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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Insulating ground state and 2−𝑘 magnetic structure of candidate Weyl hydrogen-atom K2⁢Mn3⁢(AsO4)3

The ideal Weyl "hydrogen-atom" semimetal exhibits only a single pair of Weyl nodes and no other trivial states at the Fermi energy. Such a material would be a panacea in the study of Weyl quasi-particles, allowing direct unambiguous observation of their topological properties. The alluaudite-like K2⁢Mn3⁢(AsO4)3 compound was recently proposed as such a material. Here, we use comprehensive experimental work and first-principle calculations to assess this prediction. We find K2⁢Mn3⁢(AsO4)3 crystallizes in the 𝐶⁢2/𝑐 symmetry with a quasi-one-dimensional Mn sublattice, growing as small needle-like crystals. Bulk property measurements reveal magnetic transitions at ≈8 and ≈4 K, which neutron scattering experiments show correspond to two distinct magnetic orders, first a partially ordered ferrimagnetic 𝐤𝟏=(0,0,0) structure at 8 K and a second transition of 𝐤𝟐=(1,0,0) at 4 K to a fully ordered state. Below the second transition, both ordering vectors are necessary to describe the complex magnetic structure with modulated spin magnitudes. Both of the best-fit magnetic structures in this work are found to break the symmetry necessary for the generation of Weyl nodes, though one of the magnetic structures allowed by 𝐤𝟏 does preserve this symmetry. However, the crystals are optically transparent and ellipsometry measurements reveal a large band gap, undermining expectations of semimetallic behavior. Density functional theory calculations predict an insulating antiferromagnetic ground state, in contrast to previous reports, and suggest potential frustration on the magnetic sublattice. Given the wide tunability of the alluaudite structure, we consider ways to push the system closer to a semimetallic state.

Taddei, Keith M [Argonne National Laboratory]↗
DOE OSTI2024

Nucleon axial and pseudoscalar form factors using twisted-mass fermion ensembles at the physical point

We compute the nucleon axial and pseudoscalar form factors using three N f = 2 + 1 + 1 twisted-mass fermion ensembles with all quark masses tuned to approximately their physical values. The values of the lattice spacings of these three physical point ensembles are 0.080, 0.068, and 0.057 fm and spatial sizes 5.1, 5.44, and 5.47 fm, respectively, yielding m π L > 3.6 . Convergence to the ground-state matrix elements is assessed using multistate fits. We study the momentum dependence of the three form factors and check the partially conserved axial-vector current (PCAC) hypothesis and the pion pole dominance (PPD). We show that in the continuum limit, the PCAC and PPD relations are satisfied. We also show that the Goldberger-Treimann relation is approximately fulfilled and determine the Goldberger-Treiman discrepancy. Our final results are g A = 1.245 ( 28 ) ( 14 ) for the nucleon axial charge, ⟨ r A 2 ⟩ = 0.339 ( 48 ) ( 06 ) fm 2 for the axial radius, g π N N ≡ lim Q 2 → − m π 2 G π N N ( Q 2 ) = 13.25 ( 67 ) ( 69 ) for the pion-nucleon coupling constant, and G P ( 0.88 m μ 2 ) ≡ g P * = 8.99 ( 39 ) ( 49 ) for the induced pseudoscalar form factor at the muon capture point. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Search for vector-like leptons coupling to first- and second-generation Standard Model leptons in pp collisions at s = 13 TeV with the ATLAS detector

A search for pair production of vector-like leptons coupling to first- and second-generation Standard Model leptons is presented. The search is based on a dataset of proton-proton collisions at s$$ \sqrt{s} $$ = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb−1. Events are categorised depending on the flavour and multiplicity of leptons (electrons or muons), as well as on the scores of a deep neural network targeting particular signal topologies according to the decay modes of the vector-like leptons. In each of the signal regions, the scalar sum of the transverse momentum of the leptons and the missing transverse momentum is analysed. The main background processes are estimated using dedicated control regions in a simultaneous fit with the signal regions to data. No significant excess above the Standard Model background expectation is observed and limits are set at 95% confidence level on the production cross-sections of vector-like electrons and muons as a function of the vector-like lepton mass, separately for SU(2) doublet and singlet scenarios. The resulting mass lower limits are 1220 GeV (1270 GeV) and 320 GeV (400 GeV) for vector-like electrons (muons) in the doublet and singlet scenarios, respectively.

Aad, G↗
DOE OSTI2026

Nonmonotonic-potential description of polarization effects, fusion, and nuclear rainbows in elastic scattering of 6 Li + 12 C at 4.5–600 MeV

The experimental differential cross-section (CS) and analyzing power (AP) data of the 6 Li + 12 C elastic scattering over a wide laboratory energy scale (4.5MeV≤𝐸 lab ≤600MeV) are analyzed within the framework of the optical model (OPM) using nonmonotonic (NM) nucleus–nucleus potentials. The real part of the NM potentials is derived from the Pauli-embodied energy density-functional (EDF) formalism with the sudden approximation. The real part of the noncentral spin-orbit and tensor terms, as well as the imaginary parts, are treated phenomenologically. The effect of the radius of sensitivity on the CS and AP data is found to be more important at lower energies. The diffractive and refractive scattering with Airy structures in the whole angular region of the elastic scattering across the studied energy range is successfully described within the OPM using the NM 6 Li + 12 C potential. The near- and far-side (N and F) decomposition of the total elastic-scattering amplitudes has also been studied using our NM potentials. The evolution of the Airy minima in the angular distributions, coupled with the fitting of the AP data, provides an accurate description of Airy minima of different orders. The OPM calculations with the NM potentials describe exceptionally well the CS, vector analyzing power (VAP), and tensor analyzing power data at 𝐸 lab =9.0,19.24,20,30, and 50MeV. In agreement with our past successful descriptions of CS and the opposite signs of the VAP data for the 6 Li and 7 Li elastic scattering using NM potentials in OPM, the present results appear to provide a better fit, so far, than those obtained from the coupled-channels method. The fusion cross sections of 6 Li + 12 C have been predicted in the energy range (4.5MeV≤𝐸 lab ≤20MeV), fitting the experimental data well in the range 𝐸 lab =2.97–11.77MeV. The EDF potential without any energy dependence and renormalization is also found to describe satisfactorily the experimental CS and AP data at energies up to several hundreds of MeV.

6 ≤ A ≤ 19↗
DOE OSTI2023

Robust Vector BOTDA Signal Processing with Probabilistic Machine Learning

This paper presents a novel probabilistic machine learning (PML) framework to estimate the Brillouin frequency shift (BFS) from both Brillouin gain and phase spectra of a vector Brillouin optical time-domain analysis (VBOTDA). The PML framework is used to predict the Brillouin frequency shift (BFS) along the fiber and to assess its predictive uncertainty. We compare the predictions obtained from the proposed PML model with a conventional curve fitting method and evaluate the BFS uncertainty and data processing time for both methods. The proposed method is demonstrated using two BOTDA systems: (i) a BOTDA system with a 10 km sensing fiber and (ii) a vector BOTDA with a 25 km sensing fiber. The PML framework provides a pathway to enhance the VBOTDA system performance.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Complex multicomponent spectrum analysis with Deep Neural Network

Here, in this paper, we present the use of deep neural networks to estimate physical parameters from complex optical emission spectra of the D β /H β transition. Specifically, we focus on estimating the radio frequency electric field vector of the lower hybrid wave and isotope ratio within the scrape-off-layer plasma of the WEST tokamak. Fitting the spectral data using a traditional non-linear least squares analysis requires many free parameters and is computationally expensive, rendering the data unusable for real-time control. By implementing relatively small neural networks, the physical parameters can be directly extracted from the spectral data with reasonable accuracy in a few milliseconds. The deep neural network prediction can serve as input for a reduced model using least-squares fitting or for real-time control. We show that deep neural networks can be an effective tool for analyzing complex multicomponent spectra, providing a speedup of more than 10 5 times compared to least residual analysis, with an accuracy of 0.5% for the isotope ratio, and 0.09 kV/cm and 0.38 kV/cm for the RF radial and poloidal electric field respectively.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Quality and Loss Factor Characterization of YBCO Superconducting Transmission Lines for Axion Dark Matter Detection

Axion haloscope experiments aim to detect the conversion of axions into microwave photons under a strong magnetic field through resonant cavity techniques. The conversion produces an extremely small signal, requiring a cryogenic environment to reduce thermal noise, and low-loss superconducting transmission lines for minimal attenuation in the readout chain. Yttrium barium copper oxide (YBCO) cables are a promising candidate. Unlike commonly used low-loss cryogenic cables such as niobium (Nb) and niobium titanium (NbTi), which have low critical fields, YBCO is a high-temperature superconductor that can remain stable in strong magnetic fields. We characterized the quality and loss of five stripline resonators from the Brookhaven Technology Group: three YBCO, a copper reference, and a silver reference. Experimental methodology included collecting scattering parameter data on a vector network analyzer for the samples at 77 K along with room temperature baseline measurements, and employing both Lorentzian-fit and circle-fitting techniques to confirm the coupling regime and corroborate results. We achieved quality factors on the order of $10^3$ with corresponding loss factors on the order of $10^{-1}$ dB/m. Trends were comparable with literature data on Nb and NbTi at 4 K, which did have lower loss under these conditions, but suggested similar or perhaps better loss for YBCO when accounting for the temperature difference. We also developed a cryogenic probe for future measurements in a 14 T applied field at 30 mK. This will serve to directly evaluate YBCO's durability in magnetic fields, and we expect significantly improved performance at millikelvin temperatures.

Marinos, Z. [UCLA]↗
DOE OSTI2022

$\mathrm{SIM}$-$\mathrm{STEM}$ $\mathrm{Lab}$: Incorporating Compressed Sensing Theory for Fast STEM Simulation

We report recently it has been shown that precise dose control and an increase in the overall acquisition speed of atomic resolution scanning transmission electron microscope (STEM) images can be achieved by acquiring only a small fraction of the pixels in the image experimentally and then reconstructing the full image using an inpainting algorithm. In this paper, we apply the same inpainting approach (a form of compressed sensing) to simulated, sub-sampled atomic resolution STEM images. We find that it is possible to significantly sub-sample the area that is simulated, the number of g-vectors contributing the image, and the number of frozen phonon configurations contributing to the final image while still producing an acceptable fit to a fully sampled simulation. Here we discuss the parameters that we use and how the resulting simulations can be quantifiably compared to the full simulations. As with any Compressed Sensing methodology, care must be taken to ensure that isolated events are not excluded from the process, but the observed increase in simulation speed provides significant opportunities for real time simulations, image classification and analytics to be performed as a supplement to experiments on a microscope to be developed in the future

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

In this paper, we report on a study of the spectral features associated with dipole resonances in medium mass nuclei (E ≤ 12 MeV), as revealed in the framework of the spd-interacting boson model. The effect of pairing correlations on the theory follows from solutions obtained through an application of the Bethe Ansatz Equation. In general, calculated spectra around the critical point of the vibrational to γ-soft transitions appears to approach that of a Gaussian Orthogonal Ensemble, while near the rotational and vibrational limits of the theory the spectra show more regular behavior. Specifically, the results reveal that the statistical features of the spectra are sensitive to the vector boson pairing strength, c p , in the transition region; that is, when c p is zero, or when the system approaches one of its dynamical symmetries limits the spectrum display regular features, while for stronger c p values, or when near to the critical phase transition region, the spectral feature show more chaotic behavior. Overall, our results indicate that the statistical features are governed by the interplay between dipole resonant energies, pairing correlations, and interactions between and among the single and vector bosons modes of the theory. As part of this work we also found out that chaoticity occurs when results were fit to a Berry-Robnik distribution. Throughout our analyses, we used experimentally known information about both positive and negative parity states. Our findings suggest that dipole resonances appear to be best-described by Poisson statistics for A ≈ 32-138 nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

QCD+QED PDF implications for the Higgs sector

In this work, we examine the implications of electroweak corrections beyond leading order for processes of special interest in the Higgs sector. We especially explore the role of these corrections given the introduction of an explicit parton distribution function (PDF) for the photon in the proton, an object which emerges necessarily in global PDF fits which include QED effects (i.e., ‘QCD+QED PDFs’). We concentrate on several representative cases, including total Higgs-production cross sections through gluon fusion, gg → H, vector-boson fusion (VBFH), and associated production, pp → V H; we also examine differential distributions, taking a representative Higgs-strahlung process, pp → W + H. We find that the recently developed LUX formalism for the photon PDF significantly stabilizes the PDF dependence of both QED-PDF and electroweak corrections in the Higgs sector, while leaving overall ~ 3–4% cross-section-level variations, depending on the chosen QCD+QED PDF. We illustrate this QCD+QED PDF dependence by exploring predictions based upon recent analyses of the CTEQ-TEA, MSHT, and NNPDF analysis groups, fitted either at NNLO or approximate N3LO in QCD.

Higgs production↗
DOE OSTI2025

Amplitude Analysis of ωπ0 Photoproduction at GlueX

spectrum of light mesons produced from a linearly polarized photon beam. The production and decays of a light meson resonance X such as γp → Xp′ →ωπ0p′ can be modeled with polarized vector-pseudoscalar ampli- tudes, which can describe the contribution of individual amplitudes to the total measured intensity. The status of mass-independent fits to the ωπ0 mass spectrum over a wide range of mass and momentum transfer−twill be presented, with an emphasis on interactions with the b1(1235) meson. We will also present in parallel an analysis of moments of the angular dis- tributions for the same process, as a means of verifying the stability of the amplitude-based results. These results will help to improve the broader knowledge of light meson states and how they are produced.

Scheuer, Kevin [College of William and Mary, Willi↗
DOE OSTI2022

High bias machine learning for antineutrino-based safeguards for small reactors

The statistical methods used for antineutrino detection will need to be improved to effectively monitor the inventory of next-generation nuclear reactors. In this sensitivity study, we evaluate machine learning models compared to previously used statistical approaches to identify diversion scenarios in a simulated Advanced Fast Reactor (AFR)-100. A chi-square goodness-of-fit technique, which individually compares the simulated antineutrino yields to the expected antineutrino yield, resulted in precise but low diversion detection probability. Various support vector machine (SVM) models were applied with diverse training datasets to evaluate the robustness of the method towards unexpected or “unseen” diversion scenarios. Furthermore, our results indicate that while the SVM models significantly improved the detection probability of near-field antineutrino-based safeguards, up to a probability of ~0.04, for the simulated small reactor, the detection system still needs improvements to reach the 0.2 detection limit established by the International Atomic Energy Agency.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2025

A 28 nm multiply-accumulate ASIC architecture for on-chip data compression in MHz frame rate X-ray and electron pixel detectors

Modern X-ray detector systems urgently require compact, efficient, and fast data compression schemes to handle the transmission of big data from pixel arrays, enabling frame rates in the MHz regime. Here, in this work, a data compression ASIC that implements a streaming fixed-length lossy compression scheme is introduced and analyzed, proving the feasibility and benefits of on-chip compression. The compression scheme utilizes a vector matrix product logic, which performs a number of floating-point multiplications, additions, and accumulations. The logic is verified, synthesized, and shown to fit in the area resource available for the X-ray detector under study, which comprises 192 × 168 pixels each of 12-bit width, and having a total area of 20 mm× 20 mm, about 2 mm× 20 mm of which are available for the digital logic. Several system architectures, precisions, and compression ratios ranging from 100 to 250 were analyzed to pave the way for on-chip fixed-length compression (e.g., principal component analysis, singular value decomposition) and data reduction (e.g., azimuthal integration) for X-ray and electron detectors.

Data compression↗
DOE OSTI2023

Xylella fastidiosa modulates exopolysaccharide polymer length and the dynamics of biofilm development with a β-1,4-endoglucanase

Xylella fastidiosa is a Gram-negative bacterium that causes disease in many economically important crops. It colonizes the plant host xylem and the mouthparts of its insect vectors where it produces exopolysaccharide (EPS) and forms robust biofilms. Typically, the ability to form a biofilm enhances virulence, but X. fastidiosa does not fit neatly into that paradigm. Instead, X. fastidiosa enters into biofilms to attenuate its movement in the xylem, which, in turn, slows disease progression. In most of its over 600 known plant hosts, X. fastidiosa behaves as a benign commensal, but in some hosts like Vitis vinifera grapevines, it acts as a pathogen. Its ability to attenuate its own virulence in susceptible hosts may be a remnant of its commensal lifestyle in other hosts. Here, we demonstrate that X. fastidiosa utilizes a β-1,4 endoglucanase to cleave its self-produced β-1,4-glucan exopolysaccharide polymer to process it from a higher molecular weight to a lower molecular weight polymer. This processing mediates surface adherence of the cells and ultimately governs overall biofilm architecture, indicating enzymatic pruning of the EPS plays a key role in biofilm-mediated attenuation of X. fastidiosa in planta and, thus, is a key vestige that links its commensal behaviors to its parasitic behaviors in specific hosts.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Using Downwelling Far- and Thermal-Infrared Hyperspectral Radiance for Cloud Phase Classification in the Antarctic

The cloud phase is one of the most important parameters of clouds. In this paper, we propose a method for cloud phase classification that synergistically utilizes the far- and thermal-infrared bands based on the Atmospheric Emitted Radiance Interferometer (AERI) at the Atmospheric Radiation Measurement West Antarctic Radiation Experiment (AWARE) observatory in 2016. The possible features in the far- and thermal-infrared bands are analyzed based on the differences in the simulated cloud brightness temperature (BT) spectra with different cloud phases. Using the support vector machine (SVM) algorithm, four features are determined to identify the cloud phase, which include the BT at 900 cm -1 , the slope of the fitted function of BT in the 900–1000 cm -1 interval, the BT difference (BTD) between 512 cm -1 and 726 cm -1 , and the BTD between 550 cm -1 and 726 cm -1 . Here, the performance of the proposed method is evaluated with Shupe’s and Turner’s method. The monthly average accuracy of the proposed method, the method without the two far-infrared features, and Turner’s method are about 76%, 36%, and 49%, respectively, which infer the good performance of the proposed method and also indicate that the far-infrared band features can effectively enhance cloud phase classification. It is notable that, compared to Shupe’s method, the accuracy for the proposed method is only 61% during the Antarctic summer, which results from the definitions of cloud phase and radiative effect. In addition, the accuracy is only 44% for Turner’s method in seasons with a low frequency of mixed clouds due to the significant effect of water vapor.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Rare Higgs Processes at CMS and Precision Timing Detector Studies for HL-LHC CMS Upgrade

This thesis describes the search for two rare Higgs processes. The first analysis describes the CMS Run 2 search for $H$ $\rightarrow$ $\mu$$\mu$ decays, with 137.3 fb$^{-1}$ of data at $\sqrt{s}$ = 13 TeV. The analysis targeted four different Higgs production modes: the gluon fusion (ggH), the vector boson fusion (VBF), the Higgs-strahlung process (VH), and the production in association with a pair of top quarks (ttH). Each category used a dedicated machine learning based classifier to separate the signal from the background processes. A combined fit from all these categories saw a slight excess in the data corresponding to 3.0 standard deviations at $M$$_{H}$ = 125.38 GeV, and gave the first evidence for the Higgs boson decay to second-generation fermions. The best-fit signal strength and the corresponding 68% CL interval was found to be +0.17?????? = 1.19 $_{-0.39}^{+0.41}$ (stat)$_{-0.16}^{+0.17}$(syst) at $M$$_{H}$ = 125.38 GeV. The second analysis describes the CMS Run 2 search for 𝐻𝐻 → 𝑏𝑏𝑏𝑏 with highly boosted Higgs bosons. This analysis used a dedicated jet identification algorithm based on graph neural networks (ParticleNet) to identify boosted H→ bb jets. This search targeted the gluon fusion and the vector boson fusion HH production modes, and put constraints on the allowed values of the various Higgs couplings as: 𝜅𝜆 ∈ [−9.9, 16.9] when 𝜅𝑉 = 1, 𝜅2𝑉 = 1; 𝜅𝑉 ∈ [−1.17, −0.79] ∪ [0.81, 1.18] when 𝜅𝜆 = 1, 𝜅2𝑉 = 1; 𝜅2𝑉 ∈ [0.62, 1.41] when 𝜅𝜆 = 1, 𝜅𝑉 = 1. A scenario with 𝜅2𝑉 = 0 was excluded with a significance of 6.3 standard deviations for the first time, when other H couplings are fixed to their SM values. The combined observed (expected) 95% upper limit on the HH production cross section was found to be 9.9 (5.1) × SM. Finally, this thesis also discusses the planned MIP Timing Detector (MTD) upgrade for CMS at the HL-LHC. The MTD will be a time-of-flight (TOF) detector, designed to provide a precision timing information for charged particles using SiPMs + LYSO scintillating crystals, with a time resolution of ∼30 ps. This thesis describes several R&D tests that have been performed for characterizing the sensor properties (time resolution, light yield, etc.) and optimizing the sensor design geometry. This thesis also contains a description of mock test setups for cooling the sensors, since it is known to be an effective way of mitigating the increased dark current rates in the sensors due to radiation damage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Simulation of the Impact of Point Defects and Edge Dislocations on X-Ray Diffraction in Hexagonal (Ni,Co) 1+2 x Ti 1– x O 3 Thin Films

In this work, a computer code for simulating high-resolution X-ray diffraction (XRD) data from disordered crystals with arbitrary spatial composition and local lattice parameters is developed. Simulated patterns are compared with the experimental data collected on a single phase, highly crystalline (Ni 0.42 Co 0.58 ) 2.22 Ti 0.39 O 3 solid-solution thin film exhibiting a large number of subsidiary minima. As a case study, the edge dislocations in hexagonal (Ni,Co) 3 O 3 thin films with Burgers vector parallel and perpendicular to the a-axis and c-axis, respectively, are modeled. No peak profiles are assumed and thus issues related to profile fitting are avoided. Both macroscopic features, such as film thickness, and atomic-scale structure, such as dislocations, are simultaneously modeled. Simulations are run on a desktop machine. Commonly applied database-based phase identification routines can result in wrong phase identification, unless intensities are properly modeled. Modeling tools of diffractometer manufacturers are compared with the present approach. An example of how simulated reciprocal lattice patterns can be used to choose relevant measurement geometries in defected thin films is given.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗