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At least 631 records · Page 35

Material and Interface Engineering Strategies to Mitigate Decoherence in Superconducting Qubits

While significant strides have been made to increase the coherence time of superconducting qubits, further advancements are essential for realizing scalable quantum computing. Decoherence is often a result of loss and noise stemming from two-level systems and excess quasiparticles, arising due to material defects, fabrication processes, and ambient exposure, particularly at surfaces and interfaces. Our recent efforts to mitigate these decoherence mechanisms have employed a variety of strategies, including low-loss surface encapsulation materials, advanced substrate preparation techniques, modifications to metal film growth, and the development of novel fabrication processes. The structural and chemical properties of materials, surfaces, and interfaces are studied using scanning probe microscopy, electron microscopy, photoelectron spectroscopy, mass spectrometry, and X-ray diffraction, which is correlated to device performance metrics, including superconducting resonator internal quality factor and qubit T1 time. This information is used to identify and understand material sources of loss and their origins in the device fabrication process. Through multi-institution efforts within SQMS we have identified the loss mechanism of interstitial hydrogen in niobium-based devices and shown how standard fabrication processes introduce these hydrides, developing strategies to mitigate their formation.1 Furthermore, we have characterized the metal-substrate interface, including the loss of niobium-silicides formed at that interface, and developed silicon surface treatments that reduce atomic scale roughness and oxygen content at the metal-substrate and Josephson junction interfaces.2-4 By developing the connection between materials properties and the overall performance of superconducting quantum circuitry, we can develop fabrication strategies to mitigate material losses, thus supporting the ongoing efforts to enhance coherence time in superconducting quantum devices. 1. Torres-Castanedo, C. G.*, Goronzy, D. P.*, et al., Adv. Funct. Mater., 2401365 (2024) 2. Lu, X., et al., Phys. Rev. Materials 6, 064402 (2022) 3. Berti, G., Appl. Phys. Lett. 122, 192605 (2023) 4. Kopas, C. J., Goronzy, D. P., et al., arXiv:2408.02863 (2024)

Goronzy, Dominic P.↗

Topological Antiferromagnetic Van der Waals Phase in Topological Insulator/Ferromagnet Heterostructures Synthesized by a CMOS-Compatible Sputtering Technique

Breaking time-reversal symmetry by introducing magnetic order, thereby opening a gap in the topological surface state bands, is essential for realizing useful topological properties such as the quantum anomalous Hall and axion insulator states. In this work, a novel topological antiferromagnetic (AFM) phase is created at the interface of a sputtered, c-axis-oriented, topological insulator/ferromagnet heterostructure—Bi 2 Te 3 /Ni 80 Fe 20 because of diffusion of Ni in Bi 2 Te 3 (Ni-Bi 2 Te 3 ). The AFM property of the Ni-Bi2Te3 interfacial layer is established by observation of spontaneous exchange bias in the magnetic hysteresis loop and compensated moments in the depth profile of the magnetization using polarized neutron reflectometry. Analysis of the structural and chemical properties of the Ni-Bi2Te3 layer is carried out using selected-area electron diffraction, electron energy loss spectroscopy, and X-ray photoelectron spectroscopy. These studies, in parallel with first-principles calculations, indicate a solid-state chemical reaction that leads to the formation of Ni=Te bonds and the presence of topological antiferromagnetic (AFM) compound NiBi 2 Te 4 in the Ni-Bi 2 Te 3 interface layer. The Neél temperature of the Ni-Bi 2 Te 3 layer is ≈ 63 K, which is higher than that of typical magnetic topological insulators (MTIs). The presented results provide a pathway toward industrial complementary metal-oxide-semiconductor (CMOS)-process-compatible sputtered-MTI heterostructures, leading to novel materials for topological quantum devices.

36 MATERIALS SCIENCE↗

Magnetic properties of the Ising-like rare earth pyrosilicate: D-Er 2 Si 2 O 7

Ising-like spin-1/2 magnetic materials are of interest for their ready connection to theory, particularly in the context of quantum critical behavior. In this work we report detailed studies of the magnetic properties of a member of the rare earth pyrosilicate family, D-Er 2 Si 2 O 7 , which is known to display a highly anisotropic Ising-like g-tensor and effective spin-1/2 magnetic moments. We used powder neutron diffraction, powder inelastic neutron spectroscopy (INS), and single crystal AC susceptibility to characterize its magnetic properties. Neutron diffraction enabled us to determine the magnetic structure below the known transition temperature (T N = 1.9 K) in zero field, confirming that the magnetic state is a four-sublattice antiferromagnetic structure with two non-collinear Ising axes, as was previously hypothesized. Our powder INS data revealed a gapped excitation at zero field, consistent with anisotropic (possibly Ising) exchange. An applied field of 1 T produces a mode softening, which is consistent with a field-induced second order phase transition. To assess the relevance of D-Er 2 Si 2 O 7 to the transverse field Ising model, we performed AC susceptibility measurements on a single crystal with the magnetic field oriented in the direction transverse to the Ising axes. This revealed a transition at 2.65 T at 0.1 K, a field significantly higher than the mode-softening field observed by powder INS, showing that the field-induced phase transitions are highly field-direction dependent as expected. Furthermore, these measurements suggest that D-Er 2 Si 2 O 7 may be a candidate for further exploration related to the transverse field Ising model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nanoscale strain wave generation by a piezoelectric grating from polar vortices

Nanostructures formed by spontaneously broken symmetry have provided new ways to manipulate quantum states. Specifically, topological structures with periodic spatial ordering, such as polar vortices and skyrmions, can be ideal hosts for creating engineered responses in both spatial and frequency domains. So far, however, only a few examples of such hierarchical engineering have been reported in the literature. Here we demonstrate that the spatially modulated piezoelectric response of a polar vortex structure can create strain waves with a characteristic nanoscale wavefront. Using time-resolved pump–probe resonant X-ray scattering and diffraction measurements, coupled with dynamical phase-field simulations, we show that the piezoelectric modulation of the spontaneously formed polar vortex crystal functions as an acoustic diffraction grating. This system converts incoming laterally uniform strain waves into outgoing waves with a characteristic sub-terahertz frequency, driven by an intrinsic excitation of the polar vortex crystal. Moreover, our phase-field simulations suggest that the dynamic mechanical displacements exhibiting vortex textures are generated from both space- and time-varying piezoelectric responses. Our findings illustrate a new method for generating nanoscale strain waves with unique spatial textures by tuning the hierarchical order of polar topologies to engineer new collective modes, allowing for a wide range of control through the topological lattice.

ferroelectrics↗

Short-range order in the quantum XXZ honeycomb lattice material BaCo 2 ( PO 4 ) 2

In this paper, we present observations of highly frustrated quasi-two-dimensional (2D) magnetic correlations in the honeycomb lattice layers of the S eff =1/2 compound γ-BaCo 2 (PO 4 ) 2 (γ-BCPO). Specific heat shows a broad peak comprised of two weak kink features at T N1 ~6 K and T N2 ~3.5 K, the relative weights of which can be modified by sample annealing. Neutron powder diffraction measurements reveal short range quasi-2D order that is established below T N1 and T N2 , at which two separate, incompatible, short range magnetic orders onset: commensurate antiferromagnetic correlations with correlation length ξ c =60±2 Å (T N1 ) and in quasi-2D helical domains with ξ h =350±11 Å (T N2 ). The ac magnetic susceptibility response lacks frequency dependence, ruling out spin freezing. Inelastic neutron scattering data on γ-BCPO is compared with linear spin wave theory, and two separate parameter regions of the XXZ J 1 -J 2 -J 3 model with ferromagnetic nearest-neighbor exchange J 1 are favored, both near regions of high classical degeneracy. High energy coherent excitations (~10 meV) persist up to at least 40 K, suggesting strong in-plane correlations persist above TN. Finally, these data show that γ-BCPO is a rare highly frustrated, quasi-2D S eff =1/2 honeycomb lattice material which resists long range magnetic order and spin freezing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Structure Transformation and Cerium-Substituted Optical Response across the Carbonitridosilicate Solid Solution (La δ Y 1–δ ) 2 Si 4 N 6 C(δ = 0–0.5)

Following an investigation proving La 2 Si 4 N 6 C crystallizes in a monoclinic space group, isostructural to Y 2 Si 4 N 6 C, the reportedly hexagonal (La 0.5 Y 0.5 ) 2 Si 4 N 6 C was reinvestigated to examine the apparent crystal structure change across the solid solution. Initially, calculating the electronic structure and phonon density of states of (La 0.5 Y 0.5 ) 2 Si 4 N 6 C in the P6 3 mc space group revealed an imaginary phonon mode, which is indicative of a structural instability. Displacing the atoms along the pathway of the imaginary vibration led to a previously unreported space group for carbonitridosilicates, trigonal P31c. The assignment of the trigonal space group was subsequently confirmed by synthesizing (La 0.5 Y 0.5 ) 2 Si 4 N 6 C using high-temperature, solid state synthesis and analyzing the crystal structure with high-resolution synchrotron X-ray powder diffraction. Preparing the solid solution, (La δ Y 1–δ ) 1.98 Ce 0.02 Si 4 N 6 C (δ = 0–0.5), showed that the crystal structure changes from the monoclinic to the trigonal space group at δ ≈ 0.25. Finally, substituting Ce 3+ in the crystal structure to investigate the optical response via steady-state luminescent and photoluminescent quantum yield measurements reveals severe luminescent quenching with increasing La 3+ content, due to a combination of absorption of luminescence by the host structure and thermal quenching. Here, these results display the virtue of combining computational and experimental techniques to solve inorganic crystal structures and assess potential phosphor hosts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Giant reversible barocaloric response of (MnNiSi) 1- x (FeCoGe) x ( x = 0.39, 0.40, 0.41)

MnNiSi-based alloys and isostructural systems have traditionally demonstrated impressive magnetocaloric properties near room temperature associated with a highly tunable first-order magnetostructural transition that involves large latent heat. However, these materials are limited by a small field-sensitivity of the transition, preventing significant reversible effects usable for cooling applications. Instead, the concomitant large transition volume changes prompt a high pressure-sensitivity, and therefore, promise substantial barocaloric performances, but they have been sparsely studied in these materials. Here, we study the barocaloric response in a series of composition-related (MnNiSi) 1-x (FeCoGe) x (x = 0.39, 0.40, 0.41) alloys that span continuously over a wide temperature range around ambient. We report on giant reversible effects of ~40 J K -1 kg -1 and up to ~4 K upon application of ~2 kbar and find a degradation of the first-order transition properties with pressure that limits the barocaloric effects at high pressures. Our results confirm the potential of this type of alloys for barocaloric applications, where multicaloric and composite possibilities, along with the high density and relatively high thermal conductivity, constructively add to the magnitude of the caloric effects.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Single-Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin-Ice Candidate Ce 2⁢ Zr 2 ⁢O 7 : No Apparent Octupolar Correlations Above 𝑇 = 0.05 K

The insulating magnetic pyrochlore Ce 2 ⁢Zr 2 ⁢O 7 has gained attention as a quantum spin-ice candidate with dipole-octupole character that arises from the crystal-electric-field ground-state doublet for the Ce 3+ Kramers ion. This dipole-octupole character permits both spin-ice phases based on magnetic dipoles and those based on more-exotic octupoles. This work reports low-temperature neutron diffraction measurements on single-crystal Ce 2 ⁢Zr 2⁢ O 7 with 𝑄 coverage both at low 𝑄, where the magnetic form factor for dipoles is near maximal, and at high 𝑄, covering the region where the magnetic form factor for Ce 3+ octupoles is near maximal. This study was motivated by recent powder neutron diffraction studies of other Ce-based dipole-octupole pyrochlores, Ce 2 ⁢Sn 2 ⁢O 7 and Ce 2 ⁢Hf 2 ⁢O 7 , which each showed temperature-dependent diffuse diffraction at high 𝑄, interpreted as arising from octupolar correlations. Our measurements use an optimized single-crystal diffuse scattering instrument that allows us to screen against strong Bragg scattering from Ce 2 ⁢Zr 2 ⁢O 7 . The temperature-difference neutron diffraction reveals a low-𝑄 peak consistent with dipolar spin-ice correlations reported in previous work, and an alternation between positive and negative net intensity at higher 𝑄. These features are consistent with our numerical-linked-cluster calculations using pseudospin interaction parameters previously reported for Ce 2 ⁢Zr 2⁢ O 7 , Ce 2 ⁢Sn 2 ⁢O 7 , and Ce 2 ⁢Hf 2 ⁢O 7 . Importantly, neither the measured data nor any of the NLC calculations show evidence for increased scattering at high 𝑄 resulting from octupolar correlations. We conclude that at the lowest attainable temperature for our measurements (𝑇 = 0.05 K), scattering from octupolar correlations in Ce 2 ⁢Zr 2 ⁢O 7 is not present in the neutron diffraction signal on the level of our observation threshold of around 0.1% of the low-𝑄 dipole scattering. We compare these results to those obtained earlier on powder Ce 2 ⁢Sn 2 ⁢O 7 and Ce 2⁢ Hf 2⁢ O 7 , and to low-energy inelastic neutron scattering from single-crystal Ce 2 ⁢Zr 2 ⁢O 7 .

36 MATERIALS SCIENCE↗

One-step model of photoemission from single-crystal surfaces

In our paper, we present a three-dimensional one-step photoemission model that can be used to calculate the quantum efficiency and momentum distributions of electrons photoemitted from ordered single-crystal surfaces close to the photoemission threshold. Using Ag(111) as an example, we also show that the model can not only calculate the quantum efficiency from the surface state accurately without using any ad hoc parameters, but also provides a theoretical quantitative explanation of the vectorial photoelectric effect. This model in conjunction with other band structure and wave function calculation techniques can be effectively used to screen single-crystal photoemitters for use as electron sources for particle accelerator and ultrafast electron diffraction applications.

36 MATERIALS SCIENCE↗

Ultrafast Events in Electrocyclic Ring-Opening Reactions

Electrocyclic reactions are characterized by the concerted formation and cleavage of multiple σ and π bonds in a molecular system and have been extensively studied since they were introduced by Robert Burns Woodward and Roald Hoffmann in 1965. Recent advances and the integration of time-resolved experiments and nonadiabatic quantum molecular dynamics simulations have transformed the traditional understanding of electrocyclic reactions beyond the Woodward–Hoffmann rules. In this review, we focus on recent studies of 1,3-cyclohexadiene and two of its derivatives, α-phellandrene and α-terpinene, to shed light on the underlying mechanisms of electrocyclic photochemical reactions. We highlight recent progress in ultrafast electron diffraction techniques and the simulation approach of ab initio multiple spawning. Together, these approaches can elucidate molecular structure dynamics from femtosecond to picosecond timescales as well as nuclear and electronic responses at conical intersections.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Materials genome innovation for computational software (magics) center

Functional layered material (LM) architectures will dominate nanomaterials science in this century. We have developed theory, modeling, simulation, and software and data tools that enhance understanding and AI guide synthesis, enable characterization of complex structures, and improve capabilities in the predictive design and growth of LMs. Research at the Center has focused on: Computational synthesis and characterization: AI guided synthesis and experimental synthesis of stacked LMs with tailored properties via optimized chemical vapor deposition (CVD) growth and liquid-phase exfoliation; study defects, edges, grain boundaries, wrinkling of atomic layers and their effects on chemical, mechanical, electrical, and optical properties. Far-from-equilibrium processes: Joint experimental and simulation based probe of electronic processes with NAQMD and ultrafast X-ray free-electron laser (XFEL) and ultrafast electron diffraction (UED) facilities at Stanford. Experimentally validate NAQMD by ultrafast electron diffraction and X-ray spectroscopy studies of structural and excited state dynamics, shape fluctuations, and phonon dynamics. Scalable software: Simulation engines for desktop-to-exascale platforms using low-overhead, linear-scaling QMD algorithms; divide-conquer-recombine NAQMD with electronic excitations; extended-Lagrangian reactive molecular dynamics (RMD), machine learning (ML) based neural-network quantum molecular dynamics (NNQMD), and super-state accelerated molecular dynamics (AMD) and kinetic Monte Carlo codes; thermal and electrical transport software; and design 3D architectures of LMs with desired functionality using scalable software. Distribution of software and data, and training: Software and simulation-experimental data generated within the Center are distributed to the materials science community via Berkeley Materials Project (MP) framework. We have also organized three workshops for software distribution and training at USC (Nov. 2017, Mar. 2018) and Gaithersburg, MD (Nov. 2018) to train researchers, with the last one in focused on underrepresented groups, in collaboration with Howard University which is one of the largest HBCUs. The Center supported a total of 46 personnel and 6 undergraduate students. These include 14 faculty, 11 postdoctoral research associates, 20 graduate research assistants, and mentored 6 undergraduate students. This resulted in the publications of 63 research papers that include 46 publications on Reactive and Quantum Dynamics Simulations, 13 publications on Machine Learning for Quantum Materials, and 4 publications on Quantum Computing.

2D Materials↗

Topological phase transition to a hidden charge density wave liquid

Charge density waves (CDWs), electronic crystals that form within a host solid, have long been speculated to melt into a spatially textured electronic liquid. Though they have not been previously detected, liquid CDWs may nonetheless be fundamental to the phase diagrams of many correlated electron systems, including high temperature superconductors and quantum Hall states. In one of the most promising candidate materials capable of hosting a liquid CDW, 1T-TaS2, a structural phase transition impedes its observation. Here, by irradiating the material with a femtosecond light pulse, we circumvent the structural phase transition to reveal how topological defect dynamics govern the otherwise invisible CDW correlations. Upon photoexcitation, the CDW diffraction peaks broaden azimuthally, initially revealing a hexatic state. At higher temperatures, photoexcitation completely destroys translational and orientational order and only a ring of diffuse scattering is observed, a key signature of a liquid CDW. Our work provides compelling evidence for a defect-unbinding transition to a CDW liquid and presents a protocol for uncovering states that are hidden by other transitions in thermal equilibrium.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Optimized in situ crystal growth and disordered quasi-one-dimensional magnetism in Li 2 Mn 2 ( MoO 4 ) 3

We present that the quasi-one-dimensional structure of Li 2 Mn 2 ( MoO 4 ) 3 consists of three mutually distinct chains of Li 1 - x Mn x -centered polyhedra in which Mn ostensibly adopts a J = 5 / 2 Mn 2 + configuration. In situ x-ray scattering experiments carried out as crystallites emerge from a molten oxide solution facilitate the synthesis of large single crystals. Ex situ x-ray diffraction finds no evidence of long-range Li/Mn occupancy ordering, suggesting that the structure is effectively composed of finite chains of Mn moments of statistically varying lengths. UV/visible diffuse reflectance spectroscopy measurements establish a wide 3.43(12)-eV direct charge gap consistent with the local polyhedral coordination of the nominally Mn 2 + species. The temperature T dependence of the DC magnetic susceptibility χ reveals a fluctuating moment of only 2.74 μ B ± 0.01 μ B /Mn, dramatically reduced from the 5.9 μ B /Mn expected for Mn 2 + . Meanwhile, the Weiss temperature Θ W = - 89 ± 1 K reveals antiferromagnetic fluctuations that are stymied from reaching an ordered state apparently by the chemical disorder intrinsic to the polyhedral chains. Measurements of magnetization vs field H at T ≤ 10 K are far from saturation even at H = 5 T and are strongly non-Brillouin-like, instead scaling as H / T 0.24 ( 3 ) and suggesting the presence of quantum fluctuations associated with an eventual quasi-one-dimensional, disordered magnetic phase.

1-dimensional systems↗

Study of nonlinear optical properties of TiO{sub 2} – polystyrene nanocomposite films

We consider an ex-situ prepared TiO{sub 2} − polystyrene (TiO{sub 2} − PS) nanocomposite, with different concentration of TiO{sub 2} nanoparticles (NPs), deposited by the spin-coating method on quartz substrates. Nonlinear optical properties of the TiO{sub 2} − PS nanocomposite films are studied using the Z-scan technique. Structural properties of the films are investigated using scanning electron microscopy (SEM) and X-ray diffraction (XRD) measurements. The optical band gap energy of the TiO{sub 2} − PS films are determined from the optical absorption spectra. The relation between the optical nonlinearities and the bandgap energy, as a microscopic electronic property of the semiconductor nanocomposite, is established. It is shown that an increase in the content of TiO{sub 2} NPs in the nanocomposite films results in bandgap narrowing and concomitant enhancement of optical nonlinearities. It is proposed that bandgap narrowing and enhancement of optical nonlinearities can be ascribed to the introduction of mid-gap states as a result of the formation of surface defects in TiO{sub 2} NPs. The results of this work indicate that incorporation of TiO{sub 2} NPs in the PS polymeric matrix can be a new way for bandgap narrowing of TiO{sub 2} NPs toward the visible light region, which is of great interest for their application in this part of the spectrum. Furthermore, enhancement of the optical nonlinearities of the spin-coated TiO{sub 2} − PS films by increasing the TiO{sub 2} NP content can open up new avenues for their use as nonlinear optical films in photonics applications. (nonlinear optical phenomena)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Dirac equation as a model of topological insulators

The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a three-dimensional Topological Insulator. For a bulk system, the sign of the mass determines the parity at the only time-reversal point ( k _ = 0 ) and, thus, leads to the designation of the bulk as being topologically trivial or non-trivial. Since the mass changes sign at the interface between a topologically trivial and non-trivial materials, topological surface states appear on that boundary. We present that electron scattering experiments may provide an alternate probe of the topological character of the surface states. For infinitely thick slabs, the states on the opposite sides of the slab decouple. The spatial decoupling results in the surface states become gapless, non-degenerate and, due to the Rashba spin–orbit coupling generated by the loss of inversion symmetry, exhibit spin-momentum locking. We review several characteristic properties of the topological surface states which are dependent on the topological quantum numbers and show that, using this model, they can be calculated exactly using simple approaches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Magnetic structure and Ising-like antiferromagnetism in the bilayer triangular lattice compound NdZnPO

Here, the complex interplay of spin frustration and quantum fluctuations in low-dimensional quantum materials leads to a variety of intriguing phenomena. This research focuses on a detailed analysis of the magnetic behavior exhibited by NdZnPO, a bilayer spin-1/2 triangular lattice antiferromagnet. The investigation employs magnetization, specific heat, and powder neutron scattering measurements. At zero field, a long-range magnetic order is observed at T N = 1.64 K. Powder neutron diffraction experiments show the Ising-like magnetic moments along the c-axis, revealing a stripe like magnetic structure with magnetic propagation vector (1/2, 0, 1/2). Application of a magnetic field along the c-axis suppresses the antiferromagnetic order, leading to a fully polarized ferromagnetic state above B c = 4.5 T. This transition is accompanied by notable enhancements in the nuclear Schottky contribution. Moreover, the absence of spin frustration and expected field-induced plateau-like phases are remarkable observations. Detailed calculations of magnetic dipolar interactions revealed complex couplings reminiscent of a honeycomb lattice, suggesting the potential emergence of Kitaev-like physics within this system. This comprehensive study of the magnetic properties of NdZnPO highlights unresolved intricacies, underscoring the imperative for further exploration to unveil the underlying governing mechanisms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Method for Describing the Angular Distribution of Optical Radiation Scattered by a Monolayer of Ordered Spherical Particles (Normal Illumination)

We have developed a method for describing the angular distribution of intensity of radiation scattered by a monolayer of homogeneous spatially ordered monodisperse spherical particles normally illuminated by a plane circularly polarized electromagnetic wave. The method is based on the quasicrystalline approximation (QCA) of the theory of multiple scattering of waves (TMSW) using the multipole expansion of fields and the tensor Green function in vectorial spherical wavefunctions. The method is applied for analyzing the characteristics of radiation scattered by a partially ordered monolayer and a monolayer with a nonideal lattice. The results of calculations are compared with the available experimental data on the position of the first-order diffraction peak on the angular and spectral dependences of the intensity of radiation scattered by a closely packed monolayer with a nonideal triangular lattice of SiO{sub 2} particles. Good conformity of the results has been established.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗