Thin Inclusions Research Articles

Genesis of Fibrous Calcite in the Chang 7 Member of the Yanchang Formation, Ordos Basin

AbstractTo explore the genesis of the laminated calcite veins developed in the black shale of Chang 73 submember of the Ordos Basin, the petrology, microstructure and geochemistry of calcite veins are studied using thin sections, fluid inclusions, trace elements and isotopic geochemistry. The source, the time of formation, the mechanism of formation, and the dynamic background of the veins are discussed. The veins are mostly made up of calcite, mixed with lenticular or spindle‐shape solid wall rock inclusions. Three structures are identified in the calcite minerals: fibrous, rhombic cleavage, and wedge‐like structure. Trace elements and isotopes of carbon and oxygen confirm that the calcite veins were formed from a high density hydrothermal fluid. It is assumed that calcite veins formed prior to wall rock consolidation during the formation of the Qinling Orogenic Belt in the Middle and Late Triassic. The results show that the sedimentary sources of Chang 73 submember were influenced by hydrothermal materials besides terrigenous detritus. The fibrous calcite is different from the fibrous calcite reported in the morphology and mechanism of formation. In this way, the research complements and improves the morphology and the mechanism of formation of fibrous calcite.

Effect of Surface Stresses on the Antiplane Stress-Strain State of a Thin Ribbon-Like Interface Inclusion

On the basis of the theory of functions of complex variable and the method of jump functions, we propose a procedure of taking into account the additional influence of surface stresses in the problem of thin interface inclusion in the bimaterial. In this problem, we take into account the possibility of imperfect contact between the inclusion and the matrix and, in particular, the possibility of contact with surface tension. This significantly extends the field of applicability of the results of simulation within the framework of the concept of representative volume element in micro- and macromechanics. We propose a generalized model of thin inclusion with arbitrary mechanical properties. The analysis of test problems reveals high accuracy and efficiency of the proposed approach. We present the results of numerical analyses of the stress fields in the case of interaction of the inclusion with concentrated forces and screw dislocations.

Noncoercive problems for elastic bodies with thin elastic inclusions

The paper concerns boundary value problems for an elastic body with a thin elastic inclusion for a noncoercive case. The inclusion is assumed to be delaminated thus forming a crack between the inclusion and the surrounding elastic body. To provide a mutual nonpenetration between crack faces, we consider inequality type boundary conditions with unknown set of a contact. In the paper, a solution existence of the equilibrium problems is proved for the cases when one or two given points of the inclusion are fixed as well as and for the case without these restrictions.

Elasticity Tensor Identification in Elastic Body with Thin Inclusions: Non-coercive Case

Elasticity Tensor Identification in Elastic Body with Thin Inclusions: Non-coercive Case

Genesis and Fluid Evolution of the Hongqiling Sn-W Polymetallic Deposit in Hunan, South China: Constraints from Geology, Fluid Inclusion, and Stable Isotopes

The Hongqiling is a vein-type Sn-W polymetallic deposit in southern Hunan (South China). It is geologically located on the northern margin of the Nanling metallogenic belt. Based on the mineral assemblage and vein crosscutting relationship, three mineralization stages were identified: Sn-W mineralization (S1: cassiterite, wolframite, scheelite, arsenopyrite, molybdenite, pyrite, chalcopyrite, and quartz), Pb-Zn mineralization (S2: chalcopyrite, pyrrhotite, galena, sphalerite, pyrite, quartz, and fluorite), and late mineralization (S3: quartz, fluorite, calcite, galena, sphalerite, and pyrite). According to laser Raman probe analysis, H2O dominates the fluid inclusions in the S1 and S2 stage quartz, with CO2 and trace N2 following close behind. The ore fluid has low salinity, low density, and a wide temperature range, as per our microthermometric data: the S1 stage has homogenization temperatures (Th) of 236–377.6 °C (average 305.3 °C) and salinity of 3.5–10.7 wt.% NaCleqv; the S2 stage has Th of 206.5–332 °C (average 280.7 °C) and salinity of 1.6–5.1 wt.% NaCleqv; and the S3 stage has Th of 170.9–328.7 °C (average 246 °C) and salinity of 0.2–5.9 wt.% NaCleqv. Based on the results of the aforementioned investigation, the fluid inclusions in quartz, fluorite, and calcite are mainly H2O-NaCl vapor-liquid two-phase. Additionally, examinations of inclusions in S1 wolframite and coexisting quartz using infrared and microthermometry show that the mineralizing fluid likewise belongs to the NaCl-H2O system. The Th of inclusions in wolframite is ~40 °C higher than that of coexisting quartz. Moreover, the fluid experienced a decrease in temperature accompanied by nearly constant salinity, which indicates that wolframite precipitation is due to fluid mixing and simple cooling, and the precipitation is earlier than quartz. In situ S and H-O isotope data show that the samples have δ34S = −2.58‰ to 1.84‰, and the ore fluids have δD = −76.6 to −51.5‰ (S1 and S2), and δ18Ofluid = −6.6 to −0.9‰ (S1) and −12.9 to −10.2‰ (S2). All these indicate that the mineralizing fluid was derived from the granitic magma at Qianlishan, with substantial meteoric water incursion during the ore stage. Such fluid mixing and subsequent cooling are most likely the primary controls for ore deposition.

The Problem of the Location of an Inclusion in a Two-Dimensional Elastic Body with Two Thin Rigid Inclusions

The Problem of the Location of an Inclusion in a Two-Dimensional Elastic Body with Two Thin Rigid Inclusions

Elastic body with thin nonhomogeneous inclusion in non-coercive case

The paper addresses analysis of equilibrium state of an elastic body with a thin nonhomogeneous inclusion in a non-coercive case. We assume that a part of the inclusion is located outside the elastic body, and the traction free boundary condition at the external boundary of the elastic body does not provide a coercivity of the problem. The inclusion is delaminated from the surrounding elastic material that implies a presence of the interfacial crack. Constraint boundary conditions at the crack faces describe a mutual nonpenetration and have an inequality type form. We prove a solution existence of the equilibrium problem, analyze a passage to the limit as the rigidity parameter of the inclusion tends to zero, and prove a solution existence of an inverse problem. The inverse problem assumes that along with the displacement field we have to find an elasticity coefficient for the inclusion provided that an additional information is given which can be found from a measurement.

Asymptotic Approach in the Dynamic Problems of the Theory of Elasticity for Bodies with Thin Elastic Inclusions

Asymptotic Approach in the Dynamic Problems of the Theory of Elasticity for Bodies with Thin Elastic Inclusions

Physico-chemical studies of technogenic gold-containing wastes of the Aksu deposit

To develop a comprehensive technology for processing technogenic gold-containing waste, a representative sample of technogenic mineral formations of the Aksu deposits was selected. The average representative sample was studied using chemical, X-ray phase, mineralogical, X-ray spectral and electron microscopic analysis methods. The article presents physico-chemical studies of gold-bearing technogenic mineral formations of the Aksu deposit. According to the results of X-ray phase analysis, it was found that the main phase components are the following minerals: α-quartz - 63.2%, barite - 26.8%, muscovite - 6.3% and gypsum - 3.8%. Electron probe scanning revealed the presence of gold in the form of thin inclusions in rock-forming minerals. With the help of rational analysis, it was found that the proportion of free gold in the form of accretions with ore components in them is 7.18%. It was found that the main part of gold - 64.7% - is in the sulfide sample in the form of films coated with quartz, iron hydroxides, carbonates, chlorites and other minerals. According to the results of assay and atomic adsorption, gold in technogenic mineral formations varies from 1.11 to 1.28 g/t. The sieve analysis of technogenic mineral formations of the Aksu deposit showed that the initial sample is mainly represented by a class of -0.25+0.074 mm. Based on the data of analytical studies, it can be seen that the studied samples of stale tails of TMOS are a rather complex object for extracting gold, which is associated with the above-described features of the material composition. As well as the thin inclusiveness of gold in sulfides determine the persistent nature of the raw material under study. The results obtained in the physico-chemical study of technogenic mineral formations of the Aksu deposit will become the basis for choosing the technology for processing this raw material.

Особенности сферических электроэрозионных порошков сплавов Mo и Nb

Сharacteristics of spherical powders of (Mo,Nb) and (Nb,Mo) alloys prepared by spark erosion technique are described. Two regimes (U = 24 V, I = 10 A and U = 24 V, I = 20 A in distilled water) were chosen for powder preparation. The pyrolysis of dielectric liquid during spark erosion leads to the formation of stable oxides NbO and NbO2 as thin crusts and spherical inclusions from 10 nm to 10 µm in powder particles. The largest deviations from electrode compositions (from 3 to 7 wt.% Nb) are inherent to Mo alloys with 9 and 10 wt.% of Nb. The number of NbO and to a lesser extent NbO2 inclusions in spherical powder increase with increasing of Nb content in alloy, but only in series of (Mo,Nb) samples. Such regularity is not observed for (Nb,Mo) series. Decrease of current value results the change of granulometric compositions of spherical powders. The main fraction of powders at I = 20 A is 40-80 µm and I = 10 A is 20-50 µm.

Periodic system of rigid inclusions in a spatial elastic wedge

A periodic contact problem (tangential contact) on a chain of thin rigid inclusions located along the edge of a three-dimensional elastic wedge of a dihedral angle in its middle half-plane (rigid sealing of the wedge faces, the axis of the chain of inclusions is parallel to the edge of the wedge) is considered. To derive the integral equation, the previously obtained fundamental solution of the problem of the action of a concentrated force inside a three-dimensional elastic wedge is used. The nucleus has latent symmetry, then it is reduced to a form with explicit symmetry. To solve the integral equation, a regular asymptotic method is used, which is effective for relatively sparse and far from the edge chains of inclusions in a three-dimensional elastic wedge. Contact characteristics are calculated for different values of dimensionless geometric parameters. Previously, similar problems were considered about one inclusion (stringer) in a strip [1] and a three-dimensional wedge [2], as well as in an unbounded elastic body [1].

Preparation and characterization of very thin polymer inclusion membranes (PIMs) and their application to the transport of thiocyanate

The possibility of reproducible fabrication of functioning polymer inclusion membranes (PIMs) thinner than 10 μm, referred to as very thin PIMs (VT-PIMs), was demonstrated with four membrane compositions used successfully in previous studies for the extraction of thiocyanate. These compositions included Aliquat 336 as extractant (carrier) and 70 wt% of one of the following base polymers: poly(vinyl chloride) (PVC), cellulose triacetate (CTA) or poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP). One PVC- and one CTA-based PIMs contained 10 wt% 1-tetradecanol as modifier and 20 wt% Aliquat 336, while another CTA-based PIM and the PVDF-HFP-based PIM contained only 30 wt% Aliquat 336.The PVDF-HFP-based membrane (effective thickness 7.4 μm) exhibited the highest rate of transport of thiocyanate between a feed and a receiving solution among the newly developed VT-PIMs. Its initial flux was found to be more than twice that of a conventional thickness PIM (50 μm) of the same composition while the long-term stability of these two PIMs, studied in consecutive transport experiments, was virtually identical. The results obtained indicated that VT-PIMs offered a promising way of significantly improving the transport performance of PIMs, thus making them attractive to separation applications in industry.The paper also reports on the development of a reliable method for determining the effective thickness of PIMs using their density, which is particularly useful for VT-PIMs where thickness measurements using optical microscopy are difficult to perform.

Effect of the Transverse Functional Gradient of the Thin Interfacial Inclusion Material on the Stress Distribution of the Bimaterial under Longitudinal Shear.

The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress-strain state of a piecewise homogeneous linear-elastic matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is constructed. An analytic-numerical analysis of the stress fields for some typical cases of the continuous functional gradient dependence of the mechanical properties of the inclusion material is performed. It is proposed to apply the constructed solutions to select the functional gradient properties of the inclusion material to optimize the stress-strain state in its vicinity under the given stresses. The derived equations are suitable with minor modifications for the description of micro-, meso- and nanoscale inclusions. Moreover, the conclusions and calculation results are easily transferable to similar problems of thermal conductivity and thermoelasticity with possible frictional heat dissipation.

Permian-Triassic flood basalts in the pre-Jurassic basement of the Arctic zone of the West Siberian platform

Research subject. Permian-Triassic flood basalts in the basement of the Arctic zone of the West Siberian Platform locate mainly in graben-rift structures. Flood basalts in this region remain to be understudied in comparison with other areas of its distribution, mainly due to the significant depth of their occurrence (4–6 km).Materials and methods. 36 core samples from 11 superdeep and deep boreholes were studied. Isotopic ratios were measured on mass spectrometers NEPTUNE PLUS (Nd, Sm) and TRITON PLUS (Rb, Sr). Bitumen were studied using a Raman spectrometer LabRAM HR800 Evolution. The Raman spectra were deconvoluted (“Peak fitting” procedure), and the bitumen conversion temperature was estimated.Results. About half of the samples of volcanic rocks underwent metamorphism of the prehnite-pumpellite and locally greenschist facies or intense low-temperature hydrothermal alteration. The studied basalts are close to typical flood basalts and are somewhat similar to island-arc volcanic rocks in terms of their geochemical characteristics. For the first time, thin inclusions of bitumen were found in the amygdalae of Permian-Triassic basalts in the superdeep borehole Tyumenskaya SG-6 at a depth of 7310.6 m. A high similarity of the studied volcanics by geochemical characteristics and the isotopic composition of Sr and Nd with the flood basalts of the Siberian platform is shown.Conclusions. The presence of a negative Ta, Nb, Ti anomaly, as well as a negative Ce anomaly, in some of the analyzed samples indicates a possible contamination of the basalts by island arc volcanics and volcanogenic-sedimentary rocks. The temperature of transformation of bitumen in inclusions in basalts from the well Tyumenskaya SG-6 according to Raman spectroscopy is estimated at 150–300°C and generally corresponds to the temperature of metamorphism of the host basalts. The presence of bitumen in the amygdalae may indicate the migration of hydrocarbons through the basalts.

Membranes with thin and heavy inclusions: Asymptotics of spectra

We study the asymptotic behaviour of eigenvalues of 2D vibrating systems with mass density perturbed in a vicinity of closed curves. The threshold case in which the resonance frequencies of the membrane and the frequencies of thin inclusion coincide is investigated. The perturbed eigenvalue problem can be realized as a family of self-adjoint operators acting on varying Hilbert spaces. However the so-called limit operator is non-self-adjoint and possesses the Jordan chains of length 2. Apart from the lack of self-adjointness, the operator has non-compact resolvent. As a consequence, its spectrum has a complicated structure, for instance, the spectrum contains a countable set of eigenvalues with infinite multiplicity. The complete asymptotic analysis of eigenvalues has been carried out.

Junction problem for thin elastic and volume rigid inclusions in elastic body.

The article concerns a junction problem for two-dimensional elastic body with a thin elastic inclusion and a volume rigid inclusion. It is assumed that the inclusions have a common point. A delamination of the thin inclusion from the surrounding elastic body is assumed thus forming an interfacial crack. Constraint-type boundary conditions are imposed at the crack faces to prevent interpenetration between the faces. Moreover, a connection between the crack faces is characterized by a positive damage parameter. Limit transitions are justified as the damage parameter tends to infinity and to zero. In addition to this, a transition to limit is analysed as a rigidity parameter of the thin inclusion tends to infinity. Limit models are investigated. In particular, junction conditions at the common point are found for all cases considered. This article is part of the theme issue 'Non-smooth variational problems and applications'.

Multiscale analysis of stationary thermoelastic vibrations of a composite material.

The problem of description of stationary vibrations is studied for a planar thermoelastic body incorporating thin inclusions. This problem contains two small positive parameters [Formula: see text] and [Formula: see text], which describe the thickness of an individual inclusion and the distance between two neighbouring inclusions, respectively. Relying on the variational formulation of the problem, by means of the modern methods of asymptotic analysis, we investigate the behaviour of solutions as [Formula: see text] and [Formula: see text] tend to zero. As the result, we construct two models corresponding to the limit cases. At first, as [Formula: see text], by the version of the method of formal asymptotic expansions we derive a limit model in which inclusions are thin (of zero width). Then, from this limit model, as [Formula: see text], we derive a homogenized model, which describes effective behaviour on the macroscopic scale, i.e. on the scale where there is no need to take into account each individual inclusion. The limiting passage as [Formula: see text] is based on the use of the two-scale convergence theory. This article is part of the theme issue 'Non-smooth variational problems and applications'.

Influence of Imperfect Interface of Anisotropic Thermomagnetoelectroelastic Bimaterial Solids on Interaction of Thin Deformable Inclusions

Abstract This work studies the problem of thermomagnetoelectroelastic anisotropic bimaterial with imperfect high-temperature conducting coherent interface, whose components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus, the Somigliana-type integral formulae and the corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high-temperature conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented for single and multiple inclusions.

Mathematical modeling of the dynamic interaction of thin piezoceramic inclusion of variable thickness with elastic medium under axisymmetric torsion

Mathematical modeling of the dynamic interaction of thin piezoceramic inclusion of variable thickness with elastic medium under axisymmetric torsion

Interactions between multiple rigid lamellae in a ductile metal matrix: Shear band magnification and attenuation in localization patterns

A ductile matrix material containing an arbitrary distribution of parallel and stiff lamellar (’rigid-line’) inclusions is considered, subject to a prestress state provided by a simple shear aligned parallel to the inclusion lines. Because the lamellae have negligible thickness, the simple shear prestress state remains uniform and its amount can be high enough to drive the matrix material on the verge of ellipticity loss. Close to this critical stage, a uniform remote Mode I perturbation realizes shear band formation, growth, interaction, thickening or thinning. This two-dimensional problem is solved through the derivation of specific boundary integral equations, holding for a nonlinear elastic matrix material uniformly prestressed; the related numerical treatment is specifically tailored to capture the stress singularity present at the inclusion tips. Results show how complex localized deformation patterns form, so explaining features related to the failure mechanisms of ductile materials reinforced with stiff and thin inclusions. In particular, the influence of the inclusion distribution on the shear bands pattern is disclosed. Conditions for the magnification (the attenuation) of the localized deformations are revealed, fostering the progress (the setback) of the failure process.