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At least 1,279 records · Page 71

Development of Simplified Model Test Methods for Creep-Fatigue Evaluation

The Simplified Model Test (SMT) approach is an alternative creep-fatigue evaluation method that no longer requires the use of the damage interaction diagram, or D-diagram. The reason is that the combined effects of creep and fatigue are accounted for in the test data by means of a SMT specimen that is designed to replicate or bound the stress and strain redistribution that occurs in actual components when loaded in the creep regime. However, creep-fatigue experiments on SMT key feature articles are specialized and difficult to perform by the general research community. In this paper, two innovative SMT based creep-fatigue experimental methods are developed and implemented. These newly-developed SMT test methods have resolved all the critical challenges in the SMT key feature article testing and enable the potential of further development of the SMT based creep-fatigue evaluation method into a standard testing method. Scoping test results on Alloy 617 and SS 316H using the newly developed SMT methods are summarized and discussed. The concepts of the SMT methodology for creep-fatigue evaluation are explained.

Wang, Yanli↗

Generic and robust method for automatic segmentation of PET images using an active contour model

Purpose: Although positron emission tomography (PET) images have shown potential to improve the accuracy of targeting in radiation therapy planning and assessment of response to treatment, the boundaries of tumors are not easily distinguishable from surrounding normal tissue owing to the low spatial resolution and inherent noisy characteristics of PET images. The objective of this study is to develop a generic and robust method for automatic delineation of tumor volumes using an active contour model and to evaluate its performance using phantom and clinical studies. Methods: MASAC, a method for automatic segmentation using an active contour model, incorporates the histogram fuzzy C-means clustering, and localized and textural information to constrain the active contour to detect boundaries in an accurate and robust manner. Moreover, the lattice Boltzmann method is used as an alternative approach for solving the level set equation to make it faster and suitable for parallel programming. Twenty simulated phantom studies and 16 clinical studies, including six cases of pharyngolaryngeal squamous cell carcinoma and ten cases of nonsmall cell lung cancer, were included to evaluate its performance. Besides, the proposed method was also compared with the contourlet-based active contour algorithm (CAC) and Schaefer’s thresholding method (ST). The relative volume error (RE), Dice similarity coefficient (DSC), and classification error (CE) metrics were used to analyze the results quantitatively. Results: For the simulated phantom studies (PSs), MASAC and CAC provide similar segmentations of the different lesions, while ST fails to achieve reliable results. For the clinical datasets (2 cases with connected high-uptake regions excluded) (CSs), CAC provides for the lowest mean RE (−8.38% ± 27.49%), while MASAC achieves the best mean DSC (0.71 ± 0.09) and mean CE (53.92% ± 12.65%), respectively. MASAC could reliably quantify different types of lesions assessed in this work with good accuracy, resulting in a mean RE of −13.35% ± 11.87% and −11.15% ± 23.66%, a mean DSC of 0.89 ± 0.05 and 0.71 ± 0.09, and a mean CE of 19.19% ± 7.89% and 53.92% ± 12.65%, for PSs and CSs, respectively. Conclusions: The authors’ results demonstrate that the developed novel PET segmentation algorithm is applicable to various types of lesions in the authors’ study and is capable of producing accurate and consistent target volume delineations, potentially resulting in reduced intraobserver and interobserver variabilities observed when using manual delineation and improved accuracy in treatment planning and outcome evaluation.

60 APPLIED LIFE SCIENCES↗

New method for taking into account radiative events in the MOLLER inclusive experiment

A new method (N-method) for taking into account radiative events in inclusive polarized experiments that, in principle, makes no use of an unphysical separation into soft-and hard-photon regions is demonstrated. A procedure for taking into account bremsstrahlung in theMOLLER forthcoming ultraprecise experiment at the Thomas Jefferson Laboratory is developed on the basis of this method. The algorithm of the method is described in detail, and the results obtained by means of the N method are compared with the results of applying traditional methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Adaptive Time Step Control for Multirate Infinitesimal Methods

Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased computational efficiency. Generally, such methods select these different step sizes based on experimentation or stability considerations. For problems that evolve on a single time scale, adaptivity approaches that strive to control local temporal error are widely used to achieve numerical results of a desired accuracy with minimal computational effort, while alleviating the need for manual experimentation with different time step sizes. However, there is a notable gap in the publication record on the development of adaptive time step controllers for multirate methods. In this paper, we extend the single-rate controller work of Gustafsson [ACM Trans. Math. Software, 20 (1994), pp. 496-517] to the multirate method setting. Specifically, we develop controllers based on polynomial approximations to the principal error functions for both the "fast" and "slow" time scales within multirate infinitesimal (MRI) methods. We additionally investigate a variety of approaches for estimating the errors arising from each time scale within MRI methods. We then numerically evaluate the proposed multirate controllers and error estimation strategies on a range of multirate test problems, comparing their performance against an estimated optimal performance. Through this work, we combine the most performant of these approaches to arrive at a set of multirate adaptive time step controllers that robustly achieve desired solution accuracy with minimal computational effort.

97 MATHEMATICS AND COMPUTING↗

A substandard candle: the low-$$\nu $$ method at few-GeV neutrino energies

Abstract As accelerator-based neutrino oscillation experiments improve oscillation parameter constraints with more data, control over systematic uncertainties on the incoming neutrino flux and interaction models is increasingly important. The intense beams offered by modern experiments permit a variety of options to constrain the flux using in situ “standard candle” measurements. These standard candles must use very well understood interaction processes to avoid introducing additional interaction model dependence. One option often discussed in this context is the “low- $$\nu $$ ν ” method, which is designed to isolate neutrino interactions where there is low energy-transfer to the nucleus, such that the interaction cross section is expected to be approximately constant as a function of neutrino energy. The shape of the low-energy transfer event sample can then be used to extract the flux shape. Applications of the method at high neutrino energies (many tens of GeV) are well understood. However, the applicability of the method at the lower energies of current and future few-GeV accelerator neutrino experiments remains unclear due to the presence of nuclear and form-factor effects inherent in the interaction models.In this analysis we examine the prospects for improving constraints on the accelerator neutrino fluxes in situ with the low- $$\nu $$ ν method in an experiment-independent way, using (anti)neutrino interactions on argon and hydrocarbon targets from the GENIE, NEUT, NuWro and GiBUU event generators. We begin by investigating the extent to which deviations from the constant cross-section assumption are dependent on poorly understood aspects of the neutrino interaction model. We then assess whether a low energy-transfer event sample can be confidently identified using experimentally accessible observables. We finally consider how the practicalities of reconstructing the energy spectrum of interacting neutrinos in realistic detectors might further limit the utility of low- $$\nu $$ ν flux constraints. The results show that flux constraints from the low- $$\nu $$ ν method would be severely dependent on the interaction model assumptions used in an analysis of neutrinos with energies below 5 GeV, and anti-neutrinos below at least 15 GeV. The spread of model predictions show that a low- $$\nu $$ ν analysis is unlikely to offer much improvement on typical neutrino flux uncertainties, even with a perfect detector. Notably—running counter to the assumption inherent to the low- $$\nu $$ ν method—the model-dependence increases with decreasing energy transfer for experiments in the few-GeV region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

An Assessment of GCM Performance at a Regional Scale Using a Score-Based Method

A multicriteria score-based method was developed to assess the performances of 18 general circulation models (GCMs) in the study region from 1970 to 2005. The results indicate the following. (1) GCMs simulate temperature better than rainfall. The temporal and spatial distributions of simulated temperature performed well compared with those from the observations. In comparison to temperature, the spatial distribution of simulated precipitation performed poorly. Most of the GCMs underestimated temperature and overestimated precipitation. (2) The Grubbs test was used to detect anomalous moving changes in the rank score (RS) results; the inm-cm4 and ipsl-cm5b-lr models were rejected when simulating temperature, while the bnu-esm and canesm2 models performed poorly when simulating precipitation. (3) Adding or removing any criterion does not significantly influence the RS result, which indicates that the multicriteria score-based method is robust. The advantages of using multicriteria score-based method to assess GCMs performance were demonstrated, and this method also provides a more comprehensive assessment when compared with the single-criterion method. The multicriteria method could replace other criteria as the research requirements and could be easily extended to different study regions; the results could be used for better informed regional climate change impact analyses.

Shi, Fangxin↗

Removing cosmic spikes using a hyperspectral upper-bound spectrum method

Cosmic ray spikes are especially problematic for hyperspectral imaging, due to the large number of spikes often present and their negative effects upon subsequent chemometric analysis. Fortunately, while the large number of spectra acquired in a hyperspectral imaging data set increases the probability and number of cosmic spikes observed, the multitude of spectra can also aid in the effective recognition and removal of the cosmic spikes. Dongmao Zhang and Dor Ben-Amotz were perhaps the first to leverage the additional spatial dimension of hyperspectral data matrices (DM). They integrated principal component analysis (PCA) into the upper bound spectrum method (UBS), resulting in a hybrid method (UBS-DM) for hyperspectral images. Here, we expand upon their use of PCA, recognizing that principal components primarily present in only a few pixels most likely correspond to cosmic spikes. Eliminating the contribution of those principal components in those pixels improves the cosmic spike removal. Both simulated and experimental hyperspectral Raman image data sets are used to test the newly developed UBS-DM-hyperspectral (UBS-DM-HS) method which extends the UBS-DM method by leveraging characteristics of hyperspectral datasets. Lastly, a comparison is provided between the performance of the UBS-DM-HS method and other methods suitable for despiking hyperspectral images, evaluating both their ability to remove cosmic ray spikes and the extent to which they introduce spectral bias.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A nondestructive method to estimate the chlorophyll content of Arabidopsis seedlings

Chlorophyll content decreases in plants under stress conditions, therefore it is used commonly as an indicator of plant health. Arabidopsis thaliana offers a convenient and fast way to test physiological phenotypes of mutations and treatments. But, chlorophyll measurements with conventional solvent extraction are not applicable to Arabidopsis leaves due to their small size, especially when grown on culture dishes. We provide a nondestructive method for chlorophyll measurement whereby the red, green and blue (RGB) values of a color leaf image is used to estimate the chlorophyll content from Arabidopsis leaves. The method accommodates different profiles of digital cameras by incorporating the ColorChecker chart to make the digital negative profiles, to adjust the white balance, and to calibrate the exposure rate differences caused by the environment so that this method is applicable in any environment. We chose an exponential function model to estimate chlorophyll content from the RGB values, and fitted the model parameters with physical measurements of chlorophyll contents. As further proof of utility, this method was used to estimate chlorophyll content of G protein mutants grown on different sugar to nitrogen ratios. Our method is a simple, fast, inexpensive, and nondestructive estimation of chlorophyll content of Arabidopsis seedlings. This method lead to the discovery that G proteins are important in sensing the C/N balance to control chlorophyll content in Arabidopsis.

59 BASIC BIOLOGICAL SCIENCES↗

A rapid thioacidolysis method for biomass lignin composition and tricin analysis

Abstract Background Biomass composition varies from plant to plant and greatly affects biomass utilization. Lignin is a heterogeneous phenolic polymer derived mainly from p -coumaryl, coniferyl, and sinapyl alcohols and makes up to 10–25% of lignocellulosic biomass. Recently, tricin, an O -methylated flavone, was identified as a lignin monomer in many grass species. Tricin may function as a nucleation site for lignification and is advocated as a novel target for lignin engineering to reduce lignin content and improve biomass digestibility in grasses. Thioacidolysis is an analytical method that can be adapted to analyze both lignin monomeric composition and tricin content in the lignin polymer. However, the original thioacidolysis procedure is complex, laborious, and time consuming, making it difficult to be adopted for large-scale screening in biomass research. In this study, a modified, rapid higher throughput thioacidolysis method was developed. Results In combination with gas chromatography–mass spectrometry (GC–MS) and liquid chromatography–mass spectrometry (LC–MS), the modified thioacidolysis method can be used to simultaneously characterize the lignin composition and tricin content using 2–5 mg of dry samples. The modified method eliminates the solvent extraction and drastically improves the throughput; 80 samples can be processed in one day per person. Our results indicate that there is no significant difference in the determination of lignin S/G ratio and tricin content between the original and modified methods. Conclusions A modified thioacidolysis protocol was established. The results demonstrate that the modified method can be used for rapid, high-throughput, and reliable lignin composition and tricin content analyses for screening transgenic plants for cell wall modifications or in large-scale genome-wide association studies (GWAS).

09 BIOMASS FUELS↗

Benchmarking the performance of uncertainty quantification methods for neural network-based interatomic potentials

Machine-learned interatomic potentials (ML-IAPs) continue to gain popularity as accurate, computationally efficient replacements for traditional, physics-based interatomic potentials and expensive ab initio methods. Uncertainty quantification (UQ) of ML-IAPs is a growing area of research as UQ is critical in many applications of IAPs, such as developing curated datasets, active learning-based data augmentation, self-improving models, and estimating the uncertainty of molecular dynamics simulations. In this paper, we construct and benchmark a series of different neural network potentials (NNPs) with varying network architectures to determine the performance of these models with respect to both the mean and uncertainty calibration error. Each NNP method is specifically designed to predict either epistemic or aleatoric uncertainty with particular focus on the differences in behavior between the epistemic and aleatoric uncertainty estimates. We benchmark these methods using multiple datasets common in the ML-IAP literature. The results show that the aleatoric uncertainty from single-shot model architectures is a competitive alternative to ensemble-based epistemic uncertainty predictions in regions of sufficient data-density. However, in regions where the representative data is sparse, aleatoric uncertainty models tend to overpredict and epistemic methods tend to underpredict the actual model error. We conclude that the type of UQ is crucial when discussing performance of probabilistic model results as different methods have different performance characteristics depending on the regime in which they are evaluated. Therefore, the type of UQ method should be carefully evaluated against both the data characteristics and requirements for the intended application.

97 MATHEMATICS AND COMPUTING↗

Radiation Source Mapping with Bayesian Inverse Methods

In this work, we present a method to map the spectral and spatial distributions of radioactive sources using a limited number of detectors. Locating and identifying radioactive materials is important for border monitoring, in accounting for special nuclear material in processing facilities, and in cleanup operations following a radioactive material spill. Most methods to analyze these types of problems make restrictive assumptions about the distribution of the source. In contrast, the source mapping method presented here allows an arbitrary three-dimensional distribution in space and a gamma peak distribution in energy. To apply the method, the problem is cast as an inverse problem where the system’s geometry and material composition are known and fixed, while the radiation source distribution is sought. A probabilistic Bayesian approach is used to solve the resulting inverse problem since the system of equations is ill-posed. The posterior is maximized with a Newton optimization method. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint, discrete ordinates flux solutions, obtained in this work by the Denovo code, is required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes form the linear mapping from the state space to the response space. The test of the method’s success is simultaneously locating a set of 137 Cs and 60 Co gamma sources in a room. This test problem is solved using experimental measurements that we collected for this purpose. Because of the weak sources available for use in the experiment, some of the expected photopeaks were not distinguishable from the Compton continuum. However, by supplanting 14 flawed measurements (out of a total of 69) with synthetic responses computed by MCNP, the proof-of-principle source mapping was successful. The locations of the sources were predicted within 25 cm for two of the sources and 90 cm for the third, in a room with an ~4-x 4-m floor plan. Finally, the predicted source intensities were within a factor of ten of their true value.

07 ISOTOPE AND RADIATION SOURCES↗

Proposal and application of ROM-Lasso method for sensitivity coefficient evaluation

We propose a novel method for evaluating sensitivity coefficients of neutronics parameters to cross sections, so-called the reduced-order modeling technique ROM-Lasso. In this method, cross sections of interest are randomly sampled, and corresponding perturbed core analyses are performed. Then, the sensitivity coefficient vector of the higher-level model is expanded via the active subspace bases obtained with the lower-level model whose dimensional complexity is smaller than that of the higher-level model, and the expansion coefficients are estimated by the Lasso regression. A unique feature of the ROM-Lasso method allows the use of different bases optimized for each neutronics parameter. We conducted a verification calculation for an accelerator-driven system and demonstrated that the ROM-Lasso method can reproduce the sensitivity coefficients with a much smaller number of forward calculations than the direct method. The proposed method can be used to practically evaluate sensitivity coefficients. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

New Methods for Dispersion Measurement and Correction for 12GeV CEBAF

This paper discusses methods for dispersion measurement and correction for the Continuous Electron Beam Accelerator Facility (CEBAF) for the 12GeV era. New methods will be compared with methods used during the 6GeV era. New software tools which implement the new methods will be discussed, along with a method for automating dispersion measurement and correction. New dispersion measurement and correction methods and tools are being implemented to provide more deterministic results and to reduce machine setup time.

Turner, Dennis L.↗

Low Temperature Metal Coating Method Final Report CRADA No. TSB-1155-95

A new metal coating method, cidled KEM (kinetic energy metal.lization), demonstrated in the laboratory by lnovati, utilized fast-moving solid particIes entrained in a gas that are caused to fiow through a nozzIe to effect particle deposition on metal surfaces at room temperature conditions. This method (US Patent 5,795,626) was an attractive and viabIe alternative to the currentIy available high-temperature coating methods avaiIabIe. Since it differs significantly from existing metal coating technologies, a brief description of the method is incIuded here. The proposed method, KEM, achieves cohesive and adhesive metallurgical bonding through the high-speed coUision of powder with a substrate and the subsequent discharge of electrical charge at the substrate. Such coating is effected by entraining metal powder in a gas and accelerating this mixture through a supersonic nozzle. The gas/powder is directed towards the substrate to be coated. Collisions occur, initiaIly between the powder and the substrate, and, as the first Iayer of the coating forms, between the powder and the coating. During these collisions the powder is rapidly deformed, causing the exposure of fresh (oxide free) active metal surface. When these’active surfaces contact one another, they agglomerate and form true metaIIurgicaI bonds. The resultant coating has Iow porosity and high adhesive and cohesive strength. The formation of metaIIurgicaI bonds is potentiated by the discharge of electrical energy. This electrical energy is the result of triboeIectric charging of the particIes during acceleration and transit to the nozzIe. An advantage of the method is that it does not raise the temperature of the powder being appLiedor that of the substrate. Consequently, materials sensitive to high temperature may be applied without changing Me properties of the materkd or substrate.

36 MATERIALS SCIENCE↗

Development and Optimization of Voltammetric Methods for Real Time Analysis of Electrorefiner Salt with High Concentrations of Actinides and Fission Products

This project addresses the problem of achieving accurate material control and accountability (MC&A) around pyroprocessing electrorefiner systems. Spent nuclear fuel pyroprocessing poses a unique challenge with respect to reprocessing technology in that the fuel is never fully dissolved in the process fluid. In this case, the process fluid is molten, anhydrous LiCl-KCl salt. Therefore, there is no traditional input accountability tank. However, electrorefiners (ER) accumulate very large quantities of fissile nuclear material (including plutonium) and should be well safeguarded in a commercial facility. Idaho National Laboratory (INL) currently operates a pyroprocessing facility for treatment of spent fuel from Experimental Breeder Reactor-II with two such ER systems. INL implements MC&A via a mass tracking model in combination with periodic sampling of the salt and other materials followed by destructive analysis. This approach is projected to be insufficient to meet international safeguards timeliness requirements. A real time or near real time monitoring method is, thus, direly needed to support commercialization of pyroprocessing. A variety of approaches to achieving real time monitoring for ER salt have been proposed and studied to date—including a potentiometric actinide sensor for concentration measurements, a double bubbler for salt depth and density measurements, and laser induced breakdown spectroscopy (LIBS) for concentration measurements. While each of these methods shows some promise, each also involves substantial technical complexity that may ultimately limit their implementation. Yet another alternative is voltammetry —a very simple method in theory that has previously been tested for this application to a limited extent. The equipment for a voltammetry system consists of off-the-shelf components (three electrodes and a potentiostat), which results in substantial benefits relative to cost and robustness. Based on prior knowledge of electrochemical reduction potentials for each of the species of interest, voltammetry can be used to quantify concentrations of a variety of elemental species—including uranium, plutonium, minor actinides, and rare earths. Various methods have been tested by other researchers to date—including cyclic voltammetry, square wave voltammetry, normal pulse voltammetry, etc. In most cases, it has been observed that there is a very limited concentration range for which the output can be readily correlated with concentration in the salt. Furthermore, testing to date has been limited to simple ternary salts with only a single element being quantified. While incomplete for application to MC&A for pyroprocessing, these results lead us to believe that voltammetry can be optimized based on salt properties and fundamental electrochemical rate processes to yield a highly accurate and robust method. This project is divided into four tasks jointly executed by three university research groups. This includes experimental measurement of key physical data on the systems of interest, development of a predictive voltammetry model, experimental validation of the voltammetry model, and design/verification of an optimized measurement method. This project supports the goals of the US-ROK Joint Fuel Cycle Study in addition to the NA-24 Office of the National Nuclear Security Agency and the International Atomic Energy Agency (IAEA).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Atomistic simulation methods for long-time dynamics in materials for nuclear energy systems

Many important processes in materials systems are intrinsically atomistic in nature but involve time scales that span many orders of magnitude, thus exceeding what can be directly simulated using molecular dynamics. This is especially true for materials in nuclear energy applications, in which defects created by collision cascades on the femtosecond-picosecond time scale cause microstructural changes that continue to evolve for years, in many cases leading to failure of the material. In this chapter, we review atomistic methods for reaching long time scales in systems like these. These accelerated molecular dynamics and adaptive kinetic Monte Carlo methods exploit the infrequent-event nature of the diffusive events that comprise this long-time evolution. In favorable cases, these methods can predict state-to-state evolution that approximates what would result from an extremely long molecular dynamics simulation, and the most accurate of the methods can do this to arbitrary accuracy. We present some examples of applications of these methods to problems relevant to nuclear energy materials, the subject of this volume. We then discuss situations that are difficult for the methods, causing them to be less efficient, and we conclude with a short list of the most pressing issues in the further development of these approaches to make them as powerful and predictive as possible for realistic problems.

36 MATERIALS SCIENCE↗

On the Development of Godunov Methods and Their Application to Gasdynamics

We are interested in developing the most accurate numeral models to simulate Gadynamics of explosions. But we must first recognize that there is no unique way to discretize the partial differential equations (PDEs) of gas dynamics, and also, there is no unique method to integrate the discretized forms of these equations. This has spawned a variety of numerical methods (religions*) that attempt to solve this conundrum, for example: Artificial Viscosity method created by the American mathematician John von Neumann, Flux-Corrected-Transport (FCT) method invented by Dr. Jay Boris, founder of the Laboratory for Computational Physics (LCP) at NRL, WENO method developed by Professor Stan Osher of UCLA and Professor Bjorn Enquist of U. Texas, and Godunov method by Academician Sergei Konstantinovich Godunov, Professor of the Sobolev Institute of Mathematics, RAS, in Novosibirsk to name just a few.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tight-Binding-Based Method for Simulations of Complex Materials with Accompanying Database

The NRL-Tight-Binding (NRL-TB) method has been applied successfully to many monatomic, binary, and a few ternary systems. The method consists of a fit to Density Functional Theory (DFT) results and has transferability beyond the fitted DFT database including performing tight-binding molecular dynamics simulations. We are working on a new website with a detailed guide of how to use the method in performing the fit to DFT results (Fitting Code) and obtaining non-orthogonal TB parameters expressed in a polynomial form as environment-dependent Slater-Koster parameters (on-site terms), and neighbor distance-dependent Hamiltonian and Overlap terms. These parameters are then used in a Static Code to verify or make predictions for large systems often beyond the computational capabilities of standard DFT codes. Our starting point was a website developed at NRL some years ago which NRL no longer supports. We have now been augmenting that website with new examples of expanding the original capabilities of the method such as incorporating in the codes f-electron states. Our website (esd.cos.gmu.edu/tb) contains two separate branches: One named NRL-TB with the full documentation of the method including source codes and examples. The other branch, named ESD-dB, is a library of electronic structure calculations for all the monatomic elements (a subset of the elements also found in a recent book by the author of this proposal. See reference 22) and an approximately 700 hundred compounds in specific crystal structures. We discuss below the progress made so far in improving and expanding the capabilities of our TB method and the plans for further extensions of our approach.

36 MATERIALS SCIENCE↗