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At least 73 records · Page 4

Theoretical Prediction and Experimental Verification of IrO x Supported on Titanium Nitride for Acidic Oxygen Evolution Reaction

Reducing iridium (Ir) catalyst loading for acidic oxygen evolution reaction (OER) is a critical strategy for large-scale hydrogen production via proton exchange membrane (PEM) water electrolysis. However, simultaneously achieving high activity, long-term stability, and reduced material cost remains challenging. To address this challenge, we develop a frame-work by combining density functional theory (DFT) prediction using model surfaces and proof-of-concept experimental ver-ification using thin films and nanoparticles. DFT results predict that oxidized Ir monolayers over titanium nitride (IrO x /TiN) should display higher OER activity than IrO x while reducing Ir loading. Further, this prediction is verified by depositing Ir monolayers over TiN thin films via physical vapor deposition. The promising thin film results are then extended to commercially viable powder IrO x /TiN catalysts, which demonstrate a lower overpotential and higher mass activity than commercial IrO 2 , and a long-term stability of 250 hours to maintain a current density of 10 mA cm -2 . The superior OER performance of IrO x /TiN is further confirmed using proton exchange membrane water electrolyzer (PEMWE), which shows a lower cell voltage than commercial IrO 2 to achieve a current density of 1 A cm -2 . Both DFT and in situ X-ray absorption spectroscopy reveal that the high OER performance of IrO x /TiN strongly depends on the IrO x - TiN interaction via direct Ir-Ti bonding. This study highlights the importance of close interaction between theoretical prediction based on mechanistic understanding and experimental verification based on thin film model catalysts to facilitate the development of more practical powder IrO x /TiN catalysts with high activity and stability for acidic OER.

08 HYDROGEN↗

Low-thermal-budget synthesis of monolayer molybdenum disulfide for silicon back-end-of-line integration on a 200 mm platform

Two-dimensional (2D) materials are promising candidates for future electronics due to their excellent electrical and photonic properties. Although promising results on the wafer-scale synthesis (≤150 mm diameter) of monolayer molybdenum disulfide (MoS 2 ) have already been reported, the high-quality synthesis of 2D materials on wafers of 200 mm or larger, which are typically used in commercial silicon foundries, remains difficult. The back-end-of-line (BEOL) integration of directly grown 2D materials on silicon complementary metal–oxide–semiconductor (CMOS) circuits is also unavailable due to the high thermal budget required, which far exceeds the limits of silicon BEOL integration (<400 °C). This high temperature forces the use of challenging transfer processes, which tend to introduce defects and contamination to both the 2D materials and the BEOL circuits. Here we report a low-thermal-budget synthesis method (growth temperature < 300 °C, growth time ≤ 60 min) for monolayer MoS 2 films, which enables the 2D material to be synthesized at a temperature below the precursor decomposition temperature and grown directly on silicon CMOS circuits without requiring any transfer process. We designed a metal–organic chemical vapour deposition reactor to separate the low-temperature growth region from the high-temperature chalcogenide-precursor-decomposition region. We obtain monolayer MoS 2 with electrical uniformity on 200 mm wafers, as well as a high material quality with an electron mobility of ~35.9 cm 2 V -1 s -1 . Finally, we demonstrate a silicon-CMOS-compatible BEOL fabrication process flow for MoS 2 transistors; the performance of these silicon devices shows negligible degradation (current variation < 0.5%, threshold voltage shift < 20 mV). We believe that this is an important step towards monolithic 3D integration for future electronics.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Ultrathin Ruthenium Films on Graphene Buffered SiO 2 via Quasi Van der Waals Epitaxy

In this study, we demonstrate a quasi van der Waals epitaxy approach to prepare single crystalline Ru ultrathin film on large scale, monolayer graphene. Physical and epitaxial properties of bulk, near surface and surface of ultrathin Ru films were comprehensively studied using various structural, morphological, compositional, and electrical characterization techniques. Here, we confirm that Ru can epitaxially grow on single, monolayer graphene using magnetron sputtering at elevated temperature of 600 °C. The epitaxial Ru films with film thickness ranging from 94.2 nm down to 3.9 nm show the (0001) out-of-plane orientation. The epitaxial relationships between Ru and graphene are out-of-plane Ru(0001) || graphene(0001) and in-plane Ru[$11\bar20$] || graphene[$11\bar20$]. All the Ru films show smooth surfaces with root-mean-square roughness less than 0.8 nm and have negligible oxide layer on the surfaces. The Ru films on graphene demonstrate significantly reduced electrical resistivity comparing to their counterpart grown on bare SiO 2 , which show polycrystalline nature. For 7.1 to 3.9 nm film thicknesses, the resistivity of Ru on graphene shows 38 to 45% resistivity decrease from that of Ru film on bare SiO 2 without graphene. Our observations suggest the existence of the above-classical van der Waals interaction between Ru and graphene. On the other hand, graphene is capable of effectively blocking the inter-diffusion/interaction between Ru and SiO 2 during a 1000 °C annealing process.

36 MATERIALS SCIENCE↗

Lead Adsorption and Desorption at the Barite (001) Surface in the Presence of EDTA

Scaling minerals, such as barite, can cause detrimental consequences for oil/gas pipelines and water systems, but their formation can be inhibited by organic chelators such as ethylenediaminetetraacetic acid (EDTA). Here, we resolve how EDTA affects sorption and desorption of Pb at the barite (001) surface using a combination of X-ray scattering and microscopy measurements. In the presence of EDTA, Pb incorporated in the topmost part of the barite surface and adsorbed as inner-sphere complexes on the surface. In barite saturated solutions containing [Pb] ≥ 100 μM, overgrowth films grew along step edges. These films were exclusively monolayer thick, indicating that their growth was a self-limiting process. Approximately half of the Pb was removed after 14.5 h reaction with a Pb-free EDTA solution where most of the desorption occurred to adsorbed Pb rather than incorporated Pb. Dissolution proceeded primarily via step retreat and etch pit formation in EDTA, but in deionized water, the secondary phase was quickly removed within 3 min. Together these results suggest EDTA binds to both the surface and Pb in solution, which limits Pb sorption. However, EDTA binding to the surface also inhibits removal of the secondary phase that formed at higher Pb concentrations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Picoscale structural insight into superconductivity of monolayer FeSe/SrTiO 3

Remarkable enhancement of the superconducting transition temperature ( c ) has been observed for monolayer (ML) FeSe films grown on SrTiO 3 substrates. The atomic-scale structure of the FeSe/SrTiO 3 interface is an important determinant of both the magnetic and interfacial electron-phonon interactions and is a key ingredient to understanding its high- T c superconductivity. We resolve the atomic-scale structure of the FeSe/SrTiO 3 interface through a complementary analysis of scanning transmission electron microscopy and in situ surface x-ray diffraction. We find that the interface is more strongly bonded for a particular registration, which leads to a coherently strained ML. We also determine structural parameters, such as the distance between ML FeSe and the oxide, Se-Fe-Se bond angles, layer-resolved distances between Fe-Se, and registry of the FeSe lattice relative to the oxide. This picoscale structure determination provides an explicit structural framework and constraint for theoretical approaches addressing the high- T c mechanism in FeSe/SrTiO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantitative evaluation of perfluorinated alkanethiol molecular order on gold surfaces

Self-assembled monolayers (SAMs) of perfluoroalkanethiols [CF3(CF2)xCH2CH2SH (x = 3, 5, 7, and 9)] on gold were characterized by x-ray photoelectron spectroscopy (XPS), near edge x-ray absorption fine structure (NEXAFS), and static time-of-flight secondary ion mass spectrometry (ToF-SIMS). Perfluoroalkanethiols of several chain lengths were synthesized using a known hydride reduction method for transforming commercially available perfluoroalkyliodides to corresponding perfluoroalkanethiols. This strategy provides improved product yields compared to other known routes based on hydrolysis from the common thioacetyl perfluoroalkyl intermediate. Angle-dependent XPS analysis revealed that CF3(CF2)xCH2CH2SH (x = 5, 7, and 9; F6, F8, and F10, respectively) SAMs on gold exhibited significant enrichment of the terminal CF3 group at the outer monolayer surface with the sulfur present as a metal-bound thiolate located at the monolayer-gold interface. XPS of the CF3(CF2)3CH2CH2SH (F4) monolayer revealed a thin film with a significant (>50%) amount of hydrocarbon contamination consistent with poorly organized monolayers, while the longest thiol (F10) showed XPS signals attributed to substantial ordering and anisotropy. ToF-SIMS spectra from all four SAMs contained molecular ions representative of the particular perfluorinated thiol used to prepare the monolayer. NEXAFS methods were used to determine degrees of ordering and average tilt for molecules comprising monolayers. The SAMs prepared from the longest (F10) thiols exhibited the highest degree of ordering with the molecular axis nearly perpendicular to the gold surface. The degree of ordering decreased significantly with decreasing length of the perfluorocarbon tail.

Biophysics↗

Efficient light-emitting diodes based on oriented perovskite nanoplatelets

Solution-processed planar perovskite light-emitting diodes (LEDs) promise high-performance and cost-effective electroluminescent devices ideal for large-area display and lighting applications. Exploiting emission layers with high ratios of horizontal transition dipole moments (TDMs) is expected to boost the photon outcoupling of planar LEDs. However, LEDs based on anisotropic perovskite nanoemitters remain to be inefficient (external quantum efficiency, EQE <5%) due to the difficulties of simultaneously controlling the orientations of TDMs, achieving high photoluminescence quantum yields (PLQYs) and realizing charge balance in the films of assembled nanostructures. Here, we demonstrate efficient electroluminescence from an in situ grown perovskite film composed of a monolayer of face-on oriented nanoplatelets. The ratio of horizontal TDMs of the perovskite nanoplatelet film is ~84%, which leads to a light-outcoupling efficiency of ~31%, substantially higher than that of isotropic emitters (~23%). In consequence, LEDs with a peak EQE of 23.6% are achieved, representing highly efficient planar perovskite LEDs.

36 MATERIALS SCIENCE↗

Interfacial Charge Transfer and Substrate-Dependent Oxidation States Drive SMSI Enhancements in Cobalt Oxide Films

Here, we investigated the mechanisms underlying strong metal-support interactions in CO oxidation using model systems where noble metal crystals support reducible, monolayer-thick CoO x films. The effect of the Co oxidation state, film thickness, and substrate identity were studied in varying reaction conditions using ambient pressure X-ray photoelectron spectroscopy. At low O 2 pressures, the same oxide phase forms on both Pt(111) and Au(111) surfaces. But when heated at higher O 2 pressures, the oxide phase depends on the substrate. We found that CoO x /Pt is more active for the CO oxidation reaction than CoO x /Au, even when both surfaces stabilize the same oxide phase. DFT calculations on these and related noble-metal-supported CoO x films reveal an SMSI-induced reactivity enhancement that strongly depends on the oxide film thickness and which is mediated by charge transfer between the metal and oxide. Charge transfer is also found to correlate with the reaction energy and activation barrier for CO oxidation. This effect was found to be greatest for oxide films on Pt, decreasing on other noble metal supports in the order Pt > Pd > Au > Ag, in agreement with the experiments. The role of charge transfer in the activation barriers and reaction energies provides insight into the nature of SMSI-induced catalytic activity, and suggests that the noble metal work function can serve as an indicator for the strength of SMSI effects.

36 MATERIALS SCIENCE↗

Evolution of spin excitations from bulk to monolayer FeSe

Abstract In ultrathin films of FeSe grown on SrTiO 3 (FeSe/STO), the superconducting transition temperature T c is increased by almost an order of magnitude, raising questions on the pairing mechanism. As in other superconductors, antiferromagnetic spin fluctuations have been proposed to mediate SC making it essential to study the evolution of the spin dynamics of FeSe from the bulk to the ultrathin limit. Here, we investigate the spin excitations in bulk and monolayer FeSe/STO using resonant inelastic x-ray scattering (RIXS) and quantum Monte Carlo (QMC) calculations. Despite the absence of long-range magnetic order, bulk FeSe displays dispersive magnetic excitations reminiscent of other Fe-pnictides. Conversely, the spin excitations in FeSe/STO are gapped, dispersionless, and significantly hardened relative to its bulk counterpart. By comparing our RIXS results with simulations of a bilayer Hubbard model, we connect the evolution of the spin excitations to the Fermiology of the two systems revealing a remarkable reconfiguration of spin excitations in FeSe/STO, essential to understand the role of spin fluctuations in the pairing mechanism.

36 MATERIALS SCIENCE↗

Adsorption Processes during Electrochemical Atomic Layer Deposition of Gold

Electrochemical atomic layer deposition (e-ALD) technique offers a simple and effective "wet chemistry" approach enabling high-precision monolayer-by-monolayer deposition of metal films. The process of e-ALD of Au involves lead underpotential deposition (PbUPD) followed by its redox replacement by a Au monolayer. The time evolution of the deposit mass during "one-pot" Au e-ALD is known to exhibit a unique three-stage response that is presently not well understood. In this work, we probe this response using voltammetry, electrochemical quartz crystal microgravimetry (e-QCM), and chronoamperometry to unravel the underlying mechanistic events during Au e-ALD. Furthermore, the presence of adsorbed Au +3 -ligand complex(es) (Au-L) on the Au surface is established. In stage I of e-ALD, this Au-L adsorbed layer is reduced to Au while a Pb UPD adlayer is formed. In stage II, the Pb UPD adlayer undergoes spontaneous surface-limited redox replacement by nobler Au under open-circuit conditions. Finally, in stage III, re-adsorption of the Au-L occurs on the newly deposited Au. Quantitative analysis of the deposit mass transients obtained under a variety of conditions provides an estimate of the Au-L mass and its molecular weight.

36 MATERIALS SCIENCE↗

Controllable Thin‐Film Approaches for Doping and Alloying Transition Metal Dichalcogenides Monolayers

Abstract Two‐dimensional (2D) transition metal dichalcogenides (TMDs) exhibit exciting properties and versatile material chemistry that are promising for device miniaturization, energy, quantum information science, and optoelectronics. Their outstanding structural stability permits the introduction of various foreign dopants that can modulate their optical and electronic properties and induce phase transitions, thereby adding new functionalities such as magnetism, ferroelectricity, and quantum states. To accelerate their technological readiness, it is essential to develop controllable synthesis and processing techniques to precisely engineer the compositions and phases of 2D TMDs. While most reviews emphasize properties and applications of doped TMDs, here, recent progress on thin‐film synthesis and processing techniques that show excellent controllability for substitutional doping of 2D TMDs are reported. These techniques are categorized into bottom–up methods that grow doped samples on substrates directly and top–down methods that use energetic sources to implant dopants into existing 2D crystals. The doped and alloyed variants from Group VI TMDs will be at the center of technical discussions, as they are expected to play essential roles in next‐generation optoelectronic applications. Theoretical backgrounds based on first principles calculations will precede the technical discussions to help the reader understand each element's likelihood of substitutional doping and the expected impact on the material properties.

36 MATERIALS SCIENCE↗

Dual–Interface–Reinforced Flexible Perovskite Solar Cells for Enhanced Performance and Mechanical Reliability

Two key interfaces in flexible perovskite solar cells (f-PSCs) are mechanically reinforced simultaneously: one between the electron-transport layer (ETL) and the 3D metal-halide perovskite (MHP) thin film using self-assembled monolayer (SAM), and the other between the 3D-MHP thin film and the hole-transport layer (HTL) using an in situ grown low-dimensional (LD) MHP capping layer. The interfacial mechanical properties are measured and modeled. This rational interface engineering results in the enhancement of not only the mechanical properties of both interfaces but also their optoelectronic properties holistically. As a result, the new class of dual-interface-reinforced f-PSCs has an unprecedented combination of the following three important performance parameters: high power-conversion efficiency (PCE) of 21.03% (with reduced hysteresis), improved operational stability of 1000 h T90 (duration at 90% initial PCE retained), and enhanced mechanical reliability of 10 000 cycles n88 (number of bending cycles at 88% initial PCE retained). Furthermore, the scientific underpinnings of these synergistic enhancements are elucidated.

14 SOLAR ENERGY↗

Picometer sensitivity metrology for EUV absorber phase

With growing interest in EUV attenuated phase-shift masks due to their superior image quality for applications such as dense contact and pillar arrays, it is becoming critical to model, measure, and monitor the intensity and relative phase of multilayer and absorber reflections. We present a solution based on physical modeling of reflectometry data, which can achieve single picometer phase precision and sensitivity to changes in average film thickness below one atomic monolayer. We measure absorber and multilayer reflectivity to determine thin-film parameters with a multidimensional optimization and then acquire a new measurement of either multilayer or absorber to determine perturbations in surface contamination thickness. While it is difficult to assess the accuracy of the first step, the simplicity of the second step allows us to characterize our sensitivity to changes in contamination thickness. Thus, we apply this analysis using an initial set of measurements and repeated measurements after a period of storage. For the multilayer, the total contamination growth was 1068 pm, which occurred almost exclusively during storage (1085 pm) and decreased very slightly during repeated measurements (-17 pm). For the absorber, the behavior was quite different, with a total growth of 126 pm, which occurred much less during storage (28 pm) and primarily during repeated measurements (98 pm). Ultimately, the change in relative phase (absorber minus multilayer) was -0.86 deg for the multilayer and -1.12 deg for the absorber. We estimate the precision of the surface contamination measurement to be 3σ < 6 pm for measuring thickness and 3σ < 0.2 deg for measuring phase.

36 MATERIALS SCIENCE↗

Sieving Hydrogen Isotopes via Machine Learning Assisted Chemical Vapor Deposition (CVD) of High‐Quality Monolayer Hexagonal Boron Nitride (h‐BN) on Iron Foils

Atomically thin two-dimensional (2D) ceramics, such as monolayer hexagonal boron nitride (h-BN), present potential for disruptive advances in separations. However, sub-atomic scale separation of hydrogen isotopes (H + /D + ) require near pristine 2D material membranes, and scalable synthesis of such high-quality h-BN comparable to mechanically exfoliated crystals remains a significant challenge. Here, we report a scalable Fe-catalyzed chemical vapor deposition (CVD) process for bottom-up synthesis of large-area, high-quality monolayer h-BN films, overcoming key limitations of conventional ammonia-based routes. By leveraging mechanistic insights and higher CVD temperatures, we suppress multilayer formation and achieve uniform monolayer h-BN coverage on commercially available Fe foils. Machine learning enables systematic exploration of the complex, multi-dimensional CVD parameter space (growth time, temperature, precursor temperature, multilayer faction, coverage), providing data-driven approaches to visualize and identify process regimes facilitating predominantly monolayer h-BN growth with minimal secondary nuclei/ad-layers. The optimized Fe-catalyzed CVD h-BN membranes show high-quality as observed by proton/deuteron (H + /D + ) selectivity ≈8.45, approaching the highest quality benchmark of mechanically exfoliated h-BN (H + /D + selectivity ≈10) as well as significantly outperforming Cu-catalyzed CVD h-BN membranes (H + /D + selectivity ≈3.62, control selectivity ≈1.7). Our work provides a scalable cost-effective route for high-quality monolayer h-BN synthesis for sub-atomic scale separations (H + /D + ) and demonstrates the broader potential of machine learning-guided optimization of CVD for advancing synthesis of 2D materials.

36 MATERIALS SCIENCE↗

Uptake of Pb and the Formation of Mixed (Ba,Pb)SO 4 Monolayers on Barite During Cyclic Exposure to Lead-Containing Sulfuric Acid

Barite (BaSO 4 ) is a common additive in lead-acid batteries, where it acts as a nucleating agent to promote the reversible formation and dissolution of PbSO 4 during battery cycling. However, little is known about the molecular-scale mechanisms the nucleation and cyclic evolution of PbSO 4 over a battery’s lifetime. In this study, we explore the responses of a barite (001) surface to cycles of high and low lead concentrations in the presence of 100 mM sulfuric acid using in-situ atomic force microscopy and high-resolution X-ray reflectivity. Here we find that PbSO 4 epitaxial films readily nucleate on the barite surface, even from solutions that are undersaturated relative to bulk PbSO 4 . Despite this, barite (001) proves to be an ineffective nucleator of bulk PbSO 4 , as multilayer growth is suppressed even in highly supersaturated solutions. Instead, we find evidence that Pb 2+ ions can directly exchange with Ba 2+ to create mixed (Ba,Pb)SO 4 surfaces. These chemically mixed surfaces do not host PbSO4 monolayers as readily as pristine barite, and the original reactivity is not regained until a fresh surface is reestablished by aggressive etching. Our results can be partly explained by traditional models of Stranski-Krastanov (S-K) growth, in which monolayer films are stabilized by a reduction in surface energy, but multilayer growth is inhibited by epitaxial strain. Complementary density functional theory calculations confirmed the basic energetic-terms of traditional S-K models, but also showed evidence form more complex, thickness-dependent, energetics than would be predicted from the S-K models. The experimental results can be better understood by extending the S-K model to consider the formation of mixed surfaces and films, which can have reduced strain and interfacial energies relative to pure films, while also being stabilized by entropy of mixing. These insights into non-stoichiometric heteroepitaxy will enable better predictions of how barite affects PbSO 4 nucleation in battery environments.

25 ENERGY STORAGE↗

Engineering Self-Assembled Domain Asymmetry in Solvent Vapor Annealed Block Copolymer–Homopolymer Blend Films

Thin-film block copolymer (BCP) self-assembly is a powerful approach to generate highly uniform nanopatterns across large areas, yet the symmetries of these nanopatterns are constrained by the relative volume occupied by each polymer block. Here, we present a conceptually new approach to circumvent this limitation by combining homopolymer (HP) blending with solvent vapor annealing (SVA), demonstrated here for ternary blends of a near-symmetric BCP with athermal, low molar mass HPs. Screening of BCP–HP interactions by a weakly selective solvent promotes entropically driven delocalization of HP throughout both blocks and enables assembly of metastable lamellae for volume fractions as high as 0.78. Subsequent brief thermal annealing induces HPs to withdraw to their enthalpically favored domains, sharpening domain interfaces on a time scale much shorter than pattern coarsening. This renders lamellar nanopatterns with tunable widths that can be transferred to other materials with high fidelity. Furthermore, the persistence of the metastable asymmetric lamellae upon thermal annealing is sensitive to film confinement, as they are preserved in submonolayer films but transition to horizontal cylinders in films more than one monolayer thick. SVA using a strongly selective solvent results in assembled morphologies aligned closely with expectations based on the total polymer blend composition, underscoring the key role of BCP–HP interactions in dictating domain asymmetry. Overall, this work details important principles for using SVA to mediate BCP–HP interactions in thin films, thereby presenting opportunities to engineer pathways for the assembly of well-ordered nanopatterns with designer feature asymmetry for lithographic or nanotexturing applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Water film-driven Mn (oxy)(hydr)oxide nanocoating growth on rhodochrosite

Minerals exposed to moist air stabilize thin water films that drive a score of chemical reactions of great importance to water-unsaturated terrestrial environments. In this study, we identified Mn (oxy)(hydr)oxide nanocoatings formed by the dissolution, oxidation and precipitation of Mn in oxygenated water films grown on rhodochrosite (MnCO 3 ) microparticles. Nanocoatings that could be identified by vibrational spectroscopy, X-ray diffraction, X-ray photoelectron spectroscopy, and (scanning and transmission) electron microscopy formed in water films containing the equivalent of at least 7 monolayers (~84 H 2 O/nm 2 ). These films were formed by exposing microparticles to moist air with at least 50% relative humidity (RH). Films of neutral pH reacted up to 14% of the Mn II located in the topmost ~5 nm region of the microparticles in atmospheres of up to 90% RH for 7 d. These reactions produced MnOOH, birnessite (MnO 2 ) and hausmannite (Mn 3 O 4 ) nanoparticles of low crystallinity, while exposure to atmospheric air for 1 yr. converted only 2% of Mn II in this region to MnOOH. In contrast, reactions in alkaline water films converted up to ~75% of the Mn II but only after 16 d of reaction. These films produced MnOOH and MnO 2 of low crystallinity, as well as crystalline hausmannite. Kinetic modeling of the time-resolved growth of the Mnsingle bondO stretching vibrational bands of these nanocoatings revealed two concurrent reaction processes. A 1 rst -order process was assigned to nucleation events terminating only after a few hours, and a 0-order process was assigned to the sustained growth of nanocoatings from these nuclei over longer reaction time. By identifying nanocoatings formed by water film-driven reactions on rhodochrosite, our study adds new insight into mineralogical transformations relevant to anoxic–oxic boundaries in water-unsaturated environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗