Isotropic Line Research Articles

Synthesis of Tetrahedrite Zincian Nanocomposites via solvothermal process at low temperature

This study presents a novel hydrothermal method for synthesizing Cu11Zn1Sb4S13 (tetrahedrite, zincian) nanoparticles at a low temperature of 185 °C for a 6 h annealing at 400 °C for 2 h. CuCl2, ZnCl2, SbNO3, and CH4N2S, and NaBH4 were used for the innovative synthesis of Cu11Zn1Sb4S13 (Tetrahedrite, Zincian) Copper Zinc Antimony Sulfide nanoparticles ink. Structural, morphological and optical properties (optical energy gap) were studied for thin-film Cu11Zn1Sb4S13 deposited the nanoparticles via drop-casting method onto glass substrates are investigated. The structure and characterization of Cu11Zn1Sb4S13 by XRD powder diffraction provide evidence for a cubic structure. The optical calculations indicate that the absorption coefficient (α > 104 cm−1) and optical energy gap Eg are equivalent to 1.68 eV. Comparative work of Crystalline diameters of synthesis was obtained from XRD diffraction powder. The Debye-Scherrer procedure, modified Scherrer procedure and Williamson–Hall inspection are used to examine the individual participatory of the crystalline diameters, lattice stress and dislocation to isotropic line expansion widening reflection peaks of Cu11Zn1Sb4S13 nanoparticles. The modified Scherrer approach is appropriate, with all points along the fitting line. The crystallite size estimated from XRD was 5.798 nm and the particle size calculated from the FESEM method 8–9 nm. This slight difference reflects a spherical shape of the nanoparticles.

Jahn-Teller effect and features of divalent copper ion behavior in multicomponent borate crystals

Crystals of YGa3(BO3)4, YAl3(BO3)4, EuGa3(BO3)4 and EuAl3(BO3)4 with copper alloy were studied by electron paramagnetic resonance and X-ray diffraction analysis. The lattice parameters and coordinates of copper-doped boron atoms were determined. The study of EPR spectra showed that copper is in the divalent state and replaces aluminum ions with C2 node symmetry. In YAl3(BO3)4:Cu crystals, a ligand structure exists due to the interaction of copper electrons with yttrium nuclei. The parameters of the spin Hamiltonian describing the behavior of the Cu2+ spectrum have been determined. The deviation of the Z-axis spectra from the C3 axis by 54(1)° is due to Jahn-Teller vibronic interaction and monoclinic distortion. In the EuGa3(BO3)4 crystal, a new spectrum 2 was found, which also belongs to divalent copper but is observed at an excited state 31 cm−1 away from the ground state. Above 70 K, an isotropic EPR line with a width of 450 Gs, g = 2.1, appears and exists up to room temperature.

A unified thermo-mechanical bounding surface model for saturated clay and sand

To accurately predict soil thermal effects is of great importance for simulations of complex boundary value problems such as the energy foundations and nuclear waste disposal. Existing thermo-mechanical constitutive models only account for clay, and cannot simulate the sand’s behaviour under thermo-mechanical conditions. In this study, a unified thermo-mechanical bounding surface (UTMBS) model is proposed for saturated clay and sand. Based on the thermal effects on the isotropic compression line, the model proposes a new unified thermal softening relationship and a plastic modulus for clay and sand, with the thermal cyclic behaviour replicated by a memory surface. The unified model considers the thermal effects on the critical state line and the shape of the bounding surface, accounting for both drained and undrained shearing of clay and sand at different temperatures. In addition, the non-linear elasticity relationship represents the hysteresis loops of the stress–strain relationship in the mechanical cycles. The performance of the proposed model is evaluated against existing experimental results for clay and sand in terms of their thermal cyclic behaviour, drained/undrained triaxial compression, and mechanical cyclic behaviour at different temperatures. It is evident that the UTMBS model is able to simulate various thermo-mechanical behaviours of clay and sand.

Octonionic Magical Supergravity, Niemeier Lattices, and Exceptional & Hilbert Modular Forms

AbstractThe quantum degeneracies of Bogomolny‐Prasad‐Sommerfield (BPS) black holes of octonionic magical supergravity in five dimensions are studied. Quantum degeneracy is defined purely number theoretically as the number of distinct states in charge space with a given set of invariant labels. Quantum degeneracies of spherically symmetric stationary BPS black holes are given by the Fourier coefficients of modular forms of exceptional group . Their charges take values in the lattice defined by the exceptional Jordan algebra over integral octonions. The quantum degeneracies of rank 1 and rank 2 BPS black holes are given by the Fourier coefficients of singular modular forms and . The rank 3 (large) BPS black holes will be studied elsewhere. Following the work of N. Elkies and B. Gross on embeddings of cubic rings A into the exceptional Jordan algebra we show that the quantum degeneracies of rank 1 black holes described by such embeddings are given by the Fourier coefficients of the Hilbert modular forms (HMFs) of . If the discriminant of the cubic ring A is with p a prime number then the isotropic lines in the 24 dimensional orthogonal complement of A define a pair of Niemeier lattices which can be taken as charge lattices of some BPS black holes. The current status of the searches for the M/superstring theoretic origins of the octonionic magical supergravity is also reviewed.

The sensitivity of Prazeres clay – some results on reconstituted samples

Soil’s structure is defined as the issue responsible for the differences observed in the mechanical response of natural soil samples compared to the intrinsic behaviour of reconstituted samples. The parameter that incorporates the differences in microstructure of intact and reconstituted clays is designated by stress sensitivity. The influence of microstructure and fabric on the behaviour of soils has been evaluated by comparing strength and compressibility characteristics of intact and reconstituted samples of the same material. Included on a broad characterization study of Lisbon Miocene Prazeres clay held at Porto University, some oedometer and triaxial tests were undertaken on intact and reconstituted samples. In this paper, the process of preparing reconstituted samples and consolidating them in a large oedometer to the in-situ stress is thoroughly described. The results of oedometer and triaxial tests on reconstituted samples are presented and compared with results for intact samples from the same site. A proposal for parameterisation of the intrinsic characteristics of this clay is established on the basis of test results. Concerning compressibility, oedometer test results show good adjustment to the isotropic compression line (ICL). Triaxial test results for intact samples in the light of critical states soil mechanics are similar to those obtained in s’-t space for the reconstituted samples. The intrinsic parameters show good agreement with those described in the literature for soils of the same nature.

Electron paramagnetic resonance of VN–VGa complex in BGaN

A metastable photoinduced electron paramagnetic resonance (EPR) signal at low temperatures is reported for GaN alloyed with boron (i.e., BxGa1−xN) epitaxial layers grown at temperatures ranging from 840 to 1090° C. An isotropic EPR line with g = 2.004 is observed with an intensity depending on the growth temperature for all the samples with boron content between 0.73% and 2.51%. The temperature dependence of EPR intensities is compared with the results of high-resolution photoinduced transient spectroscopy. This enables a link between particular traps and the EPR signal. The activation energies of these traps are consistent with the theoretical position of the VN–VGa complex. Thermal annihilation of the EPR signal with 30 meV activation energy corresponds to shallow donor ionization. A model explaining the light-induced EPR signal that involves redistribution of electrons between deep and shallow donors, mediated by photoionization to the conduction band, is proposed.

Cation distribution, Fe2+/Fe3+ valence states and oxygen vacancies detection in the Y2.98Er0.02Fe5−yCryO12 compound

The appropriate physical properties of yttrium iron garnet (YIG), make it an excellent soft magnetic material for applications in microwave, magneto-optical devices, and spintronic. In this sense, the scientific community has made and continues to make numerous investigations to improve the YIG properties. Here, we have presented a study on the cation's distribution, valence states and oxygen vacancies (OV) in the Y2.98Er0.02Fe5−yCryO12 (0.00 ≤ y ≤ 0.05) compound. The coral type structures were observed by Transmission Electron Microscopy (TEM), whereas the Selected Area Electron Diffraction (SAED) confirmed the YIG crystalline nature, by means of bright points corresponding to the (004), (123), (024), (224), (022) and (112) YIG family planes. The valence states of the different atoms and oxygen vacancies defects were identified by the deconvolution of the X-ray Photoelectron Spectroscopy (XPS) spectra. For all YIG samples, the coexistence of Fe3+ and Fe2+ ions were observed and the Fe2+ cations and OV decrease as the Cr3+ cations concentration increases. By using the Electronic Paramagnetic Resonance (EPR) measurements, was detected the magnetic contribution of the Fe cations, while an isotropic line obtained near to 3440 Oe was associated with the Cr3+ cations presence. Finally, an increase of the Cr content led to a decrease in the saturation magnetization (Ms), which was explained in terms of the cation’s occupation, obtained from a phenomenological model.

Implicit Algorithm of the SBSP-R Model for Predicting the Non-Unique Critical State of Soils

The non-unique critical state represents the distance between the critical state line (CSL) and the isotropic consolidation line (ICL) that significantly varies with stress paths and particle size distribution of soils. A structural bounding surface plasticity model with spacing ratio r (SBSP-R model) was implemented using an explicit algorithm. However, the explicit algorithm did not well capture the non-unique critical state of soils with a large spacing ratio r, which prevented the soil mechanics research on non-unique critical state via finite element analysis. To overcome the limitation, the implicit algorithm of the SBSP-R model is formulated, and it mainly includes elastic prediction and plastic correction. The plastic correction is realized using the Newton–Simpson scheme with a controlling equation set related to consistency condition, plastic flow, hardening parameter, structural bounding surface, plastic modulus, and mapping rule. Case studies indicate that the implicit algorithm of the SBSP-R model is right and stable in predicting non-unique critical states. Comparisons between predicted and tested results indicate that the implicit algorithm of the SBSP-R model not only captures the critical state, stress-strain, and stress paths of various soils but also shows higher computational accuracy and efficiency compared with the previous explicit algorithm. These results indicate that the formulated implicit algorithm of the SBSP-R model is an alternative approach to the previous explicit algorithm.

Micro- and nanostructured layered-kagome zinc orthovanadate BaZn3(VO4)2(OH)2.

Pure micro- and nanocrystalline powders of the layered-kagome zinc orthovanadate BaZn3(VO4)2(OH)2 have been successfully prepared and thoroughly characterised. Microstructured samples (BaZn3-MPs) have been produced by hydrothermal reaction using synthetic martyite Zn3V2O7(OH)2·2H2O as the starting reagent. Nanoparticles (NPs) with an average size of ≈ 60 nm (BaZn3-NPs-7h) or ≈ 50 nm (BaZn3-NPs-25min) have been obtained by using a coprecipitation method at ambient pressure, and by varying the stirring time. Rietveld refinements of X-ray diffraction data indicate that micro- and nanostructured BaZn3(VO4)2(OH)2 both crystallize in a R3̄m structure very similar to that of the known layered-kagome compound BaCo3(VO4)2(OH)2. Transmission electron microscopy observation of BaZn3-NPs-7h and BaZn3-NPs-25min reveals crystallized NPs with homogenous distributions of Ba, Zn, and V elements. FT-IR and Raman spectra show subtle differences between micro- and nanostructured samples which cannot be linked to any differences in the average crystal structures. The high resolution 51V MAS NMR spectrum of BaZn3-MPs shows a single isotropic line attributed to VO43- groups with C3v point group. The spectra of the nanostructured samples reveal the presence of a weak additional signal which decreases in intensity with increasing the NPs size, and which has been tentatively assigned to the presence at the surface of the NPs of a small amount of V5+ ions in a different chemical environment. Nanostructuring also impacts the optical properties of BaZn3(VO4)2(OH)2. The UV-vis absorption spectra of NPs exhibit an additional weak transition in the visible domain which is not observed for the microstructured sample.

Continuous wave and pulsed EPR study of Cd1-xMnxTe crystals with different Mn content

The cadmium manganese telluride (Cd1–xMnxTe) crystals (x < 0.001 and x = 0.02, 0.04, 0.1) grown using the Bridgman method were studied by applying continuous wave and pulsed electron paramagnetic resonance (EPR) spectroscopy in the wide temperature range. The Cd1–xMnxTe crystals with x < 0.001 revealed the EPR spectrum from isolated Mn2+ with g⊥ = g∥ = 2.0074(3), |A⊥| = |A∥| = 56.97 ⋅ 10–4 cm–1, |a| = 30.02⋅10–4 cm–1, while Cd1–xMnxTe crystals with x = 0.02…0.04 are characterized by two single broad isotropic EPR lines of Lorentzian shape (g ~ 2.009 and g ~ 1.99) due to Mn clusters of different sizes. The EPR spectrum of Cd1–xMnxTe crystals with x = 0.01 consists of the single broad line at g ~ 2.01 due to higher level of homogeneity inherent to these crystals. The temperature dependence of spin relaxation times for the isolated Mn2+ center in the Cd1–xMnxTe crystals with x < 0.001 has been described using the conceptions of Orbach process for TM–1 and two-phonon Raman process for T1–1.

Reflection Principles for Zero Mean Curvature Surfaces in the Simply Isotropic 3-space

Zero mean curvature surfaces in the simply isotropic 3-space $${\mathbb {I}}^3$$ naturally appear as intermediate geometry between geometry of minimal surfaces in $${\mathbb {E}}^3$$ and that of maximal surfaces in $${\mathbb {L}}^3$$ . In this paper, we investigate reflection principles for zero mean curvature surfaces in $${\mathbb {I}}^3$$ as with the above surfaces in $${\mathbb {E}}^3$$ and $${\mathbb {L}}^3$$ . In particular, we show a reflection principle for isotropic line segments on such zero mean curvature surfaces in $${\mathbb {I}}^3$$ , along which the induced metrics become singular.

Новые задачи начертательной геометрии. Продолжение

Complex geometry is a synthesis of Euclidean E-geometry (circle geometry) and pseudo-Euclidean M-geometry (hyperbola geometry). Each of them individually defines a non-closed system in which a correctly posed problem may not give a solution. Analytical geometry represents a closed system. In it, a correctly posed problem always gives solutions in the form of complex numbers, for each of which, one of the parts may be equal to zero. Finding imaginary solutions and imaginary figures formed by a set of such solutions is a new problem in descriptive geometry. Degenerated conics and quadrics, or curves and surfaces of higher orders, constitute a new class of figures and a new class of problems in descriptive geometry. For example, null-circle, null-sphere, null-cylinder, null-torus. In this paper the problem for studying the shape of second (conics, quadrics), third (conoid), and fourth (torus) order figures is posed. The latest suggest a meeting with new geometric properties of figures. Geometric operations are still immersed in the complex space E + M or real - imaginary. The examples under consideration continue a series of degenerated figures in which the null-circle splits into isotropic lines. Isotropic lines are taken as generators of surfaces. They form a cone of revolution and a hyperbolic paraboloid (an oblique plane).

On the pinned distances problem in positive characteristic

We study the Erdős–Falconer distance problem for a set A ⊂ F 2 $A\subset \mathbb {F}^2$ , where F $\mathbb {F}$ is a field of positive characteristic p $p$ . If F = F p $\mathbb {F}=\mathbb {F}_p$ and the cardinality | A | $|A|$ exceeds p 5 / 4 $p^{5/4}$ , we prove that A $A$ determines an asymptotically full proportion of the feasible p $p$ distances. For small sets A $A$ , namely when | A | ⩽ p 4 / 3 $|A|\leqslant p^{4/3}$ over any F $\mathbb {F}$ , we prove that either A $A$ determines ≫ | A | 2 / 3 $\gg |A|^{2/3}$ distances, or A $A$ lies on an isotropic line. For both large and small sets, the results proved are in fact for pinned distances.

Radio continuum properties of OH megamaser galaxies

ABSTRACT We present a study of the radio continuum properties of two luminous/ultraluminous infrared galaxy samples: the OH megamaser (OHM) sample (74 objects) and the control sample (128 objects) without detected maser emission. We carried out pilot observations for 140 objects with the radio telescope RATAN-600 at 1.2, 2.3, 4.7, 8.2, 11.2, and 22.3 GHz in 2019–2021. The OHM sample has two times more flat-spectrum sources (32 per cent) than the control sample. Steep radio spectra prevail in both samples. The median spectral index at 4.7 GHz α4.7 = −0.59 for the OHM sample, and α4.7 = −0.71 for the non-OHM galaxies. We confirm a tight correlation of the far-infrared (FIR) and radio luminosities for the OHM sample. We found correlations between isotropic OH line luminosity LOH and the spectral index α4.7 (ρ = 0.26, p-val. = 0.04) and between LOH and radio luminosity P1.4 (ρ = 0.35, p-val. = 0.005). Reviewing subsamples of masers powered by active galactic nuclei (AGNs) and star formation revealed insignificant differences for their FIR and radio properties. None the less, AGN-powered galaxies exhibit larger scatter in a range of parameters and their standard deviations. The similarities in the radio and FIR properties in the two samples are presumably caused by the presence of a significant amount of AGN sources in both samples (47 and 30 per cent in the OHM and control samples) and/or possibly by the presence of undetected OH emission sources in the control sample.

Vibrational relaxation of monomeric and self-associated acrylonitrile species in solutions

The dynamic interactions between acrylonitrile and carbon tetrachloride in solutions were investigated by means of Raman spectroscopy in a wide concentration range. We progress on the comprehensive understanding of vibrational frequency modulation and dephasing by analyzing the spectra and the time correlation functions of vibrational relaxation. Unlike to the usual Raman line profile analysis, we used an alternative approach to extract valuable parameters related to vibrational short-time dynamics of the system by applying a fitting procedure of the spectra directly in the frequency domain without prejudging the Lorentzian or Gaussian character of the analytical function. We focused on the CN symmetric stretching mode of acrylonitrile, which was used as a probe of the dynamics of these solutions. This relatively complex mode appears as an asymmetric line profile that was decomposed into two individual components assigned to monomeric and self-associated species. Systematic analysis of the dynamic parameters revealed a strong dependence of vibrational relaxation on the local environment around the acrylonitrile species in solutions with carbon tetrachloride. The vibrational relaxation time τV and the frequency modulation time τω increase from dilute to dense solutions implying modification of interactions upon dilution. The variations observed in the second moments of vibrations imply an interplay between repulsive and attractive forces acting on monomeric and self-associated species in solution environment. The relative contribution of the homogeneous and inhomogeneous broadening to the isotropic Raman line profile of the CN symmetric stretching mode of acrylonitrile has been analyzed and discussed in view of the recent phenomenological status of the field.

Soil Fabric and Transitional Behavior in Completely Decomposed Granite: An Example of Well-Graded Soil

Unlike sedimentary soils, limited studies have dealt with completely decomposed granite (CDG) soils, even though they are plentiful and used extensively in several engineering applications. In this paper, a set of triaxial compression tests have been conducted on well-graded intact and disturbed CDG soils to study the impact of the fabric on soil behavior. The soil behavior was robustly affected by the soil fabric and its mineral composition. The intact soil showed multiple parallel compression lines, while a unique isotropic compression line was present in the case of disturbed soil. Both the intact and disturbed soils showed unique critical state lines (CSL) in both the e-log p′ and q-p′ spaces. The intact soil showed behavior unlike other transitional soils that have both distinct isotropic compression lines ICLs and CSLs. The gradient of the unique ICL of the disturbed soil was much more than that of the parallel compression lines of the intact soil. In the intact soil, the slope of the unique CSL (M) in the q-p′ space was higher than that of the disturbed soil. The isotropic response was present for both the intact and disturbed soils after erasing the inherited anisotropy as the stress increased with irrecoverable volumetric change. Soil fabric is considered the dominant factor in the transitional behavior and such a mode of soil behavior is no longer restricted to gap-graded soil as previously thought.

Efficient polynomial analysis of magic-angle spinning sidebands and application to order parameter determination in anisotropic samples.

Chemical shift tensors in C solid-state NMR provide valuable localized information on the chemical bonding environment in organic matter, and deviations from isotropic static-limit powder line shapes sensitively encode dynamic-averaging or orientation effects. Studies in C natural abundance require magic-angle spinning (MAS), where the analysis must thus focus on spinning sidebands. We propose an alternative fitting procedure for spinning sidebands based upon a polynomial expansion that is more efficient than the common numerical solution of the powder average. The approach plays out its advantages in the determination of CST (chemical-shift tensor) principal values from spinning-sideband intensities and order parameters in non-isotropic samples, which is here illustrated with the example of stretched glassy polycarbonate.

Measurements of pressure broadening of N2 in the anisotropic tensor component of spontaneous Raman spectra

Spontaneous Raman scattering from nitrogen is well-suited for temperature measurements in combustion experiments, especially at high pressure which increases the Raman signal because of the higher density in the measurement volume. In this work we investigate high density effects on the anisotropic tensor component of ro-vibrational spontaneous Raman scattering, which must be understood to obtain accurate thermometry in high pressure gases using high-fidelity Raman simulations. We measure the collision broadening for the anisotropic component of spontaneous Raman scattering from room temperature nitrogen over the pressure range 10–70 atm for three gas compositions: pure nitrogen, air, and nitrogen in argon. Line broadening coefficients inferred from these measurements were found to be 14 ± 5% larger than the corresponding broadening coefficients of the isotropic Q branch. Air broadening coefficients were found to be very similar and about 2.5% smaller than nitrogen self-broadening coefficients. Argon broadening coefficients were 25% smaller at rotational quantum number 7 and about 50% smaller at rotational quantum number 21. Additionally, we found that our unmixed line model for the O and S branches gave good fits for all pressures, which indicates that line mixing effects are not significant in the O and S branches over this range of pressures. Using indirect experimental evidence we infer that line mixing effects in the anisotropic component of the Q branch were below the threshold set by our experimental spectral resolution at pressures up to 70 atm at room temperature. Assuming that the anisotropic Q branch lines mix like the isotropic lines results in a small systematic error in the inferred temperature at flame temperatures, with the error increasing slowly with pressure. The bias can be easily removed by modeling the anisotropic spectrum separately from the isotropic spectrum. Line mixing effects should be included in the model of the isotropic part of the Raman spectrum, but can probably be neglected in the anisotropic part of the spontaneous Raman spectrum of N 2 for pressures below 400 atm at flame temperatures.

Structural, paramagnetic centres and luminescence investigations of the UV radiation-emitting BaZrO3:Gd3+ perovskite ceramic prepared via sol-gel route

Perovskite-type ceramic materials have been widely studied due to their potential use in such applications as electrical, thermal, optical, and immobilizing host materials in nuclear waste. In this work, Gd3+-doped BaZrO3 perovskite samples were prepared by sol-gel method and characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), electron paramagnetic resonance (EPR) spectroscopy, and photoluminescence (PL) analysis. Our XRD analysis confirmed the formation of the sol-gel products, and the SEM data implicated the prepared porous compound as the cause of the gases that evolved during the preparation. Upon excitation at 275 nm, the ceramic material displayed UVB emission at 315 nm (6P7/2 → 8S7/2). The EPR technique was used to study the undoped and gadolinium-doped perovskite BaZrO3 ceramics. The lines in the undoped system were caused by two defect centers. Center I displayed an isotropic line with a g-factor of 1.973 and a linewidth of 48 Gauss, and the center was assigned to an F+ center. Center II exhibited an axially symmetric g-tensor with principal values g|| = 1.895 and g⊥ = 1.978. This center was identified as the Zr3+ ion. The single dominant EPR line with an effective g-value of 1.976 that was observed in the Gd-doped system was attributed to the Gd3+ ion experiencing a weak cubic symmetry crystal field.

Interplay between spatial anisotropy and next-nearest-neighbor exchange interactions in the triangular Heisenberg model

We investigate the interplay between spatial anisotropy and further exchange interactions in the spin-$\frac{1}{2}$ Heisenberg antiferromagnetic model on a triangular lattice. We use the Schwinger boson theory by including Gaussian fluctuations above the mean-field approach. The phase diagram exhibits a strong reduction of the long range collinear and incommensurate spirals regions with respect to the mean-field ones. This reduction is accompanied by the emergence of its short range order counterparts, leaving an ample room for $0$-flux and nematic spin liquid regions. Remarkably, within the neighborhood of the spatially isotropic line, there is a range where the spirals are so fragile that only the commensurate $120^{\circ}$ N\'eel ones survive. The good agreement with recent variational Monte Carlo predictions gives support to the rich phase diagram induced by spatial anisotropy.