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Essential barrier height and a probabilistic approach in characterizing potential landscape

In this work we propose a probabilistic approach to investigate the shape of landscapes of multi-dimensional potential functions. Under a suitable coupling scheme, two copies of the overdamped Langevin dynamics associated with the potential function are coupled, and the coupling times are collected. Assuming a set of intuitive yet technically challenging conditions on the coupling scheme, it is shown that the tail distributions of the coupling times exhibit qualitatively different dependencies on the noise magnitude for single-well versus multi-well potential functions. More specifically, for convex single-well potentials, the negative tail exponent of the coupling time distribution is uniformly bounded away from zero by the convexity parameter and is independent of the noise magnitude. In contrast, for multi-well potentials, the negative tail exponent decreases exponentially as the noise vanishes, with the decay rate governed by the essential barrier height, a quantity introduced in this paper to characterize the non-convex nature of the potential function. Numerical investigations are conducted for a variety of examples, including the Rosenbrock function, interacting particle systems, and loss functions arising in artificial neural networks. These examples not only illustrate the theoretical results in various contexts but also provide crucial numerical validation of the conjectured assumptions, which are essential to the theoretical analysis yet lie beyond the reach of standard technical tools.

97 MATHEMATICS AND COMPUTING↗

How Does HF-DFT Achieve Chemical Accuracy for Water Clusters?

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy , we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r 2 SCAN 50, a 50% global hybrid of exact exchange with r 2 SCAN, which may be less correct than r 2 SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r 2 SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense and become large in an absolute sense only due to an increase in cluster size. SCAN@HF, short for SCAN evaluated on the Hartree–Fock (HF) density, produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r 2 SCAN@HF, as in the composite method HF-r 2 SCAN-DC4, makes its FE more negative than in r 2 SCAN@HF, permitting a near-perfect cancellation of FE and DE. r 2 SCAN by itself (and even more so, r 2 SCAN evaluated on the r 2 SCAN 50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus, the accuracy of composite methods like SCAN@HF and HF-r 2 SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Lastly, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn–Sham inversion of the CCSD(T) density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

From Well Log to Formation Model: A Novel Laboratory Calibrated Methodology with Demonstration

This work demonstrates how the characterization and modeling of both elastic and creep properties are essential to describe zones in layered rock formations as either low-stress targets for stimulation or high-stress barriers to fracture growth. Prediction of fracture height is critical for designing stimulation operations in oil and gas wells. Ideally, fractures are placed in target zones which will produce hydrocarbons and should not propagate into zones expected to be unproductive or to produce unwanted fluids such as water which in turn must be treated and/or disposed. The essential task in designing stimulation plans is predicting which zones have low horizontal stresses and which will be high-stress barriers to fracture growth. Despite this importance, there are gaps in current knowledge and a complete workflow from laboratory characterization to a finite element model which includes time dependent rock deformation is required. While the research and methodology presented here also have application to CO 2or hydrogen storage, wastewater injection, and geothermal applications, the focus will be on hydrocarbon extraction. This thesis presents the results of a characterization-to-prediction workflow for the Caney shale, which is an emerging hydrocarbon resource in Oklahoma, USA. It begins with an investigation to enable critical evaluation of the Caney zonation into nominally “brittle” and “ductile” zones based on properties observed from well logs. It shows none of the zones are consistently “brittle” or “ductile” mechanical behavior based on the variety of definitions of these terms. However, the nominally ductile zones are weaker and more prone to creep. A laboratory investigation of samples including strength, elastic, and creep properties, is then used in a finite element model of stress evolution. The model includes both elastic deformation and viscoplastic creep. Results predict the least creep-prone layers to have the lowest horizontal stresses, therefore comprising hydraulic fracturing targets. The most creep-prone layers attain a horizontal stress similar to the vertical stress and therefore are predicted to be high stress barriers to hydraulic fracture stimulation. In addition to defining stimulation target intervals, the model shows how as tectonic strain rate increases, there is a transition from creep-dominated stresses to stresses dominated by elasticity.

Benge, Margaret↗

Model for the Solid–Liquid Interfacial Free Energy at High Pressures

The free energy involved in the formation of an interface between two phases (e.g., a solid–liquid interface) is referred to as the interfacial free energy. For the case of solidification, the interfacial free energy dictates the height of the energy barrier required to nucleate stable clusters of the newly forming solid phase and is essential for producing an accurate solidification kinetics model using classical nucleation theory (CNT)-based methods. While various methods have been proposed for modeling the interfacial free energy for solid–liquid interfaces in prior literature, many of these formulations involve making restrictive assumptions or approximations, such as the system being at or near equilibrium (i.e., the system temperature is approximately equal to the melt temperature) or that the system is at pressures close to atmospheric. However, these approximations and assumptions may break down in highly non-equilibrium situations, such as in dynamic-compression experiments where metastable liquids that are undercooled by hundreds of kelvin or over-pressurized by several gigapascals or more are formed before eventually solidifying. We derive a solid–liquid interfacial free-energy model for such high-pressure conditions by considering the enthalpies of interactions between pairs of atoms or molecules. We also consider the contribution of interface roughness (disordering) by incorporating a multilayer interface model known as the Temkin n-layer model. Our formulation is applicable to a diverse variety of materials, and we demonstrate it by developing models specifically for two different materials: water and gallium. We apply our interfacial free-energy formulation to CNT-based kinetics simulations of several suites of dynamic-compression experiments that cause liquid water to solidify to the high-pressure solid polymorph ice VII and have found good agreement to the observed kinetics with only minor empirical fitting.

36 MATERIALS SCIENCE↗

Full CI studies of the collinear transition state for the reaction F + H2 yields HF + H

Full CI calculations on the collinear transition state for the reaction F + H2 yields HF + H are reported. The full CI results are compared with those obtained from single-reference and multireference CI calculations and from single-reference CPF calculations. In general, only those methods which attempt to account for the effects of higher excitations, such as CPF or CI plus the Davidson correction, yield a transition-state location and barrier height in good agreement with the full CI. In an extended basis, the effect of higher excitations is estimated to lower the barrier by as much as 1.5 kcal/mol; such an effect would essentially eliminate the present discrepancy between theory and experiment.

Bauschlicher, Charles W., Jr.↗

Energy distribution among reaction products. V.

Discussion of three reactions, one point of theoretical interest being the predicted correlation between barrier height and barrier location. The H + Br 2 reaction having a lower activation barrier than H + Cl 2, should have an earlier barrier, and hence a greater percentage attractive energy release and higher efficiency of vibrational excitation. Information is developed concerning the effect of isotopic substitution in the pair of reactions H + Cl 2 and D + Cl 2. The 'arrested relaxation' method was used. Essentially, the method involves reacting two diffuse reagent beams in a reaction vessel with background pressure less than 0.001 torr, and with walls cooled by liquid nitrogen or liquid helium.

Anlauf, K. G.↗

Internal Photoemission Spectroscopy Measurements of Interfacial Energy Barriers in Operating TaN/Hf 0.5 Zr 0.5 O 2 /TaN Metal/Ferroelectric/Metal (MFM) Devices

The effect of the "waking" and subsequent "poling" operations on the electron barriers at both top and bottom electrode interfaces in operating ferroelectric hafnium zirconium oxide (Hf 0.5 Zr 0.5 O 2 , HZO) metal/ferroelectric/metal (MFM) devices are measured for the first time via internal photoemission (IPE) spectroscopy. Top and bottom (TaN/HZO and HZO/TaN) barriers for pristine devices were measured at 2.6 eV and 2.9 eV, respectively. The waking operation (10 kHz bipolar voltage cycling above the coercive field) increased the top barrier to 2.8 eV while leaving the bottom barrier essentially unchanged. Poling operations (application of a longer 10 msec unipolar pulse) were found to significantly decrease both top and bottom barriers. Here, the poling direction (polarity) had relatively little impact. The barrier for the top interface under positive (P↓) and negative poling (P↑) was 2.1 and 2.2 eV, respectively, while the bottom barrier was 2.3 eV for P↓ and 2.4 eV for P↑. All barrier heights remained unchanged after several months at room temperature. Potential physical mechanisms responsible for the changes observed under electrical operation are consistent with movement and/or creation of charged oxygen vacancy defects.

36 MATERIALS SCIENCE↗

Acoustic Barrier Facilitates Inlet Noise Measurements for Aft-Dominated Fans

Noise levels for modern high-bypass-ratio subsonic turbofans tend to be aft dominated. That is, the highest flyover noise levels radiate from the fan exit. Measuring fan inlet sound radiation without aft radiation contamination requires selective suppression of the aft noise. In NASA Lewis Research Center's 9- by 15-Foot Low-Speed Wind Tunnel, an acoustic barrier was used to effectively isolate the inlet noise field for a model of an advanced turbofan. This proof-of-concept test was performed on a model turbofan manufactured for NASA Lewis by the Allison Engine Company as part of the Advanced Subsonic Technology program. The 8-cm-thick acoustic barrier was constructed in sections that were joined upon installation. These sections, which were composed of a wood frame with typically 0.64-cm tempered fiberboard skins, extended from the tunnel's floor to its ceiling and had an axial length of 61 cm. On the fan side of the barrier just downstream of the leading edge, the upstream section had an acoustic treatment--a bulk absorber with a perforated metal skin. It had a nominal full height and an axial length of 46 cm. In addition, an elliptical leading edge was faired into the upstream barrier section. The barrier was mounted on tracks on the tunnel floor and ceiling at a sideline distance of 15 cm from the fan nacelle. Tests were made with the barrier leading edge at the fan inlet highlight plane and 15 cm further aft. The barrier extended downstream essentially to the end of the treated tunnel test section.

Source record↗

Analytic model of electron transport through and over non-linear barriers

Tunneling barriers are an essential component of electron sources, sensors, detectors, and vacuum nanoelectronics, and a pivotal factor in their performance, but the barriers themselves routinely depart from the analytic models used to model their behavior. Here, a new formalism is developed to analytically and accurately model emission through and over barriers associated with depletion layers, nanotip barriers, and MIM structures. The transmission probability for depletion layer and metal-insulator-metal (MIM) and metaloxide-semiconductor (MOS) barriers is accurately modeled as the electron energy exceeds the barrier height using approaches designed for rapid implementation demanded by simulation codes, and extensible to general barriers. The models supersede conventional thermal and field models in depletion and MIM/MOS barrier studies. Thermal-field methods are used to treat the transmission probability, and shape factor methods to treat the tunneling factor. Analytic formulae for current density are obtained. The methods ease device simulation and characterization of current-voltage relations for emerging technologically interesting barriers with better accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Tunneling Barrier-Integrated Gold Nanofilms for Negative Strain Gauging with Near-Zero Energy Consumption

Wireless strain sensors with minimal power needs are essential for long-term monitoring in energy-limited environments. We present a soft tunneling barrier-integrated gold thin film for negative strain sensing with near-zero energy consumption. The device features a strain-induced transition from an insulating to a metallic state, increasing conductivity by 9 orders of magnitude under a controlled strain. It consists of Au-PDMS-Au nanofilm layers, where the Au structures are near the percolation threshold and the PDMS layer acts as a tunneling barrier. Under strain, thinning due to the Poisson effect lowers the barrier’s potential height, enabling electron tunneling and forming an electrical path. Further, with a standby power consumption of ~10 –5 mW over 10 6 times lower than conventional sensors (~12.5 mW), this device is ideal for real-time, long-term stationary structural monitoring in multiple locations.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Performance of Heterostructural TaC/AlGaN Schottky Diodes Based on First Principles Electronic Structure Properties

Advances in ultra-wide bandgap materials, such as high Al-content AlxGa1-xN (AlGaN), are essential for next generation power electronics, but the requirement for lattice matched substrates is currently a significant obstacle. Recently, conductive TaC has emerged as a promising virtual substrate for AlGaN heteroepitaxy, with wurtzite (0001) AlxGa1-xN lattice-matched to rocksalt (111) TaC at x ~ 0.5. Thus, understanding and controlling the electronic properties of the TaC/AlGaN interface is key for developing technological applications based on TaC/AlGaN devices. Using density functional theory and electronic structure calculations, we here investigate TaC/Al0.5Ga0.5N interfaces, where we include explicit alloy models in the slab calculations. We predict the Schottky barrier height and the electric field discontinuity resulting from interface charges. Considering all possible combinations of (Ta, C) substrate termination, (Al/Ga, N) nucleation, and (Al/Ga, N) polarity, we construct a chemical potential phase diagram to identify the stable interfaces that can be accessed through variation of the synthesis conditions. The predicted interface electronic properties are implemented in device performance simulations to demonstrate a practical design for a strain-free, high-efficiency TaC/AlGaN Schottky diode with a low barrier height and without interface charges, underscoring the potential of TaC as a substrate for ultra-wide bandgap devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗