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At least 667 records · Page 37

Modeling Equilibrium Solid–Liquid Interfaces under Effective Constant Chemical Potential Using Machine Learning Interatomic Potentials

The chemical potential (μ) of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot maintain constant chemical potential with reference to a targeted concentration or chemical potential under nonequilibrium or dynamic conditions, as solute species can migrate to the interface and deplete (or enrich) the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative quasi-constant chemical potential molecular dynamics (iqCμMD) simulation, which helps simulate targeted molar concentrations of species in solution. iqCμMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target bulk concentration (chemical potential), which allows simulation of the interface under the bulk conditions comparable to experiment. We demonstrate our approach using machine learning interatomic potential (MLIP)-based MD simulations of the Na 2 SO 4,aq –graphene interface, and to show the transferability of our approach, we also perform classical force field-based MD simulations of NaCl aq –air and NaCl aq –graphite interfaces, which produce comparable results to previous CμMD simulations. Our results also show that the iqCμMD approach efficiently achieves the desired bulk ion concentration within two iterations, and by utilizing MLIPs, we can achieve converged results using relatively small-scale simulations compared to previous CμMD simulations. By combining iqCμMD with MLIP-driven simulations, solid–liquid interfaces can be modeled under an effective constant chemical potential with DFT-level accuracy. Here, we show that iqCμMD offers a robust and simple computational framework for constant chemical potential simulations, as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Chemical structure↗

Manipulating Ferroelectrics through Changes in Surface and Interface Properties

Ferroelectric materials are used in many applications of modern technologies including information storage, transducers, sensors, tunable capacitors, and other novel device concepts. In many of these applications, the ferroelectric properties, such as switching voltages, piezoelectric constants, or stability of nanodomains, are crucial. For any application, even for material characterization, the material itself needs to be interfaced with electrodes. On the basis of the structural, chemical, and electronic properties of the interfaces, the measured material properties can be determined by the interface. This is also true for surfaces. However, the importance of interfaces and surfaces and their effect on experiments are often neglected, which results in many dramatically different experimental results for nominally identical samples. Therefore, it is crucial to understand the role of the interface and surface properties on internal bias fields and the domain switching process. Here, the nanoscale ferroelectric switching process and the stability of nanodomains for Pb(Zr,Ti)O 3 thin films are investigated by using scanning probe microscopy. Interface and surface properties are modulated through the selection/redesign of electrode materials as well as tuning the surface-near oxygen vacancies, which both can result in changes of the electric fields acting across the sample, and consequently this controls the measured ferroelectric and domain retention properties. By understanding the role of surfaces and interfaces, ferroelectric properties can be tuned to eliminate the problem of asymmetric domain stability by combining the effects of different electrode materials. Lastly, this study forms an important step toward integrating ferroelectric materials in electronic devices.

30 DIRECT ENERGY CONVERSION↗

Structure Prediction of Ionic Epitaxial Interfaces with Ogre Demonstrated for Colloidal Heterostructures of Lead Halide Perovskites

Colloidal epitaxial heterostructures are nanoparticles composed of two different materials connected at an interface, which can exhibit properties different from those of their individual components. Combining dissimilar materials offers exciting opportunities to create a wide variety of functional heterostructures. However, assessing structural compatibility–the main prerequisite for epitaxial growth–is challenging when pairing complex materials with different lattice parameters and crystal structures. This complicates both the selection of target heterostructures for synthesis and the assignment of interface models when new heterostructures are obtained. Here, we demonstrate Ogre as a powerful tool to accelerate the design and characterization of colloidal heterostructures. To this end, we implemented developments tailored for the high-efficiency prediction of epitaxial interfaces between ionic/polar materials, which encompass most colloidal semiconductors. These include the use of pre-screening candidate models based on charge balance at the interface and the use of a classical potential for fast energy evaluations, with parameters automatically calculated based on the input bulk structures. These developments are validated for perovskite-based CsPbBr 3 /Pb 4 S 3 Br 2 heterostructures, where Ogre produces interface models in excellent agreement with density functional theory and experiments. Furthermore, we use Ogre to rationalize the templating effect of CsPbCl 3 on the growth of lead sulfochlorides, where perovskite seeds induce the formation of Pb 4 S 3 Cl 2 rather than Pb 3 S 2 Cl 2 due to better epitaxial compatibility. Finally, combining Ogre simulations with experimental data enables us to unravel the structure and composition of the hitherto unsolved CsPbBr 3 /Bi x Pb y S z interface, and to assign a structure to several other reported metal halide- and oxide-based interfaces. The Ogre package is available on GitHub or via the OgreInterface desktop application, available for Windows, Linux, and Mac.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Atomically Resolved Electrically Active Intragrain Interfaces in Perovskite Semiconductors

Deciphering the atomic and electronic structures of interfaces is key to developing state-of-the-art perovskite semiconductors. However, conventional characterization techniques have limited previous studies mainly to grain-boundary interfaces, whereas the intragrain-interface microstructures and their electronic properties have been much less revealed. Herein using scanning transmission electron microscopy, we resolved the atomic-scale structural information on three prototypical intragrain interfaces, unraveling intriguing features clearly different from those from previous observations based on standalone films or nanomaterial samples. These intragrain interfaces include composition boundaries formed by heterogeneous ion distribution, stacking faults resulted from wrongly stacked crystal planes, and symmetrical twinning boundaries. The atomic-scale imaging of these intragrain interfaces enables us to build unequivocal models for the ab initio calculation of electronic properties. Our results suggest that these structure interfaces are generally electronically benign, whereas their dynamic interaction with point defects can still evoke detrimental effects. This work paves the way toward a more complete fundamental understanding of the microscopic structure-property-performance relationship in metal halide perovskites.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Emergent interface vibrational structure of oxide superlattices

As the length scales of materials decrease, the heterogeneities associated with interfaces become almost as important as the surrounding materials. This has led to extensive studies of emergent electronic and magnetic interface properties in superlattices. However, the interfacial vibrations that affect the phonon-mediated properties, such as thermal conductivity, are measured using macroscopic techniques that lack spatial resolution. Although it is accepted that intrinsic phonons change near boundaries, the physical mechanisms and length scales through which interfacial effects influence materials remain unclear. Here we demonstrate the localized vibrational response of interfaces in strontium titanate–calcium titanate superlattices by combining advanced scanning transmission electron microscopy imaging and spectroscopy, density functional theory calculations and ultrafast optical spectroscopy. Structurally diffuse interfaces that bridge the bounding materials are observed and this local structure creates phonon modes that determine the global response of the superlattice once the spacing of the interfaces approaches the phonon spatial extent. Our results provide direct visualization of the progression of the local atomic structure and interface vibrations as they come to determine the vibrational response of an entire superlattice. Direct observation of such local atomic and vibrational phenomena demonstrates that their spatial extent needs to be quantified to understand macroscopic behaviour. Tailoring interfaces, and knowing their local vibrational response, provides a means of pursuing designer solids with emergent infrared and thermal responses.

36 MATERIALS SCIENCE↗

The effect of ZnO surface conditions on the electronic structure of the ZnO/CuPc interface

The interfacial electronic structures of zinc oxide (ZnO)/copper-phthalocyanine (CuPc) were investigated by in situ x-ray and ultraviolet photoelectron spectroscopy (UPS) to determine the effects of air contamination on the ZnO substrate. UPS spectra showed that the 0.2 eV of the interface dipole is generated at the interface of the air exposed ZnO/CuPc while the interface of the annealed ZnO/CuPc generated -0.2 eV. In both cases, no band bending was observed. On the other hand, band bending at 0.3 eV and an interface dipole of 0.2 eV were observed at the interface of the sputter cleaned ZnO/CuPc. The energy offset between the conduction band maximum of ZnO and the highest occupied molecular orbital of CuPc was determined to be 0.6-0.7 eV for the contaminated ZnO interface while the offset was 1.0 eV for the cleaned ZnO interface. Contaminating moisture has little effect on the offset while the charge transfer was blocked and the offset was decreased in the presence of hydrocarbons.

36 MATERIALS SCIENCE↗

Ge interface engineering using ultra-thin La{sub 2}O{sub 3} and Y{sub 2}O{sub 3} films: A study into the effect of deposition temperature

A study into the optimal deposition temperature for ultra-thin La{sub 2}O{sub 3}/Ge and Y{sub 2}O{sub 3}/Ge gate stacks has been conducted in this paper with the aim to tailor the interfacial layer for effective passivation of the Ge interface. A detailed comparison between the two lanthanide oxides (La{sub 2}O{sub 3} and Y{sub 2}O{sub 3}) in terms of band line-up, interfacial features, and reactivity to Ge using medium energy ion scattering, vacuum ultra-violet variable angle spectroscopic ellipsometry (VUV-VASE), X-ray photoelectron spectroscopy, and X-ray diffraction is shown. La{sub 2}O{sub 3} has been found to be more reactive to Ge than Y{sub 2}O{sub 3}, forming LaGeO{sub x} and a Ge sub-oxide at the interface for all deposition temperature studied, in the range from 44 °C to 400 °C. In contrast, Y{sub 2}O{sub 3}/Ge deposited at 400 °C allows for an ultra-thin GeO{sub 2} layer at the interface, which can be eliminated during annealing at temperatures higher than 525 °C leaving a pristine YGeO{sub x}/Ge interface. The Y{sub 2}O{sub 3}/Ge gate stack deposited at lower temperature shows a sub-band gap absorption feature fitted to an Urbach tail of energy 1.1 eV. The latter correlates to a sub-stoichiometric germanium oxide layer at the interface. The optical band gap for the Y{sub 2}O{sub 3}/Ge stacks has been estimated to be 5.7 ± 0.1 eV from Tauc-Lorentz modelling of VUV-VASE experimental data. For the optimal deposition temperature (400 °C), the Y{sub 2}O{sub 3}/Ge stack exhibits a higher conduction band offset (>2.3 eV) than the La{sub 2}O{sub 3}/Ge (∼2 eV), has a larger band gap (by about 0.3 eV), a germanium sub-oxide free interface, and leakage current (∼10{sup −7} A/cm{sup 2} at 1 V) five orders of magnitude lower than the respective La{sub 2}O{sub 3}/Ge stack. Our study strongly points to the superiority of the Y{sub 2}O{sub 3}/Ge system for germanium interface engineering to achieve high performance Ge Complementary Metal Oxide Semiconductor technology.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Theoretical vibrational sum-frequency generation spectroscopy of water near lipid and surfactant monolayer interfaces

Understanding the structure of water near cell membranes is crucial for characterizing water-mediated events such as molecular transport. To obtain structural information of water near a membrane, it is useful to have a surface-selective technique that can probe only interfacial water molecules. One such technique is vibrational sum-frequency generation (VSFG) spectroscopy. As model systems for studying membrane headgroup/water interactions, in this paper we consider lipid and surfactant monolayers on water. We adopt a theoretical approach combining molecular dynamics simulations and phase-sensitive VSFG to investigate water structure near these interfaces. Our simulated spectra are in qualitative agreement with experiments and reveal orientational ordering of interfacial water molecules near cationic, anionic, and zwitterionic interfaces. OH bonds of water molecules point toward an anionic interface leading to a positive VSFG peak, whereas the water hydrogen atoms point away from a cationic interface leading to a negative VSFG peak. Coexistence of these two interfacial water species is observed near interfaces between water and mixtures of cationic and anionic lipids, as indicated by the presence of both negative and positive peaks in their VSFG spectra. In the case of a zwitterionic interface, OH orientation is toward the interface on the average, resulting in a positive VSFG peak.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inherent interface defects in thermal (211)Si/SiO{sub 2}:{sup 29}Si hyperfine interaction

Low temperature electron spin resonance (ESR) studies were carried out on ‘higher index’ (211)Si/SiO{sub 2} interfaces thermally grown in the temperature range T{sub ox} = 400–1066°C. The data reveal the presence of two species of a P{sub b}-type interface defect, exhibiting a significant difference in defect density. On the basis of the pertinent ESR parameters and interface symmetry, the basic defect is typified as P{sub b0}{sup (211)}, close to the Pb0 center observed in standard (100)Si/SiO{sub 2}. The dominant type is found to pertain to defected Si atoms at (111)Si-face terraces with the dangling bond along the [111] direction at ∼19.5°C with the interface normal, these sites thus apparently predominantly accounting for interface mismatch adaptation. The total of the P{sub b}-type defect appearance clearly reflects the higher-index nature of the interface. It is found that T{sub ox} = 750°C is required to minimize the P{sub b0}{sup (211)} defect density through relaxation of the oxide (interface). Q-band ESR saturation spectroscopy reveals an anisotropic {sup 29}Si (nuclear spin I=1/2) hyperfine (hf) doublet associated with the central P{sub b0}{sup (211)} Zeeman signal, with hf parameters closest to those of the similar hf structure of the P{sub b0}{sup (110)} defect in thermal (110)Si/SiO{sub 2}, adducing independent support to the P{sub b0}{sup (211)} typification.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

TaN interface properties and electric field cycling effects on ferroelectric Si-doped HfO{sub 2} thin films

Ferroelectric HfO{sub 2}-based thin films, which can exhibit ferroelectric properties down to sub-10 nm thicknesses, are a promising candidate for emerging high density memory technologies. As the ferroelectric thickness continues to shrink, the electrode-ferroelectric interface properties play an increasingly important role. We investigate the TaN interface properties on 10 nm thick Si-doped HfO{sub 2} thin films fabricated in a TaN metal-ferroelectric-metal stack which exhibit highly asymmetric ferroelectric characteristics. To understand the asymmetric behavior of the ferroelectric characteristics of the Si-doped HfO{sub 2} thin films, the chemical interface properties of sputtered TaN bottom and top electrodes are probed with x-ray photoelectron spectroscopy. Ta-O bonds at the bottom electrode interface and a significant presence of Hf-N bonds at both electrode interfaces are identified. It is shown that the chemical heterogeneity of the bottom and top electrode interfaces gives rise to an internal electric field, which causes the as-grown ferroelectric domains to preferentially polarize to screen positively charged oxygen vacancies aggregated at the oxidized bottom electrode interface. Electric field cycling is shown to reduce the internal electric field with a concomitant increase in remanent polarization and decrease in relative permittivity. Through an analysis of pulsed transient switching currents, back-switching is observed in Si-doped HfO{sub 2} thin films with pinched hysteresis loops and is shown to be influenced by the internal electric field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Influence of interface potential on the effective mass in Ge nanostructures

The role of the interface potential on the effective mass of charge carriers is elucidated in this work. We develop a new theoretical formalism using a spatially dependent effective mass that is related to the magnitude of the interface potential. Using this formalism, we studied Ge quantum dots (QDs) formed by plasma enhanced chemical vapour deposition (PECVD) and co-sputtering (sputter). These samples allowed us to isolate important consequences arising from differences in the interface potential. We found that for a higher interface potential, as in the case of PECVD QDs, there is a larger reduction in the effective mass, which increases the confinement energy with respect to the sputter sample. We further understood the action of O interface states by comparing our results with Ge QDs grown by molecular beam epitaxy. It is found that the O states can suppress the influence of the interface potential. From our theoretical formalism, we determine the length scale over which the interface potential influences the effective mass.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

2D heterodyne-detected sum frequency generation study on the ultrafast vibrational dynamics of H{sub 2}O and HOD water at charged interfaces

Two-dimensional heterodyne-detected vibrational sum-frequency generation (2D HD-VSFG) spectroscopy is applied to study the ultrafast vibrational dynamics of water at positively charged aqueous interfaces, and 2D HD-VSFG spectra of cetyltrimethylammonium bromide (CTAB)/water interfaces in the whole hydrogen-bonded OH stretch region (3000 cm{sup −1} ≤ ω{sub pump} ≤ 3600 cm{sup −1}) are measured. 2D HD-VSFG spectrum of the CTAB/isotopically diluted water (HOD-D{sub 2}O) interface exhibits a diagonally elongated bleaching lobe immediately after excitation, which becomes round with a time constant of ∼0.3 ps due to spectral diffusion. In contrast, 2D HD-VSFG spectrum of the CTAB/H{sub 2}O interface at 0.0 ps clearly shows two diagonal peaks and their cross peaks in the bleaching region, corresponding to the double peaks observed at 3230 cm{sup −1} and 3420 cm{sup −1} in the steady-state HD-VSFG spectrum. Horizontal slices of the 2D spectrum show that the relative intensity of the two peaks of the bleaching at the CTAB/H{sub 2}O interface gradually change with the change of the pump frequency. We simulate the pump-frequency dependence of the bleaching feature using a model that takes account of the Fermi resonance and inhomogeneity of the OH stretch vibration, and the simulated spectra reproduce the essential features of the 2D HD-VSFG spectra of the CTAB/H{sub 2}O interface. The present study demonstrates that heterodyne detection of the time-resolved VSFG is critically important for studying the ultrafast dynamics of water interfaces and for unveiling the underlying mechanism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Observation of interface dependent spin polarized photocurrents in InAs/GaSb superlattice

In this letter, we investigated the spin polarized photocurrents excited by mid-infrared radiation and near-infrared radiation, respectively, in InAs/GaSb type II superlattices with different kinds of interfaces. By periodically varying the polarization state of the radiation, we analyzed Rashba-type and Dresselhaus-type spin polarized photocurrents, which present different features depending on the interface types and excitation conditions. Under mid-infrared excitation, the ratio of Rashba-type and Dresselhaus-type spin polarized photocurrents of the superlattice with InSb-like interface is obviously larger than that of the superlattice with GaAs-like interface, the ratio of the superlattice with alternate interface is in the middle. Whereas under near-infrared excitation, the ratios of the three superlattices are nearly the same. Further researches reveal the synactic effects of interface dependent strain and asymmetric interface potential on the spin splitting. Besides, the polarized Raman spectroscopies of these structures were also analyzed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Vortex-sheet modeling of hydrodynamic instabilities produced by an oblique shock interacting with a perturbed interface in the HED regime

In this work, we consider hydrodynamic instabilities produced by the interaction of an oblique shock with a perturbed material interface under high-energy-density (HED) conditions. During this interaction, a baroclinic torque is generated along the interface due to the misalignment between the density and pressure gradients, thus leading to perturbation growth. Our objective is to understand the competition between the impulsive acceleration due to the normal component of the shock velocity, which drives the Richtmyer–Meshkov instability, and the shear flow across the interface due to the tangential component of the shock velocity, which drives the Kelvin–Helmholtz instability, as well as its relation to perturbation growth. Since the vorticity resulting from the shock-interface interaction is confined to the interface, we describe the perturbation growth using a two-dimensional vortex-sheet model. We demonstrate the ability of the vortex-sheet model to reproduce roll-up dynamics for non-zero Atwood numbers by comparing to past laser-driven HED experiments. We determine the dependence of the interface dynamics on the tilt angle and propose a time scaling for the perturbation growth at early time. Eventually, this scaling will serve as a platform for the design of future experiments. This study is the first attempt to incorporate into a vortex-sheet model the time-dependent interface decompression and the deceleration (as well as the corresponding Rayleigh–Taylor instability) arising from laser turn-off.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Atomically thin interlayer phase from first principles enables defect-free incommensurate SnO2/CdTe interface

Advancing optoelectronic and emerging technologies increasingly requires control and design of interfaces between dissimilar materials. However, incommensurate interfaces are notoriously defective and rarely benefit from first-principles predictions, because no explicit atomic-structure models exist. Here, we adopt a bulk crystal structure prediction method to the interface geometry and apply it to SnO2/CdTe heterojunctions without and with the addition of CdCl2, a ubiquitous and beneficial, but abstruse processing step in CdTe photovoltaics. Whereas the direct SnO2/CdTe interface is highly defective, we discover a unique two-dimensional CdCl2 interphase, unrelated to the respective bulk structure. It facilitates a seamless transition from the rutile to zincblende lattices and removes defect-states from the interface bandgap. Implementing the predicted interface electronic structure in device simulations, we demonstrate the theoretical feasibility of bufferless oxide-CdTe heterojunction solar cells approaching the Shockley–Queisser limit. Our results highlight the broader potential of designing atomically thin interlayers to enable defect-free incommensurate interfaces.

14 SOLAR ENERGY↗

Modeling the aqueous interface of amorphous TiO 2 using deep potential molecular dynamics

Amorphous titanium dioxide (a-TiO 2 ) is widely used as a coating material in applications such as electrochemistry and self-cleaning surfaces where its interface with water has a central role. However, little is known about the structures of the a-TiO 2 surface and aqueous interface, particularly at the microscopic level. In this work, we construct a model of the a-TiO 2 surface via a cut-melt-and-quench procedure based on molecular dynamics simulations with deep neural network potentials (DPs) trained on density functional theory data. After interfacing the a-TiO 2 surface with water, we investigate the structure and dynamics of the resulting system using a combination of DP-based molecular dynamics (DPMD) and ab initio molecular dynamics (AIMD) simulations. Both AIMD and DPMD simulations reveal that the distribution of water on the a-TiO 2 surface lacks distinct layers normally found at the aqueous interface of crystalline TiO 2 , leading to an ~10 times faster diffusion of water at the interface. Bridging hydroxyls (Ti 2 –O b H) resulting from water dissociation decay several times more slowly than terminal hydroxyls (Ti–O w H) due to fast Ti–O w H 2 → Ti–O w H proton exchange events. These results provide a basis for a detailed understanding of the properties of a-TiO 2 in electrochemical environments. Moreover, the procedure of generating the a-TiO 2 -interface employed here is generally applicable to studying the aqueous interfaces of amorphous metal oxides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Validating first-principles molecular dynamics calculations of oxide/water interfaces with x-ray reflectivity data

Metal oxide/water interfaces play a crucial role in many electrochemical and photocatalytic processes, such as photoelectrochemical water splitting, the creation of fuel from sunlight, and electrochemical CO 2 reduction. First-principles electronic structure calculations can reveal unique insights into these processes, such as the role of the alignment of the oxide electronic energy levels with those of liquid water. An essential prerequisite for the success of such calculations is the ability to predict accurate structural models of these interfaces, which in turn requires careful experimental validation. Here we report a general, quantitative validation protocol for first-principles molecular dynamics simulations of oxide/aqueous interfaces. The approach makes direct comparisons of interfacial x-ray reflectivity (XR) signals from experimental measurements and those obtained from ab initio simulations with semilocal and van der Waals functionals. The protocol is demonstrated here for the case of the Al 2 O 3 (001)/water interface, one of the simplest oxide/water interfaces. We discuss the technical requirements needed for validation, including the choice of the density functional, the simulation cell size, and the optimal choice of the thermodynamic ensemble. Our results establish a general paradigm for the validation of structural models and interactions at solid/water interfaces derived from first-principles simulations. Furthermore, while there is qualitative agreement between the simulated structures and the experimental best-fit structure, direct comparisons of simulated and measured XR intensities show quantitative discrepancies that derive from both bulk regions (i.e., alumina and water) as well as the interfacial region, highlighting the need for accurate density functionals to properly describe interfacial interactions. Our results show that XR data are sensitive not only to the atomic structure (i.e., the atom locations) but also to the electron-density distributions in both the substrate and at the interface.

36 MATERIALS SCIENCE↗

A refraction correction for buried interfaces applied to in situ grazing-incidence X-ray diffraction studies on Pd electrodes

In situ characterization of electrochemical systems can provide deep insights into the structure of electrodes under applied potential. Grazing-incidence X-ray diffraction (GIXRD) is a particularly valuable tool owing to its ability to characterize the near-surface structure of electrodes through a layer of electrolyte, which is of paramount importance in surface-mediated processes such as catalysis and adsorption. Corrections for the refraction that occurs as an X-ray passes through an interface have been derived for a vacuum–material interface. In this work, a more general form of the refraction correction was developed which can be applied to buried interfaces, including liquid–solid interfaces. Furthermore, the correction is largest at incidence angles near the critical angle for the interface and decreases at angles larger and smaller than the critical angle. Effective optical constants are also introduced which can be used to calculate the critical angle for total external reflection at the interface. This correction is applied to GIXRD measurements of an aqueous electrolyte–Pd interface, demonstrating that the correction allows for the comparison of GIXRD measurements at multiple incidence angles. This work improves quantitative analysis of d-spacing values from GIXRD measurements of liquid–solid systems, facilitating the connection between electrochemical behavior and structure under in situ conditions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗