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Final Reports of the 2021 Los Alamos National Laboratory Computational Physics Student Summer Workshop

Since 2011, the Los Alamos National Laboratory Computational Physics Student Summer Workshop has been bringing together a highly talented and diverse group of students every summer. Students work in teams of two, alongside typically two mentors, on research projects reflecting a broad range of topics within computational physics. In addition, students attend a series of lectures on topics within computational physics, facility tours, and networking events. The program lasts ten weeks, with this year’s workshop running from June 7 to August 13. At the end of the summer, students give a final presentation, along with a written report. Those reports are what make up the remaining sections of this document. Admission to the workshop is by a competitive process, with the mentors forming the selection committee. One of the important accomplishments of the workshop has been to create a student pipeline from diverse schools that sometimes are not normally tapped by LANL recruiting. Many workshop students maintain a continuing relationship with LANL, returning as student interns, post-doctoral researchers, and staff members. Additionally, workshop alumni act as ambassadors for LANL. The result is a wider awareness both of LANL as a potential employer, and of the technical work that happens at LANL. This year, the workshop was once again in an off-site, virtual format. Students worked on LANL virtual desktop systems remotely, also accessing LANL HPC resources. In order to facilitate communication, student were given accounts on both Webex, a video teleconferencing platform, and Mattermost, an online team collaboration and chat platform, similar to Slack. Daily communication between students and mentors was primarily on Mattermost, with Webex conferencing as needed. The lectures were all done on Webex. Given the difficulty of the virtual format, and a concern that students might have video teleconferencing burn-out, all lectures were optional this year. In spite of this, the attendance was generally high. Lecturers were asked to try to move to a more high-level, ”What is it?,” format. Once again, the students did a tremendous job. Over the course of ten weeks, they did important research across a staggering array of disciplines. The following pages contain the final report for each team’s research efforts. Enjoy!

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Classification of Dissolution Events Using Fusion of Effluents Measurements and Classifiers

Classifiers for dissolution events at a radiochemical processing facility are studied using gamma spectra measurements of effluents collected by a high purity germanium detector located at its off-gas stack. Data sets collected at the Oak Ridge National Laboratory’s Radiochemical Engineering Development Center under a Pu dissolution campaign spanning a three months period are utilized. Features corresponding to the activity levels of 15 radionuclides, including isotopes of iodine, krypton, and xenon, that are indicated by the target decay chains, are computed from the spectra at 1 hour intervals. A conceptualization diagram is developed to reflect the steps from the source to measurement to feature computation that depend on fission products indicated by decay chains, chemical processing, and effluents transport to the off-gas stack. A diverse set of eight classifiers based on different design principles are trained using the ground truth data for this campaign, and the outputs of top three classifiers, namely, classification trees, Ensemble of Trees (EOT), and k-nearest neighbor, are combined using EOT classifier-fuser. Our results show that for 5-fold cross validation, features associated with isotopes of xenon provide the lowest classification error among the different elements across the classifiers; the classification error is furthered improved when all 15 isotope features are used by each classifier, and it is again improved by the fusion of three classifiers. Further reduction in classification error is achieved by using a measurement window of 1-2 days which is identified based on half-life time estimates of the isotopes; it is long enough for the stabilization of feature estimates while being short enough not to be affected by the follow on dissolution events. As a net result of feature and classifier fusion, combined with the incorporation of decay chain and isotope half-life information, this approach achieves 98% detection rate while maintaining a false alarm rate under 2% for this data set.

Rao, Nageswara↗

Insight into the Fast-Rechargeability of a Novel Mo 1.5 W 1.5 Nb 14 O 44 Anode Material for High-Performance Lithium-Ion Batteries

Wadsley–Roth phased niobates are promising anode materials for lithium-ion batteries, while their inherently low electrical conductivity still limits their rate-capability. Herein, a novel doped Mo 1.5 W 1.5 Nb 14 O 44 (MWNO) material is facilely prepared via an ionothermal-synthesis-assisted doping strategy. The detailed crystal structure of MWNO is characterized by neutron powder diffraction and aberration corrected scanning transmission electron microscope, unveiling the full occupation of Mo 6+ -dopant at the t1 tetrahedral site. In half-cells, MWNO exhibits enhanced fast-rechargeability. In this work, the origin of the improved performance is investigated by ultraviolet–visible diffuse reflectance spectroscopy, density functional theory (DFT) computation, and electrochemical impedance spectroscopy, revealing that bandgap narrowing improves the electrical conductivity of MWNO. Furthermore, operando X-ray diffraction elucidates that MWNO exhibits a typical solid-solution phase conversion-based lithium-ion insertion/extraction mechanism with reversible structural evolution during the electrochemical reaction. The boosted lithium-ion diffusivity of MWNO, due to the Mo 6+ /W 6+ doping effect, is confirmed by a galvanostatic intermittent titration technique and DFT. With the simultaneously enhanced electrical conductivity and lithium-ion diffusivity, MWNO successfully demonstrates its fast-rechargeability and practicality in the LiNi 0.5 Mn 1.5 O 4 -coupled full-cells. Therefore, this work illustrates the potential of ionothermal synthesis in energy storage materials and provides a mechanistic understanding of the doping effect on improving material's electrochemical performance.

25 ENERGY STORAGE↗

Defect Complexes in CrSBr Revealed Through Electron Microscopy and Deep Learning

Atomic defects underpin the properties of van der Waals materials, and their understanding is essential for advancing quantum and energy technologies. Scanning transmission electron microscopy is a powerful tool for defect identification in atomically thin materials, and extending it to multilayer and beam-sensitive materials would accelerate their exploration. Here, we establish a comprehensive defect library in a bilayer of the magnetic quasi-1D semiconductor CrSBr by combining atomic-resolution imaging, deep learning, and calculations. We apply a custom-developed machine learning work flow to detect, classify, and average point vacancy defects. This classification enables us to uncover several distinct Cr interstitial defect complexes, combined Cr and Br vacancy defect complexes, and lines of vacancy defects that extend over many unit cells. We show that their occurrence is in agreement with our computed structures and binding energy densities, reflecting the intriguing layer interlocked crystal structure of CrSBr. Our ab initio calculations show that the interstitial defect complexes give rise to highly localized electronic states. These states are of particular interest due to the reduced electronic dimensionality and magnetic properties of CrSBr and are, furthermore, predicted to be optically active. Our results broaden the scope of defect studies in challenging materials and reveal new defect types in bilayer CrSBr that can be extrapolated to the bulk and to over 20 materials belonging to the same FeOCl structural family.

deep learning↗

Diffraction of radio-frequency waves by plasma turbulence in the edge of a tokamak

The Mie-Lorenz-Debye theory of scattering of radio frequency waves (RF) by filamentary structures in the edge of a tokamak plasma has been established in prior publications. These results have been verified. Theory and computations show that RF can be reflected, refracted, and diffracted by turbulence. Furthermore, the filamentary structures lead to side scattering of waves and excitation of wave modes different from the launched RF. It is important to quantify the overall effect of turbulence on the propagation of RF since efficiency of heating and current drive by RF waves depends upon the wave characteristics. The commonly used RF ranges vary from the low frequency ion-cyclotron (IC) waves, to medium frequency lower-hybrid (LH) waves, to high-frequency electron cyclotron (EC) waves with wavelengths respectively, large, comparable, or smaller than the radial dimensions of the filaments. Currently, we discuss the scattering as well as the forces exerted by different RF in the edge plasma. Also, we present a code for 3D full wave scattering analysis of arbitrary tensor permittivity and plasma density profiles. The study is applicable to ITER-like plasmas, as well as to plasmas in medium sized tokamaks such as TCV, ASDEX-U and DIII-D and high field concepts like SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Low rank approximation in simulations of quantum algorithms

Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits can be simulated efficiently on a classical computer if the input quantum state is a low rank tensor and all intermediate states of the quantum algorithm can be represented or approximated by low rank tensors. Here, in this paper, we examine the possibility of simulating a few quantum algorithms by using low-rank canonical polyadic (CP) decomposition to represent the input and all intermediate states of these algorithms. Two rank reduction algorithms are used to enable efficient simulation. We show that some of the algorithms preserve the low rank structure of the input state and can thus be efficiently simulated on a classical computer. However, the rank of the intermediate states in other quantum algorithms can increase rapidly, making efficient simulation more difficult. To some extent, such difficulty reflects the advantage or superiority of a quantum computer over a classical computer. As a result, understanding the low rank structure of a quantum algorithm allows us to identify algorithms that can benefit significantly from quantum computers.

97 MATHEMATICS AND COMPUTING↗

Nuclear Forces for Precision Nuclear Physics: A Collection of Perspectives

This is a collection of perspective pieces contributed by the participants of the Institute for Nuclear Theory’s Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. Please note the contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Evaluation of the Sum-of-Fractions Methodology for Water and Polyethylene Moderated Systems

Sum-of-Fractions is a method intended to assure a subcritical margin for aqueous solutions and slurries of fissionable isotopes. The method indicates that a system is subcritical if the sum of the ratios of the mass of each isotope in a mixture to its individual minimum subcritical mass limit is less than or equal to one. The basis of the Sum-of Fractions has historically been derived from allowances given in ANSI/ANS-8.15-1981. However, the allowance was removed in ANSI/ANS-8.15-2014 due to a lack of technical basis. A methodology was developed to assess the validity of using the Sum-of-Fractions for water or polyethylene moderated systems for the following nuclides: 232 U, 233 U, 234 U, 235 U, 237 Np, 236 Pu, 238 Pu, 239 Pu, 240 Pu, 241 Pu, 242 Pu, 241 Am, 242 mAm, 243 Am, 242 Cm, 243 Cm, 244 Cm, 245 Cm, 246 Cm, 247 Cm, 249 Cf, and 251 Cf. The methodology uses available benchmark data for mixtures of 233 U, 235 U, and 239 Pu to establish the calculational margin, and a mass limit reduction to establish the margin of subcriticality. Water or polyethylene moderated and reflected mixtures containing the nuclides are evaluated with SCALE 6.2.4. Including the calculational margin, subcritical mass limits for each nuclide were computed for optimally water or polyethylene moderated and fully reflected systems. These masses were used to create nuclide mixtures in which the sum of the mass to subcritical mass limit ratios is one. The various nuclide mixtures were modeled over a range of moderation and demonstrate the k eff does not exceed the calculational margin. For additional assurance of subcriticality, a significant mass reduction is applied to each computed minimum critical mass of the nuclides without adequate benchmark data consistent with the method in ANSI/ANS-8.15-2014.

07 ISOTOPE AND RADIATION SOURCES↗

Determining the Concentration of Free Electrons in n-InSb from Far-Infrared Reflectance Spectra with Allowance for Plasmon–Phonon Coupling

Contactless nondestructive testing is a means for determining the concentration of free electrons N in indium antimonide (InSb) samples from far-infrared reflectance spectra recorded at room temperature. A computer program capable of determining the characteristic wave number from the Kramers–Kronig relation is developed. The calculated calibration dependence makes it possible to determine the electron concentration from the known characteristic wave number. It is shown that this dependence is described by a cubic polynomial. In the calculations, the energy dependence of the electron effective mass is taken into account. It is established that, in determining the electron concentration, account must be taken of plasmon–phonon coupling, specifically at N ≤ 5 × 10{sup 17} cm{sup –3}. The systematic error introduced into the determination of N by disregard of plasmon–phonon coupling is estimated. The software elaborated here makes it possible to calculate the electron concentration N from experimental reflectance spectra and to store and process the results. The software is tested by the example of the reflectance spectrum of heavily doped n-InSb.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Engineering the temporal dynamics of all-optical switching with fast and slow materials

Abstract All-optical switches control the amplitude, phase, and polarization of light using optical control pulses. They can operate at ultrafast timescales – essential for technology-driven applications like optical computing, and fundamental studies like time-reflection. Conventional all-optical switches have a fixed switching time, but this work demonstrates that the response-time can be controlled by selectively controlling the light-matter-interaction in so-called fast and slow materials. The bi-material switch has a nanosecond response when the probe interacts strongly with titanium nitride near its epsilon-near-zero (ENZ) wavelength. The response-time speeds up over two orders of magnitude with increasing probe-wavelength, as light’s interaction with the faster Aluminum-doped zinc oxide (AZO) increases, eventually reaching the picosecond-scale near AZO’s ENZ-regime. This scheme provides several additional degrees of freedom for switching time control, such as probe-polarization and incident angle, and the pump-wavelength. This approach could lead to new functionalities within key applications in multiband transmission, optical computing, and nonlinear optics.

42 ENGINEERING↗

Refinements for Bragg coherent X-ray diffraction imaging: electron backscatter diffraction alignment and strain field computation

Bragg coherent X-ray diffraction imaging (BCDI) allows the 3D measurement of lattice strain along the scattering vector for specific microcrystals. If at least three linearly independent reflections are measured, the 3D variation of the full lattice strain tensor within the microcrystal can be recovered. However, this requires knowledge of the crystal orientation, which is typically attained via estimates based on crystal geometry or synchrotron microbeam Laue diffraction measurements. Presented here is an alternative method to determine the crystal orientation for BCDI measurements using electron backscatter diffraction (EBSD) to align Fe–Ni and Co–Fe alloy microcrystals on three different substrates. The orientation matrix is calculated from EBSD Euler angles and compared with the orientation determined using microbeam Laue diffraction. The average angular mismatch between the orientation matrices is less than ∼6°, which is reasonable for the search for Bragg reflections. The use of an orientation matrix derived from EBSD is demonstrated to align and measure five reflections for a single Fe–Ni microcrystal via multi-reflection BCDI. Using this data set, a refined strain field computation based on the gradient of the complex exponential of the phase is developed. This approach is shown to increase accuracy, especially in the presence of dislocations. The results demonstrate the feasibility of using EBSD to pre-align BCDI samples and the application of more efficient approaches to determine the full lattice strain tensor with greater accuracy.

42 ENGINEERING↗

Rapid Computational Identification of Therapeutic Targets for Pathogens

Biological threats continue to persist and evolve as an important challenge to national security. There are multiple ways in which novel viral pathogens could emerge to pose a serious threat to human health. This project developed a pathogen target identification tool that can rapidly respond to a novel or emerging viral biological threat. A set of computational tools were developed that provide detailed information on the newly sequenced genes, their protein products and the drug target sites for the proteins that are best suited for biological countermeasure development. Three key innovations were developed in the project. 1) Development of a new extensive database of protein pocket structures with structure-based search algorithms to rapidly link novel protein targets with the complete collection of previously experimentally solved protein structures. 2) A novel clustering pipeline was introduced to group matching structures and associated small-molecule binding ligands into a consensus protein pocket with the associated small-molecule chemotypes predicted to fit in the pocket site. The matching experimentally solved structures were used to inform the value of different target sites. 3) Where there are viral protein targets with pockets structurally matched to similar human proteins, a biological knowledge graph, which links molecular interactions with human disease, was used to further assess the potential negative impact of a viral protein target with similarities to human proteins that could have important off target side effects. In total, the project produced a new resource for rapid and detailed assessment of promising targets for countermeasures, reflecting the ongoing wet lab, clinical, and computational data being collected. These capabilities will improve the ability to respond to a biological threat in multiple domains.

59 BASIC BIOLOGICAL SCIENCES↗

Contactless Position Measurement System for Remote Alignment of Highly Reflective Objects

The Contactless Position Measurement System (CPMS) permits automatic alignment of highly-reflecting components that cannot or should not be touched by human hands, such as those used in SRF cavities. CPMS also has application during maintenance of fusion reactors, when the components in the reactor are radioactive. The length of time for which humans can handle the components in order to carry out maintenance or repairs is limited. We would like to measure the relative positions of such objects so we can bring them into alignment with motorized stages, thus eliminating the need for human contact. The CPMS is a computer vision system that measures the location of highly reflective components to within a fraction of a millimeter by finding the edges of silhouette images. This is done by placing a uniform, infrared backlight behind the components, and viewing each component with two low-aberration, infrared cameras. Each of these stereoscopic cameras are located within a coordinate system we set up with reference platforms, light sources, and survey cameras distributed around the perimeter of the string assembly room, or fusion reactor. We obtain stereoscopic silhouette images of each component, and we use these to determine the position of the component within our string assembly coordinate system. The CPMS combines the silhouette images with knowledge of the dimensions of the objects to obtain the relative positions of components in its field of view. These position measurements then allow us to mechanically maneuver the components into contact. Once we know where they are, we can move the components to where they are supposed to be with motorized stages or other mechanical means, check they are in the right place, and bolt them together. In Phase I, we built a prototype infrared backlights and cameras, tested it, wrote an analysis program to fit the images. At a range of 50 cm, we are able to measure the relative positions of two stainless steel flanges with an accuracy of 150 μm rms. The next steps are to test the analysis program with motorized stages, build a full-size prototype, and implement it in an cleanroom with SRF cavity assembly. This can be done in a cost effective way given the materials with which the system is designed. As Open Source Instruments achieved more in Phase I than anticipated, despite not receiving a Phase II SBIR grant, we hope to move forward with product development and sales with a testing partner.

43 PARTICLE ACCELERATORS↗

Sensor system that uses embedded optical fibers

Sensor systems including an interferometer system are disclosed herein. In a general embodiment, the sensor system includes an optical fiber that is embedded into a sample, where the optical fiber has a reflective tip. The optical fiber is optically coupled to a sensor and a detector of the laser interferometer system. The sensor system further includes a computing device or circuit that is configured to receive electrical signals generated by the detector. The laser source is configured to emit light, which is coupled into the optical fiber. The light travels through the optical fiber until the light reaches the reflective tip, where it is reflected back through the optical fiber. The detector is impacted by the reflected light, and generates an electrical signal based upon the reflected light. The computing device generates a value that is indicative of a behavior of the sample based upon the electrical signal.

Chavez, Marcus Alexander↗

Sum-of-Fractions Methodology for Actinides in Water- and Polyethylene-Moderated and -Reflected Systems

Sum-of-fractions is a method intended to make sure a subcritical margin for aqueous solutions and slurries of fissionable isotopes exists. The method indicates that a system is subcritical if the sum of the ratios of the mass of each isotope (in a mixture) to its individual minimum subcritical mass limit is less than or equal to one. Historically, the basis of the sum-of-fractions has been derived from allowances given in the American National Standards Institute (ANSI)/ American Nuclear Society (ANS)-8.15-1981. However, the allowance was removed in ANSI/ANS-8.15-2014 due to a lack of technical basis. A methodology was developed to assess the validity of using the sum-of-fractions for water- or polyethylene-moderated systems for the following nuclides: 232 U, 233 U, 234 U, 235 U, 237 Np, 236 Pu, 238 Pu, 239 Pu, 240 Pu, 241 Pu, 242 Pu, 241 Am, 242 m Am, 243 Am, 242 Cm, 243 Cm, 244 Cm, 245 Cm, 246 Cm, 247 Cm, 249 Cf, and 251 Cf. The methodology uses available benchmark data for mixtures of 233 U, 235 U, and 239 Pu to establish the calculational margin, and a mass limit reduction to establish the margin of subcriticality. Water- or polyethylene-moderated and -reflected mixtures containing the nuclides are evaluated with the code system, SCALE 6.2.4. Including the calculational margin, subcritical mass limits for each nuclide were computed for optimally water- or polyethylene-moderated and fully reflected systems. These masses were used to create nuclide mixtures in which the sum of the mass to subcritical mass limit ratios is one. The various nuclide mixtures were modeled over a range of moderation and demonstrate the keff does not exceed the calculational margin. For additional assurance of subcriticality, a significant mass reduction is applied to each computed minimum critical mass of the nuclides without adequate benchmark data consistent with the method in ANSI/ANS-8.15-2014.

07 ISOTOPE AND RADIATION SOURCES↗

Sum-of-Fractions Method

Sum-of-fractions is a method intended to make sure a subcritical margin for aqueous solutions and slurries of fissionable isotopes exists. The method indicates that a system is subcritical if the sum of the ratios of the mass of each isotope (in a mixture) to its individual minimum subcritical mass limit is less than or equal to one. Historically, the basis of the sum-of-fractions has been derived from allowances given in the American National Standards Institute (ANSI)/ American Nuclear Society (ANS)-8.15-1981. However, the allowance was removed in ANSI/ANS-8.15-2014 due to a lack of technical basis. A methodology was developed to assess the validity of using the sum-of-fractions for water- or polyethylene-moderated systems for the following nuclides: 232U, 233U, 234U, 235U, 237Np, 236Pu, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 241Am, 242mAm, 243Am, 242Cm, 243Cm, 244Cm, 245Cm, 246Cm, 247Cm, 249Cf, and 251Cf. The methodology uses available benchmark data for mixtures of 233U, 235U, and 239Pu to establish the calculational margin, and a mass limit reduction to establish the margin of subcriticality. Water- or polyethylene-moderated and -reflected mixtures containing the nuclides are evaluated with the code system, SCALE 6.2.4. Including the calculational margin, subcritical mass limits for each nuclide were computed for optimally water- or polyethylene-moderated and fully reflected systems. These masses were used to create nuclide mixtures in which the sum of the mass to subcritical mass limit ratios is one. The various nuclide mixtures were modeled over a range of moderation and demonstrate the keff does not exceed the calculational margin. For additional assurance of subcriticality, a significant mass reduction is applied to each computed minimum critical mass of the nuclides without adequate benchmark data consistent with the method in ANSI/ANS-8.15-2014.

criticality safety, Actinide↗

Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

In Pursuit of 2D Materials for Maximum Optical Response

Despite being only a few atoms thick, single-layer two-dimensional (2D) materials display strong electron–photon interactions that could be utilized in efficient light modulators on extreme subwavelength scales. In various applications involving light modulation and manipulation, materials with strong optical response at different wavelengths are required. Using qualitative analytical modeling and first-principles calculations, we determine the theoretical limit of the maximum optical response such as absorbance ($A$) and reflectance ($R$) in 2D materials and also conduct a computational survey to seek out those with best $A$ and $R$ in various frequency ranges, from mid-infrared to deep-ultraviolet. We find that 2D boron has broadband reflectance R > 99% for >100 layers, surpassing conventional thin films of bulk metals such as silver. Moreover, we identify 2D monolayer semiconductors with maximum response, for which we obtain quantitative estimates by calculating quasiparticle energies and accounting for excitonic effects by solving the Bethe–Salpeter equation. We found several monolayer semiconductors with absorbances ≳30% in different optical ranges, which are more than half of the maximum possible value, Alim = 1/2, for a freestanding 2D material. Our study predicts 2D materials which can potentially be used in ultrathin reflectors and absorbers for optoelectronic application in various frequency ranges.

36 MATERIALS SCIENCE↗