Ca L2,3-edge near edge X-ray absorption fine structure of tricalcium aluminate, gypsum, and calcium (sulfo)aluminate hydrates

Abstract Tricalcium aluminate (cement clinker phase), gypsum, katoite, ettringite, and calcium monosulfoaluminate hydrate (abbreviated as kuzelite) are the major minerals in the hydration reaction of tricalcium aluminate in the presence of gypsum and have critical impacts on the kinetics and thermodynamics of early-age cement hydration mechanisms. Here, spectroscopic analysis of these minerals is conducted using scanning transmission X-ray microscopy (STXM). Their Ca L2,3-edge near edge X-ray absorption fine structure (NEXAFS) spectra are measured and correlated to the known Ca coordination environments. The results indicate that these minerals have unique Ca environments that can be differentiated from one another based on the intensities and positions of the absorption peaks at 346.5–348.5 and 350.5–351.5 eV. It is concluded that Ca in tricalcium aluminate (cubic and orthorhombic polymorphs) and katoite is in cubic-like coordination with negative 10Dq, whereas Ca is in an octahedral-like coordination with positive 10Dq in ettringite, gypsum, and kuzelite. For tricalcium aluminate, the Ca atoms in both polymorphs are in similar chemical environments with slightly more distortion in the orthorhombic polymorph. As a common issue in STXM experiments, absorption saturation of NEXAFS spectra is also investigated. It is demonstrated that the optical density difference between pre- and post-edge absorption levels provides a reliable indication of the sample thickness in the systems studied. The present work provides a reference for the STXM study of the calcium (sulfo)aluminate reactions in cement hydration and natural aqueous environments, and in the former case, provides a more complete understanding of a system that may serve as a low-C alternative to Portland cement.

intRoDuction Calcium (sulfo)aluminate hydrates are found in geological formations (Bell and Rossman 1992;Nelson 1982), wet near-surface environments (Puppala et al. 2005;van Aardt and Visser 1977), and complex composite materials such as hydrated Portland cement (PC) (Taylor 1997;Mehta and Monteiro 2014). Recent studies suggest that heavy metal oxyanions, such as chromate (Hashem and Amin 2014), arsenate (Sasaki et al. 2014), and selenate (Baur and Johnson 2003), can be immobilized using calcium (sulfo)aluminate hydrates, e.g., ettringite (Chrysochoou and Dermatas 2006;Zhou et al. 2006;Hillier et al. 2007), as these elements can be directly substituted into the structures of these minerals. The substitution extent of heavy metal oxyanions has been shown to depend on the coordination environment of Ca with respect to sulfate. It has also been suggested that the coordination environment of Ca is a critical parameter in determining the reactivity of minerals (Davidovits 1994;Skibsted et al. 1993;Black et al. 2003). The Ca coordination symmetry of many natural and synthetic solid phases has been studied by Ca L 2,3 -edge NEXAFS (Solomon et al. 2012;Ha et al. 2012;Jackson et al. 2013;Geng et al. 2015;Fleet and Liu 2009). The peak structures and separations at the absorption edges are affected by the crystal field splitting and spin-orbit effects (Stöhr 2013). Nanometer-resolved identification of Ca coordination environments in complex composite materials (e.g., hydrated cement) has been reported but seems challenging due to the lack of direct links between NEXAFS spectra and coordination configurations (Solomon et al. 2012;Jackson et al. 2013). The efficient assignment of spectra to mineral phases greatly relies on understanding the reference spectra of known minerals and semi-empirical prediction of coordination environment from the spectra details.
Scanning transmission X-ray microscopy (STXM) combines spatially resolved measurements with X-rays of tunable energy at synchrotron radiation facilities (Warwick et al. 2002;Kilcoyne et al. 2003). The bonding and coordination environments of Ca in calcium (sulfo)aluminate hydrates intermixed on the nano-and microscales can be spatially determined by STXM using coupled near edge X-ray absorption fine structure (NEXAFS) measurements (Stöhr 2013). This technique has gained significant interest in geology (Wan et al. 2007), environmental and material research applications (Chen et al. 2014), photovoltaics (McNeill et al. 2008, and cosmological chemistry (Sandford et al. 2006). Cement hydration systems have submicrometer chemical and structural heterogeneities that greatly influence their macroscopic performances, e.g., rheology, hydration heat release and volumetric stability. STXM provides a powerful analytical tool for measuring both spectroscopic and spatial information down to the micro-or nanometer scales for cementitious materials; however, collecting reference spectra of cement-based minerals is critical for analyzing the spatially resolved spectroscopic data.
Tricalcium aluminate (3CaO⋅Al 2 O 3 , abbreviated as C 3 A) is a clinker mineral whose hydration determines the early age performance of fresh concrete mixtures. It is cubic (C 3 A cub ) when the Na 2 O mass content is less than 1.9 wt% and orthorhombic (C 3 A orth ) when the Na 2 O doping is between 3.5 and 4.2 wt% (Barnes and Bensted 2002). Its direct reaction with water rapidly forms metastable calcium aluminate hydrates, which quickly become katoite (3CaO⋅Al 2 O 3 ⋅6H 2 O, a garnet structure type mineral). In the presence of gypsum (CaSO 4 ⋅2H 2 O), the hydration speed is adjusted by the slow formation of ettringite (3CaO⋅Al 2 O 3 ⋅3CaSO 4 ⋅32H 2 O), which is later transformed into calcium monosulfoaluminate hydrate, i.e., kuzelite (3CaO⋅Al 2 O 3 ⋅CaSO 4 ⋅12H 2 O) through reaction with remnant C 3 A after the gypsum is completely consumed (Barnes and Bensted 2002). In this project, STXM is used to collect the reference Ca L 2,3 -edge NEXAFS spectra of several calcium (sulfo)aluminate hydrate mineral phases. The correlations between the spectral features and Ca coordination environments are discussed. The influence of the absorption saturation on the correct interpretation of the Ca L 2,3 -edge NEXAFS spectra is also studied. This work provides reference spectra for the STXM study of calcium (sulfo)aluminate reaction systems in cement hydration and natural aqueous environments.

cA L 2,3 -eDGe neXAFs theoRy
The crystal field splitting of d 0 compounds such as Ca 2+ has been investigated experimentally and theoretically ( Fig. 1) to understand the link between coordination symmetry and nearedge adsorption fine structure (de Groot et al. 1990;Burns 1993;Albright et al. 2013). The lowest unoccupied molecular orbitals (LUMOs) in the CaO x complex are t 2g and e g . They are close in energy but distinct in symmetry. The t 2g state is mainly composed of d xy , d yz , and d xz orbitals and therefore has the same symmetry as these orbitals, whereas e g is mainly composed of d z 2 and d x 2 -y 2 orbitals. In the isolated Ca 2+ ion, the t 2g and e g states share the same energy, but when approached by coordinating O atoms, their energies become significantly different. The t 2g state is at a higher energy than the e g state when Ca coordination is in cubic symmetry whereas the opposite is true for octahedral symmetry. Therefore, the energy gap (e g -t 2g ), equivalently termed 10Dq, is negative for cubic symmetry and positive for octahedral symmetry. A typical Ca L 2,3 -edge NEXAFS spectra has two major peaks (a 2 and b 2 ), two minor peaks (a 1 and b 1 ), and several leading peaks (1, 2 possibly). The spin-orbital interaction splits the Ca L 2,3 -edge NEXAFS spectra into two doublets. The lower-energy doublet (a 1 and a 2 ) corresponds to excitation from 2p 3/2 orbitals, whereas the higher-energy doublet (b 1 and b 2 ) corresponds to excitation from 2p 1/2 orbitals. In each doublet, the major peak corresponds to a final state of the higher energy state in t 2g and e g , while the lower one corresponds to the minor peak. The peak position differences a 2 -a 1 and b 2 -b 1 are determined by, but not identical to, 10Dq (de Groot et al. 1990). The leading peaks 1, 2, and b 1o are part of the multiplet spectrum and can be accounted for by the Coulomb repulsion and exchange terms (de Groot et al. 1990). In cubic coordination, the minor peak 2 occurs between the energies of the a 1 and a 2 peaks, which can be used to distinguish between cubic and octahedral coordination symmetries.
In a Ca L 2,3 NEXAFS spectrum, peak broadening is caused by the solid-state broadening effect when the sample becomes thicker and disorder appears in the crystal structures, which increases the number of inter-peak absorption states ). The intensities of the minor peaks also increase more rapidly than those of the major peaks with increasing sample thickness. A previous study concluded that peak heights should not exceed 0.30 ± 0.05 optical density (OD) to obtain reliable spectra with no absorption saturation artifacts, corresponding to a sample thickness of 30 nm (Hanhan et al. 2009). However, conditions vary from beamline to beamline. Quantitative NEXAFS spectra with no saturation artifacts can be obtained using beamline 5.3.2.2 at the ALS of the Lawrence Berkeley National Laboratory for OD values of ∼1.0, corresponding to a sample thickness of ∼200 nm. Saturation effects are generally significant in the analysis of NEXAFS spectra of cement systems, as the typical grain size distribution in cement varies from ∼100 nm to ∼100 µm.

MAteRiALs AnD MethoDs
To ensure purity, all samples studied here were lab-prepared phases, rather than from natural sources. Katoite, ettringite, C 3 A cub , and C 3 A orth powders were purchased from Mineral Research Processing (http://www.mineralresearchprocessing.fr/). The crystal structures and chemical compositions of these minerals were verified by powder X-ray diffraction (XRD) (Electronic Supplemental Material 1 ). Gypsum was purchased from Fisher Scientific (no. S76764). Ca L 2,3 -edge NEXAFS spectra of katoite, ettringite, C 3 A cub , and C 3 A orth were measured on samples prepared by drop-casting small amounts of these precursors directly onto Si 3 N 4 windows. Ca L 2,3 -edge NEXAFS spectra of kuzelite was obtained by spectromicroscopic analysis of samples produced by mixing gypsum, C 3 A cub , and deionized water by hand at a mass ratio of 0.4:1:14 in sealed plastic vials under ambient conditions (1 atm, 25 ± 2 °C). Small volumes (∼0.2 µL) of the hydrated mixtures were drop-cast onto 100 nm thick Si 3 N 4 windows (Norcada) after 9 days of reaction. The reactions were stopped by removing excess water immediately after drop-casting by gently contacting the mixtures with Kimwipes (Kimtech Science), leaving a thin layer of hydrated solids ( Fig. 2) (Kilcoyne et al. 2003). Ca L 2,3 -edge NEXAFS spectra of katoite and C 3 A cub were measured on samples prepared by drop-casting small amounts of these precursors directly onto Si 3 N 4 windows.
The STXM and Ca L 2,3 -edge NEXAFS measurements were conducted at beamline 5.3.2.2 of the Advanced Light Source (Lawrence Berkeley National Laboratory), which operates at 1.9 GeV and 500 mA using a bending magnet source and an active servo-stabilized toroidal pre-mirror. Two computer-controlled slits are placed on each side of a low dispersion spherical grating monochromator. Within the energy range of 250-780 eV, the resolving power of the radiation source at beamline 5.3.2.2 is E/∆E ~ 5000 when using slit dimensions of approximately 20 × 10 × 10 µm and decreases to E/∆E ∼ 2000 with slit dimensions of approximately 60 × 30 × 30 µm, where E is the incident beam energy and ∆E is the resolvable energy step size. The scanning transmission X-ray microscope installed on beamline 5.3.2.2 has a spatial scanning resolution limit of ∼31 nm utilizing a 240 µm diameter zone plate, with the transmission signal recorded using a phosphor-coated photomultiplier tube (PMT) (Stöhr 2013;Collins and Ade 2012). The photon energy is calibrated by setting the position of the Rydberg 3s peak for CO 2 to 292.74 eV as detailed in reference (Collins and Ade 2012).
Samples were measured under 0.3 atm of helium. The energy scanning range was set to 340-360 eV, with a step size of 0.1 eV between 345 and 356 eV and a step size of 0.2 eV used at the other sampled energies. The measured data were processed using aXis2000 software (Hitchcock et al. 2012).

Ca L 2,3 -edge NEXAFS spectra and crystal chemistry
The Ca L 2,3 -edge NEXAFS spectra of all the studied minerals show fine structures within the energy range of 346 to 354 eV (Fig. 3), consistent with Ca L 2,3 -edge NEXAFS spectra of many Ca-containing minerals (Solomon et al. 2012;Ha et al. 2012;Jackson et al. 2013;Geng et al. 2015;Fleet and Liu 2009). Unique spectra were repeatedly observed for each mineral phase on different sampling regions of similar thickness, indicating that FiGuRe 3. (a) Ca L 2,3 -edge NEXAFS spectra of ettringite, kuzelite, katoite, gypsum, C 3 A cub , and C 3 A orth , collected from the regions in b-g. The absorption signals of the dashed circle or straight lines in each image were averaged to yield the spectra. Insets are spectra of CaF 2 (de Groot et al. 1990) and Ca(OH) 2 (Geng et al. 2015) as examples of cubic and octahedral coordination, respectively. (Color online.) the chemical environment of Ca in each mineral is relatively homogeneous at the spatial resolution of ∼30 nm.
Katoite. The shape of the Ca L 2,3 -edge NEXAFS spectrum of katoite (Fig. 3) is similar to that of CaF 2 (de Groot et al. 1990;Naftel et al. 2001;Miedema et al. 2011), which contains Ca coordinated to eight F atoms in cubic symmetry. The cubic-like symmetry of katoite is confirmed by the larger peak energy differences of a 2 -a 1 (1.70 eV) than b 2 -b 1 (1.21 eV) in this phase. A similar a 2 -a 1 energy difference is found for CaF 2 (1.60-1.70 eV), although the b 2 -b 1 energy difference in CaF 2 (1.40-1.44 eV) is larger. According to Lager et al. (1987) (2) there is a slight misalignment of the top and bottom rectangles (Fig. 4a).
Ettringite. The Ca L 2,3 -edge NEXAFS spectrum of ettringite (Fig. 3a) resembles that of octahedrally coordinated Ca both because the peak energy differences of a 2 -a 1 and b 2 -b 1 are comparable and because no peak is observed between a 1 and a 2 . The leading peak 2 is almost indistinguishable in this spectrum. The energy differences between the peak positions a 2 and a 1 at the L 3 edge and b 2 and b 1 at the L 2 edge are 1.05 eV and 1.14 eV, respectively, which are low relative to the corresponding values for calcite and calcium hydroxide (Geng et al. 2015). The relatively low splittings of the L 3 and L 2 edges and low intensities of the minor a 1 and b 1 peaks indicate a weak crystal field.
So far three ettringite structures have been reported where Ca environments are highly comparable (Moore and Taylor 1970;Hartman and Berliner 2006;Goetz-Neunhoeffer and Neubauer 2006). Ettringite contains eightfold-coordinated Ca in two positions (Fig. 4b), with Ca-O bond lengths for Ca1 ranging from 2.356 to 2.739 Å, average of 2.464 Å, and those for Ca2 ranging from 2.317 to 2.747 Å, average of 2.491 Å (Moore and Taylor 1970). Viewing Ca1 along the (100) axis, the corners of the rectangle formed by two O1 atoms and two O3 atoms are misaligned with the corners of the rectangle formed by O6, O8, O10, and O12  (Allmann 1977), and (d) gypsum (Comodi et al. 2008), with rotation axes marked by dashed lines. The insets show color blocks that illustrate the orientations of the roughly coplanar oxygen atoms viewed down the rotation axes. Filled ellipses and triangles represent twofold and threefold axes, respectively. Bond lengths are in angstroms. (Color online.) atoms, and thus, the t 2g orbital is less destabilized by the ligands. Instead, the O8 atom and two O1 atoms can destabilize the d z 2 orbital from the axial direction and the five equatorial oxygen atoms, i.e., O6, O10, O12 and two O3 atoms can destabilize the d x 2 -y 2 and d xy orbitals (note that O6 and O12 are slightly off the equatorial plane to the O8 side). In contrast, the d yz and d xz orbitals are less likely to be destabilized because their symmetry poorly matches that of the ligand configuration. Ca2 has a very similar configuration to Ca1, with O7 and O2 in axial positions and O5, O9, O11, O4s in equatorial positions. Based on the above reasoning, we predict that Ca in ettringite is in a weak crystal field with positive 10Dq. This matches very well with the Ca L 2,3 -edge NEXAFS spectrum of ettringite in Figure 3a.
Kuzelite. The Ca L 2,3 -edge NEXAFS spectra for kuzelite and ettringite are similar, except that the positions of the a 2 , b 1 , and b 2 peaks in the former phase are shifted to lower energy, which also has a relatively smaller L 3 splitting (0.93 eV) and a relatively larger L 2 splitting (1.18 eV). The Ca L 2,3 -edge NEXAFS spectrum for kuzelite contains very well-resolved leading (1, 2) and minor (a 1 , b 1 ) peaks and has a relatively high signal-to-noise ratio, which can be attributed to the analysis of large, uniformly thick and near-perfect hexagonal crystals (Fig. 3c).
In kuzelite, there is one equivalent Ca position (Allmann 1977) (Fig. 4c). The oxygen in water (O w ) is located on the (001) Fig. 4c, where the side that the rotation axis is pointing toward is denoted as the top side). There is a misalignment of 43.7° in the orientations of the equatorial O hd regular triangle (blue triangle in Fig. 4c, inset) and the top O hd regular triangle (red triangle in Fig. 4c, inset). In this configuration, only the d z 2 orbital is likely to be significantly destabilized, axially by O w , on top by the O hd triangle, and equatorially by the equatorial O hd triangle. Compared with the strong destabilization of the perfect octahedral ligand configuration (Moore and Taylor 1970), we expect the Ca L 2,3 -edge NEXAFS spectra for kuzelite to be similar to those with small positive 10Dq, which matches the result shown in Figure 3a.
Gypsum. The Ca L 2,3 -edge NEXAFS spectrum measured for gypsum is similar to the spectra obtained for ettringite and kuzelite (Fig. 3a), although the L 3 edge peak splitting (a 2 -a 1 ) of 0.85 eV and the L 2 edge peak splitting (b 2 -b 1 ) of 0.90 eV for gypsum are smaller, indicating a weaker crystal field. Values of L 3 and L 2 edge splitting of ∼0.95 eV have previously been reported for CaSO 4 , indicating a stronger crystal field with emission of crystalliferous water (Patel and Aswath 2012). The Ca L 2,3 -edge NEXAFS spectrum for gypsum also contains weak leading 1 and 2 peaks and shows a small, positive 10Dq value because peak 2 is located between peak 1 and a 1 . There is an additional weak b 1o peak at 350.82 eV, which was not identified in the NEXAFS of perfectly octahedral coordinated compounds nor in theoretical calculations (de Groot et al. 1990). Therefore, the NEXAFS results for gypsum indicate that this phase contains Ca in distorted coordination symmetry with 3d orbitals destabilized in a way similar to octahedral coordination.
The analysis for gypsum presented above is consistent with the crystal chemistry of Ca in this phase (Comodi et al. 2008). In gypsum, Ca is coordinated to eight oxygen atoms in one equivalent position (Fig. 4d), with bond lengths ranging from 2.360 to 2.547 Å. The relative orientation of the two O2 atoms and two O w atoms to the four O1 atoms in gypsum and katoite are similar if viewed along the (010) axis (i.e., the rotation axis), although neither the O2, O w nor O1 atoms lie in the same plane. From the geometric point of view, the coordination of Ca in gypsum can be classified into neither octahedral-like nor cubic-like symme- try but rather a spherical-like symmetry, with 8 ligand O atoms distributing randomly within short range of distances from the center Ca. This leads to a much weaker splittings at the L 3 and L 2 edges than in ettringite and kuzelite.
Cubic and orthorhombic C 3 A. The Ca L 2,3 -edge NEXAFS spectrum C 3 A cub exhibits a cubic-like symmetry pattern with peak 2 located between the positions of peaks a 1 and a 2 with L 3 and L 2 edge splittings of 1.57 and 1.28 eV, respectively.
There are six Ca sites in the C 3 A cub unit cell (Mondal and Jeffery 1975) (Fig. 5). Ca1 and Ca2 have identical site symmetry and are in a distorted octahedral configuration with Ca-O bond lengths of 2.338 Å. All three oxygen pairs in Ca1 and Ca2 take Ca as the center, yet the angles between these pairs are 79.2° instead of 90°. Ca3 is also distorted from octahedral coordination with three 2.352 Å-long Ca-O bonds and three 2.356 Å-long Ca-O bonds. The angle of each O3-Ca-O4 bond is 162.52°. The four equatorial O atoms are not exactly coplanar. The coordination structures of Ca4, Ca5, and Ca6 are more complex, with Ca-O bond lengths varying between 2.258 and 3.013 Å. Therefore, Ca L 2,3 -edge NEXAFS spectrum for C 3 A cub is a superposition of contributions from octahedrally coordinated Ca (Ca1, Ca2, and Ca3) and irregularly coordinated Ca (Ca4, Ca5, and Ca6) and is not expected to show strong L 2 and L 3 edge splitting because the percentage of octahedral-like sites is relatively low (11.1% for Table 1. Numbers and locations of Ca and Na atoms in the C 3 A cub (Mondal and Jeffery 1975) and C 3 A orth unit cells (Nishi and Takeuchi 1975) (color online)  summation of Ca1 and Ca2, 11.1% for Ca3, as shown in Table 1). The Ca L 2,3 -edge NEXAFS spectrum for C 3 A cub is consistent with this line of reasoning, and the complex coordinations of Ca4, Ca5, and Ca6 produce cubic-like crystal field splitting effects with negative 10Dq.
The symmetry and size of the unit cell (Table 1) as well as the configurations of Ca atoms (Fig. 6)  The previously mentioned symmetries of Ca atoms in C 3 A orth explains the cubic-like Ca L 2,3 edge NEXAFS spectrum that was measured for this phase (Fig. 3). This spectrum differs from that for C 3 A cub by a shift in the location of peak 2 to lower energy and a more broadened peak b 1 , with otherwise minor differences in spectral line shape and peak positions. The energy differences between peaks a 2 -a 1 and b 2 -b 1 are slightly smaller in the Ca L 2,3 edge NEXAFS spectrum for C 3 A orth relative to C 3 A cub , indicating a slightly weaker crystal field of Ca in C 3 A cub . The doping of Na is not uniform on the unit-cell scale, leading to a fractional occupancy of Ca1, which breaks the perfect periodicity over long ranges (Nishi and Takeuchi 1975). This may explain the broadening of peak b 1 in the C 3 A orth spectrum. The sharpening of peak 2 in the spectrum of C 3 A orth could then be explained by the higher fraction of octahedral-like coordinated Ca3 atoms in C 3 A orth (23.5%) relative to C 3 A cub (11.1% for each of the two octahedral-like coordinated sites), whose a 1 peak is sharp (de Groot et al. 1990). Therefore, the Ca atoms in C 3 A orth are in cubic-like coordination with slightly weaker crystal fields than those in C 3 A cub .

Absorption saturation
In a transmission X-ray spectroscopy experiment, NEXAFS spectra become "saturated" once the sample thickness reaches a limiting value. Increasing sample thickness beyond this limit results in significantly broadened absorption peaks and increases the peak intensity ratio (PIR) of the minor peaks relative to the major peaks. The Ca L 2,3 -edge NEXAFS spectra collected for ettringite, gypsum, and kuzelite samples of different thickness show that the PIRs of the leading and minor peaks typically increase with increasing sample thickness (Figs. 7 and 8b). Peaks 2 and b 1o in the Ca L 2,3 -edge NEXAFS spectrum for gypsum, as well as peak 2 for ettringite, become increasingly difficult to resolve as the sample thickness increases. Most of the major peaks and some of the minor peaks in the Ca L 2,3 -edge NEXAFS spectra for ettringite and gypsum become significantly broadened with increasing sample thickness, although the minor peaks (1, 2, a 1 , a 2 ) in the Ca L 2,3 -edge NEXAFS spectra for kuzelite do not display peak broadening. This is explained by the perfect or near-perfect crystal structure of the kuzelite crystallites sampled (Fig. 3c), such that relatively low amounts of structural-disorder-induced interpeak states are encountered for this phase. Unsurprisingly, peak positions remain unchanged during absorption saturation for all measured phases, meaning that individual phases in composite geochemical systems can be resolved by STXM using this parameter. The features located between 356 and 358 eV are artifacts caused by dynamic focusing of the zone plate.
Using maximum OD values to estimate sample thickness is a common approach (Hanhan et al. 2009). However, it could be impractical when the background absorption is comparable to the resonance absorption, which frequently occurs in thick sampling regions. Here, we propose another estimation of sample thickness. Sample thickness can be estimated using the Beer-Lambert Law (see Eqs. 1-2): (1) OD = µt = -ln(I/I 0 ) (2) where I 0 and I are the incident and transmitted beam intensities, respectively, t is the sample thickness, and µ is the attenuation coefficient (Hubbell and Seltzer 1995). Although µ is a function of the incident beam energy, it can be treated as a constant if the incident beam energy ranges within several tens of electron volts outside of an absorption edge (Fig. 8a). At the absorption edge, µ changes drastically with a small range of variation in beam energy. Beyond the absorption edge, µ once again changes immeasurably with beam energy, as illustrated in Figure 8a. The difference between the pre-edge and post-edge OD, i.e., the optical density difference (∆OD), is related to t and ∆µ, i.e., the difference in µ over this same energy range: Values of minor to major PIRs in unnormalized Ca L 2,3 -edge NEXAFS spectra with different ∆OD are shown in Figure  8b. Given the same ∆OD, the PIRs of ettringite, gypsum, and kuzelite are similar despite differences in attenuation coefficients and sample densities. For example, using I(b 1 )/I(b 2 ) at ∆OD = 0.4, the PIR of these minerals vary within the range 0.75-0.8. These results indicate that the ∆OD parameter may provide a universal measurement of sample attenuation thickness in STXM studies of heterogeneous microscale systems containing these phases. The I(b 1 )/I(b 2 ) curve for kuzelite approaches its lower limit asymptotes at ∆OD < 0.1 and upper limit asymptotes at ∆OD ≥ 0.6. The same observation applies to all three curves of ettringite, where the lower limit is at ∆OD∼0.08 and the upper limit is ∆OD∼0.43. The I(a 1 )/I(a 2 ), I(2)/I(a 2 ), and I(1)/I(a 2 ) curves of kuzelite display only lower asymptotes at ∆OD < 0.1 because the ∆OD does not become large enough to cause full saturation in the minor peaks a 1 , 1, and 2. For gypsum, a lower asymptote is not clear due to lack of sampling in the low ∆OD region but an upper asymptote is obtained for ∆OD > 0.5. In the medium OD range (approximately 0.1∼0.4), the slope of all PIR curves for these phases increase approximately linearly.

iMpLicAtions
Our work has implications for cement chemistry, in demonstrating novel methods to investigate unsolved topics, such as the retardation mechanism of calcium sulfate (hydrates) on the otherwise rapid hydration of C 3 A, which is critical to understanding the early age performance of fresh concrete mixtures. Another potential application lies in the hydration dynamics of calcium sulfoaluminate cement, which is a promising alternative to ordinary Portland cement that may reduce the heavy carbon footprint of the cement industry (Justnes 2012). Clearly, STXM can be a powerful chemical and morphological probe to study rapidly evolving aqueous systems, given that the reference spectra are well resolved. ► F i G u R e 8 . ( a ) S a m p l e t h i c k n e s s parameters indicated for a Ca L 2,3 -edge NEXAFS spectrum of calcium monosulfoaluminate h y d r a t e . ( b ) P I R s f o r e t t r i n g i t e , gypsum, and calcium monosulfoaluminate hydrate as functions of ∆OD. (Color online.)