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At least 91 records · Page 5

5-2428: Coupled Investigation of Fracture Permeability Impact on Reservoir Stress and Seismic Slip Behavior [Slides]

Our goal is to develop, apply and validate a holistic thermal, hydrologic, mechanical, and chemical (THMC) workflow that also includes evaluation of induced seismic slip in EGS reservoirs. We will integrate experimental and modelling approaches to reduce parameter uncertainty and better integrate friction constitutive laws for faults to improve our ability to predict and mitigate seismic hazard at Utah FORGE and future EGS sites. We propose a novel approach that incorporates 3D physics-based Earthquake simulations in THMC models, using lab measurements of friction parameters, herein referred to as “THMC+E” models. These simulations will enable exploration of various circumstances that may hinder EGS success and develop mitigation strategies.

58 GEOSCIENCES↗

Interim results from the characterization testing of the Engineering Development (EDM) rubidium clocks for satellite applications

Some interim results from the environmental testing program to evaluate the Engineering Design Model (EDM) of the EG and G Spaceborne Rubidium Clock are presented. This effort is in support of the Global Positioning System (GPS) BLOCK IIR program and is intended to characterize the performance of EG and G design for BLOCK IIR satellite applications. Two EG and G EDM units are currently under test at NRL's Clock Test Facility to measure the long-term frequency stability, drift, and frequency versus temperature characteristics.

Powers, Edward D., Jr.↗

ROSAT guest investigator program (AO-1). On a search for coronal x ray emissions from white dwarfs

We have suggested that cool magnetic white dwarfs may be sources of X-ray coronal emission and proposed several prominent candidates for this emission. One of these candidates (EG 250) was approved for the C-category observation by the National and International Committee and was observed by ROSAT on April 17, 1991. Unfortunately, the granted exposure time (1071 s) was much shorter than that which was required by theoretical predictions to observe coronal X-ray emission from this object. The tape containing the data was send to us in November 1991. Since then we have analyzed the data visiting the ROSAT Science Center at NASA Goddard Space Flight Center. The analysis of the data taken during this short observation show, as expected, no X-rays. It is our hope that EG 250 will be observed again during the AO-2 phase of pointed observations, as 10,000 s of observing time was granted to V. Trimble for the C-category observation of this star. We have a close contact with Dr. Trimble regarding this matter. Because our all targets (GD 90, KUV 2316-123 and GD 356) proposed for the observation during the AO-2 phase of pointed observations have been approved by the National and International Committee, we have installed the required software at NASA/MSFC to be able to carry out the data analysis in Huntsville. Two of our targets have already been observed (KUV 2316-123 was observed on Dec. 3, 1991 with 10,000 s of the exposure time, and GD 356 was observed on Jan 4, 1992 with 5,000 s of the exposure time). We just received the data and will begin the analysis soon. The results of our analysis will be reported to the scientific community by publishing papers in the Astrophysical Journal Letters. Our intention is to submit a paper when the analysis of the data taken during AO2 is completed. The data taken during the observation of EG 250 will be a part of this paper.

Musielak, Z. E.↗

A comparison of small and larger mesoscale latent heat and radiative fluxes: December 6 case study

Because of the small amounts of water vapor, the potential for rapid changes, and the very cold temperatures in the upper troposphere, moisture measuring instruments face several problems related to calibration and response. Calculations of eddy moisture fluxes are, therefore, subject to significant uncertainty. The purpose of this study is to examine the importance of latent heat (moisture) fluxes due to small and larger mesoscale circulations in comparison to radiative fluxes within cirrus. Scale separation is made at about 1 km because of significant changes in the structures within cirrus. Only observations at warmer than -40 C are used in this study. The EG&G hygrometer that is used for measuring dewpoint temperature (Td) is believed to be fairly accurate down to -40 C. On the other hand, Lyman-Alpha (L-alpha) hygrometer measurements of moisture may include large drift errors. In order to compensate for these drift errors, the L-alpha hygrometer is often calibrated against the EG&G hygrometer. However, large errors ensue for Td measurements at temperatures less than -40 C. The cryogenic hygrometer frost point measurements may be used to calibrate L-alpha measurements at temperatures less than -40 C. In this study, however, measurements obtained by EG&G hygrometer and L-alpha measurements are used for the flux calculations.

Gultepe, I.↗

Phototransistor (PT) in the 2 Micron Region

Within the framework of the project the University of Delaware has developed InGaAsSb-based heterojunction phototransistors (HPT) structure with a large (1000 micron diameter) photosensitive/photoactive area. Two different compositions of quaternary alloys were used to provide the cutoff wavelength (50% of maximum quantum efficiency) of 2.4 micron (Type 1) and 2.15 micron (Type 2). The Type 1 HPT was composed of Al0.25Ga0.75As0.02Sb0.98 and In0.18Ga0.82As0.17Sb0.83 layers with room-temperature bandgaps of Eg approximates 1.0 eV and Eg approximates 0.54 eV, respectively. The layers are lattice-matched to a GaSb substrate. The growth started with a 0.15micron-thick n+-GaSb buffer layer and was completed with a 0.1 m-thick n+- GaSb contact layer doped with Te. The HPT structure includes a 0.5 m-thick n-type AlGaAsSb emitter, 0.8 micron-thick p-type composite base consisting of AlGaAsSb (0.3 m) and InGaAsSb (0.5 m) layers, and a 1.5micron - thick n type InGaAsSb collector. The Type 2 HPT differed by a higher bandgap In0.16Ga0.84As 0.14Sb0.86 layers with a room-temperature bandgap of Eg approximates 0.555 eV.

Prather, Dennis↗

Comparative Study of Enhanced Geothermal System Supply Curves Across CONUS from Two Temperature Models Using the Renewable Energy Potential Model (reV)

Enhanced geothermal systems (EGS) have had recent breakthroughs within the geothermal sector. These breakthroughs are reflected in the National Renewable Energy Laboratory (NREL) 2024 Annual Technology Baseline and will result in updated EGS supply curves (i.e., the available resource capacity relative to cost). Our research uses NREL's Renewable Energy Potential (reV) model to compare EGS supply curves across the conterminous United States (CONUS) for two different temperature models: the Stanford temperature model (STM) and the Southern Methodist University temperature model (SMU). The reV model provides the levelized cost of energy (LCOE) at a consistent resolution across CONUS, taking into consideration transmission costs and constraints as well as technical exclusions pertaining to sensitive cultural, ecological, or infrastructure locations. In addition to a countrywide analysis of both models, we also conducted a regional analysis of Texas. We observed the STM had, on average, lower temperatures across different depths, resulting in slightly higher mean and median LCOEs as compared to the SMU temperature model at the same depths. In the regional analysis for Texas, however, when we compared only the common points between the two temperature models, the STM had lower median and mean LCOEs compared to SMU due to higher temperatures at depths greater than 5 km.

enhanced geothermal systems↗

Stochastic fracture generation and thermo-hydro-mechanical modeling in an equivalent continuum framework for enhanced geothermal systems

Enhanced geothermal systems (EGS) involve fracturing low permeability material to establish well connectivity and then injecting and circulating fluid into the fractured subsurface for geothermal power production. Changes in fracture aperture from contraction of the cooling matrix rock may alter network connectivity and risk thermal short-circuiting. Thermo-hydro-mechanical (THM) models are a useful tool to study these processes. However, as fracture networks are complex, and data may be limited, fracture networks in THM models are often stochastically generated. Given reliance on stochastic fracture networks and THM modeling to represent the subsurface and assess productivity of EGS, increased understanding of the influence of such statistically derived fracture networks on flow and heat transport in THM models is needed. Here, a new fracture process model is developed in the reactive transport code PFLOTRAN to stochastically generate fracture families and simulate changes in fracture aperture over time due to temperature changes of the rock matrix. Sixty-four different fracture networks ranging from well to poorly-connected, are modeled in PFLOTRAN with and without mechanical processes (THM vs TH). Results indicate that for well-connected fracture networks, thermal short-circuiting is less of a concern due to the abundance of available alternative flowpaths. For poorly-connected fracture networks, inclusion of mechanical processes showed steep thermal drawdown coincident with increase in fracture aperture along developing colder flowpaths, demonstrating the risk of thermal short-circuiting. Simulations with additional, larger fractures engineered to establish connectivity in a poorly-fractured subsurface, indicate that while stochastic variation of fracture orientation of the background network had limited influence, such variation in the engineered fractures significantly affected flow and heat transport.

Discrete fracture networks (DFN)↗

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗

Design Principles in Engineering of Multigrain Nanocatalysts via Multiscale Electronic Structure Characterization

Engineering grain boundary (GB) strain provides a promising pathway to tune the catalytic properties of nanocrystals. However, structural heterogeneity from random grain orientation and geometry has limited clear structure–property correlations. Here, we utilize a multigrain Co3O4/Mn3O4 core/shell nanocrystal platform as a model system to systematically investigate how geometric misfit strain at GBs serves as catalytically active sites for the oxygen reduction reaction. Through precise subnanometer-level control over grain morphology and by integrating multiscale electronic structure characterization, we identify the electronic structural signature of GB defects and establish a direct correlation between localized strain fields and modified electronic states. Strain modulation at GBs alters the eg orbital energy levels, with elongation along the z-axis combined with shear strain stabilizing the eg states, in contrast to the destabilization observed under pure shear strain. This stabilization mechanism enhances the electrocatalytic activity and selectivity of strained GBs compared with strain-relaxed grain surfaces. Furthermore, we reveal that GBs exhibit a radial strain gradient, producing a spatial energy shift that further modulates local electronic structures, as resolved through the classification of electron energy loss spectroscopy data. Together, these findings demonstrate that geometric misfit strain enables precise tuning of grain geometry and the resulting electronic structures, offering a robust strategy for engineering next-generation nanocatalysts.

Cho, Min Gee↗

Machine Learning‐Assisted Microearthquake Location Workflow for Monitoring the Newberry Enhanced Geothermal System

Abstract Enhanced geothermal systems (EGS) offer a sustainable energy source but face challenges in accurately locating microearthquakes induced during reservoir stimulation. Locating these microearthquakes provides reliable feedback on the stimulation progress. Current deep learning methods for locating earthquakes require extensive data sets for training, which is problematic as detected microearthquakes are often limited. To address the scarcity of training data, we propose a practical workflow using probabilistic multilayer perceptron (PMLP) which predicts microearthquake locations from cross‐correlation time lags in waveforms. Utilizing a 3D velocity model of Newberry site derived from ambient noise interferometry, we generate numerous synthetic microearthquakes and 3D acoustic waveforms for PMLP training. Accurate synthetic tests prompt us to apply the trained network to the 2012 and 2014 stimulation field waveforms. To enhance the accuracy of source localization, we carefully handpick the P‐arrival times. Predictions on the 2012 stimulation data set show major microseismic activity at depths of 0.5–1.2 km, correlating with a known casing leakage scenario. In the 2014 data set, the majority of predictions concentrate at 2.0–2.9 km depths, consistent with results obtained from conventional physics‐based inversion, and align with the presence of natural fractures from 2.0 to 2.7 km. We validate our findings by comparing the synthetic and field picks, demonstrating a satisfactory match for the first arrivals. By combining the benefits of quick inference speeds and accurate location predictions, we demonstrate the feasibility of using realistic synthetic data set to locate microseismicity for EGS monitoring.

15 GEOTHERMAL ENERGY↗

Electronic structure, self-doping, and superconducting instability in the alternating single-layer trilayer stacking nickelates La 3 ⁢Ni 2 ⁢O 7

Motivated by the recently proposed alternating single-layer trilayer stacking structure for the nickelate La 3 ⁢Ni 2 ⁢O 7 , we comprehensively study this system using ab initio and random-phase approximation techniques. Here, our analysis unveils similarities between this novel La 3⁢ Ni 2 ⁢O 7 structure and other Ruddlesden-Popper nickelate superconductors, such as a similar charge-transfer gap value and orbital-selective behavior of the eg orbitals. Pressure primarily increases the bandwidths of the Ni e g bands, suggesting an enhancement of the itinerant properties of those e g states. By changing the cell volume ratio V/V 0 from 0.9 to 1.10, we found that the bilayer structure in La 3 ⁢Ni 2 ⁢O 7 always has lower energy than the single-layer trilayer stacking La 3 ⁢Ni 2 ⁢O 7 . In addition, we observe a “self-doping” effect (compared to the average 1.5 electrons per eg orbital per site of the entire structure) from the trilayer to the single-layer sublattices and this effect will be enhanced by overall electron doping. Moreover, we find a leading d x 2 -y 2 -wave pairing state that is restricted to the single layer. Because the effective coupling between the single layers is very weak, due to the nonsuperconducting trilayer in-between, this suggests that the superconducting transition temperature T c in this structure should be much lower than in the bilayer structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

FORGE STRESS annual report

The project's goal is to combine high-fidelity numerical models and true-triaxial block fracturing tests at high temperatures to understand the relationship between in situ stress, thermal effects, wellbore orientations and hydraulic fracture patterns. The numerical models are calibrated against field data, such as well pressures and microseismic data, and employed to estimate the in situ stress at the FORGE site. Laboratory experiments investigate the complex physics driving hydraulic fracture nucleation in EGS, enhancing understanding of the role of parameters like temperature, well orientation, and stress. Additionally, they are employed to validate some of the numerical tools used in the project. The project will have a significant impact by: (1) improving the characterization of the in-situ stress field at FORGE; (2) demonstrating the use of high-fidelity modeling tools for EGS; (3) providing a unique set of high-temperature hydraulic fracturing results to identify key components for in-situ stress estimation, validate current theories, and propose new ones; (4) offering a validated set of numerical tools within an open-source simulation framework, GEOS, that will be available to any future user.

15 GEOTHERMAL ENERGY↗

Land of Opportunity: Potential for Renewable Energy on Federal Lands

Renewable energy (RE) in the United States has historically been deployed primarily on private lands, but the growing interest in RE development, generally across the country and specifically on federal lands, raises questions about the potential for RE on public lands. This study seeks to estimate RE technical potential on federal lands and project the amount of RE to be developed on federal lands under decarbonization scenarios for the contiguous United States. The study applied a combination of high-resolution geospatial analysis and power sector modeling and relied on multiple partner federal agencies and land administrators from the Bureau of Land Management, the U.S. Fish and Wildlife Service, the U.S. Forest Service, the U.S. Department of Defense, and the U.S. Department of Energy. In our reference siting access case, we estimate 44 million acres of federal land across the contiguous United States is potentially suitable for UPV development, which corresponds to a capacity technical potential of 5,750 gigawatts (GW) (Figure ES-1). Federal land area available for wind development is similar to UPV but wind’s generating capacity technical potential is lower (875 GW). The technical potential is estimated for two geothermal technologies, hydrothermal and enhanced geothermal systems (EGS), both of which have a smaller amount of federal land available for development (12 and 27 million acres, respectively). However, in terms of capacity, the technical potential for EGS (975 GW) is approximately equal to wind’s technical potential and there is an estimated 130 GW of hydrothermal potential. We also developed cases with more-limited land available for UPV and wind (for federal and non-federal lands) resulting in 96% reduction of wind capacity potential and 70% reduction for UPV. In a case with additional constraints applied to non-federal lands only (Limited Private), the overall (federal and non-federal) technical potential declines but the share of that technical potential on federal lands is higher than in the other siting cases. The technical potential is the maximum amount that could be developed, but only a small fraction would be developed or needed in the future. Across seven scenarios that achieve 100% carbon-free electricity by 2035, we estimate 26 GW to 270 GW of RE capacity could be deployed on federal lands by 2035. The three central scenarios have 51–84 GW of RE deployed by 2035 and requiring about 500,000 to 1,000,000 acres of total land area. Direct land consumption is less than total land use required, thus enabling co-use opportunities. The large technical potential estimates and the increasing deployment projections from the collection of scenarios show the opportunities for RE development on federal lands. Capturing these opportunities-while minimizing conflicts with other land uses, federal department or agency missions, and public interest, and simultaneously maximizing the economic, grid, and social value of the projects-would require collaborative planning among federal land administrators, grid planners, project developers, the public, and other stakeholders.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Prediction and Analysis of Utah FORGE Injection Activities using a Coupled Thermo-hydro-mechanical and Earthquake (THM+E) Modeling Workflow

A coupled thermo-hydro-mechanical (THM) numerical workflow that is capable of modeling seismic slip is critical for the successful development of enhanced geothermal systems (EGS). By integrating key physical processes, this workflow enables accurate simulation of temperature and pressure diffusions, stress changes, and induced seismicity. As a result, it serves as a vital tool for predicting induced seismicity and optimizing reservoir stimulation strategies. The Utah FORGE (Frontier Observatory for Research in Geothermal Energy) project, located near Milford, Utah, is a U.S. Department of Energy initiative aimed at advancing EGS technology. In April 2024, eight new stimulation stages (Stages 3R-10) were conducted in well 16A (injection well) subsequent to the first series of stimulation (Stages 1-3) performed in April, 2022. To monitor the induced seismicity, geophones were deployed in wells 58-32, 56-32, and 78B-32, while fiber optic cables were also installed in wells 16B, 78-32, and 78B-32 to collect microseismic data and detect frac hits Preliminary analyses of microseismic catalogs and fiber optic data suggest that the stimulated fractures in Stages 3R–6 closely align with that generated during Stage 3, indicating that the new stimulations were likely reactivating the previously stimulated fracture. To better understand the underlying process, a comprehensive modeling approach that can accurately capture thermal, hydrological, mechanical, and seismic responses is essential. In this work, we propose and utilize a coupled thermo-hydro-mechanical and earthquake (THM+E) simulation workflow to numerically investigate the stimulation activities on well 16A. The specific objective is to confirm whether the new stimulation stages (Stages 3R–6) reactivated fractures previously stimulated during Stage 3. For this purpose, we perform THM+E simulations individually for Stages 3, 3R, 4, and 5, incorporating the discrete fracture networks (DFNs) created by the plane-fitting technique based on the microseismic catalogs. The simulation workflow consists of two separate models: a THM model and an earthquake model, coupled in a one-way manner. Detailed descriptions of the workflow are provided in Section 3. Simulation results are presented in terms of injection pressure, permeability evolution, and predicted seismic catalogs, which are then compared with field data for further analyses. This report is structured as follows. In Section 2, we present detailed analyses of the field data and propose the hypothesis that the new stimulation stages (Stages 3R–6) were probably reactivating the previously stimulated fractures in Stage 3. In Section 3, we introduce the coupled THM+E workflow and the problem setup to validate our hypothesis, followed by the simulation results for each stage in Section 4. Meanwhile, discussions are included to analyze the model predictions and their comparison with field data. Lastly, we conclude the report and outline future plans in Section 5.

15 GEOTHERMAL ENERGY↗

Tuning Solvation Dynamics of Electrolytes at Their Eutectic Point Through Halide Identity

Deep eutectic solvents (DESs) are regarded as highly promising solvent systems for redox flow batteries. DESs, composed of choline halides (ChX, X = F − , Cl − , Br − , I − ) and ethylene glycol (EG), exhibit distinct physicochemical properties at their eutectic points, including halide-dependent phase behavior, viscosity, polarity, conductivity, and solvation dynamics. In this study, we investigate the effects of the halide identity on the solvation properties of ChX:EG mixtures at varying mol % of ChX salt content. The solvatochromic polarity based on ET(30) measurements indicates higher polarity for larger halides (I − > Br − ) than for smaller halides (Cl − > F − ), which exhibit larger compensating solvation shells. The ionic conductivity follows the trend of the solvent fluidity (the inverse of the viscosity), namely ChCl > ChBr > ChI > ChF, influenced by the ion mobility and solvodynamic radii. Measurements of the liquidus temperatures (T L ) reveal that the system with ChCl exhibits the deepest eutectic point (at ~20 mol % ChCl), while ChBr and ChI have shallower minima at ~10 mol % ChBr and ~3 mol % ChI, respectively. ChF does not display a eutectic transition but instead appears to readily supercool at salt concentrations above 30 mol % ChF. Consistent with the phase transition measurements, femtosecond transient absorption spectroscopy shows that in the ChCl system, the solvation dynamics become faster with an increasing salt concentration up to ~16.67 mol %, after which the dynamics slow down with further increases in the salt content. The ChF-based system exhibits similar behavior, though with slower dynamics. In contrast, the solvation dynamics of the systems containing ChBr and ChI monotonously slow down with an increasing salt concentration, in agreement with the phase transition measurements, which show that the eutectic points occur at low salt concentrations. These measurements suggest that the solvent composition and, in particular, the identity of the halide anion play a significant role in the solvation behavior of these ethylene-glycol-based DESs, offering a foundation for tuning the DES properties for specific applications.

Biochemistry & Molecular Biology↗

Value of Geothermal Energy Storage for Supply-Side and Demand-Side Applications

This report presents the results of a study examining the value potential for geothermal energy storage (GES), a long-duration energy storage resource that stores thermal and/or geomechanical energy in the subsurface. GES could benefit the overall U.S. power system by temporally shifting electricity generation (supply-side) or meeting building heating and cooling load (demand-side). This report analyzes supply-side and demand-side opportunities independently because of differences in applications and models. Currently there is significant uncertainty about the development costs for GES, with only a limited number of demonstration plants for electric energy storage and building heating and cooling storage developments. In this report, we estimate the value of supply-side and demand-side GES to the bulk power system in the contiguous United States. Because of the significant uncertainty about GES development costs, this analysis does not consider GES deployment costs but instead focuses on the value of GES to the U.S. electricity system. The estimated values of GES provide reference points for economically competitive commercial cost targets. Supply-side GES is modeled as part of an enhanced geothermal system (EGS) generation plant in NREL's Regional Energy Deployment System (ReEDS) capacity expansion model (Ho et al. 2021). In contrast to conventional geothermal plants, which generate constant power, EGS plants have unique features that may allow for in-reservoir energy storage for flexible generation. Demand-side GES for heating and cooling, including seasonal hot and cold storage and short-duration heat pump storage, is incorporated into a price-taker model using Cambium electricity marginal cost projections. To establish an upper bound for the value of GES, analysis focused on favorable scenarios for storage with high generation from zero marginal cost, variable renewable energy resources. High penetrations of variable renewable energy generation can increase hourly electricity price variability, which increases the value of temporal energy arbitrage for storage technologies like GES.

15 GEOTHERMAL ENERGY↗

Brief search for low-mass objects

Observations of the nearby white dwarfs EG 5 (van Maanen 2) and EG 290 obtained in the J, H, K, L, L-prime, and M bands using an RC1 photometer at the Cassegrain focus of the 3.3-m IR telescope at Mauna Kea on Dec. 2, 1983 are reported. The L-band fluxes are analyzed to search for low-mass companion objects, but none is found. Upper limits of Te = 850 K and L = 5 x 10 to the -6th solar luminosity are established for the putative companions of both dwarfs, corresponding to a mass of 0.027 solar mass or less for an age of 3 Gyr.

Krishna Kumar, C.↗

Optical dispersion relations for diamondlike carbon films

Ellipsometric measurements on plasma deposited diamondlike amorphous carbon (a-C:H) films were taken in the visible, (E=1.75 to 3.5 eV). The films were deposited on Si and their properties were varied using high temperature (up to 750 C) anneals. The real (n) and imaginary (k) parts of the complex index of refraction N were obtained simultaneously. Following the theory of Forouhi and Bloomer, a least squares fit was used to find the dispersion relations n(E) and k(E). Reasonably good fits were obtained, showing that the theory can be used for a-C:H films. Moreover, the value of the energy gap (Eg) obtained in this way was compared to the Eg value using conventional Tauc plots and reasonably good agreement was obtained.

Alterovitz, Samuel A.↗