The dynamic nature of crystal growth in pores

Micro- and milli-fluidic sample environments for in situ X-ray analysis in the chemical and materials sciences

X-ray-based methods are powerful tools for structural and chemical studies of materials and processes, particularly for performing time-resolved measurements. In this critical review, we highlight progress in the development of X-ray compatible microfluidic and millifluidic platforms that enable high temporal and spatial resolution X-ray analysis across the chemical and materials sciences. With a focus on liquid samples and suspensions, we first present the origins of microfluidic sample environments for X-ray analysis by discussing some alternative liquid sample holder and manipulator technologies. The bulk of the review is then dedicated to micro- and milli-fluidic devices designed for use in the three main areas of X-ray analysis: (1) scattering/diffraction, (2) spectroscopy, and (3) imaging. While most research to date has been performed at synchrotron radiation facilities, the recent progress made using commercial and laboratory-based X-ray instruments is then reviewed here for the first time. This final section presents the exciting possibility of performing in situ and operando X-ray analysis in the 'home' laboratory and transforming microfluidic and millifluidic X-ray analysis into a routine method in physical chemistry and materials research.

Robust surface-correlation-function evaluation from experimental discrete digital images

Correlation functions (CFs) are universal structural descriptors; surface-surface F_{ss} and surface-void F_{sv} CFs are a subset containing additional information about the interface between the phases. The description of the interface between pores and solids in porous media is of particular importance and recently Ma and Torquato [Phys. Rev. E 98, 013307 (2018)2470-004510.1103/PhysRevE.98.013307] proposed an elegant way to compute these functions for a wide variety of cases. However, their "continuous" approach is not always applicable to digital experimental 2D and 3D images of porous media as obtained using x-ray tomography or scanning electron microscopy due to nonsingularities in chemical composition or local solid material's density and partial volume effects. In this paper we propose to use edge-detecting filters to compute surface CFs in the "digital" fashion directly in the images. Computed this way, surface correlation functions are the same as analytically known for Poisson disks in case the resolution of the image is adequate. Based on the multiscale image analysis we developed a C_{0.5} criterion that can predict if the imaging resolution is enough to make an accurate evaluation of the surface CFs. We also showed that in cases when the input image contains all major features, but do not pass the C_{0.5} criterion, it is possible with the help of image magnification to sample CFs almost similar to those obtained for high-resolution image of the same structure with high C_{0.5}. The computational framework as developed here is open source and available within the CorrelationFunctions.jl package developed by our group. Our "digital" approach was applied to a wide variety of real porous media images of different quality. We discuss critical aspects of surface correlation functions computations as related to different applications. The developed methodology allows applying surface CFs to describe the structure of porous materials based on their experimental images and enhance stochastic reconstructions or super-resolution procedures, or serve as an efficient metrics in machine learning applications due to computationally effective GPU implementation.

Hierarchical synchrotron diffraction and imaging study of the calcium sulfate hemihydrate-gypsum transformation

The mechanism of hydration of calcium sulfate hemihydrate (CaSO4·0.5H2O) to form gypsum (CaSO4·2H2O) was studied by combining scanning 3D X-ray diffraction (s3DXRD) and phase contrast tomography (PCT) to determine in situ the spatial and crystallographic relationship between these two phases. From s3DXRD measurements, the crystallographic structure, orientation and position of the crystalline grains in the sample during the hydration reaction were obtained, while the PCT reconstructions allowed visualization of the 3D shapes of the crystals during the reaction. This multi-scale study unfolds structural and morphological evidence of the dissolution-precipitation process of the gypsum plaster system, providing insights into the reactivity of specific crystallographic facets of the hemihydrate. In this work, epitaxial growth of gypsum crystals on the hemihydrate grains was not observed.

Assessing an aqueous flow cell designed for in situ crystal growth under X-ray nanotomography and effects of radiolysis products

Nucleation and growth of minerals has broad implications in the geological, environmental and materials sciences. Recent developments in fast X-ray nanotomography have enabled imaging of crystal growth in solutions in situ with a resolution of tens of nanometres, far surpassing optical microscopy. Here, a low-cost, custom-designed aqueous flow cell dedicated to the study of heterogeneous nucleation and growth of minerals in aqueous environments is shown. To gauge the effects of radiation damage from the imaging process on growth reactions, radiation-induced morphological changes of barite crystals (hundreds of nanometres to ∼1 µm) that were pre-deposited on the wall of the flow cell were investigated. Under flowing solution, minor to major crystal dissolution was observed when the tomography scan frequency was increased from every 30 min to every 5 min (with a 1 min scan duration). The production of reactive radicals from X-ray induced water radiolysis and decrease of pH close to the surface of barite are likely responsible for the observed dissolution. The flow cell shown here can possibly be adopted to study a wide range of other chemical reactions in solutions beyond crystal nucleation and growth where the combination of fast flow and fast scan can be used to mitigate the radiation effects.

Application of percolation, critical-path, and effective-medium theories for calculation of two-phase relative permeability

There has been active development of numerical pore-network simulation of two-phase immiscible flows in porous media in recent years. These models allow for generation of capillary pressure and relative permeability curves. However, percolation models provide an efficient alternative, with reduced reliance on numerical techniques. Implementation of effective medium or critical path theory along with the percolation model allows for evaluation of the relative permeability curves. Both approximations failed to match the irreducible water saturation for water relative permeability. While the effective medium approximation poorly matches the pore network simulator, the critical path approximation is shown to match the result of the oil relative permeability. Despite the difference in end points, there is qualitative agreement between critical path approximation and the pore network simulator. Moreover, observed differences are not necessarily a drawback due to important boundary effects as discussed in the paper. Our results indicate that percolation-theory based predictions have the potential to become an efficient tool for upscaling by computing two-phase flow properties for numerous porosity subdomains.

Direct characterization of solute transport in unsaturated porous media using fast X-ray synchrotron microtomography

Solute transport in unsaturated porous materials is a complex process, which exhibits some distinct features differentiating it from transport under saturated conditions. These features emerge mostly due to the different transport time scales at different regions of the flow network, which can be classified into flowing and stagnant regions, predominantly controlled by advection and diffusion, respectively. Under unsaturated conditions, the solute breakthrough curves show early arrivals and very long tails, and this type of transport is usually referred to as non-Fickian. This study directly characterizes transport through an unsaturated porous medium in three spatial dimensions at the resolution of 3.25 μm and the time resolution of 6 s. Using advanced high-speed, high-spatial resolution, synchrotron-based X-ray computed microtomography (sCT) we obtained detailed information on solute transport through a glass bead packing at different saturations. A large experimental dataset (>50 TB) was produced, while imaging the evolution of the solute concentration with time at any given point within the field of view. We show that the fluids' topology has a critical signature on the non-Fickian transport, which yet needs to be included in the Darcy-scale solute transport models. The three-dimensional (3D) results show that the fully mixing assumption at the pore scale is not valid, and even after injection of several pore volumes the concentration field at the pore scale is not uniform. Additionally, results demonstrate that dispersivity is changing with saturation, being twofold larger at the saturation of 0.52 compared to that at the fully saturated domain.

Crystallization in Confinement

Many crystallization processes of great importance, including frost heave, biomineralization, the synthesis of nanomaterials, and scale formation, occur in small volumes rather than bulk solution. Here, the influence of confinement on crystallization processes is described, drawing together information from fields as diverse as bioinspired mineralization, templating, pharmaceuticals, colloidal crystallization, and geochemistry. Experiments are principally conducted within confining systems that offer well-defined environments, varying from droplets in microfluidic devices, to cylindrical pores in filtration membranes, to nanoporous glasses and carbon nanotubes. Dramatic effects are observed, including a stabilization of metastable polymorphs, a depression of freezing points, and the formation of crystals with preferred orientations, modified morphologies, and even structures not seen in bulk. Confinement is also shown to influence crystallization processes over length scales ranging from the atomic to hundreds of micrometers, and to originate from a wide range of mechanisms. The development of an enhanced understanding of the influence of confinement on crystal nucleation and growth will not only provide superior insight into crystallization processes in many real-world environments, but will also enable this phenomenon to be used to control crystallization in applications including nanomaterial synthesis, heavy metal remediation, and the prevention of weathering.

Hydraulic and Mechanical Impacts of Pore Space Alterations within a Sandstone Quantified by a Flow Velocity-Dependent Precipitation Approach

Geochemical processes change the microstructure of rocks and thereby affect their physical behaviour at the macro scale. A micro-computer tomography (micro-CT) scan of a typical reservoir sandstone is used to numerically examine the impact of three spatial alteration patterns on pore morphology, permeability and elastic moduli by correlating precipitation with the local flow velocity magnitude. The results demonstrate that the location of mineral growth strongly affects the permeability decrease with variations by up to four orders in magnitude. Precipitation in regions of high flow velocities is characterised by a predominant clogging of pore throats and a drastic permeability reduction, which can be roughly described by the power law relation with an exponent of 20. A continuous alteration of the pore structure by uniform mineral growth reduces the permeability comparable to the power law with an exponent of four or the Kozeny–Carman relation. Preferential precipitation in regions of low flow velocities predominantly affects smaller throats and pores with a minor impact on the flow regime, where the permeability decrease is considerably below that calculated by the power law with an exponent of two. Despite their complete distinctive impact on hydraulics, the spatial precipitation patterns only slightly affect the increase in elastic rock properties with differences by up to 6.3% between the investigated scenarios. Hence, an adequate characterisation of the spatial precipitation pattern is crucial to quantify changes in hydraulic rock properties, whereas the present study shows that its impact on elastic rock parameters is limited. The calculated relations between porosity and permeability, as well as elastic moduli can be applied for upscaling micro-scale findings to reservoir-scale models to improve their predictive capabilities, what is of paramount importance for a sustainable utilisation of the geological subsurface.

Growth of faceted pores in a multi-component crystal by applying mechanical stress

The theory for controllable growth of pores in a multicomponent crystal using mechanical stress is proposed.

Calculation of tensorial flow properties on pore level: Exploring the influence of boundary conditions on the permeability of three-dimensional stochastic reconstructions

While it is well known that permeability is a tensorial property, it is usually reported as a scalar property or only diagonal values are reported. However, experimental evaluation of tensorial flow properties is problematic. Pore-scale modeling using three-dimensional (3D) images of porous media with subsequent upscaling to a continuum scale (homogenization) is a valuable alternative. In this study, we explore the influence of different types of boundary conditions on the external walls of the representative modeling domain along the applied pressure gradient on the magnitude and orientation of the computed permeability tensor. To implement periodic flow boundary conditions, we utilized stochastic reconstruction methodology to create statistically similar (to real porous media structures) geometrically periodic 3D structures. Stochastic reconstructions are similar to encapsulation of the porous media into statistically similar geometrically periodic one with the same permeability tensor. Seven main boundary conditions (BC) were implemented: closed walls, periodic flow, slip on the walls, linear pressure, translation, symmetry, and immersion. The different combinations of BCs amounted to a total number of 15 BC variations. All these BCs significantly influenced the resulting tensorial permeabilities, including both magnitude and orientation. Periodic boundary conditions produced the most physical flow patterns, while other classical BCs either suppressed crucial transversal flows or resulted in unphysical currents. Our results are crucial to performing flow properties upscaling and will be relevant to computing not only single-phase but also multiphase flow properties. Moreover, other calculation of physical properties such as some mechanical, transport, or heat conduction properties may benefit from the technique described in this study.

Mineral Precipitation in Fractures and Nanopores within Shale Imaged Using Time-Lapse X-ray Tomography

Barite precipitation in fractures and nanopores within a shale sample is analysed in situ, in 3D, and over time. Diffusion of barium and sulphate from opposite sides of the sample creates a supersaturated zone where barium sulphate crystals precipitate. Time-lapse synchrotron-based computed tomography was used to track the growth of precipitates over time, even within the shale’s matrix where the nanopores are much smaller than the resolution of the technique. We observed that the kinetics of precipitation is limited by the type and size of the confinement where crystals are growing, i.e., nanopores and fractures. This has a major impact on the ion transport at the growth front, which determines the extent of precipitation within wider fractures (fast and localised precipitation), thinner fractures (non-localised and slowing precipitation) and nanopores (precipitation spread as a front moving at an approximately constant velocity of 10 ± 3 µm/h). A general sequence of events during precipitation in rocks containing pores and fractures of different sizes is proposed and its possible implications to earth sciences and subsurface engineering, e.g., fracking and mineral sequestration, are discussed.

Hierarchical Optimization: Fast and Robust Multiscale Stochastic Reconstructions with Rescaled Correlation Functions

Stochastic reconstructions based on universal correlation functions allow obtaining spatial structures based on limited input data or to fuse multiscale images from different sources. Current application of such techniques is severely hampered by the computational cost of the annealing optimization procedure. In this study we propose a novel hierarchical annealing method based on rescaled correlation functions, which improves both accuracy and computational efficiency of reconstructions while not suffering from disadvantages of existing speeding-up techniques. A significant order of magnitude gains in computational efficiency now allows us to add more correlation functions into consideration and, thus, to further improve the accuracy of the method. In addition, the method provides a robust multiscale framework to solve the universal upscaling or downscaling problem. The novel algorithm is extensively tested on binary (two-phase) microstructures of different genesis. In spite of significant improvements already in place, the current implementation of the hierarchical annealing method leaves significant room for additional accuracy and computational performance tweaks. As described here, (multiscale) stochastic reconstructions will find numerous applications in material and Earth sciences. Moreover, the proposed hierarchical approach can be readily applied to a wide spectrum of constrained optimization problems.

New software protocols for enabling laboratory based temporal CT

Temporal micro-computed tomography (CT) allows the non-destructive quantification of processes that are evolving over time in 3D. Despite the increasing popularity of temporal CT, the practical implementation and optimisation can be difficult. Here, we present new software protocols that enable temporal CT using commercial laboratory CT systems. The first protocol drastically reduces the need for periodic intervention when making time-lapse experiments, allowing a large number of tomograms to be collected automatically. The automated scanning at regular intervals needed for uninterrupted time-lapse CT is demonstrated by analysing the germination of a mung bean (vigna radiata), whilst the synchronisation with an in situ rig required for interrupted time-lapse CT is highlighted using a shear cell to observe granular segregation. The second protocol uses golden-ratio angular sampling with an iterative reconstruction scheme and allows the number of projections in a reconstruction to be changed as sample evolution occurs. This overcomes the limitation of the need to know a priori what the best time window for each scan is. The protocol is evaluated by studying barite precipitation within a porous column, allowing a comparison of spatial and temporal resolution of reconstructions with different numbers of projections. Both of the protocols presented here have great potential for wider application, including, but not limited to, in situ mechanical testing, following battery degradation and chemical reactions.

Deciphering pore-level precipitation mechanisms

Mineral precipitation and dissolution in aqueous solutions has a significant effect on solute transport and structural properties of porous media. The understanding of the involved physical mechanisms, which cover a large range of spatial and temporal scales, plays a key role in several geochemical and industrial processes. Here, by coupling pore scale reactive transport simulations with classical nucleation theory, we demonstrate how the interplay between homogeneous and heterogeneous precipitation kinetics along with the non-linear dependence on solute concentration affects the evolution of the system. Such phenomena are usually neglected in pure macroscopic modelling. Comprehensive parametric analysis and comparison with laboratory experiments confirm that incorporation of detailed microscale physical processes in the models is compulsory. This sheds light on the inherent coupling mechanisms and bridges the gap between atomistic processes and macroscopic observations.