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At least 73 records · Page 4

Simple and Sophisticated Models of Taylor's Cylinder Impact

We present a study based on the simplest possible models for Taylor’s cylinder impact problem, in addition to examination of using convolutional neural networks (CNNs) to map cylinder profiles to strength calibrations. We find that the approximate treatments of Taylor and Hawkyard compare well with hydrodynamic simulations using an equivalent assumption of constant flow stress. The CNN models prove to be well suited to successfully infer parameterizations of the Preston-Tonks-Wallace model of plastic deformation based on the deformed profile of an impacted cylinder

36 MATERIALS SCIENCE↗

Long-term thermal aging behavior and strength reduction in a laser powder bed fusion 316H stainless steel

The long-term thermal stability of structural alloys is essential for ensuring the safe and reliable operation of nuclear reactors and other power plants. While extensive research has explored the effects of thermal aging on conventional stainless steels, the behavior of additively manufactured (AM) alloys remains less understood. This study examines the thermal aging response of laser powder bed fusion (LPBF) 316H stainless steel (SS) at temperatures ranging from 550 °C to 750 °C over durations of up to 10,000 h (approximately 1.14 years). Advanced characterization techniques, including electron microscopy and synchrotron X-ray diffraction, were used to investigate dislocation recovery and phase evolution. Based on these findings, a time-temperature-precipitation (TTP) diagram was developed for LPBF 316H SS, revealing a 10- to100-fold acceleration in precipitation kinetics compared to wrought 316H SS. A physics-informed model was calibrated using the short-term experimental data, enabling predictions of average precipitate sizes, volume fractions of M 23 C 6 and Laves phases, and changes in molybdenum solute concentration for aging up to 1 × 10⁶ h (114 years). These microstructural insights were further utilized to estimate yield strength and extrapolate strength reduction factors over the extended aging period. Despite the accelerated aging kinetics, LPBF 316H SS demonstrated superior yield strength retention compared to its wrought counterpart. In conclusion, this study establishes a framework for evaluating long-term performance using short-term experimental data and supports the accelerated qualification of AM materials for high-temperature structural applications.

Laser powder bed fusion↗

A TOPAS model for lens-based proton radiography

Abstract Objective. Proton Radiography can be used in conjunction with proton therapy for patient positioning, real-time estimates of stopping power, and adaptive therapy in regions with motion. The modeling capability shown here can be used to evaluate lens-based radiography as an instantaneous proton-based radiographic technique. The utilization of user-friendly Monte Carlo program TOPAS enables collaborators and other users to easily conduct medical- and therapy- based simulations of the Los Alamos Neutron Science Center (LANSCE). The resulting transport model is an open-source Monte Carlo package for simulations of proton and heavy ion therapy treatments and concurrent particle imaging. Approach. The four-quadrupole, magnetic lens system of the 800-MeV proton beamline at LANSCE is modeled in TOPAS. Several imaging and contrast objects were modelled to assess transmission at energies from 230–930 MeV and different levels of particle collimation. At different proton energies, the strength of the magnetic field was scaled according to βγ, the inverse product of particle relativistic velocity and particle momentum. Main results. Materials with high atomic number, Z, (gold, gallium, bone-equivalent) generated more contrast than materials with low-Z (water, lung-equivalent, adipose-equivalent). A 5-mrad collimator was beneficial for tissue-to-contrast agent contrast, while a 10-mrad collimator was best to distinguish between different high-Z materials. Assessment with a step-wedge phantom showed water-equivalent path length did not scale directly according to predicted values but could be mapped more accurately with calibration. Poor image quality was observed at low energies (230 MeV), but improved as proton energy increased, with sub-mm resolution at 630 MeV. Significance. Proton radiography becomes viable for shallow bone structures at 330 MeV, and for deeper structures at 630 MeV. Visibility improves with use of high-Z contrast agents. This modality may be particularly viable at carbon therapy centers with accelerators capable of delivering high energy protons and could be performed with carbon therapy.

60 APPLIED LIFE SCIENCES↗

Comparison of atomized mass and crater volume in laser ablation

The extent and dynamics of laser ablation are typically studied using crater imaging or by invoking the relationship between atomic emission and the mass removed. The former is a static view of a dynamic process and requires the accumulation of multiple shots in one location. The latter is complex and not absolute without calibration of the optical system with a standard of spectral radiance. We measure the mass of the atomized plume by laser atomic-absorption spectroscopy at 2 µs without external mass calibration; mass uncertainty in laser-ablation atomic absorption spectroscopy (LA-AAS) results from uncertainties in line area fitting, tabulated oscillator strengths, and partition functions as well as a <10% underrepresentation of the mass due to treating the plasma as a single thermodynamic equilibrium. The LA-AAS-measured mass pertains to the atoms in the probed charge states and does not include condensed or molecular species. The ablation efficiency at 300 mbar of helium varies significantly between the two focusing conditions used. A comparison of crater-derived masses and LA-AAS masses suggests that more defocused ablation may result in significant redeposition of material in the crater, distorting the conclusions from drilling studies and crater imaging. More focused ablation conditions result in crater-derived masses that exceed those measured with LA-AAS and suggest melt expulsion or phase explosion.

Merten, Jonathan [Arkansas State University, Jones↗

A Continuum Dislocation Dynamics Crystal Plasticity Approach to Irradiated Body-Centered Cubic α-Iron

Radiation-induced embrittlement of reactor pressure vessel (RPV) steels can potentially limit the operating life of nuclear power plants. Over extended exposure to radiation doses, these body-centered cubic (BCC) irons demonstrate irradiation damage. Here, we present a continuum dislocation density (CDD) crystal plasticity model to capture the interaction among dislocations and self-interstitial atom (SIA) loops in α-iron. We demonstrate the importance of modeling cross slip using a combined stochastic Monte Carlo approach and the role of slip system strength anisotropy in capturing stochastic cross slip interactions. Through these captured interactions, the CDD crystal plasticity model can capture both the stress response and the physical evolution of dislocations on different slip system planes. Single-crystal verification experiments are used to calibrate the CDD crystal plasticity model, and a set of simplified polycrystalline simulations demonstrates the model’s ability to capture the stress response from tensile experiments on α-iron.

36 MATERIALS SCIENCE↗

A combined experimental and computational analysis of failure mechanisms in open-hole cross-ply laminates under flexural loading

In this work, integrated experimental tests and computational modeling are proposed to investigate the failure mechanisms of open-hole cross-ply carbon fiber reinforced polymer (CFRP) laminated composites. In particular, we propose two effective methods, which include width-tapered double cantilever beam (WTDCB) and fixed-ratio mixed-mode end load split (FRMMELS) tests, to obtain the experimental data more reliably. We then calibrate the traction-separation laws of cohesive zone model (CZM) used among laminas of the composites by leveraging these two methods. The experimental results of fracture energy, i.e. G Ic and G Tc , obtained from WTDCB and FRMMELS tests are generally insensitive to the crack length thus requiring no effort to accurately measure the crack tip. Moreover, FRMMELS sample contains a fixed mixed-mode ratio of G IIc /G Tc depending on the width taper ratio. Examining comparisons between experimental results of FRMMELS tests and failure surface of B–K failure criterion predicted from a curve fitting, good agreement between the predictions and experimental data has been found, indicating that FRMMELS tests are an effective method to determine mixed-mode fracture criterion. In addition, a coupled experimental-computational modeling of WTDCB, edge notched flexure, and FRMMELS tests are adopted to calibrate and validate the interfacial strengths. Finally, failure mechanisms of open-hole cross-ply CFRP laminates under flexural loading have been studied systematically using experimental and multi-scale computational analyses based on the developed CZM model. The initiation and propagation of delamination, the failure of laminated layers as well as load-displacement curves predicted from computational analyses are in good agreement with what we have observed experimentally.

36 MATERIALS SCIENCE↗

Quality Control of Additively Manufactured Metallic Structures with Machine Learning of Thermography Images

Additive manufacturing (AM) of high-strength metals is currently based on the laser powder bed fusion (LPBF) process, which can introduce internal material flaws, such as pores and anisotropy. Quality control (QC) requires nondestructive evaluation of actual AM structures. Flash thermography is a potentially promising QC technique because it is scalable to arbitrary structure size. However, the detection sensitivity of this method is limited by noise. We investigate separation of signal from noise in thermography images using several machine learning (ML) methods, including new spatial–temporal blind source separation and spatial–temporal sparse dictionary learning methods. Performance of the ML methods is benchmarked using thermography data obtained from imaging stainless steel 316L and Inconel 718 specimens produced by the LPBF method with imprinted calibrated porosity defects. The ML methods are ranked by F-score and execution runtime. Finally, the ML methods with higher accuracy require a longer runtime. However, this runtime is sufficiently short to perform QC within a realistic time frame.

36 MATERIALS SCIENCE↗

Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al

Several theoretical studies have reported that the geometry and structure of grain boundaries in polycrystalline materials could impose a significant effect on the Hall-Petch slope. However, experimental observations are primarily limited by the ability of the techniques to accurately quantify the grain boundary strength and validate these theoretical models. Using high-resolution electron backscatter diffraction (HR-EBSD), the local stress tensor ahead of a slip band blocked by a grain boundary was quantified and coupled with a continuum dislocation pile-up model to assess the barrier strength of specific grain boundaries to specific slip systems, referred to as micro-Hall-Petch coefficient. For basal slip system in a deformed Mg-4Al alloy, the micro-Hall-Petch coefficient ($k^{basal}_{μ}$) varied significantly, from 0.054 to 0.184 MPa - m 1/2 for nine different grain boundaries. These results were correlated with geometric descriptors of the respective grain boundaries, with three-dimensional GB profile additionally measured via focused ion beam milling. It was found that the angle between the two slip plane traces on the grain boundary plane was the most sensitive parameter affecting $k^{basal}_{μ}$, followed by the angle between the slip directions. A functional form for calculation of $k^{basal}_{μ}$ depending on these two angles is proposed to augment crystal plasticity constitutive models with slip resistance dependent on some measure of the grain size. The method allows a new pathway to calibrate grain size strengthening parameters in crystal plasticity models, allowing further computational investigations of the interrelationship between texture, grain morphology, and the Hall Petch effect.

36 MATERIALS SCIENCE↗

Relationships between lineal fracture intensity and chemical composition in the Marcellus Shale, Appalachian Basin

Within mudrock reservoirs, brittle zones undergo failure during hydraulic stimulation, creating numerous artificial fractures which enable hydrocarbons to be liberated from the reservoir. Natural fractures in mudrock reduce the tensile strength of the host rock, creating planes of weaknesses that are hypothesized to be reactivated during hydraulic stimulation. Combined, brittleness and natural fractures contribute to creating more abundant and complex fracture networks during hydraulic stimulation. Research efforts toward quantifying rock brittleness have resulted in numerous mineral-/compositional-based indices, which are used during petrophysical analysis to predict zones most conducive to hydraulic stimulation. In contrast, investigations on the relationship between chemical composition and core-scale natural fractures are limited. For this study, we collected high-resolution energy-dispersive X-ray fluorescence (XRF) data, calibrated with a wave-dispersive XRF, from a Marcellus Shale core. Additionally, we characterized corescale natural fractures in terms of length, width, in-filling material or lack thereof, and orientation. Following the characterization, we transformed the natural fracture data into a continuous P10 (lineal fracture intensity) curve, expressed as the number of fractures per a one-half foot window. Using these data sets, we investigated the relationship between rock composition and natural fracture intensity. Regression analyses recorded positive relationships between natural fracture intensity and calcium, silicon/aluminum, and total organic carbon (TOC), and negative relationships with silicon and aluminum. Aluminum recorded the strongest (negative) relationship ([Formula: see text]) with natural fracture intensity. To access the degree to which natural fractures can be predicted based on chemical composition, we applied a partial least-squares analysis, a multivariate method, and recorded an [Formula: see text]. Our study illustrates that although numerous factors are responsible for natural fracture genesis, such fractures predictively concentrate in areas of similar chemical composition, largely in zones with low aluminum concentrations.

Geochemistry & Geophysics↗

In-Situ Laser-Induced-Desorption-Spectroscopy Diagnostic Deployment on the Linear Plasma Device CSDX

A calibrated laser induced desorption diagnostic (LIDS) concept is developed under this award for application to fusion relevant plasma materials interactions studies. Small areal amounts of hydrogenic release from a deuterium filled PMI target are measured and quantified when irradiated by a LID flash heat event on the target surface. Good success was demonstrated by this project with the PISCES-E rf plasma device at UCSD by fully quantified measurement and removal of D from W-D co-deposit layers in experiments. However, adapting the LIDS technique to D plasma exposed W targets in the linear plasma CSDX device, now labelled PISCES-Rf, was prone to several technical challenges ranging from target line of sight access, laser focusing, and loss of optical spectroscopic signal strength in the larger PISCES-Rf vacuum system. The results are summarized in this report.

08 HYDROGEN↗

The intrinsic mechanical properties of hydromagnesite, Mg 5 (CO 3 ) 4 (OH) 2 ·4H 2 O, a key phase of reactive MgO carbonate cement

To potentially enable CO 2 sequestration, reactive MgO carbonate cement is emerging as an alternative binder to Portland cement. Understanding the mechanical properties of its binding phase is critical for understanding the strength development and performing materials design for reactive MgO cement systems; however, the intrinsic mechanical properties of hydromagnesite (Mg 5 (CO 3 ) 4 (OH) 2 ·4H 2 O), a key binding phase, remain unexplored. Here the present study utilized synchrotron-based high-pressure X-ray diffraction to determine the unit cell-scale, intrinsic mechanical properties of hydromagnesite for the first time. Up to hydrostatic loading of 7.7 GPa, the bulk modulus of hydromagnesite was determined as 59 GPa or 71 GPa fitted using the second-order or third-order Birch-Murnaghan equation of state, which we contextualize with binding phases in various cement systems. The experiment results are applicable in materials design of low-carbon concrete and valuable for the validation and calibration of atomistic models.

36 MATERIALS SCIENCE↗

Constrained model calibration of grain structure dependent spall dynamics in shock-loaded tantalum

Here, we perform a gas gun experiment by shock loading tantalum samples of varying grain structures to assess the suitability of a numerical model for simulating spall behavior. The observed differences in spall strength, as well spallation and re-compression history, are not captured in uncalibrated hydrodynamic simulations. An optimization is performed on the Johnson spall model to determine the best parameters that fit the observed trends. Linear stability analysis is employed to motivate bounds on those parameters. Herein, optimized simulations agree well with the experimental results, reproducing pullback depth and recompression timescales across the different samples tested. Further, the observed pullback time of the single crystal sample was found to imply, via the stability analysis, a percolation threshold in good agreement with the theoretical value for a body centered cubic lattice. Therefore, the combined linear stability and percolation analysis shows promise and may be applied to other materials with diverse microstructures. Collectively, the findings demonstrate that the model is suitable for reproducing spall-induced free surface behavior across various microstructures, but also points to caution in using model coefficients for uncalibrated microstructures.

58 GEOSCIENCES↗

First Annual Report on Pulsed Thermal Tomography Nondestructive Evaluation of Additively Manufactured Reactor Materials and Components: Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials and Components

Additive manufacturing (AM, or 3D printing) for commercial nuclear energy applications is an emerging method for cost-efficient manufacturing aimed at replacing aging nuclear reactor parts and reducing costs for new construction. Because of the geometry of metallic structures of interest for nuclear applications, which consist of planar primitives with no symmetry of revolution, limited options are available for nondestructive evaluation (NDE), either during or post manufacturing. Known material flaws in AM include low-density regions consisting of non-sintered powder, which have to be detected to ensure the safety of long-term performance nuclear reactor components. As a solution to NDE of AM, we are developing pulsed thermal tomography (PTT) models and depth inversion algorithms for 3D imaging. PTT has many advantages because the method is non-contact and allows for in-service, NDE of AM nuclear reactor parts. By analyzing transients of surface temperature response due to internal thermal resistances, one can obtain 3D reconstructions of material effusivity using a unique inversion algorithm developed at Argonne. This report provides results of preliminary performance evaluation of PTT capability in detection of flaws in metallic structures, as well imaging complex geometry AM structures. Performance of PTT was investigated through modeling and experiments, Computer models of PTT were developed using COMSOL Heat Transfer module. Defects were modeled as cylindrical flat bottom holes (FBH), which is a common model of calibrated material flaws in thermal tomography experiments. Materials considered in this study include stainless steel 316 (SS316), stainless steel 304 (SS304), and Inconel 718. Theoretical analyses were conducted to validate inversion of simulated PTT data with COMSOL for a plate. Subsequently, 3D reconstructions were performed on COMSOL simulations for FBH, revealing a decrease in spatial resolution over depth due to thermal diffusion. The results of this study show that the performance of the inversion algorithm for detecting smaller defects depends strongly on the depth of the defect as well as the incident heat flux. The size of detectable defect was estimated by fitting a Gaussian function to surface temperature profile. The criteria for detectability was taken as 20mK noise equivalent temperature difference (NETD), which is currently the sensitivity limit of high-performance infrared cameras. It was determined through computer simulations that the smallest detectable FBH in SS316 has a 50µm diameter and is located 0.5mm below the plate surface. Preliminary experimental studies were performed to evaluate PTT performance in detecting calibrated flaws using metallic specimens with AM defects simulated as drilled-in FBH’s. High strength Stainless Steel 316 and Inconel 718 alloys were considered, as well as lower grade Stainless Steel 304, Nickel 200, and Hastelloy C276. Specimens investigated in this report consisted of approximately 1/4in-thick plates made out of these alloys using conventional manufacturing methods. The diameters of FBH’s varied from 1mm to 8mm, and their depths below the plate flat surface varied between 1mm and 6mm. The size of the smallest FBH was limited to 1mm because conventional mechanical drills were used for creating the holes. PTT imaging results have shown that 1mm-diameter FBH located 1mm and 2mm below the surface were detectable. Larger size FBH were detectable at greater depth. For example, 6mm-diameter FBH could be detected at 8mm depth. Image contrast varied slightly between the specimens, with the best reconstructions obtained in SS316 and C276 plates. Finally, PTT capability in imaging several AM structures fabricated from Inconel 718 (IN718) powder feedstock was investigated. The AM structures have complex geometry, but do not have calibrated internal defects. The objective is to determine PTT settings, such as the total integration time, for imaging of representative AM structures. A new FLIR X8500sc IR camera with higher spatial resolution (1280x1024 at 181Hz frame rate) was integrated into the PTT laboratory setup. Software tools were developed to ensure compatibility of new camera files with legacy effusivity reconstruction codes. The new camera was used to obtain 3-D reconstructions of AM IN718 nozzle plate and a particle filter plate. It was shown that PTT can scan through 2/3in-thick Inconel 718 plates in approximately 15s. Several modes of 3-D data visualization were explored, including using ImageJ and MATLAB software packages. The results demonstrate the capability of PTT in 3-D imaging of complex geometry AM structures. Intermediate results demonstrated in this report will be developed further to investigate detection of flaws in AM specimens.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

On the high-temperature stability of the Al 8 Cu 3 Ce intermetallic in an additively manufactured Al-Cu-Ce-Zr alloy

High-temperature resistant eutectic Al alloys are crucial materials for lightweight and energy efficient design in the automotive and aviation industries. Additive manufacturing offers a pathway to refine eutectic microstructures and develop novel alloys with superior high-temperature strength. High-volume fraction intermetallic Al-Cu-Ce alloys have been developed to deliver high-temperature strength in combination with reduced hot-tearing susceptibility. Zr is added to provide additional strengthening via nanoscale Al 3 Zr precipitation, and to stabilize and avoid coarsening of the Al 8 Cu 3 Ce phase. However, the detailed interaction between Zr and Al 8 Cu 3 Ce remains unexplored. In this work, we show with synchrotron X-ray diffraction that laser powder bed fusion fabricated Al-Cu-Ce and Al-Cu-Ce-Zr alloys contain predominantly the Al 8 Cu 3 Ce intermetallic in the as-fabricated condition. Heat treatment of the Al-Cu-Ce alloy results in the Al 8 Cu 3 Ce → Al 8 Cu 4 Ce phase transformation. In the Al-Cu-Ce-Zr alloy, minor fractions of (Al,Cu,Si) 4 Ce and Al 2 Cu-θ are found in the as-fabricated condition, while Al 8 Cu 3 Ce remains stable during heat treatment. Atom probe microscopy quantifies intermetallic stoichiometries and reveals how Zr is enriched at the Al-matrix/Al 8 Cu 3 Ce interface acting as a diffusion barrier against solute exchange. Calibrated thermodynamic modeling underpins this as a kinetic effect. Here, a qualitative microstructural model summarizes, how Zr stabilizes Al 8 Cu 3 Ce against phase transformations and coarsening.

36 MATERIALS SCIENCE↗

Experimental study of compaction localization in carbonate rock and constitutive modeling of mechanical anisotropy

Abstract Sedimentary rocks are inherently anisotropic and prone to strain localization. While the influence of rock anisotropy on the brittle/dilative regime has been studied extensively, its influence on the ductile/compactive regime is much less explored. This paper discusses the anisotropic behavior of a high‐porosity carbonate rock from central Europe (the Maastricht Tuffeau). A set of triaxial tests with concurrent x‐ray tomography has been performed at different confining pressures. The anisotropic characteristics of this rock have been investigated by testing samples cored at different inclinations of the bedding, thus revealing non‐negligible effects of the coring direction on yielding and compaction behavior. Specifically, samples cored perpendicular to bedding display higher strength and longer stages of post‐yielding deformation before manifesting re‐hardening. Despite such alterations of the inelastic response, Digital Image Correlation has revealed that the strain localization mode is independent of the coring direction, thus being primarily affected by the confinement level. To capture the observed interaction between material anisotropy and compaction behavior at the continuum‐scale, an elastoplastic constitutive law has been proposed. For this purpose, a set of tensorial bases has been introduced to replicate how the oriented rock fabric modulates the yielding and plastic flow characteristics of the material. The analyses show that the impact of the coring direction on yield function and plastic flow rule is fundamentally different, thus requiring the use of distinct projection strategies (a strategy here defined heterotopic mapping). The performance of the model, studied through parametric analyses and by calibrating the experimental results, illustrates the improved capability of the proposed constitutive approach when applied to strongly anisotropic porous rocks.

Shahin, Ghassan↗

Development of High-Performance Ni-base Alloys for Gas Turbine Wheels Using a Coprecipitation Approach (Final Technical Report)

In this project, a synergistic approach involving experiments informed by modelling was used to develop γ'/γ'' coprecipitation-strengthened Ni-base superalloys for land-based gas turbine wheels. In thick sections of such turbine wheels, the slow cooling rate normally observed, as well as variations in cooling rate could potentially result in drastically inhomogeneous and coarsened microstructure. Thus, ten alloy compositions were selected based on coprecipitation and sluggish γ’ growth and coarsening during three iterations of alloy development, assisted by extensive CALPHAD modeling. Phase equilibrium calculations, informed by the characterization of early alloys, were successful in predicting suitable aging treatments to obtain bimodal coprecipitate distribution in several alloys. These aging treatments were applied to the subsequent round of alloys and the resulting microstructures were characterized in detail. Two different cooling rates were used during each of these heat treatments to simulate the range of cooling rates observed in a thick section forging. The microstructures were used to calibrate a multi-phase field model (MPF), which was used to study the formation mechanisms of various coprecipitate morphologies observed in the experiments. Following this, the most promising alloys in each round were selected and studied using high temperature tensile and creep tests. Considering that a slower cooling rate would lead to a strength debit, while a faster cooling rate might lead to a decline in creep rupture life of a full-scale wheel, tensile tests were carried out for slower cooled samples, while creep tests were carried out for faster cooled samples. The deformation microstructures were then characterized using advanced characterization techniques such as Diffraction Contrast-Scanning Transmission Electron Microscopy (DC-STEM) and Electron Channeling Contrast Imaging (ECCI). Further, a mean-field creep model was developed and calibrated using these experimental findings to predict long-term creep behavior of these coprecipitation-strengthened alloys.

36 MATERIALS SCIENCE↗

Electric field dependence of nanoscale cathodoluminescence inside Cr doped β-Ga 2 O 3 interfaces

Chromium (Cr) is a common impurity in β-Ga 2 O 3 crystals, where its characteristic R1 and R2 luminescence lines are susceptible to both the host crystal field and externally applied fields. Here, in this work, we demonstrate that the Cr cathodoluminescence (CL) quenches toward the bulk of the crystal but enhances with applied reverse bias, reflecting the effect of free carrier depletion with increasing electric field. Furthermore, we illustrate that the R1/R2 CL intensity ratio, measured as the integrated area ratio of R1 to R2, can be used as a direct probe of the electric field in a Ni-β-Ga 2 O 3 : Cr Schottky diode. This optical calibration method provides a complementary approach to conventional C–V and I–V measurements for determining electric field strength in the depletion region of β-Ga 2 O 3 -based Schottky diodes and can be extended to other semiconductors and multilayer device structures.

36 MATERIALS SCIENCE↗