attenuated by the sample yield the absorption-contrast, whereas the phase shifts between the incident and the transmitted wavefields, due to the X-rays refraction by the sample, generate phase contrast images [START_REF] Da Silva | X-ray Computed Microtomography technique applied for cementitious materials: A review[END_REF][START_REF] Aranda | Recent studies of cements and concretes by synchrotron radiation crystallographic and congnate methods[END_REF]. The absorption-contrast imaging of the individual phases, present in low-absorbing materials, consisting of atoms with low atomic number is challenging. In this case, phase-contrast imaging can be used to achieve a high compositional contrast within samples consisting of materials with similar linear attenuation coefficients [START_REF] Stampanoni | Coherent X-ray Imaging: Bridging the Gap between Atomic and Micro-scale Investigations[END_REF]. However, this property is only accessible by applying imaging techniques using spatially coherent probe beams, such as 3 rd -generation-synchrotron radiation and electron beam or laser, which allows the generation of interference, and by the use of appropriate phase retrieval algorithms.

For high resolution X-ray imaging (2D and 3D), the high brilliance of synchrotron radiation was shown to be advantageous to study multi-hierarchical materials like cement pastes [START_REF] Parisatto | Examining microstructural evolution of Portland cements by in-situ synchrotron micro-tomography[END_REF] in scattering experiments [START_REF] Cuberos | Phase development in conventional and active belite cement pastes by Rietveld analysis and chemical constraints[END_REF][START_REF] Álvarez-Pinazo | In-situ early-age hydration study of sulfobelite cements by synchrotron powder diffraction[END_REF][START_REF] Artioli | Powder Diffraction and Synchrotron Radiation[END_REF][START_REF] De La Torre | The superstructure of C3S from synchrotron and neutron powder diffraction and its role in quantitative phase analyses[END_REF][START_REF] Garbev | Cell Dimensions and Composition of Nanocrystalline Calcium Silicate Hydrate Solid Solutions. Part 1: Synchrotron-Based X-Ray Diffraction[END_REF][START_REF] Merlini | The early hydration and the set of Portland cements: In situ X-ray powder diffraction studies[END_REF][START_REF] Schlegel | First Seconds in a Building's Life-In Situ Synchrotron X-Ray Diffraction Study of Cement Hydration on the Millisecond Timescale[END_REF][START_REF] Gutberlet | New insights into water bonding during early tricalcium silicate hydration with quasielastic neutron scattering[END_REF] and spectroscopic investigations, both reviewed elsewhere [START_REF] Aranda | Recent studies of cements and concretes by synchrotron radiation crystallographic and congnate methods[END_REF][START_REF] Chae | Advanced Nanoscale Characterization of Cement Based Materials Using X-Ray Synchrotron Radiation: A Review[END_REF][START_REF] Monteiro | Characterizing the nano and micro structure of concrete to improve its durability[END_REF][START_REF] Provis | Nanostructural characterization of geopolymers by advanced beamline techniques[END_REF][START_REF] Brisard | Multiscale X-ray tomography of cementitious materials: A review[END_REF]. In Holographic X-ray Computed Tomography (HXCT), the detector is placed at 4 different distances from the sample permitting the detection of both the incident and refracted radiation (near-field inline holography). With this setup, the attenuation and the phase shift can be detected. By varying the sample-detector distance, the phase of the wave field can be determined (phase retrieval) solving a mathematically ill-posed problem. The 3D information (tomography) is obtained by rotating the sample and recording images at a series of projection angles for different sample-detector distances [START_REF] Stampanoni | Coherent X-ray Imaging: Bridging the Gap between Atomic and Micro-scale Investigations[END_REF]. Synchrotron based HXCT was used in several studies dealing with cement. These studies, for example, focussed on the impact of organic admixtures (dispersants or (super)plasticizers) on the formation of C-S-H during the hydration of ordinary Portland cement. The pore size distribution in the hardened samples was also analysed [START_REF] Parisatto | Examining microstructural evolution of Portland cements by in-situ synchrotron micro-tomography[END_REF][START_REF] Artioli | Direct Imaging of Nucleation Mechanisms by Synchrotron Diffraction Micro-Tomography: Superplasticizer-Induced Change of C-S-H Nucleation in Cement[END_REF].

In Near-Field Ptychographic X-ray Computed Tomography (NF-PXCT), X-ray absorption and X-ray phase-contrast imaging of the samples are obtained also in the holographic regime. The near-field ptychographic approach is based on the acquisition of holograms of the sample at different lateral positions within a structured incoming coherent beam to solve the ill-posed problem in phase-retrieval [START_REF] Stark | Zement und Kalk: Der Baustoff Als Werkstoff[END_REF]. With the use of appropriate phase retrieval algorithms, NF-PXCT permits an inherent quantitative 3D imaging of the sample regarding the electron density distribution and by that the mass density at voxel resolution below 20 nm [START_REF] Aranda | Recent studies of cements and concretes by synchrotron radiation crystallographic and congnate methods[END_REF][START_REF] Stockmar | Near-field ptychography: phase retrieval for inline holography using a structured illumination[END_REF][START_REF] Monteiro | Advances in characterizing and understanding the microstructure of cementitious materials[END_REF]. Far-field Ptychographic X-ray Computed Tomography (FF-PXCT) was, for example, used to determine the mass density of different phases in Portland cement pastes [START_REF] Trtik | Density mapping of hardened cement paste using ptychographic X-ray computed tomography[END_REF][START_REF] Da Silva | Mass Density and Water Content of Saturated Never-Dried Calcium Silicate Hydrates[END_REF][START_REF] Cuesta | Quantitative disentanglement of nanocrystalline phases in cement pastes by synchrotron ptychographic X-ray tomography[END_REF]. Another study showed the distribution of C3S, C-S-H, and portlandite in hardened C3S pastes, proving the strength of the method in phase contrast [START_REF] Da Silva | X-ray Computed Microtomography technique applied for cementitious materials: A review[END_REF][START_REF] Da Silva | Mass Density and Water Content of Saturated Never-Dried Calcium Silicate Hydrates[END_REF]. The microstructure including AFm, AFt, and aluminium hydroxide was analysed by PXCT in ye'elimite containing materials after hydration [START_REF] Cuesta | Chemistry and Mass Density of Aluminum Hydroxide Gel in Eco-Cements by Ptychographic X-ray Computed Tomography[END_REF]. PXCT experiments were also performed with the aim of determining the mass density and to study the reaction of ye'elimite in-situ [START_REF] Cuesta | In situ hydration imaging study of a ye'elimite paste by ptychographic x-ray computed tomography[END_REF]. Finally, the radius of ettringite needles formed during the hydration of C3A in the presence of gypsum was investigated by PXCT [START_REF] Geng | Synchrotron X-ray nanotomographic and spectromicroscopic study of the tricalcium aluminate hydration in the presence of gypsum[END_REF].

Although the experimental determination of the evolution of the particle size distribution of C3S remains a challenging task, hypotheses were proposed to address this important issue. In the first hypothesis, it is assumed that the degree of hydration of the bulk material is equal to that of the median particle size. Based on this assumption, the median particle radius was used to calculate the reacted rim of C3S (e), the C-S-H layer thickness (E) and the full particle size (RP, consisting of a C3S core overgrown by C-S-H) [START_REF] Garrault | Formation of the C-S-H Layer during Early Hydration of Tricalcium Silicate Grains with Different Sizes[END_REF] (abbreviations in Figure 1). The second hypothesis deals with the formation of C-S-H fibres at the surface of C3S during the acceleration and deceleration period without assuming a diffusion barrier or impingement ('needle model' [START_REF] Ouzia | The needle model: A new model for the main hydration peak of alite[END_REF]). Such models may account for a constant C-S-H layer thickness for all particles at a given degree of hydration. The third hypothesis (Figure 1) states that the hydration proceeds faster for small C3S particles as a result of an identical reacted rim thickness for all particle sizes. This reacted rim thickness increases with hydration progress ('reaction zone hypothesis') [START_REF] Masoero | A Reaction Zone Hypothesis for the Effects of Particle Size and Water-to-Cement Ratio on the Early Hydration Kinetics of C3S[END_REF]. The assumption of a constant reacted rim thickness was originally developed for the formation of a C-S-H layer around C3S particles and is used here to describe the thickness of the dissolved layer from the C3S particles. As a result, smaller particles are fully dissolved earlier than larger particles, and the degree of hydration of the bulk sample is unequally distributed over the different particle size classes. It should be clarified that the first hypothesis mentioned above deals only with the median particle size and not with the full particle size distribution. Furthermore, the calculation of the C3S particle size distribution during the main hydration period is in principle possible with the 'needle model'. However, the input parameters need to be changed dramatically and are outside the range of reasonable values when this model is used for the present data. For these reasons, only the 'reaction zone hypothesis' is addressed in this work. The first aim of the present work is to fill the mentioned experimental gaps regarding the measurement of the specific surface area of C3S during the main hydration period. Therefore, the C3S particle size distribution is measured by state-of-the-art 3D X-ray nanoimaging technology, uniquely available in 3 rd generation synchrotron facilities such as ESRF including the novel near-field ptychographic X-ray computed tomography (NF-PXCT) and holographic X-ray computed tomography (HXCT). The present work is thus the first application of NF-PXCT for characterization of cementitious samples. The used techniques provide an unprecedented high sensitivity to sample morphology and unprecedented high resolution to study dynamics in cement. Thereby, the particle size distribution data are obtained from the analysis of local distribution of the particle morphology by measuring each particle individually.

The second aim of the present work is to evaluate the 'reaction zone hypothesis' by simulation of the development of the C3S particle size distribution during hydration based on the gathered data. The degree of hydration of C3S is needed as an input parameter for this purpose, which is independently analysed by X-ray diffraction (XRD), 29 Si nuclear magnetic resonance spectroscopy (NMR) and thermal analysis (TA). Additionally, the C-S-H layer thickness at the C3S surface is evaluated by SEM imaging. The latter approach is complicated by the fact that SEM is a 2D-method which is discussed in section 3.2. The reliability of the 'reaction zone hypothesis' is explored by comparison of the measured and predicted control parameters: C3S particle size distribution and specific surface area of C3S. The aqueous phase composition is measured by means of inductively coupled plasma-optical emission spectroscopy (ICP-OES) during the main hydration period. Combination of the various results allows us to discuss the development of the C3S particle size distribution during hydration with additional information on the liquid phase composition.

Materials and methods

Raw material preparation and properties

Synthesis of tricalcium silicate

Tricalcium silicate was produced by high temperature solid state reaction from a blend of calcium carbonate (Merck p.a.) and highly dispersed silicon dioxide (Merck p.a.). The raw materials were homogenized and fired at 1520 °C for 8 hours in a platinum crucible and subsequently quenched at 20 °C. This procedure was repeated twice and the material was ground between the high temperature treatments to improve its homogeneity. For high resolution synchrotron X-ray tomography, the volume of the sample has to be very small. To guarantee that a sufficient number of particles are in that volume, the particle size of the C3S has to be below 10 µm. For this purpose, the material was ground in batches of 25 g for 20 min in a zirconia disk mill at 700 rpm under the addition of 0.08 g diethylene glycol as a grinding aid. The particle size was further reduced in an air classifier to remove particles larger than 10 µm. The individual batches of C3S were finally homogenized. The particle size distribution measured by Laser scattering is provided in the supplementary information (Figure S1). These results cannot be directly compared to the particle size distribution obtained by X-ray tomography as both methods are based on different physical methods and use different definitions to extract the particle size from the experimental data.

The C3S produced in this study has the following chemical composition (determined by chemical wet analysis based on titration of calcium , gravimetric determination of silicon as well as ICP-OES analysis for all other elements except silicon): 72.8 wt.-% CaO, 26.1 wt.-% SiO2 and 1.0 wt.-% LOI, whereas the concentration of foreign oxides was below the limit of detection (0.1 wt.-%). The free lime concentration determined by Franke-method [START_REF] Franke | Bestimmung von Calciumoxyd und Calciumhydroxyd neben wasserfreiem und wasserhaltigem Calciumsilikat[END_REF] was 0.3 wt.-%. Analysis by QXRD indicated the presence of pure C3S in the triclinic modification and the concentration of belite and free lime were below the limit of quantification (LOQ: 5 wt.-% for belite and 0.5 wt.-% for CaO).

Hydration of C3S

All experiments were designed to match the requirements of synchrotron X-ray nanotomography. As stated before, particle sizes below 10 µm are specifically prepared in order to increase the spatial resolution of the tomography. Therefore, a relatively high water/C3S-ratio (by mass) of 3.0 was required to produce a workable suspension as the surface area of the starting material is very high. This water/solid-ratio is higher than normally used for hydration studies on pastes but it was recently confirmed that hydration kinetics of C3S are not affected by the water/solid-ratio [START_REF] Naber | Influence of w/s ratio on alite dissolution and C-S-H precipitation rates during hydration[END_REF]. Accordingly, 15 g of C3S was mixed with 45 g filtered saturated calcium hydroxide solution and 0.10 g superplasticizer. Superplasticizer (SP1 from reference [START_REF] Sowoidnich | Calcium complexation and cluster formation as principal modes of action of polymers used as superplasticizer in cement systems[END_REF]) was added to the starting solution prior to mixing to avoid the formation of agglomerates due to the surface charge of the C3S particles [START_REF] Jiang | Studies on mechanism and physico-chemical parameters at the origin of the cement setting II. Physico-chemical parameters determining the coagulation process[END_REF][START_REF] Jönsson | Controlling the Cohesion of Cement Paste[END_REF]. This superplasticizer is a methacrylic acid-co-polyethylene glycol type polycarboxylate with the following parameters: 8.2 repeating units, 3.9 monomers per repeating unit, 23 monomers in the side chain with a total molecular weight of 10,930 g/mol.

The closed vessel filled with the suspension was stirred for 24 hours at a temperature of 25 °C. Samples (approx. 6 ml suspension) taken after 4, 8, 12, and 16 hours of hydration were filtered in a gaseous nitrogen pressure filtration unit using filters with a pore width of 15 nm. This relatively small pore width of the filter was used to avoid C-S-H particles from passing through the filter, especially when superplasticizers are present [START_REF] Sowoidnich | Calcium complexation and cluster formation as principal modes of action of polymers used as superplasticizer in cement systems[END_REF]. As a consequence, the filtration process took 30-45 min at a pressure of approx. 2 bar. The solid residue of the filtration was dried at 60 °C for X-ray nano-tomography, QXRD, 29 Si-NMR, SEM, and thermal analysis. It was not possible to extract pore solution after 20 and 24 hours by this method. Additional samples (< 100 mg) were taken after 6, 10, 14, 18, and 22 hours only for thermal analysis by drying at 60 °C without prior filtration.

Preparation of the hydrated C3S samples for Scanning Electron Microscopy (SEM)

Sample preparation for SEM characterisation included embedding of the hydrated samples in epoxy resin and mechanical polishing using diamond slurries of 15, 9, 3, and 1 µm particle size. The polished samples were coated with gold to ensure electric conductivity of the sample surface.

Preparation of the hydrated C3S samples for synchrotron X-Ray nano-tomography

The samples for synchrotron X-ray nano-tomography were produced by embedding the samples in a commercial two-component epoxy resin. Thin filaments composed of epoxy resin and sample material were pulled while the epoxy-C3S mix was already stiff but still workable. After hardening of these filaments containing the samples embedded in epoxy resin, these were cut into small segments with a length of 1-2 mm. Segments with a diameter of approximately 100 µm were selected under an optical microscope and glued to the sample post of the device by epoxy resin. Thus, the final length of the filaments was approximately 1 mm and the diameter was approximately 100 µm. Only the anhydrous C3S was mixed with a highly adsorbing polymer before embedding in resin as described before. This was done to produce an organic film on the surface that enables the observation of individual C3S particles instead of agglomerates. For this purpose, 1.00 g C3S was mixed with 2.00 g polymer dispersion (styrene-acrylate co-polymer model latex in [START_REF] Kong | Retardation effect of styrene-acrylate copolymer latexes on cement hydration[END_REF]) and treated by ultrasound (frequency: 20 kHz, amplitude 43 mm) for 20 seconds and quickly dried after 1 minute at 50 °C to avoid a reaction with water. A schematic illustration of the sample preparation steps and the nano-tomography as well as simulation is provided in the supplementary information (Figure S2).

Analytical methods

Degree of hydration of C3S and aqueous phase composition during hydration X-ray diffraction

XRD patterns of the hydrated samples were obtained in a D8 Advance diffractometer (BRUKER-AXS) equipped with a LynxEye detector using a Cu-tube operating at 40 mA and 40 kV. The scans from 7 to 70 °2θ were recorded with a step size of 0.011 °2θ and a counting time of 0.5 seconds per step. The concentration of individual phases was calculated using the Rietveld-software Topas 5.0 (BRUKER-AXS), using a recently developed external standard method [START_REF] O'connor | Application of the Rietveld Refinement Procedure in Assaying Powdered Mixtures[END_REF][START_REF] Jansen | A remastered external standard method applied to the quantification of early OPC hydration[END_REF]. The respective crystal structures were applied to describe the tricalcium silicate [START_REF] Golovastikov | Crystal Structure of Tricalcium Silicate, 3CaOSiO2 = C3S[END_REF] and portlandite [START_REF] Busing | Neutron Diffraction Study of Calcium Hydroxide[END_REF] contribution to the diffraction pattern, while a PONKCS approach by Bergold et al. [START_REF] Bergold | Quantitative analysis of C-S-H in hydrating alite pastes by in-situ XRD[END_REF] was employed to describe the C-S-H contribution. The amorphous content in the anhydrous tricalcium silicate was not increased by the intense milling.

Thermal analysis (TA)

Thermogravimetry data were obtained in a TA instruments SDT Q600 device at a heating rate of 10 K/min under a stream of nitrogen. The water content of C-S-H was determined by subtraction of the change in mass related to dehydration of portlandite and the decarbonation of calcium carbonate from the loss on ignition at the final temperature (1000 °C). It was revealed in this calculation that the C-S-H of the hydrated C3S sample contains 2.6 moles of water. Under the assumption of a Ca/Si molar ratio of 1.7 for C-S-H, the hydration reaction of C3S can be written as:

𝐶 ! 𝑆 + 3.9 𝐻 → 𝐶 ".$ 𝑆𝐻 %.& + 1.3 𝐶𝐻 Equation 1
Equation 1 was used for the calculation of the C3S content in the hydrated samples.

29 Si-NMR spectroscopy 29 Si solid-state magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy was performed in a spectrometer equipped with an Oxford wide bore magnet (11.7 T), a Bruker Avance III 500 console and a Doty triple resonance probehead for 7 mm (O.D.) zirconia rotors.

Single-pulse and cross-polarization ( 29 Si{ 1 H} CP) experiments were conducted by 29 Si solidstate NMR to quantify the concentrations of C3S, C-S-H and metastable hydrate phase [START_REF] Bellmann | Improved evidence for the existence of an intermediate phase during hydration of tricalcium silicate[END_REF], which can be interpreted as a first form of C-S-H [START_REF] Sowoidnich | New insights into tricalcium silicate hydration in paste[END_REF]. The single-pulse experiments used a MAS spinning rate of 4 kHz, a π/2 pulse length of 6.4 µs, 128 scans, and a recycle delay time of 600 s. This recycle delay time is too short for complete relaxation of the silicon sites in C3S resulting in an underestimation of the intensity of this phase compared to C-S-H which has a much lower relaxation time. Thus, the intensities extracted from the deconvolution need to be multiplied by a factor of 3.62, which was obtained by comparing a fully relaxed spectrum (recycle delay time 4 hours, 24 scans) with a spectrum acquired at the same degree of relaxation (recycle delay time 600 s, 24 scans) as the samples used for quantitative analysis. The chemical shifts associated to the different phases and the recorded spectra obtained by the single-pulse experiments are provided in the supplementary information (Figure S3).

The 29 Si{ 1 H} CP experiments were conducted using parameters that were adjusted using a sample of α-C2SH at the same MAS frequency of 4 kHz. The spectra were recorded using an initial 1 H pulse (π/2 pulse length of 4.5 µs), a contact time of 4 ms with a 1 H rf field strength of 38.3 kHz (ramp 10090) and a 29 Si rf field strength of 30.9 kHz, 1 H decoupling during acquisition for 10 ms, a recycle delay time of 3 s and 1024 scans.

The concentration of C3S, C-S-H, and a metastable hydration product containing Q 0 sites was computed from the (corrected) relative intensities from the deconvolution of the spectra, the silicon concentration in the sample and the molar weight of the phases. The molar weight of C-S-H and the metastable hydration product is based on the composition of these phases assuming 1.7 CaO • SiO2 • 2.6 H2O and 1.3 CaO • SiO2 • 2H2O [START_REF] Sowoidnich | New insights into tricalcium silicate hydration in paste[END_REF], respectively.

All chemical shift data are reported relative to tetramethylsilane (TMS) as an external standard. The software DMFit was used for the deconvolution of the spectra [START_REF] Massiot | Modelling one-and two-dimensional solid-state NMR spectra[END_REF].

The 29 Si{ 1 H} MAS NMR (CP) spectra and the chemical shifts of the phases are presented in the supplementary information of this article (Figure S4 & S5, Table S2).

ICP-OES

Ion concentrations in the filtered aqueous solutions were analysed by ICP-OES using a Horiba Jobin Yvon, active M with radial observation. Calcium and silicon concentrations were measured at a wavelength of 373.69 nm and 251.61 nm, respectively. The aqueous phase was obtained by filtration of the suspensions after 4 h, 8 h, 12 h, and 16 h of hydration. The filtered solutions were diluted and stabilized by the addition of 0.2 g of 5 M HNO3 for analysis by means of ICP-OES. This dilution was taken into account.

C-S-H layer analysis by means of Scanning Electron Microscopy (SEM)

Microstructural characterisation was carried out using a SEM equipped with a field emission gun (Nova NanoSEM 230 FEI). For the detection of backscatter electron images, 12 kV acceleration voltage and 1.8 nA probe current were used (high vacuum mode of the instrument). The C-S-H layer thickness was measured by manually selecting undisturbed (by sample preparation and vacuum) hydration rims. For each sample more than 50 particles have been analysed. It is known that C-S-H can lose water when exposed to high vacuum but it is not expected that the morphology is significantly affected by this dehydration (measurements were taken in areas were no significant shrinkage cracking was observed).

C3S particle size distribution during hydration by holo-and near-field ptychographic nano-tomography using synchrotron radiation

The experiments were carried out at the ID16A nano-imaging beamline of the European Synchrotron Radiation Facility (ESRF) [START_REF] Da Silva | Efficient concentration of high-energy x-rays for diffraction-limited imaging resolution[END_REF]. This end-station is optimized for efficient hard X-ray nano-focusing and designed to provide coherent X-rays for nanoimaging. During the experiments, the sample was exposed to vacuum (around 10 -7 mbar) at room temperature. However, the C3S and C-S-H particles are not directly exposed to the vacuum and subsequent water loss as the material is fully enclosed in epoxy resin. The beamline offers a piezo-driven short-range hexapod stage for the accurate positioning and scanning of the sample under the control of capacitive sensors. Two sets of tomographic experiments were conducted, namely, HXCT and NF-PXCT. Details of the experiments using those two techniques are given in the supplementary information of this article.

Results

Degree of hydration of C3S and aqueous phase composition during hydration

The samples obtained during the hydration experiment were analysed by three independent methods to determine the degree of hydration. These include QXRD, 29 Si MAS NMR spectroscopy, and thermal analysis. The degree of hydration is calculated from the evolution of the concentration of tricalcium silicate in the samples when using QXRD and 29 Si NMR. In contrast, the C3S concentration is indirectly assessed by thermal analysis by using the determined concentrations of C-S-H and portlandite to stoichiometrically calculate the C3S concentration (equation 1). The concentration of C3S during hydration is plotted in Figure 2 as the mean value, with the corresponding standard deviation obtained from the individual methods. A method-dependent list of these results is provided in the supplementary information of this article (Table S1). The mean value of the C3S concentration against time is fitted using Equation 2:

𝐶 ! 𝑆 [𝑤𝑡. -%] = 𝐴2 + ((")(%) "+, !"!# $! Equation 2
A corrected R² = 0.99955 was achieved with the fit parameters A1 = 97.6 wt.-%, A2 = 19.5 wt.-%, t0 = 12.9 h and dt =2.1 h. This mathematical fit is also given in Figure 2 (dotted line). The first derivative of this fit corresponds to the reaction rate and is plotted on the right axis of Figure 2. The application of reaction calorimetry that is generally used for the determination of the hydration rate [START_REF] Taylor | Cement Chemistry[END_REF] was not possible because the hydration was performed in suspensions (water/C3S -ratio (by mass) of 3.0) and thus continuous stirring is needed during the measurement.

As shown in Figure 2, the concentration of C3S at the start of the experiment is slightly lower than 100 wt.-%. This can be the consequence of the adsorption of a small amount of water in the air classifier during milling or other procedures. Between 5 and 20 h, the concentration of C3S drops to a final value of 19 wt.-% as it is consumed during the main hydration period. Such a high degree of reaction (0.81) is attributed to the very small particle sizes of the used C3S powder. The maximum rate of reaction during the main hydration period is observed after approximately 13 hours. This is relatively late when compared to other studies using pure tricalcium silicate and the shift of the maximum of the main hydration peak is connected to the addition of superplasticizer that is known to retard the nucleation and growth of C-S-H. However, the retarding effect is relatively low as the concentration of superplasticizer was only 0.67% relative to C3S. Between 20 and 24 hours, the concentration of C3S decreases from 23 to 19 wt.-%, indicating that the reaction has slowed down and the main hydration period has ended. In addition to the C3S concentration, the aqueous phase of the C3S suspensions during hydration was analysed by ICP-OES (Table 1). The results show that the calcium ion concentration is already at a very high level after 4 hours hydration (32 mmol/L) and increases after 8 h to 34 mmol/L. At later hydration times, the calcium ion concentration in the aqueous phase decreases, which can be attributed to nucleation and growth of portlandite [START_REF] Barret | Fundamental hydration kinetic features of the major cement constituents: Ca[END_REF]. A calcium ion concentration of 28 mmol/L was observed after 16 hours reaction. The silicon concentration displays an opposite trend compared to the calcium ion concentration, decreasing from 20 to 16 µmol/L between 4 and 8 hours. A slight increase in silicon is observed after 12 hours, followed again by a decrease after 16 hours. A possible explanation of the observed trends in the ion concentrations of the aqueous phase can be deduced from the plot of Si against Ca (Figure S7, supplementary information). In this way the results can be interpreted that the aqueous phase is close to an equilibrium with a metastable C-S-H [START_REF] Sowoidnich | New insights into tricalcium silicate hydration in paste[END_REF] for hydration periods up to 12 h and departs towards stable C-S-H [START_REF] Haas | From C-S-H to C-A-S-H: Experimental study and thermodynamic modelling[END_REF] at later hydration times.

C-S-H layer analysis by means of SEM

The hydrated samples were investigated by SEM with the aim of evaluating the C3S particle size distribution and the C-S-H layer thickness at the surface of the C3S particles during hydration. Figure 3 shows examples of these SEM investigations.

The dark areas in the SEM images shown in Figure 3 represent the epoxy resin, which was used to fix the material. The C3S particles are light grey, C-S-H is slightly darker covering the C3S surface. Portlandite can be recognised by its shape, i.e., as elongated shapes resulting from sectioned plate-like crystals. Mean values of the C-S-H layer thickness were estimated for a number of 57 (12 h), 77 (16 h), and 70 (20 h) C3S particles providing the sum of inner and outer C-S-H. These analyses provide only semi-quantitative information as the polishing process during sample preparation cuts the particles not through the volume centre. An extraction of the true thickness of the C-S-H layer from these results is not straightforward and requires a number of assumptions for particle shape and other properties [54]. It is also complicated by the fact that the C3S particles have irregular shapes and there is a high variation in the thickness of the C-S-H layer even at the same grain. Thus, an evaluation of accurate quantitative information is complicated but a semi-quantitative approach demonstrates a growing thickness of the C-S-H layer around tricalcium silicate during hydration as predicted by the reaction zone hypothesis in Figure 1. Image analysis of the sample hydrated for 12 h shows that the C-S-H covering the C3S particles has the lowest thickness of the investigated samples with a value of 300 ± 80 nm. This C-S-H layer thickness increases after 16 h of hydration to a mean value of 670 ± 170 nm and after 20 h of hydration to 800 ± 260 nm. Although these results bear a large error, the conducted SEM investigations prove the findings [START_REF] Möser | A New Model Of Ordinary Portland Cement Hydration Derived By Means Of ESEM-FEG[END_REF][START_REF] Stark | Zement und Kalk: Der Baustoff Als Werkstoff[END_REF] that the C-S-H layer thickness increases with increasing hydration time. The values obtained for the C-S-H layer thickness are much higher than the C-S-H needle length results summarized in [START_REF] Ouzia | The needle model: A new model for the main hydration peak of alite[END_REF] but in broad agreement with layer thicknesses expected from BNG simulations [START_REF] Masoero | A Reaction Zone Hypothesis for the Effects of Particle Size and Water-to-Cement Ratio on the Early Hydration Kinetics of C3S[END_REF]. The deviation from values reported in [START_REF] Ouzia | The needle model: A new model for the main hydration peak of alite[END_REF] may be due to the fact that the C3S used in this study had a higher surface area, which resulted in a higher degree of hydration which facilitates formation of longer C-S-H needles. It was also attempted to extract the particle size distribution of tricalcium silicate from the SEM micrographs. These efforts have indicated that the size of the C3S cross sections can be analysed accurately by SEM but a recalculation of the diameter of the 3D-particles from the 2D cross sections is challenging due to irregular shaped alite cores. In addition to C3S and C-S-H, also portlandite particles are observed in all samples, especially in the 20 h sample.

C3S particle size distribution during hydration by holo-and near-field ptychographic tomography using synchrotron radiation

The first step in determining the particle size distribution of C3S during hydration is the identification of the C3S particles in the samples. Figure 4 provides a greyscale image from the HXCT (left hand) together with the processed binary image obtained by the used segmentation algorithm (right hand) [START_REF] Phansalkar | Adaptive local thresholding for detection of nuclei in diversity stained cytology images[END_REF]. It can be seen that the used segmentation algorithm showed a good performance in separating neighbouring particles and removing hydration products.

A) B)

C) The image processing from the NF-PXCT experiments is exemplarily shown in Figure 5 for the sample hydrated for 12 h. The C3S particles appear in light grey, whereas C-S-H and portlandite are dark grey and the resin still darker. Air bubbles are black spheres. The hydration products C-S-H and portlandite have almost the same grey-level but a different morphology as calcium hydroxide forms elongated particles of several micrometers in the longest dimension. Figure 5 shows that the C3S particles are clearly identified as their grey level is different from all other phases in the analysed volume. These differences in grey level between C3S and the other phases allow an extraction of the particle size distribution of tricalcium silicate. A related analysis of the C-S-H shell thickness is complicated by the fact that the grey levels of C-S-H and portlandite are almost identical. The processed images were segmented to identify the phase present in the individual voxel from the grey level. A minimum of 8 connected voxels representing tricalcium silicate was considered as the smallest particle size which could be identified in the segmentation process. These 8-voxel clusters at an individual voxel size of 50 nm reveal the volume of the smallest particles which is 10 6 nm³.

The diameter of a sphere with the identical volume is 124 nm. All particle diameters determined from nano-tomography data which are presented in the following sections are calculated as spheres with identical volume compared to the analysed volume of the irregular shaped particles. In the following, the identified C3S particles were converted into particle size distributions. The volume distributions of the anhydrous C3S particles are shown in Figure 6 obtained by HXCT and NF-PXCT. Figure 6 shows that NF-PXCT and HXCT give comparable results for the volume-based particle size distribution of the anhydrous C3S. The maximum C3S particle diameter is 6.3 µm (NF-PXCT) and the smallest measures 124 nm as defined during the post-processing procedure (minimum 8 voxels per particle are selected to avoid any possible contamination of the dataset due to the presence of noise). The HXCT results show some variation in grey level intensity complicating the segmentation process. It appears from the HXCT data that a 7.5 µm particle is present in the analysed volume which is not identified by NF-PXCT. A closer comparison of the tomographic data reveals that such a particle is not present but consists of an agglomeration of two particles in the HXCT reconstruction. This confirms the improved resolution and an enhancement in grey-level contrast of the NF-PXCT results compared to HXCT.

Results in Figure 7 show that the maximum particle size is reduced from 6.3 µm in the anhydrous sample to 5.5 µm (NF-PXCT) or 5.9 µm (HXCT) after 12 h of hydration. The same agreement between NF-PXCT and HXCT is observed for the other samples. The data also reveal a further decrease of the maximum particle size to 5.4 µm (NF-PXCT) or 5.1 µm (HXCT) after 16 h of hydration and the maximum particle size is 4.8 µm (NF-PXCT and HXCT) after 20 h of hydration. This implies that the impact of hydration is clearly visible by a reduced diameter of the largest particles. The situation is different for small particles sizes as the number of particles in a given size class is reduced by dissolution of initially anhydrous particles and increased by size reduction of particles of initially larger particles during hydration. Overall, for the observed hydration periods, both effects lead to steeper and narrower particle size distribution as shown in Figure 7. The qualitative trend to smaller particles sizes during hydration observed for the largest particles is not evident in all size classes for all hydration times. Unexpectedly, the relative concentration of medium sized particles is higher in the 20 hours sample than in the 16 hours sample.

Discussion

A hydration time dependent particle size distribution measurement during C3S hydration with full phase selectivity was achieved in this study by employing synchrotron X-ray nanotomography. As mentioned in the introduction, this experimental data was unavailable up to now for a description of the C3S hydration. The obtained data on the development of the particle size distribution are used to evaluate the 'reaction zone hypothesis'. This hypothesis claims that the hydration proceeds in an identical reacted depth (rim) for all sizes of particles (Figure 1). This reacted rim increases with the degree of hydration. The mathematical expressions are developed in the following equations.

Mathematical expression

With the reacted rim thickness e (Figure 1) and the initial diameter of particles of class i (denoted Di(0)), the diameter of the particle of class i at distinct degree of hydration Di(α) is:

𝐷 -(𝛼) = 𝐷 -(0) -2𝑒 Equation 3
With: From Di(α), the mass of particle of class i(mi) can be calculated using the corresponding volume of a sphere and the mass density of C3S (3.16 g/cm³). The degree of hydration of particle of class i at time t, αi(t), reads:

2𝑒 ≤ 𝐷 - (
𝛼 -(𝑡) = 1 - . % (/)
. %,# Equation 5With mi(t) and mi,0 being the mass of the particle i at time t and at time zero, respectively.

The sum over all particles classes i weighted by the number of particles in each class Ni of the initial bulk sample gives the degree of hydration of the bulk sample α(t):

α(𝑡) = 1 -∑ ∑ . % (/)1 % ( % ∑ . %,# 1 % ( % 2 -3" Equation 6
During simulation, the reacted rim thickness e is iterated until the global degree of hydration of the particles matches the measured degree of hydration at time t of the bulk sample (α(t), eq. 6, depicted in Figure 2). The result of this simulation gives the reacted rim thickness e and the degree of hydration distributed over all particle sizes.

Application

For the following simulation, the measured particle size distribution (NF-PXCT only) of the reference sample and the degree of hydration of the bulk samples are used as input parameters. Figure 8A shows the degree of hydration of the bulk samples distributed over all C3S particle sizes calculated from eq. 5 for the samples hydrated for 12 h, 16 h, and 20 h. In Figure 8B, the corresponding reacted rim thickness 'e' is presented.

The simulation in Figure 8A shows that the C3S particles with diameter smaller than 0.42 µm have completely reacted after 12 h of hydration. The degree of hydration of particles with diameter ranging from 0.40 µm to 6.31 µm decreases from 1.0 to 0.2 non-linearly. After 16 h of hydration, particles smaller than 0.98 µm have completely reacted and after 20 h this value is 1.22 µm. The simulated values for the distribution of the degree of hydration over the initial particle sizes (Figure 8A) correspond at the same time to the reacted rim thickness, which is depicted in Figure 8B. It can be seen that the reacted rim increases non-linearly with increasing degree of hydration. A) B)

Evaluation

The 'reaction zone hypothesis' is qualitatively evaluated by comparing the measured values of the C-S-H layer thickness and the particle size distribution in the following. A quantitative evaluation will be presented afterwards by the comparison of the measured and predicted specific surface area of C3S during hydration.

Qualitative evaluation of the simulation

The qualitative evaluation step regarding the simulation based on the 'reaction zone hypothesis' centres around the comparison of the predicted and measured particle size distribution of C3S during hydration. In addition to the particle size distribution of the starting material (measured by NF-PXCT), also the degree of hydration of the samples is taken into account as an input parameter. From this, the volume fractions of C3S in the size classes i can be calculated for the hydrated samples. The results of this calculation are compared to the measured values in Figure 9. The results from the simulation and nano-tomography are displayed in Figure 9. The simulation results are obtained using the particle size distribution from NF-PXCT, degrees of hydration from section 3.1 and the shrinking core model from section 4.1. A close agreement between the particle size distributions from simulation and nano-tomography is indicated by the cumulative curves (Figure 9A) and impressively confirmed by the differential curves (Figure 9B). The error bars in that Figure refer to the standard deviation (1σ) of the NF-PXCT results that was obtained by splitting the analysed volume in three sub-volumes followed by extraction of the particles size distribution for each sub-volume. Thus, the standard deviation is a conservative approximation for the uncertainties introduced by particle statistics.

It is evident from Figure 9B that the simulation and the experimental results agree closely and always within the standard deviation. The quality of the results is underpinned by the fact that the curves referring to the individual hydration times are distinct from each other and fall outside the standard deviation from the other hydration times. Only in the late stage of hydration when the reaction slows down, the particles size distributions are located within the standard deviation of the curve from another hydration time (16 h and 20 h samples), see Figure 9B.

It is important to point out that the simulation data obtained from the shrinking core model closely agrees with the experimental data thus confirming the validity of that model -at least for the samples analysed in this study.

Quantitative evaluation of the simulation

The qualitative evaluation of the 'reaction zone hypothesis' shown in section 4.3.1 is now followed by quantitative tests by analysing the surface area of C3S during hydration ( during hydration. A close agreement between both nano-tomography techniques and the simulation is observed. The maximum deviation between different techniques was as small as 0.06 m²/g (NF-PXCT versus HXCT for the anhydrous C3S). This difference is due to difficulties in the segmentation of the HXCT-data of this sample already noted in section 3.3. The absolute differences between the methods are even smaller for all other samples with HXCT tending to give slightly lower values. The good agreement between simulation and experimental data implies that the 'reaction zone hypothesis' can predict the specific surface area of tricalcium silicate during hydration with high accuracy. This statement applies to the samples prepared in this study and a general validation of the model would require a systematic analysis of many other samples.

The surface area data in Table 1 refers to the outer surface of the particles and may be modified by changes in micro-roughness of the particles during hydration. It has to be kept in mind that the values reported in Table 1 account for particles larger than 124 nm as smaller particles cannot be detected by the experimental methods used in this study. The presence of smaller particles will lead to higher surface areas and can be included in the simulation. Such particles smaller than 124 nm had to be removed from the present simulation to be consistent with the experimental study. A repetition of the simulation using the particle size distribution from the laser diffraction data would derive surface area data that is systematically higher than the results in Table 1. This difference is due to the fact that laser diffraction can analyse much smaller samples as it operates on a different physical basis. Such data was not included in the current study as it cannot be compared to the experimental results obtained by nanotomography.

Hydration time

Degree of hydration

Aqueous phase composition

Surface area C3S with respect to 1 g alite [m²]

[ In view of the quantitative comparison in Table 1, the reaction zone hypothesis enables to simulate the measured (HXCT and NF-PXCT) development of the C3S particle sizes during hydration (at least for the samples analysed in this study). Therefore, to predict the surface area of C3S during hydration, the starting particle size distribution and the degree of hydration of the bulk sample are sufficient as input parameters for equations (3) - [START_REF] Garrault | Study of C-S-H growth on C3S surface during its early hydration[END_REF]. These reported values can be used, for example, as parameters for the simulation of the C3S hydration kinetics during the first 24 h of hydration. For this purpose, Table 1 summarizes additionally the values obtained in the current study regarding the aqueous phase composition and related simulated surface area of C3S for the samples hydrated for 4 h, 8 h, 12 h and 16 h with respect to 1 g alite at 0 h. An integration of our results into kinetic models and the discussion of basic mechanisms for C3S hydration in the light of our data is beyond the scope of this paper.

The reaction zone hypothesis was applied here for the computation of C3S layer dissolved during hydration and showed good agreement with the experimental data for the evolution of the C3S particle size distribution during hydration. In addition to this, the reaction zone hypothesis can be applied to the thickness of the C-S-H layer formed around the C3S particles during hydration as originally proposed [START_REF] Masoero | A Reaction Zone Hypothesis for the Effects of Particle Size and Water-to-Cement Ratio on the Early Hydration Kinetics of C3S[END_REF][START_REF] Biernacki | Advanced single particle model for C3S and alite hydration[END_REF][START_REF] Honorio | Modeling hydration kinetics based on boundary nucleation and space-filling growth in a fixed confined zone[END_REF]. However, the evaluation of such a model would require the extraction of the C-S-H rim thickness from the nano-tomography data which has not been successfully realized. It was also attempted to obtain information on the thickness of the hydrated rim from the SEM data but the uncertainty in the C-S-H shell thickness results obtained by this method was too high. This has prevented an evaluation of the reaction zone hypothesis to the C-S-H layer and such an extension can be the scope of future studies.

Conclusions

The present study focuses on the measurement of the time-dependent C3S particle size distribution during the main hydration period of C3S. Since the C3S particles are overgrown by C-S-H, phase selective synchrotron radiation nano-tomography was applied for the first time to cementitious materials by combining two different operation modes (HXCT and NF-PXCT). The obtained volume distribution of C3S particles shows good accordance between HXCT and NF-PXCT results. The experimental data indicate that the C3S particles sizes decrease during hydration, which leads to a decrease of the specific surface area of C3S due to the consumption of small particles.

The obtained experimental results are used to simulate the process of C3S dissolution during hydration using a constant reacted rim thickness for all C3S particle sizes that varies with the degree of hydration ('reaction zone hypothesis' [START_REF] Masoero | A Reaction Zone Hypothesis for the Effects of Particle Size and Water-to-Cement Ratio on the Early Hydration Kinetics of C3S[END_REF]). For this purpose, the degree of hydration of the bulk samples and the C3S particle size distribution of the starting material are used as input parameters for these simulations. The degree of hydration during the first 20 hours of hydration was independently determined by means of QXRD, 29 Si MAS NMR, and TA with consistent results. The simulation of the C3S particle size distribution based on the "reaction zone hypothesis" showed good agreement with the measured values by HXCT and NF-PXCT for our samples. It has to be noted that only particles bigger than 124 nm in diameter are investigated and compared to calculated values. Thus, the 'reaction zone hypothesis' appears to be an adequate description of the development of the particle size distribution of C3S during hydration.

Figure 1 :

 1 Figure 1: 'Reaction zone hypothesis' for the development of the particle sizes of C3S during hydration with individual degree of hydration of each particle size due to constant reacted rim thickness. R0-radius of the anhydrous particle, R-radius of the hydrated particle, e-reacted rim, E-C-S-H layer thickness, RP-radius of the full particle (C3S core + C-S-H layer). The presentation focuses on details important to the present study; additional information such as formation of a gap between remaining C3S cores and C-S-H or the difference between inner and outer C-S-H are not included to increase clarity of the presentation.

Figure 2 :

 2 Figure 2: C3S concentration during 24 h of hydration given as the mean value from TA, NMR, and QXRD measurements (black squares) with its mathematical fit by Equation 2 (dotted line), and C3S reaction rate as the first derivative (multiplied by -1) of the C3S concentration fit (bold line, right hand axis).

Figure 3 :

 3 Figure 3: SEM images of embedded samples hydrated for 12 h (A), 16 h (B), and 20 h (C) with measurements of the C-S-H layer thickness.

Figure 4 :

 4 Figure 4: Grayscale (left) and binary (right) images relative to a 2D section through the reconstructed volume (12-hours hydrated sample). Black: cement particles; grey: glue; white: air voids. Segmented C3S particles in the binary image are shown in white. Scale bar: 10 µm.

Figure 5 :

 5 Figure 5: 2D view of the C3S sample hydrated for 12 h showing irregular shaped C3S particles, elongated portlandite sections, C-S-H as a hydration rim around tricalcium silicate, epoxy resin and air (black).

Figure 6 :

 6 Figure 6: Volume-based particle size distribution (cumulative and derivative) for HXCT and NF-PXCT measurements of anhydrous C3S.

Figure 7 :

 7 Figure 7: Volume-based cumulative particle size distribution obtained from NF-PXCT and HXCT measurements of C3S.

Figure 8 :

 8 Figure 8: Simulated degree of hydration of the C3S particles in dependence of their size after 12 h, 16 h, and 20 h of hydration (A). Calculated reacted rim thickness of the C3S particles in dependence on the degree of hydration (B).

Figure 9 :

 9 Figure 9: Particle size distribution (A: cumulative, B: derivative) during C3S-hydration. Measurement (NF-PXCT, HXCT) and simulation.

Table

h] [-] Ca [mmol/L] Si [µmol/L] Ptycho- graphy Holo- graphy

							Simu-
							lation
	0	0.03	-	-	0.72	0.66	-
	4	0.04	19.8	32.1	-	-	0.66
	8	0.11	15.6	33.6	-	-	0.62
	12	0.38	17.2	32.6	0.43	0.40	0.43
	16	0.69	15.5	28.2	0.24	0.21	0.22
	20	0.77	-	-	0.17	0.15	0.17
	24	0.81	-	-	-	-	0.14

Table 1 :

 1 Comparison of the measured and simulated evolution of the surface area of C3S per 1 g anhydrous material during hydration. The aqueous phase composition is additionally shown.

Acknowledgements

This work was supported by the European Synchrotron Research Facility under the project number CH 5449 "Surface area of hydrated cement calculated from SR nano-tomography" to F. Bellmann.


F Villar

L Andre

R Baker

S Bohic

Julio Cesar Da Silva

C Guilloud

J C Da Silva

O Hignette

J Meyer

A Pacureanu

M Perez

M Salome

P Van Der Linden

Y Yang

P Cloetens

Nanopositioning for the ESRF ID16A Nano-Imaging Beamline

come   L'archive ouverte pluridisciplinaire

Introduction

New scientific frontiers in biomedicine, materials science and nanotechnology make increasingly use of characterization methods at the mesoscopic and nanometer scale. These studies of heterogeneous samples are most often three-dimensional and require multiple and stable acquisitions, where the spatial and/or angular position of the sample is changed in a well-controlled way. The high average brightness of synchrotron sources, which will be further enhanced by the future diffraction limited storage rings [1], is invaluable in this context. Several nanoscale characterization methods have become available, using highly coherent probes, nanofocused probes, or both [2][3][4][5][6][7][8]. However, the required nanopositioning and stability (absence of vibrations and long term drifts) remain huge challenges, especially when the environment of the specimen needs to be controlled. The European Synchrotron has developed a number of specialised nanoprobe endstations covering energies from the tender X-ray regime (the X-ray microscopy beamline ID21 under refurbishment [9]), over moderate X-ray energies (the micro-diffraction imaging beamline ID01 [10], the microfocus beamline ID13 [11], the nano-imaging beamline ID16A [12] and the nano-analysis beamline ID16B [13]), to the high energy regime (the materials science beamline ID11 [START_REF] Vaughan | Proceedings of the 31st Risø International Symposium on Materials Science[END_REF] and the future endstation of the high energy beamline ID31 [START_REF] Dehaeze | Proceedings of MEDSI[END_REF]). Here we develop the specific case of the Nano-Imaging beamline ID16A that provides routine imaging on the nanoscale with a sub 13 nm X-ray beam with a very high flux. At the expense of flexibility, it exploits one of the most advanced nanopositioning endstations. We introduce its specifications, discuss the specific design choices and illustrate the performance with metrology and X-ray experimental results.

Experimental techniques and nanopositioning specifications

Designed for quantitative three dimensional characterization of the morphology and the elemental composition of specimens at the nanoscale, the ID16A beamline of the ESRF produces currently the world's brightest nanofocus. With the endstation located at 185 m from the source, the beamline is optimized for coherent hard X-ray imaging and X-ray fluorescence microscopy. It offers extreme focusing down to 13 nm with a very high photon flux (up to 10 12 photons/s at ΔE/E~1%) [12]. The selected energies, 17 keV and 33.6 keV, are well suited for applications in biomedicine, materials science and nanotechnology. Two coherent imaging techniques, X-ray holographic [START_REF] Khimchenko | [END_REF] and ptychographic [17] tomography, provide the distribution of the electron density through phase contrast at length scales ranging from ~130 nm down to ~10 nm, while keeping a relatively large field of view. Complementary, X-ray fluorescence microscopy delivers label-free, highly efficient trace element quantification with detection limits down to subppm level [18]. Additionally, correlative imaging is routinely performed by combining phase contrast and fluorescence microscopy [19].

The instrument attains its unique properties by combining highly performing nanofocusing optics (multilayer coated Kirkpatrick-Baez mirrors [START_REF] Morawe | Proc. SPIE[END_REF]) with a carefully designed mechanical device for stable sample positioning and accurate scanning. The fixed curvature KB optics provides a diffraction limited focus of less than 13 nm, a world-record at high energy [12]. Focusing X-rays down to this size requires the last focusing element to be very close to the sample -in our case, the last optical face of the KB mirrors is at 25 mm upstream the sample. Both the fluorescence and phase contrast measurements can be performed under cryogenic conditions to preserve the biological samples close to their native hydrated state and slow down radiation damage effects [START_REF] Kapishnikov | [END_REF]. Furthermore, free space is required around the sample to accommodate X-ray fluorescence detectors with a large solid angle and a light microscope to select the scanning region in X-ray fluorescence mode.

Concerning the requirements on the positioning, two groups of positioners can be distinguished: dedicated to alignment and dedicated to scanning. The alignment positioners are used to align the instrument, the orthogonality in tomography for example, and align the relevant position of the specimen with respect to the X-ray beam. The alignment translations typically have a large stroke: +/-5 mm transverse to the beam and -2/+85 mm along the beam for holographic phase contrast tomography. The accuracy requirements of the order of 500 nm are moderate, but the short and long term stability during the acquisition are critical. The scanning positioners include the rotation stage for tomography and small range translations transverse to the X-ray beam for mapping experiments. Tomography experiments require the parasitic translations at the level of the sample to be smaller than 50 nm over a rotation of at least 180 degrees. A continuous, 'vibration free' rotation mode is preferable. For scanning experiments (X-ray fluorescence analysis and ptychography), fast lateral positioning with an accuracy better than 5 nm over a scanning range of 50 µm x 50 µm is needed. The axis perpendicular to the rotation axis, horizontal in our case, should be compatible with continuous scanning to avoid acquisition overheads. In some cases, software corrections on the acquired data can compensate for positioning errors. We prefer to have positioners with intrinsic reasonably optimal performance, because the software corrections are a bottleneck for routine operation and they often fail in the case of weak contrast.

Design choices of the endstation

The endstation is composed of long range stages (the alignment positioners) that integrate the fine movement stages (the scanning positioners). The fine movement stages include the tomography rotation stage and a piezoelectric stage for the scanning experiments. In addition to scanning the sample, the piezo-stage is also used to compensate the parasitic motion of the rotation stage. Movements of the piezo-stage is made under the control of capacitive sensors attached to a specific metrology frame. This active correction technique is implemented in the continuation of the work made by Leleu and David at the Laboratoire National de Métrologie et d'Essais [22]. The whole endstation is placed in a vacuum enclosure reaching 10 -8 mbar in order to operate at cryogenic temperature and to limit contamination of the KB mirrors. Figure 1 shows the open vacuum enclosure revealing the long range stages and the fine movement stages.

The ID16A endstation aims at keeping the relative position of the sample with respect to the focal spot within a few tens of nanometers during experiments that can last a few hours. Main disturbances that can affect this performance have been identified as being the amplification of the ground vibration and geometric deformation due to variation in the temperature gradient of the endstation. We describe here the general design principles we have implemented to limit these disturbances and mitigate their effects on the positioning performance. To limit the amplification of ground vibration, we have decided to maximise the stiffness of the stages and support. However, due to the proximity of the nanofocusing optics, the space is limited to design stages and supporting structures with sufficient stiffness. To overcome this problem, the half-space below the X-ray horizontal beam plane has been left free to fit in the sample stages, while the KB system and the light microscope are supported above this plane. This implies to hold the KB system from the top with a support structure that spans the sample stages. Space is then available to extend the width of stages and supports in the horizontal plane in order to increase stiffness and stability.

The whole endstation is placed in an experimental hutch where the temperature is controlled to +/-0.05 K. The vacuum enclosure acts as thermal shell that smoothens remaining temperature variations. To further limit the effect of the temperature changes on the geometry on the endstation, the materials have been carefully chosen and a specific design has been implemented. Most of the endstation is made of aluminum alloy and in some specific cases, Invar and stainless steel have been used. Aluminum has been chosen because of its high thermal conductivity, compared to Invar or steel, which helps in limiting the temperature gradients that can affect the geometry of the station. However, the thermal expansion is higher and the design must be adapted to overcome this disadvantage. One possibility is to make the design symmetric, for both geometry and thermal sources. This is the case for the endstation where we tried to satisfy as much as practically possible a reflectional symmetry. Sample and X-ray beam are placed in the plane of symmetry so that parasitic displacements outside of this plane are very limited. The geometrical stability of the station in the transverse direction illustrated in the Results section reflects this design choice. However, as the station is supported on the ground, a design having a top/bottom symmetry was impractical to implement. The relative position of the sample with respect to the focal spot is then much more sensitive to temperature changes in the vertical direction than in the horizontal plane. To limit this thermal drift in the vertical direction, Invar has been used for the specific parts of the structural chain that control the vertical position of the sample. The use of different materials requires a specific design to accommodate the differential thermal expansion. A typical solution is to use kinematic constraints between the parts of the station having different materials. For the ID16A endstation this is the case for example for the connection between the concrete block that supports the whole station and its main frame made of an aluminum alloy. However, kinematic constraints can sometimes be difficult to design with sufficient stiffness in the case of long and slender parts with no rotational symmetry. This is the case for example for the translation stage which provides a 100 mm stroke to swap between the two KB systems. The dimension of the stage is 80 mm x 260 mm, it is made of stainless steel and it is attached to a frame made of an aluminum alloy. Attaching this stage on three points with exact constraints would give too much bending compliance, so we decided to overconstrain the design while still leaving free the differential thermal expansion between steel and aluminum.

The piezo actuated hexapod

We have chosen to use a vacuum compatible rotation stage made of roller bearing elements and whose typical guiding errors are a few micrometers in translation and a few hundreds of microradians in rotation. In order to reach the tomography specification of 50 nm parasitic sample displacement, a correction of the parasitic motions is thus required. This correction is made by a feedback system that measures the errors with capacitive sensors and compensates them with a piezo-actuated stage producing small displacements of the rotation stage. The piezo-stage is a custom made hexapod composed of piezo-stack actuators having an individual stroke of 60 µm. Total displacement of the hexapod is about 50 µm in each direction and 500 µrad for tilts. These strokes are much larger than necessary to correct the rotation stage parasitic motions. This is because the piezo-stage is also used to perform the X-ray scanning experiments, with the rotation stage switched off.

Measurement of the rotation stage errors (3 translations and 2 rotations) is made thanks to capacitive sensors looking at a metrology reference attached to the rotating part of the stage as shown schematically in Figure 2a. This reference is a diamond turned aluminum ring whose shape errors have been previously calibrated so that only the rotation stage parasitic motions are measured by the capacitive sensors. In order to limit the measurement noise, we use fast averaging of the individual sensors and we use a total of 12 redundant sensors. With an integration time of 10 ms, the typical standard deviation obtained on the determination of the displacement of the ring is then well below 1 nm. Increasing the number of sensors allows also to measure the thermal expansion of the ring or to continue to operate the endstation in the case a sensor fails.

The principle of the control of the fine movement stages is illustrated in Figure 2b. From a user point of view, the feedback loop runs autonomously on a dedicated Debian Linux computer. Access to the fine stage control is done through specific Tango device servers [23]. They allow to change the sample stage setpoints: all zero during a tomography scan or a continuous ramp on the Ty setpoint for an X-ray fluorescence scan. When needed, the servers also provide access to the metrology of the capacitive sensors as raw values or transformed in Cartesian coordinates. Basic parameters of the feedback loop can be set and the correction can be turned on and off, for example on changing the sample.

Results

Extensive characterisation of the piezo and rotation stages has been conducted at the Precision Engineering Laboratory of the ESRF. First the shape errors of the reference ring were calibrated. To do this, an independent system used to measure the guiding errors of rotation stages was used in conjunction with the capacitive sensors of the station. By combining the measurements performed at the same time by these two systems, it is possible to separate the shape errors of the ring from the stage guiding errors. Results show that axial, radial and tilt errors of the rotation stage are about 3 µm, 6 µm and 120 µrad respectively. The shape error of the reference ring is below 1 µm. Assuming the shape errors do not change over time, they are used as a look-up table for the measurement of the stage errors by the capacitive sensors only. The piezo-stage is then actuated so as to compensate these errors. After having implemented the feedback loop, the residual errors are measured by the independent system of the Precision Engineering Laboratory. As shown in Figure 3 the axial error is decreased from 2 µm down to less than 20 nm when the control loop is active. Similar results have been obtained for the radial and tilt errors.

The described system is in user operation since late 2014, while the capabilities, such as cryogenic operation, have been gradually enriched. The X-ray characterisation of the ID16A nanofocusing and nanopositioning performance is illustrated in Figure 4. Operated at an X-ray energy of 33.6 keV, a fluorescence knife-edge scan shows that the focus is smaller than 20 nm. A careful analysis of the focus size using farfield ptychography demonstrated the focus to be about 13 nm in both directions [12]. The reproducibility of the scanning is excellent, while performed with the piezo actuated hexapod. The stability of the focus position of 12 nm over a period of 10 hours, shows that the symmetry and materials design choices were very appropriate. After an initial settling the horizontal stability reaches amazing values as low as 2-3 nm over a period of six hours. The excellent everyday performance of the instrument is illustrated with two representative scientific results in Figure 5, obtained respectively in X-ray fluorescence mode and in holographic nanotomography mode.

Summary and outlook

We presented the specifications, design choices and some selected results of the nanopositioning for the ESRF ID16A beamline. The key solution to the requirements imposed by the scientific needs are fine movements stages with an active correction scheme. The symmetry and materials design choices result furthermore in excellent short and long term stability. The full control of the sample position has opened unexpected possibilities such as applying a random motion during tomography acquisition to avoid artefacts related to X-ray optics imperfections [25]. On the downsize, the very integrated design makes the maintenance of the system cumbersome. However, this integration is the key to an advanced system that has to reach its excellent performance routinely.

Highly specialized solutions, at the cost of flexibility, are expected to be further developed in the future for true nanoprobe operation. On the current system, three laser interferometry is being implemented to measure the vertical drift of the sample with respect to the KB system. The feedback system can integrate the compensation of this drift. Finally, the new generation of diffraction-limited storage-ring-based light sources will offer an increase of about two orders of magnitude in source brilliance and coherent fraction of the X-ray beams. The ESRF has started its upgrade to such an 'Extremely Brilliant Source' [26][27] that will be ideally suited for nanoprobe imaging applications. A major challenge will be the development of mandatory faster nanopositioning and detection schemes. Ca (blue). The step size is 50 nm x 50 nm (left panel) and 20 nm × 20nm (right panel) [18]. (b) Volume rendering of a glass spicule of a marine sponge G. cydonium revealing simultaneously the outer structure and the internal axial filament. The data was obtained by X-ray holographic nanotomography [24].

Figure captions

Figure 1

 1 Figure 1 Pictures of the ID16A endstation with open vacuum enclosure. (a) Large stroke actuators along the beam (Tx), and transverse to the beam (Ty and Tz). The Tz motion consists of a tripod that provides as well the Rx and Ry alignment degrees of freedom. The tomography scan is performed with the main rotation stage Rz, (b) Close-up of the endstation showing one of the KB nanofocusing optics (KB), the sample (S), the capacitive sensors (C) of the feedback metrology for the piezo actuated hexapod and the long working distance light microscope (LM).

Figure 2

 2 Figure2Schematic of the piezo actuated hexapod and its control. (a) Principle of the short range piezo hexapod for scanning the sample and correcting the rotation stage parasitic movement through feedback with respect to a metrology frame, (b) principle of the feedback loop including the sample stage setpoints, the capacitive sensor metrology, the correction of the ring shape errors and the control of the short range hexapod.

Figure 3

 3 Figure 3 Characterisation of the parasitic movements of the main rotation stage. (a) Axial error without compensation and (b) axial error with compensation by the piezo actuated hexapod. The axial error is reduced from 2 um to less than 20 nm.

Figure 4 X

 4 Figure 4 X-ray characterisation of the ID16A nanofocusing and nanopositioning performance. (a) Piezo actuated hexapod scan through the edge of a Ni lithography structure revealing a vertical focus size below 20 nm, (b) evaluation of the long term stability of the endstation through repetitive scanning of the structure. A stability of 12 nm over a 10 hours period is demonstrated in the horizontal direction.

Figure 5

 5 Figure 5 Selected scientific results of the ID16A instrument. (a) X-ray fluorescence maps of ovarian cancer cells treated with Os containing metallodrugs, showing the cellular distribution of Os (red), Zn (green) and Ca (blue). The step size is 50 nm x 50 nm (left panel) and 20 nm × 20nm (right panel)[18]. (b) Volume rendering of a glass spicule of a marine sponge G. cydonium revealing simultaneously the outer structure and the internal axial filament. The data was obtained by X-ray holographic nanotomography[24].

Acknowledgments

The authors would like to thank Jean-Marie David (Arts et Métiers Paristech) for his advice during the design of the endstation. Furthermore, we thank all members of the ESRF support groups for their contribution to the realization of the ID16A endstation and in particular E. Gagliardini and Y. Dabin for the beamline components and H.P. van der Kleij and L. Ducotte for the measurements at the Precision Engineering Laboratory.