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At least 109 records · Page 6

Unraveling Grain Boundary Instability in Dense Proton-Conducting Oxides

The long-term stability of protonic ceramic electrolysis cell (PCEC) materials under high-steam operating conditions remains a critical barrier to device commercialization. Here, we investigate the fundamental degradation mechanisms of dense BaCe 0.7 Zr 0.1 Y 0.1 Yb 0.1 O 3-δ (BCZYYb) electrolytes operated at 550 °C, 50% H 2 O in air. Over 1,000 h, the total electrolyte conductivity decreases by 11.1%, driven primarily by a >130% increase in grain-boundary resistivity. Post-mortem analyses reveal that damage is localized to near-surface grain boundaries extending ∼50 μm into the dense electrolyte pellet. This surface localization indicates that degradation is likely to be severe in thin, device-level electrolytes. Degradation is primarily attributed to chemo-mechanical grain-boundary weakening arising from hydration-induced chemical expansion, culminating in the formation of intergranular cracks oriented parallel to the pellet surface. These internal cracks subsequently react with steam and/or CO 2 , leading to the formation of nanoscale insulating phases, including Ba(OH) 2 , nanocrystalline BaCO 3 , and amorphous Ce/Zr/Y/Yb-containing oxides or hydroxycarbonates. After an initial degradation period of approximately 200 h, the overall conductivity stabilizes. Incorporating NiO sintering aids reduces grain-boundary density by an order of magnitude under identical sintering conditions. Although addition of NiO increases the initial resistivity by >160% at 550 °C, it substantially suppresses grain-boundary instability and mitigates chemical degradation. These findings underscore the urgent need for chemical and/or physical stabilization of BCZYYb electrolytes and offer design guidelines to enable durable, high-performance PCECs.

08 HYDROGEN↗

Mechano-chemical understanding of NaSICON for aqueous redox-flow batteries

Redox-flow batteries utilizing a sodium superionic conductor (NaSICON) can be cost-effective systems for grid energy storage by combining high sodium selectivity with reliance on abundant, low-cost elements. However, improving membrane toughness while maintaining a sufficiently thin membrane for ion conduction is needed. Addressing this issue requires deeper insight into the mechanical properties of NaSICON, its interactions with aqueous chemistries, and the chemo-mechanical degradation mechanisms that arise at the intersection of these phenomena. Here, we provide a framework for understanding these problems, strategies to address them, and highlight the potential of unconventional sintering and thin-film fabrication to optimize the performance of NaSICON in practical flow cells.

Grid energy storage↗

Resiliency of Degraded Built Infrastructure

Infrastructure resiliency depends on the ability of infrastructure systems to withstand, adapt, and recover from chronic and extreme stresses. In this white paper, we address the resiliency of infrastructure assets and discuss improving infrastructure stability through development of our understanding of cement and concrete degradation. The resiliency of infrastructure during extreme events relies on the condition, adaptability, and recoverability of built infrastructure (roads, bridges, dams), which serves as the backbone of existing infrastructure systems. Much of the built infrastructure in the US has consistently been rated D+ by the American Society of Civil Engineers (ASCE). Aged infrastructure introduces risk to the system, since unreliable infrastructure increases the likelihood of failures under chronic and extreme stress and are particularly concerning when extreme events occur. To understand and account for this added risk from poor infrastructure quality, more research is needed on (i) how the changing environment alters the aging of new and existing built infrastructure and (ii) how degradation causes unique failure mechanisms. The aging of built infrastructure is based on degradation of the structural materials, such as concrete and steel supports, which causes failure. Current work in cement/concrete degradation is based on (i) the development of high strength and degradation resistance concrete mixtures, (ii) methods of assessing the age and reliability of existing structures, and (3) modeling of structural stability and the microstructural evolution of concrete/cement from degradation mechanisms (sulfide attack, carbonation, decalcification). Sandia National Laboratories (SNL) has made several investments in studying the durability and degradation of cement based materials, including using SNL-developed codes and methodologies (peridynamics, PFLOTRAN) to focus on chemo-mechanical fracture of cement for energy applications. Additionally, a recent collaboration with the University of Colorado Boulder has included fracture of concrete gravity dams, scaling the existing work to applications in full sized infrastructure problems. Ultimately, SNL has the experience in degradation of cementitious materials to extend the current research portfolio and answer concerns about the resilience of aging built infrastructure.

36 MATERIALS SCIENCE↗

Understanding and Strategies for Controlled Interfacial Phenomena in Lithium-Ion Batteries and Beyond

Electrolyte chemistry and properties and electrode structure and chemical properties particularly at the interfaces are crucial for the development of advanced battery components. This project focused on elucidating the roles of the electrolyte and electrode on the formation and evolution of the SEI layer and cell electrochemical performance on silicon and on Li metal anodes. For Si nano/microstructures we evaluated lithiation, volume changes, reactivity, and chemo-mechanical transformations as functions of nanoparticle size, shape, presence of coatings, electrolyte composition, electron leakage to the electrolyte, and cycling. For Li metal anodes we provided detailed analyses of the electrode and electrolyte effects on interfacial reactivity and as a function of microstructural evolution and underlying stochasticity as dendrites nucleate and grow. We thoroughly investigated and simulated how the chemistry of the various components of the electrolyte and the electrode architecture may affect the electrochemical reactions as well as cell degradation. A multiscale modeling approach was utilized, where atomistic simulations informed about the microscopic behavior of the system, and intermediate time and length scales were investigated with mesoscopic models. Results were also tested against selected experiments from our collaborators. The combined theoretical-experimental strategy saves costs by utilizing predictions from computational analyses to guide experimentation.

25 ENERGY STORAGE↗

Integrated Multiphysics Modeling of Environmentally Assisted Brittle Fracture

Brittle materials, such as cement, compose major portions of built infrastructure and are vulnerable to degradation and fracture from chemo-mechanical effects. Currently, methods of modeling infrastructure do not account for the presence of a reactive environment, such as water, on the acceleration of failure. Here, we have developed methodologies and models of concrete and cement fracture that account for varying material properties, such as strength, shrinkage, and fracture toughness due to degradation or hydration. The models have been incorporated into peridynamics, non-local continuum mechanics methodology, that can model intersecting and branching brittle fracture that occurs in multicomponent brittle materials, such as concrete. Through development of new peridynamic capabilities, decalcification of cement and differential shrinkage in clay-cement composites have been evaluated, along with exemplar problems in nuclear waste cannisters and wellbores. We have developed methods to simulate multiphase phenomena in cement and cement-composite materials for energy and infrastructure applications.

36 MATERIALS SCIENCE↗

Improving Subsurface Stress Characterization for Carbon Dioxide Storage Projects by Incorporating Machine Learning Techniques

The overall objective of this project is to develop a framework for reliable characterization and prediction of the state of stress in the overburden and underburden (including the basement) in CO 2 storage reservoirs using machine learning and integrated geomechanics and geophysical methods. Specifically, we propose to develop workflow encompassing of technologies and/or methods to predict stress and pressure changes due to CO 2 injection in an active tertiary recovery site and their impacts on subtle fault activation, fractures and occurrence of microseismic events and compare responses to field observations. In this project, we anticipate using dataset from the Farnsworth field Unit (FWU) which is operated by Purdure Petroleum. A novel elastic-waveform VSP inversion technique will be used to estimate high-resolution spatial and temporal changes of elastic moduli in CO 2 storage reservoirs, which will be combined with velocity-stress relationship derived from laboratory tests to obtain subsurface pressure and stress. Clustered microseismic data will be jointly inverted for improved focal mechanisms. Least-squares reverse-time migration of microseismic waveform data will be performed to directly image fracture/fault zones. Additionally, a deep neural network machine learning technique with convolutional and recurrent layers will be used for learning the spectro-temporal structures in microseismic waveforms. The results of this geotechnical data analysis will be integrated to develop a high-resolution 3D mechanical earth model extending from the overburden sealing formations to the underburden including the basement. Mechanical properties will be derived through integration of mechanical logs, tests, available results from chemo-mechanical laboratory tests, and elastic inversion of seismic data using a combination of Bayesian and stochastic methods as well as machine learning technique. Failure features (faults/fractures) will be represented and/or modeled based on seismic and core data analysis. A transient hydrodynamic-geomechanical model will be developed through coupling with the calibrated FWU reservoir simulation model. The full physics coupled model will be used to train a reduced order proxy model using machine learning algorithm for estimating stress which will then be used with appropriate constitutive relationships and forward seismological models to simulate pressure changes and induced microseismicity. An advanced optimization framework will be developed to perform a history match to minimize error between field observations and simulated. The history matched proxy model will be verified against the full-physics equivalent. The field observations that will be used in the coupled model calibration process include pressure/stress inverted from VSP, moment magnitude from microseismic analysis, real time downhole pressure measurements, production and injection data. Parameter sensitivity and uncertainty analysis will be performed to characterize the impact of model parameter uncertainty on stress estimates. The proposed project will have significant impact on future field implementation of the proposed technology. Because the project field site is an ongoing CO 2 EOR development, the value of the new technology will be demonstrated in an operational context and evaluated as a viable risk mitigation strategy. Cost/benefit will be evaluated together with the various commercial incentives for CO 2 sequestration available to oil and gas operators. The extensive available dataset and ongoing data acquisition under the SWP Phase III work plan provides flexibility for investigation of multiple approaches and reduces technical risk.

58 GEOSCIENCES↗

Multidimensional Diagnostics of the Interface Evolutions in Solid-State Lithium Batteries

All-solid-state lithium metal batteries hold tremendous potential as next-generation energy storage solutions. However, their performance is hindered by complex chemo-mechanical instabilities at the interface, which encompass electrolyte decomposition, loss of contact due to volume changes, and the growth of lithium filaments. Given the complexity of these failure mechanisms, it is imperative to employ multidimensional diagnostics that leverage a combination of tools capable of quantifying formed voids and filaments, identifying the chemical and mechanical properties of lithium dendrites and electrolyte decomposition products, as well as monitoring the evolution of these processes in situ. The primary objective of this project is to develop a comprehensive characterization platform for solid-state battery interfaces, integrating FIB-SEM tomography, ToF-SIMS, in-SEM nanoindentation, and in-SIMS AFM-based stiffness mapping to enable structural, chemical, and mechanical analyses. The project team has accomplished significant milestones, including: 1) The successful development of a characterization platform that combines FIB-SEM, ToF-SIMS, nanoindentation, and AFM. 2) The creation of solid-state cells at various scales. 3) Real-time visualization of the plating and stripping of lithium. 4) Operando analysis of the chemical composition and evolution of electrolyte decomposition products, encompassing intermediate and metastable species, at both the cathode and anode interfaces. 5) In situ analysis of mechanical properties coupled with chemical mapping. 6) The implementation of the multiscale characterization technique has yielded valuable insights into cell failure mechanisms and has led to the development of a solid-state lithium cell that exhibits exceptional durability, surpassing 2500 cycles. This project has resulted in 10 publications, 1 invention disclosure, 8 manuscripts under review or in preparation.

25 ENERGY STORAGE↗

Chemical controls on the propagation and healing of subcritical fractures

Human activities involving subsurface reservoirs—resource extraction, carbon and nuclear waste storage—alter thermal, mechanical, and chemical steady-state conditions in these systems. Because these systems exist at lithostatic pressures, even minor chemical changes can cause chemically assisted deformation. Therefore, understanding how chemical effects control geomechanical properties is critical to optimizing engineering activities. The grand challenge in predicting the effect of chemical processes on mechanical properties lays in the fact that these phenomena take place at molecular scales, while they manifest all the way to reservoir scales. To address this fundamental challenge, we investigated chemical effects on deformation in model and real systems spanning molecular- to centimeter scales. We used theory, experiment, molecular dynamics simulation, and statistical analysis to (1) identify the effect of simple reactions, such as hydrolysis, on molecular structures in interfacial regions of stressed geomaterials; (2) quantify chemical effects on the bulk mechanical properties, fracture and displacement for granular rocks and single crystals; (3) develop initial understanding of universal scaling for individual displacement events in layered geomaterials; and (4) develop analytic approximations for the single-chain mechanical response utilizing asymptotically correct statistical thermodynamic theory. Taken together, these findings advance the challenging field of chemo-mechanics.

36 MATERIALS SCIENCE↗

EFRC-MUSE: Multi-Scale Fluid-Solid Interactions in Architected and Natural Materials

Phase interactions and fluid properties in geological and other environments are critical in applications ranging from hydrogen production and geologic storage and recovery, carbon dioxide storage and sequestration, and the sustainable use of water resources. The four goals of EFRC-MUSE: Multi-Scale Fluid-Solid Interactions in Architected and Natural Materials were based on the priority directions articulated in the Basic Research Needs documents, and the scientific needs in nanoscience. 1. Develop a fundamental understanding of confinement and surface interactions in mesoscale media with nanometer-sized pores on the phase behavior, thermodynamic and multiphase flow properties of multicomponent fluid mixtures. 2. Examine the impact of mineralogy and material heterogeneity on mechanical properties to better understand chemo-mechanical interactions in material failure. 3. Determine in-operando cross-scale structural and nanostructural material properties with fluids in confinement and flow under realistic condi

58 GEOSCIENCES↗

MgADP Promotes Myosin Head Movement toward Actin at Low [Ca 2+ ] to Increase Force Production and Ca 2+ -Sensitivity of Contraction in Permeabilized Porcine Myocardial Strips

Myosin cross-bridges dissociate from actin following Mg 2+ -adenosine triphosphate (MgATP) binding. Myosin hydrolyses MgATP into inorganic phosphate (P i ) and Mg 2+ -adenosine diphosphate (ADP), and release of these hydrolysis products drives chemo-mechanical energy transitions within the cross-bridge cycle to power muscle contraction. Some forms of heart disease are associated with metabolic or enzymatic dysregulation of the MgATP-MgADP nucleotide pool, resulting in elevated cytosolic [MgADP] and impaired muscle relaxation. We investigated the mechanical and structural effects of increasing [MgADP] in permeabilized myocardial strips from porcine left ventricle samples. Sarcomere length was set to 2.0 µm at 28 °C, and all solutions contained 3% dextran T-500 to compress myofilament lattice spacing to near-physiological values. Under relaxing low [Ca 2+ ] conditions (pCa 8.0, where pCa = -log 10 [Ca 2+ ]), tension increased as [MgADP] increased from 0-5 mM. Complementary small-angle X-ray diffraction measurements show that the equatorial intensity ratio, I 1,1 /I 1,0 , also increased as [MgADP] increased from 0 to 5 mM, indicating myosin head movement away from the thick-filament backbone towards the thin-filament. Ca 2+ -activated force-pCa measurements show that Ca 2+ -sensitivity of contraction increased with 5 mM MgADP, compared to 0 mM MgADP. These data show that MgADP augments tension at low [Ca 2+ ] and Ca 2+ -sensitivity of contraction, suggesting that MgADP destabilizes the quasi-helically ordered myosin OFF state, thereby shifting the cross-bridge population towards the disordered myosin ON state. Together, these results indicate that MgADP enhances the probability of cross-bridge binding to actin due to enhancement of both thick and thin filament-based activation mechanisms.

60 APPLIED LIFE SCIENCES↗

Formation of planar n(+) pockets in GaAs for mixer diode fabrication

A novel technique has been developed to produce n(+) 'pockets' in semiinsulating GaAs bulk material. This technique has produced thick pockets of highly conducting epitaxial material on the substrate surface. The pockets were formed by the growth of a liquid-phase epitaxial (LPE) layer into holes which had been etched into the substrate. Surface uniformity was obtained by chemo-mechanically polishing the substrate surface under tightly controlled conditions. Polishing rates as low as 0.2 micron/min have been obtained. Photographs taken of the pocket cross-sectional area have revealed that growth occurred throughout the entire pocket region. Growth was even found to have occurred along the irregularly shape walls of the packets. The continuous growth throughout the pockets coupled with the subsequent polishing of the substrate have produced exceptionally smooth and planar surfaces. Thicknesses as great as 10 microns have been obtained for the n(+) pockets using this technique. Mixer diodes have been fabricated onto these layers and tested. Preliminary dc measurements taken on these devices have yielded a zero-biased cutoff frequency (Fco) of 800 GHz with a series resistance (Rs) of 6 omega and a zero-biased capacitance (Co) of 30 fF.

Griffin, J. A.↗

The Promise of Alloy Anodes for Solid-State Batteries

Solid-state batteries are anext-generation technology that could featureimproved safety and energy density, but reliably integrating high-capacity electrode materials to enable high energy while retaining stablelong-termcycling remains a challenge. Anode materials that alloy with lithium, such as silicon, tin, and aluminum,offer high capacity that canyield high-energy battery cells. The use of alloy anodes in solid-state batteries potentially offers major mechanistic benefits compared to other anode contendersand battery systems, such as lithium metal in solid-state architectures or alloys in liquid-electrolyte batteries. This perspective discusseskey advantagesof alloy anode materials for solid-state batteries, including the avoidance of the short circuiting observed with lithium metal and the chemo-mechanical stabilization of the solid-electrolyte interphase (SEI). We further discuss open research questions and challenges in engineering alloy-anode-based solid-state batteries, with the goal of advancing our understanding and control of alloy anode materialswithin solid-state architectures toward commercial application.

John A Lewis↗

Coalescence of GaP on V-Groove Si

With an increase of control over crystalline defects, metallorganic vapor phase epitaxy (MOVPE)-grown III-V-on-Si multijunction solar cells have seen rapid increases in efficiency in recent years, pointing to a promising path to lower cost III-V solar cells. However, the cost of chemo-mechanical polishing the Si wafers to prepare them for epitaxy is high. The use of V-groove nanopatterns enables similar defect reduction to that achieved on planar wafers, but the nanopatterns can be fabricated with a low-cost process. While V-grooves offer advantages over planar Si, they add complexity to the growth process. In particular, coalescence can cause the formation of threading dislocations, and the highly-directional growth conditions required for coalescence are unusual for MOVPE. We have studied the coalescence of GaP films nucleated directly on V-groove Si by MOVPE. We observed that for optimized growth conditions (V/III=5,000 and T=800 C) two growth modes were possible, and the resulting morphology depended on the exact geometry of the SiNx cap used to cover the (0 0 1)-oriented Si at the tops of the grooves. For caps with a width >100 nm, noncoalescing, nano ridge-like growth terminating in f1 1 1g facets was observed. For narrower caps, coalescence with an RMS roughness of 0.2 nm as measured by atomic force microscopy was observed. We will discuss mechanisms responsible for this phenomenon, including the role of Si from the substrate surface. The dislocation dynamics of this system were studied with electron channeling contrast imaging (ECCI) and transmission electron microscopy (TEM). We find that V-grooves do not block dislocation glide; ECCI measurements show misfit dislocations greater than 10 micrometers long observed to continue perpendicularly across neighboring V-grooves. In addition, all threading dislocations appear to lie on f1 1 1g planes, consistent with the GaP relaxing via glided-in glissile dislocations. The dislocation dynamics and morphological evolution of the coalescence of GaP on Si, possible mechanisms behind the observed phenomenons, and further dislocation mitigation strategies for these materials will be presented.

dislocation dynamics↗

Neural Network Enhanced RKPM for Electrochemical-Mechanical Coupled Damage Modeling of Energy Storage Materials

Energy storage materials undergo significant charge cycling, which makes understanding their reliability and durability fundamental in predicting performance and service life. Strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking, largely along material interfaces and grain boundaries. For Li-ion batteries, for example, lithium moving between electrodes during charging and discharging process causes expansion and contraction of grains, and the strongly anisotropic and nonlinearly [Li]-dependent grain material properties can cause grains to expand into and contract away from each other, leading to chemo-mechanical cracking. In the first part of this work, a RKPM based computational framework for solving the coupled solid-phase lithium conservation with Fickian diffusion and the lithium concentration dependent anisotropic mechanical problem subjected to a highly nonlinear Butler-Volmer boundary condition is introduced. The choice of RKPM completeness conditions for lithium concentration and mechanical deformation fields, and the variational consistency condition for the domain integration of the coupled problem is first determined. In the second part of this work, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1] is leveraged to accurately capture damage and crack propagation throughout the material, by learning the location, orientation, and sharpness of discontinuity while allowing for a coarser nodal distribution than that is necessary for capturing sharp solution transitions using traditional mesh-based methods. NN-RKPM is used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure.

damage modeling↗

Chemo‐Mechanical Coupling in Hydrogels: Dynamics in the Diffusion‐Limited Regime

Hydrogels are characterized by substantial volume changes in response to external stimuli, making them promising candidates for developing smart materials with enhanced adaptability and responsiveness. By integrating chemical reactions, hydrogels acquire dynamic and tunable responsiveness to external stimuli through chemo‐mechanical coupling, expanding their potential in emerging applications. However, capturing their transient behavior remains challenging due to the complex interplay of chemical reactions, solvent transport, and polymer network deformation. Classical theories capture equilibrium swelling but fail to describe time‐dependent phenomena. To address this, a time‐dependent continuum model is developed that explicitly couples these processes. Volume phase transition in hydrogels with homogeneous chemical reactions is investigated, then the effects of reaction kinetics on these transitions are analyzed. The coupling of these mechanisms is further explored through a study of transient mechanical instabilities. To illustrate the impact of distinct reaction and diffusion timescales, a photo‐active gripper is studied for robotic applications. Finally, a photo‐active microswimmer that exhibits non‐reciprocal motion is proposed to highlight the solvent diffusion for locomotion at the micro‐ and nano‐ scales. The work establishes that transient dynamics of chemo‐mechanical hydrogels generate functions not accessible by steady state models and provides a predictive platform for designing adaptive materials in emerging applications.

chemo-mechanical coupling↗

Mechanical Milling – Induced Microstructure Changes in Argyrodite LPSCl Solid-State Electrolyte Critically Affect Electrochemical Stability

Microstructure of argyrodite solid-state electrolyte (SSE) critically affects lithium metal electrodeposition/dissolution. While the stability of unmodified SSE is mediocre, once optimized state-of-the-art electrochemical performance is achieved (symmetric cells, full cells with NMC811) without secondary interlayers or functionalized current collectors. Planetary mechanical milling in wet media (m-xylene) is employed to alter commercial Li 6 PS 5 Cl (LPSCl) powder. Quantitative stereology demonstrates how milling progressively refines grain and pore size/distribution in the SSE compact, increases its density, and geometrically smoothens the SSE-Li interface. Mechanical indentation demonstrates that these changes lead to reduced site-to-site variation in the compact's hardness. Milled microstructures promote uniform early-stage electrodeposition on foil collectors and stabilize solid electrolyte interphase (SEI) reactivity. Analysis of half-cells with bilayer electrolytes demonstrates the importance of microstructure directly contacting current collector, with interface roughness due to pore and grain size distribution being key. For the first time, short-circuiting Li metal dendrite is directly identified, employing 1.5 mm diameter “mini” symmetrical cell and cryogenic focused ion beam (cryo-FIB) electron microscopy. The branching sheet-like dendrite traverses intergranularly, filling the interparticle voids and forming an SEI around it. Importantly, mesoscale modeling reveals the relationship between Li-SSE interface morphology and the onset of electrochemical instability, based on underlying reaction current distribution.

25 ENERGY STORAGE↗

Concurrent measurement of strain and chemical reaction rates in a calcite grain pack undergoing pressure solution: Evidence for surface-reaction controlled dissolution

Pressure solution is inferred to be a significant contributor to sediment compaction and lithification, especially in carbonate sediments. For a sediment deforming primarily by pressure solution, the compaction rate should be directly related to the rate of calcite dissolution, transport along grain contacts, and calcite reprecipitation. Previous experimental work has shown that there is evidence that deformation in wet calcite grain packs is consistent with control by pressure solution, but considerable ambiguity remains regarding the rate limiting mechanism. We present the results of laboratory compaction experiments designed to directly measure calcite dissolution and precipitation rates (recrystallization rates) concurrently with strain rate to test whether measured rates are consistent with predicted rates both in absolute magnitude and time evolution. Recrystallization rates are measured using trace element chemistry (Sr/Ca, Mg/Ca) and isotopes (87Sr/86Sr) of fluids flowing slowly through a compacting grain pack as it is being triaxially compressed. Imaging techniques are used to characterize the grain contacts and strain effects in the post-experiment grain pack. Our data show that calcite recrystallization rates calculated from all three geochemical parameters are in approximate agreement and that the rates closely track strain rate. The geochemically inferred rates are close to predicted rates in absolute magnitude. Uncertainty in grain contact dimensions makes distinguishing between surface reaction control and diffusion control difficult. Measured reaction rates decrease faster than predicted from standard pressure solution creep flow laws. This inconsistency may indicate that calcite dissolution rates at grain contacts are more complex, and more time-dependent, than suggested by geometric models designed to predict grain contact stresses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗