Multiscale X-Ray Scattering for Probing Chemo-Morphological Coupling in Pore-to-Field and Process Scale Energy and Environmental Applications Multiscale X-Ray Scattering for Probing Chemo-Morphological Coupling in Pore-to-Field and Process Scale Energy and Environmental Applications

One of the greatest challenges of our generation is the sustainable storage of environ- mentally harmful by-products of energy production processes. High-level nuclear wastes and CO 2 produced from the energy sectors are examples of these by-products. To ensure the environmentally benign storage of these by-products in a solid form, it is essential to understand the chemical and morphological features of the materials in which these by- products are immobilized. With recent advancements in X-ray scattering, it is now possi ble to map the structure and the microstructure of architected and natural materials across four decades in spatial scale. Multiscale X-ray scattering that encompasses ultrasmall-, small-, and wide-angle X-ray scattering (USAXS/SAXS/WAXS) allows us to probe material features in the spatial ranges of ~5 μm–10 nm, ~100–1 nm, and ~1 nm–0.2 Å, respectively. This connection is illustrated using two specific examples. The first example involves determination of the changes in the porosity and the structure of beidellite, a swelling clay used in the repository design for nuclear waste disposal, on heating to temperatures above 1000°C. The second example illustrates the changes in the nanoscale porosity of heat-treated serpentine after reacting with CO 2 to form magnesium carbonate.


Introduction
Developing technological solutions for the long-term and sustainable storage of environmentally harmful by-products of energy production processes is one of the critical needs of our society. Examples of these by-products include high-level nuclear wastes and CO 2 produced from the energy or industrial sectors. A fundamental understanding of the chemo-morphological coupling in materials containing these immobilized environmentally hazardous by-products is essential for predicting the long-term fate of these contaminants. In this context, chemo-morphological coupling refers to the influence of structural changes in materials at the sub-nanoscale on the nano-and mesoscale morphological changes in materials. Understanding chemo-morphological connectivity in materials allows for establishing a fundamental basis for the bulk-scale properties such as the extent of contaminants immobilized in the solid matrix. The recent development of multiscale X-ray scattering techniques presents a non-invasive, reliable, and robust approach for probing the changes in the structure and morphology of materials from the atomicto-micrometer scales.
Other studies quantified the porosity in limestone and sandstone using ultra-small and small angle neutron scattering (USANS/SANS) measurements supported by complimentary electron microscopy imaging [12,13]. With the recent interest in energy recovery from unconventional formations, the non-invasive characterization of the porosity in shales [14][15][16] and its constituents such as clays [17][18][19] using USAXS/SAXS has received increased attention. One of the advantages of multiscale X-ray scattering is the ability to probe, in-operando, the dynamic changes across the material hierarchy. This approach is illustrated by following the dynamic morphological and structural changes during the heat treatment of beidellite, a swelling clay with a hierarchical material structure. Beidellite, a swelling clay is used in the repository design for nuclear waste disposal and for developing catalytically active materials for clean energy production [20]. Beidellite is the aluminum-rich member of the montmorillonitebeidellite series of minerals [21]. Another example illustrates the reduction in the porosity of heat-treated serpentine on reaction with CO 2 to form magnesium carbonate for the permanent storage of CO 2 . These specific examples illustrate the application of multiscale X-ray scattering techniques for probing material transformations at the crystal structural and pore-scale levels for field and process scale applications in energy and environment, as shown in Figure 1.

Analyses of ultrasmall and small angle scattering data for porous materials
Given the multiscale nature of the applications described in the previous section, powerful techniques such as ultra-small, small, and wide-angle X-ray scattering (USAXS/SAXS/WAXS) are needed to probe the structures of materials across scales. At the angstrom scale, wide angle X-ray scattering (WAXS) provides detailed insights into the internal structure of crystalline materials by modeling the Bragg diffraction peaks. At the nanometer scale, small angle X-ray scattering (SAXS) provides quantitative information regarding the shape and size of the scattering objects including the relative roughness of pore-solid interfaces in porous materials. By combining small angle X-ray scattering (SAXS) with ultra-small angle X-ray scattering (USAXS), it is now possible to quantify the particle and pore sizes across the material hierarchy in architected materials or the fractal morphology in heterogeneous materials from the nanometer to millimeter scale. The key relationships for quantifying the microstructures in materials using small angle scattering are discussed in the following paragraphs.
The measured scattering, I(Q) is related to the spatial distribution of the coherent X-ray or neutron scattering length density, ρ(r) over the sampling volume, V S using the following expression: [22][23][24] Simplification of Eq. (1) by assuming that the isotropic microstructure consists of scattering particles or features of number density, n P (i.e., volume fraction, Φ V = n P V P ) yields Eq. (2) where |Δρ| 2 , γ 0 (r), V P , F P 2 (Q), and S P (Q) represent the scattering contrast factor, the dimensionless atomic pair correlation function, the individual scattering feature volume, feature form-factor, and the interparticle structure factor, respectively.

Determination of the volume fractions using the scattering invariant
The volume fraction of a given set of scattering features is determined using the scattering invariant. The scattering invariant is obtained by integrating the small angle scattering intensity over all Q [23]. The volume fraction, Φ v and the scattering invariant are related using the following expression.

Determination of the mean volumes and radius of gyration using the guinier approximation
The mean radius of gyration of narrowly dispersed and uncorrelated scattering features is determined using the Guinier approximation. The following expression relates the scattering intensity, I(Q) to the mean radius of gyration, R G , particle volume, V P , the scattering contrast factor, |Δρ| 2 and the volume fraction, Φ v.

Determination of the morphology or roughness of solid interfaces from the porod scattering regime
The Porod region is used to probe the local structure at the higher q regimes. In porous materials, the relative roughness or smoothness of the pore-solid interface is quantified using the Porod slope [25]. The Porod slope is determined using the following relationships where I (Q) and n represent the scattering intensity and the slope, respectively: Scattering from rigid rods provides a Porod slope of 1. Porod slopes between 2 and 3 represent branched systems or networks also known as mass fractals. Porod slopes between 3 and 4 represent rough interfaces with a fractal dimension, D where n = 6 -D and n represents a surface fractal. A smooth surface has a Porod slope of 4. For a smooth surface, the surface area, S v can be directly related to the scattering intensity, I(Q) and the flat background scattering, bg using the following expression.

Shapes and size distributions
One of the challenges with USAXS and SAXS is the need for microstructural insights prior to the morphological quantification of a material. Information needed a priori includes insights into the polydispersity of the scatterers and shape features such as disks, sheets, laminar structures, cylinders, rods, or capillary pores, core-shell particles [22,23], and spheres [26,27].
Once the shape of the features is known, the size distributions can be determined by optimizing the scattering intensity from a predefined set of histogram bin sizes also known as the entropy maximization technique, using a least-squares fitting Fourier Transform method, or fitting a functional form of the size distribution and averaging the scattering over the chosen size distribution function. Homogeneous systems can be fitted using a single functional form. The morphologies of hierarchical materials, on the other hand, are better fitted by binning the scattering intensities corresponding to various sizes. Some of the challenges with this approach include the need for multiple iterations for model convergence and the generation of multiple fitting parameters [28,29].

Brief description of USAXS/SAXS instrumentation
The ability to obtain a wide Q range that spans four decades in spatial resolution from 10 −4 to 1 Å −1 is attributed to the application of Bonse-Hart crystal optics. The flexible geometry, crystal optics independent of the sample apertures, source, and size of the point detector conferred by Bonse Hart crystals allow for the detection of a wide Q range. The constituents of a typical Bonse-Hart USAXS instrument include a pair of collimating crystals, ion chamber, guard slits, analyzer crystals, and a photodiode detector. In order to obtain a monochromatic beam, the pre-monochromated beam is passed through the 2-D slits and a pair of collimating crystals set to the angle satisfying the Bragg condition. The X-rays scattered by the sample are then passed through the analyzer crystals and the intensity is measured by the point detector.

Materials and methods
Beidellite procured from The Source Clay Mineral Repositories (Purdue University, West Lafayette, IN) are ground to a size smaller than 75 μm and compacted into a pellet with a thickness of about 0.5 mm. The pellet is placed in a Linkam TS1500 heating stage (Linkam Scientific Instruments Ltd., Tadworth, UK) in alignment with the synchrotron beamline. The starting and final temperatures of 30°C and 1150°C are set with a temperature ramp rate of 3°C/min. The X-ray scattering measurements are performed at the USAXS instrument at sector 9-ID at the Advanced Photon Source (APS), Argonne National Laboratory, Argonne, IL. Using this instrument, USAXS measurements are combined with pinhole-camera based SAXS measurements and with WAXS measurements. The USAXS, SAXS and WAXS data are represented as a function of the scattering or diffracted intensity, I (q) versus q where q = (4π/λ) sinθ (and q = (2π/d) to determine a lattice spacing, d, from an XRD peak in the WAXS data), λ is the X-ray wavelength and θ is half of the scattering or diffracted angle, 2θ. Data collection times for USAXS, SAXS and WAXS are 90, 30, and 30, respectively, for a total of ≈ 3 min, including time for instrument stage motions. The sample configuration within the beam is not changed and the measurements are made within a few minutes of each other. The beam size settings of (0.8 × 0.8) mm for USAXS and (0.8 × 0.2) mm for SAXS (pinhole SAXS or pin-SAXS) and WAXS are used. The sample-to-detector distances for SAXS and WAXS are set to 547 mm and 181 mm, respectively. The X-ray energy is to 21.0 keV. The total X-ray flux at the sample is ≈10 13 photon s −1 . Silver behenate and NIST standard reference material, SRM 660c (LaB 6 ) are used for the calibration of q values and sample-to-detector distances. The collected data are reduced and analyzed using the Irena [31] and Nika [32] software packages written in IgorPro (Wavemetrics, Lake Oswego, OR).

Structural changes in beidellite on heating
One of the interesting structural features in clays is the hierarchical arrangement of the nanosheets and the characteristic interlayer basal distances. The interlayer water confined between the nanosheets contributes to the swelling behavior of these materials. In case of beidellite, a swelling clay, the characteristic interlayer basal spacing decreased from 12.5 to 9.7 Å on heating from 32 to 308°C (Figure 2). This reduction in the interlayer basal distance corresponds to the removal of the one layer of interlayer water. A progressive reduction in the intensity of the peak corresponding to the interlayer basal distance of beidellite is also noted on heating to 1150°C. The decreasing peak intensity on heating suggests a reduction in the number of interlayer nanopores on heating. On the structural front, a significant reduction in the intensity of the characteristic beidellite peak that corresponds to q = 4.22 Å −1 , d = 1.49 Å (h k l: (0 6 0), (3 3 0)) [21] is noted (Figure 3). The trend in the reduction of the peak intensity of beidellite on heating is similar to that of Na-and Ca-montmorillonite reported in previous studies [17]. It was interesting to note the onset of significant structural changes in beidellite (Figure 3) after a reduction in the interlayer basal distance (Figure 2).

Morphological changes in beidellite on heating
The USAXS and SAXS data are collected in the range (10 −4 to 1.5) Å −1 (Figure 4(a)). As the temperature is increased from 32 to 1150°C, the scattering intensity increased 43, 58, and 25% at Q = 0.1, 0.001, and 0.0001 Å −1 , respectively. While changes in the scattering contrast are noted, significant changes in the shape of the scattering curve are not evident. Another consideration is the extent of reversibility in the morphological changes in beidellite. As discussed in the previous section, the changes in the interlayer basal distance coupled with the structural changes in beidellite produce irreversible morphological changes in beidellite.
To quantify the morphologies in beidellite on heating, the scattering contrast factor, |Δρ| 2 is applied. The scattering contrast factor is the square of the difference in the scattering length  density (SLD or ρ) between the two phases. The scattering length density is a function of the chemical composition and density of the phase. In case of beidellite, the scattering contrast factor at the beginning of the experiment emerges from the contrast between the solid and interlayer water. This scattering contrast factor is determined to be 100 × 10 28 m −4 . On heating to 1105°C, the beidellite structure undergoes significant structural changes as evident in Figure 3. The loss of water and densification of the material increase the scattering contrast factor to 500 × 10 28 m −4 .
To quantify the changes in the morphology of beidellite, the void size distributions are modeled as spheroids with an aspect ratio of 0.2, which allows us to account for the layered morphology of clays. The size distributions are determined using the entropy maximization routine, MaxEnt [28,30]. These results are shown in Figure 4(b). On heating to 1105°C, the porosity in the range of 1-10 nm is reduced by nearly two orders of magnitude. These results are consistent with the reduction in the intensity of the interlayer basal distance corresponding to the porosity between the clay nanosheets as shown in Figure 2. This example illustrates one approach to quantify the changes in the nanoscale porosity corresponding to the interlayer basal spacing using USAXS measurements, the interlayer basal spacing in the SAXS regime, and the structure in the beidellite nanosheet in the WAXS regime in a single measurement.

Morphological and structural changes in heat-treated serpentine on carbon mineralization
One of the approaches for permanent carbon storage is to use highly reactive Ca-and Mg-bearing substrates that can react with CO 2 to form thermodynamically stable and environmentally benign calcium or magnesium carbonates [33][34][35][36][37]. Examples of reactive Caand Mg-bearing materials include wollastonite (CaSiO 3 ), olivine (Mg 2 SiO 4 ), and serpentine (Mg 3 Si 2 O 5 (OH) 4 ). Serpentine is widely mined for extracting nickel and the use of serpentine mine tailings for accelerated carbon mineralization has been proposed [38]. However, the kinetics of CO 2 interactions with serpentine are slow. To accelerate these kinetic interactions, the heat treatment of serpentine is proposed. Heat treating serpentine to temperatures of 625°C dehydroxylates the lattice enabling its conversion to an amorphous state [39]. This amorphous material has a higher reactivity with CO 2 compared to the unreacted material.
Recent studies have shown that heat-treated serpentine is effective in capturing and converting CO 2 from flue gas streams to magnesium carbonate [40]. However, the change in the pore size as the heat-treated serpentine is converted to magnesite is not well understood.
A reduction in the porosity of heat-treated serpentine as it is converted to magnesite may potentially limit the reactivity of the material by preventing the migration of Mg. In this context, quantification of the extent of reduction in the porosity of heat-treated serpentine on conversion to magnesium carbonate is useful. Combined ultrasmall, small, and wide angle X-ray scattering (USAXS/SAXS/WAXS) is particularly useful in linking changes in the porosity of heat-treated serpentine to the formation of magnesite. In this study, serpentine was heat-treated to 625°C and the resulting material was reacted at 185°C, P CO2 = 139 bar in 1.0 M NaCl and 0.64 M NaHCO 3 for 3 h while stirring at 300 rpm in a pressurized batch process. The extent of carbonation of heat-treated serpentine to magnesium carbonate is 48%. The particle sizes of these materials before and after carbon mineralization were determined to be in the range of 3-100 μm.
WAXS measurements of the heat-treated serpentine before and after the carbonation reaction showed the formation of magnesite. The characteristic magnesite peak corresponding to q = 2.99 Å −1 , d = 2.10 Å and hkl: 113 is shown in Figure 5. At the lower Q regions, a reduction in the scattering intensity is noted (Figure 6(a)). The scattering contrast factors are applied to determine changes in the morphology of the materials. The scattering contrast factor of the  unreacted and reacted heat-treated serpentine are 446 × 10 28 m −4 and 574 × 10 28 m −4 , respectively. The scattering contrast factors and the void size distributions with an aspect ratio of 1 are the important inputs to determine the morphological changes in these materials using the entropy maximization routine, MaxEnt [28,30]. The changes in the cumulative pore volume distributions of heat-treated serpentine before and after carbon mineralization are shown in Figure 6(b). A significant reduction in the void spaces corresponding to sizes in the range of 2-6 nm is noted. These findings are consistent with the previous observations of reduced porosity due to magnesite growth on olivine grains [35].

Conclusions
In this chapter, we have illustrated the use of combined USAXS, SAXS, and WAXS measurements to quantify reaction-driven microstructural and structural changes involving complex architected and natural materials. These materials include beidellite, a swelling clay from the smectite family of minerals, and serpentine, a layered sheet silicate that belongs to the family of phyllosilicates. The combined USAXS, SAXS, and WAXS techniques available at Sector 9-ID at the Advanced Photon Source in Argonne National Laboratory allows for measurements that span nearly four decades in spatial scale. This chapter also illustrates the need for prior knowledge about the morphological arrangement in materials to quantify the key features such as the changes in the porosity or surface area of porous materials on reaction. In this context, recent advancements in electron microscopy and X-ray tomography have aided the quantitative interpretation of the X-ray scattering measurements discussed in this chapter.