Triaxial Anisotropy Research Articles

Transitions between Segments of C- and S-Shaped Domain Walls in Magnetically Uniaxial and Triaxial Films

A three-dimensional micromagnetic computer simulation of transition structures that separate regions of C- and S-shaped vortex asymmetric domain walls in films with easy magnetization axes parallel to the surface has been performed. Films with uniaxial and triaxial magnetic anisotropy (with the surface parallel to crystallographic plane (100)) have been examined. New types of transition structures (including those containing Bloch points) have been obtained.

Permeability evolution of anthracite coal considering true triaxial stress conditions and structural anisotropy

It is critical to understand the gas flow behavior in coal under a reservoir stress condition for coal bed methane production, underground coal mining, and CO2-sequestration in deep coal seams. With respect to coal seams, the in-situ stress is anisotropic and generally exists under true triaxial stress (σ1 > σ2 > σ3) conditions. Additionally, the flow channels determining the permeability of coal are also anisotropic. This dual anisotropy produces difficulties in replicating the gas transport characteristics of coal at the laboratory scale, and there is a paucity of relevant studies. In this study, we performed a series of permeability measurements using cubic anthracite coal samples and changing the principal stresses and flow directions under various true triaxial stress conditions. The coal permeability exhibited greater anisotropy in the vertical direction as a result of the presence of minerals in cleats across the bedding plane. After each principal stress compression at a differential stress of 20 MPa, the permeability in each direction decreased by an order of magnitude. With an increase in the intermediate stress parameter, the permeability values of two horizontal cleats experienced higher decreasing rates compared with the vertical bedding permeability. This increased the significance of the horizontal permeability anisotropy. With respect to the true triaxial stress condition with a higher horizontal principal stress (σH > σh > σv), a higher permeability reduction was observed during the principal stress loading period. The butt cleat plane was more sensitive to changes in the principal stress because of the lower connectivity of the flow channels induced by the closure of the face cleat that acted as a cross-linked pathway. The anisotropic permeability data measured under true triaxial stress conditions were well expressed by an exponential equation containing different mean cleat compressibility and stress terms. The cleat compressibility values in different directions were obtained by data fitting.

Frequency dependence of susceptibility in magnets with uniaxial and triaxial anisotropy

AbstractCharacterization of minerals in rocks and soils provides a window into environmental processes and improves the interpretation of paleomagnetic measurements. Mineral composition, size, and shape can be constrained using magnetic measurements. For small minerals, a promising measurement is the frequency dependence of magnetic susceptibility. The size and shape dependence of the in‐phase componentand out‐of‐phase componentare derived for arbitrarily oriented superparamagnetic and single‐domain magnets with uniaxial and triaxial anisotropy. In a fluctuating field, a single magnet has a thermal response parallel to the easy axis and instantaneous rotation of the moment perpendicular to it. The size and temperature variations have the same form as in earlier theories in which all the magnets are aligned with the field and can be easily adapted to the methods of Shcherbakov and Fabian (2005) and Egli (2009) for finding size distributions using multiple temperatures and frequencies. These inversions are inherently nonunique and complicated by non‐SD contributions, but some robust constraints can be put on the volume distribution if the commonly used ratioχfdis 10% or greater. The anisotropy of the out‐of‐phase component (opAMS) has the same sense as thermoremanent magnetization (TRM) and can be used to correct the paleofield direction. Along with the anisotropy of the in‐phase component (ipAMS), it can be used to gain quantitative information on the deformation of the host rock. For the line/plane, or March, deformation model, opAMS and ipAMS are calculated and it is shown how they can be used to accurately represent the strain anisotropy.

Evidence of field induced slow magnetic relaxation in cis-[Co(hfac)2(H2O)2] exhibiting tri-axial anisotropy with a negative axial component.

We report a combined experimental characterization and theoretical modeling of the hexa-coordinated high-spin Co(ii) complex cis-[Co(hfac)2(H2O)2] (I). The magnetic static field (DC) data and EPR spectra (measurements were carried out on the powder samples of diluted samples cis-[Co0.02Zn0.98 (hfac)2(H2O)2]) were analyzed with the aid of the parametric Griffith Hamiltonian for the high-spin Co(ii) supported by the ab initio calculations of the crystal field (CF) parameters, g-factors and superexchange parameters between H-bonded Co(ii) ions in the neighboring molecules in a 1D network. This analysis suggests the presence of the easy axis of magnetic anisotropy and also shows the existence of a significant rhombic component. The detected frequency dependent (AC) susceptibility signal shows that complex I exhibits slow paramagnetic relaxation in the applied DC field belonging thus to the class of non-uniaxial field induced single ion magnets with a negative axial component of anisotropy. It is demonstrated that the main contributions to the relaxation come from the direct one-phonon process dominating at low temperatures, while the contribution of the two-phonon Raman process becomes important with increasing temperature.

回転変調磁場を用いた希土類系高温超伝導体の3次元結晶配向

Modulated rotating magnetic field (MRF) enables bi-axial grain arrangement of substances with tri-axial magnetic anisotropy. Even feeble magnetic (paramagnetic and diamagnetic) substances become target materials for the magnetic grain alignment by using a 10 telsa-class strong magnet. In this review article, the authors introduce high potential of the magnetic alignment technique using MRF as a fabrication process of bi-axially grain-oriented rare-earth(RE)-based cuprate superconductors. In the former topic, the bi-axial magnetic alignment of RE-based cuprate superconductors without twin microstructures at room temperature are reported for the clarification of RE-dependent magnetization axes and tri-axial magnetic anisotropies. In the latter topic, the authors show the bi-axial magnetic alignment of practical RE-based superconductors, REBa2Cu3Oy (RE123), with twin microstructures. The inplane orientation degrees in RE123 were lowered compared with those in RE-based cuprates without twin microstructures; however, bi-axial magnetic alignment has been successfully achieved even in RE123 with twin microstructures.

Fast determination and characterization of formation resistivity anisotropy, dip, and fracture using multicomponent induction data

Multicomponent induction (MCI) logging measurements have been widely used in the past decade for determining formation resistivity anisotropy (horizontal and vertical resistivities: [Formula: see text] and [Formula: see text]), dip, and azimuth. Currently, almost all MCI processing and interpretation algorithms of determining [Formula: see text], [Formula: see text], dip, and azimuth are based on simplified transversely isotropic (TI) formation models. In most geologic environments, formations are layered or laminated, making the TI model a reasonable assumption. Subsurface formations usually contain different types of fractures (natural or drilling-induced), and exhibit azimuthal resistivity anisotropy in the bedding plane, which leads to formation biaxial anisotropy (BA) in the same bedding plane. (This type of media is usually called orthorhombic or orthotropic in mechanical engineering and geomechanics.) Therefore, MCI data processing based on TI models may not be valid in complex BA formations caused by fractures. MCI processing and interpretation methods based on BA formation models are needed for more accurate descriptions of complex anisotropic formations. Fractures significantly affect fluid flow in formations, and therefore the fracture characterization with MCI logging can provide some useful information for oil/gas development and production, especially in unconventional reservoirs. We have developed a fast and practical integrated method of borehole multiarray MCI data processing for effective determination of formation BA anisotropy (or triaxial resistivities: [Formula: see text], [Formula: see text], and [Formula: see text]), dip, and azimuth. The multiple MCI data sets were further applied to fracture evaluation, and they were tested with synthetic and field log data sets. The method has the following components: the inversion algorithm based on the multiple BA models, a fracture identification function for detection of the fracture, and the corresponding approach for estimation of the fracture relative azimuth and dip angle. The application results demonstrated that accurate triaxial formation anisotropy and dip can be obtained based on the BA models compared with the TI processed logs. Furthermore, fractures can be characterized by integrating measurements and processed log data, such as the recovered horizontal resistivities [Formula: see text] and [Formula: see text], vertical resistivity [Formula: see text], and formation dips based on the BA and TI models.

Hysteresis and coercivity of hematite

AbstractIn room‐temperature hysteresis, 14 submicron hematites (0.12‐0.45 µm) had large coercive forces Hc (150‐350 mT), while 22 natural 1‐5.5 mm hematite crystals had Hc = 0.8‐23 mT (basal‐plane measurements). Single‐domain (SD) and multidomain (MD) hematites owe their high Hc mainly to magnetoelastic anisotropy, caused in fine particles by internal strains and in large crystals by defects like dislocations, with a smaller contribution by triaxial magnetocrystalline anisotropy. A strong correlation between Hc and the defect moment Md measured below hematite's Morin transition also favors magnetoelastic control. Saturation remanence/saturation magnetization ratios Mrs/Ms and coercivity ratios Hcr/Hc (Hcr is remanent coercive force) are distinctive: Mrs/Ms = 0.5‐0.9, Hcr/Hc = 1.02‐1.17 for MD hematites; Mrs/Ms = 0.5‐0.7, Hcr/Hc = 1.45‐1.62 for SD hematites. In high‐temperature (20‐690°C) hysteresis, Hc(T) ~ Ms(T) to a power 1.8‐2.4 above 385°C. Magnetoelastic wall pinning by crystal defects is thus more likely than control by domain nucleation which depends on magnetocrystalline anisotropy. Our results compare well with existing Hc vs. crystal size d data. A suggested peak in Hc around 15 µm and a proposed slope change around 100 µm are both questionable. Using only near‐saturation data, Hc varies continuously as d−0.61 from ≈0.1 µm to 2 mm. The SD threshold size d0 may be >15 µm but there is no strong evidence that d0 ≈100 µm. Direct domain observations are needed to settle the question. Augmented data sets for Hc and Mrs vs. d show that SD hematite is increasingly affected by thermal fluctuations below ≈0.3 µm and generally confirm a superparamagnetic threshold size ds of 0.025‐0.03 µm.

Tri-axial magnetic anisotropies in RE2Ba4Cu7O15−y superconductors

We report a novel quantification method of tri-axial magnetic anisotropy in orthorhombic substances containing rare earth (RE) ions using tri-axial magnetic alignment and tri-axial magnetic anisotropies depending on the type of RE in RE-based cuprate superconductors. From the changes in the axes for magnetization in magnetically aligned powders of (RE′1−xRE″x)2Ba4Cu7Oy [(RE′,RE″)247] containing RE ions with different single-ion magnetic anisotropies, the ratios of three-dimensional magnetic anisotropies between RE′247 and RE″247 could be determined. The results in (Y,Er)247, (Dy,Er)247, (Ho,Er)247, and (Y,Eu)247 systems suggest that magnetic anisotropies largely depended on the type of RE′ (or RE″), even in the heavy RE ions with higher magnetic anisotropies. An appropriate choice of RE ions in RE-based cuprate superconductors enables the reduction of the required magnetic field for the production of their bulks and thick films based on the tri-axial magnetic alignment technique using modulated rotation magnetic fields.

Behavior of Y‐Based High‐Critical‐Temperature Superconductors in Modulated Rotating Magnetic Fields

SUMMARYWe report changes in the degree of triaxial orientation as functions of the applied magnetic field and rotation rate for Y2Ba4Cu7Oy powder samples oriented in epoxy resin under modulated rotating magnetic fields (MRFs). Although the degrees of orientation were reduced as a result of a decrease in both the applied field and rotation rate, the mechanisms of the reduction of the degrees of orientation were found to be different. Optimization of the MRF conditions or quantification of triaxial magnetic anisotropy in a target substance is required for the production of triaxially oriented ceramics based on a colloidal process.

三軸結晶配向技術としての磁場配向法

Magnetic alignment technology using the modulated rotating magnetic fields (MRF) enables formation of tri-axial grain arrangement of the substances with tri-axial magnetic anisotropy. In this review, we introduce a high potential of magnetic alignment technique as the fabrication process of tri-axially grain-oriented cuprate superconductors. As the first topic, we reported the tri-axial magnetic alignment of rare-earth-based and bismuth-based cuprate superconductors operated at room temperature. In the second topic, we show the importance of single-ion magnetic anisotropy of the rare-earth ions as a determination factor of magnetization axes and the tri-axial magnetic anisotropy in rare-earth-based cuprate superconductors. The final topic is the fabrication of tri-axially grain-aligned ErBa2Cu4O8 (Er124) ceramics under a modified MRF. To date, the Er124 ceramic with the degree of in-plane orientation with ~11 degree has been successfully fabricated by controlling the viscosity of slurry and introducing the oscillation type of MRF.

Hydrological hotspots in blanket peatlands: Spatial variation in peat permeability around a natural soil pipe

[1] Measurements were made of the hydraulic conductivity (K) of peat around a natural soil pipe in a blanket bog. This is the first investigation of decimeter-scale variability in both vertical K and horizontal K in blanket peats, which were found to be higher than indicated by previous research. This information suggests that it may be appropriate to reconsider (I) the spatial sampling strategies employed to investigate subsurface flow in blanket peatlands, and (II) how field data are used to parameterize flow models. Critically, there was spatial structure in the heterogeneity, with a wedge of high-K peat directly above the pipe forming a hydrological conduit between near-surface peat and the perennially flowing pipe. There was also significantly greater horizontal K parallel to the pipe's orientation compared with horizontal K perpendicular to the pipe. Determinations of the triaxial anisotropy of K, undertaken for the first time in peat soils, revealed substantial directional variations in K. The K around the pipe-peat interface was investigated; however, sample length dependency of K for peat samples precluded the investigation of a hypothesized low-K skin around the pipe.

The degrees of tri-axial orientation in RE-doped Bi2212 powders aligned in a modulated rotation magnetic field

We report relationship between the degrees of tri-axial orientation and doping level of rare earth (RE) ions in Bi2Sr2(Ca1−xREx)Cu2Oy (RE-doped Bi2212; RE=Dy, Ho, Er and Tm) powder samples aligned under a modulated rotation magnetic field (MRF) of 10T. Tri-axial magnetic alignment of the RE-doped Bi2212 with x=0–0.5 was achieved by single-ion magnetic anisotropy of RE3+ and tri-axial magnetic anisotropy induced by modulation microstructure in a grain level. The degrees of in-plane and c-axis orientation with ∼3° were achieved for the case of the Tm-doped Bi2212 with x=0.5. The findings in the present study give us important information for the fabrication of triaxially oriented Bi-based cuprate superconductor materials by the magneto-scientific process.

Host-guest supramolecular complexes of the composition [M{NH(CH2)4O}{S2CN(C2H5)2}2] · CHCl3 (M = Zn, 63Cu(II)): Synthesis, structure, spectral properties, and thermal behavior

Solvated forms of adducts [M{NH(CH2)4O}{S2CN(C2H5)2}2] · CHCl3 (M = Zn (I), 63Cu (II)) are preparatively isolated. Nonequivalence of the dithiocarbamate groups in structure I is revealed by the 13C MAS NMR method. According to the X-ray analysis data, adduct I is a supramolecular compound, whose structure includes a system of ordered channels occupied by outer-sphere solvating guest molecules of CHCl3 (structural type of lattice clathrates). The solvation of the initial adduct is accompanied by the structural unification of its isomeric forms and an increase in the strength of binding of the morpholine molecules and in the contribution of the trigonal-bipyramidal component to the geometry of the zinc polyhedron. The character of triaxial anisotropy of the EPR parameters of isotopically substituted compound II in the magnetically dilute state is due to the geometry of the copper polyhedron, which is intermediate between a tetragonal pyramid and a trigonal bipyramid with the ground state of an unpaired electron formed by mixing of the \(3d_{x^2 - y^2 } \)- and \(3d_{z^2 } \)-atomic orbitals (AO) of copper(II). The thermal destruction of compound I studied by simultaneous thermal analysis includes stages of desorption of solvating chloroform molecules and coordinated morpholine molecules and thermolysis of the “dithiocarbamate part” of the adduct.

Theoretical Investigation of the Magnetic Order in FeAs

The magnetic structure of the iron monoarsenide FeAs is studied using first-principlescalculations. We consider the collinear and non-collinear (spin-spiral wave) magnetic orderingand magnetic anisotropy. It is analitically shown that a magnetic triaxial anisotropy resultsin a sum of two spin-spiral waves with opposite directions of wave vectors and different spinamplitudes, so that the magnetic moments in two perpendicular directions do not equal eachother.

Correlation between elastic anisotropy and magnetic susceptibility anisotropy of sedimentary and metamorphic rock

A correlation has been revealed between the types of acoustic anisotropy and magnetic susceptibility anisotropy for specimens from noncrystalline metamorphic and sedimentary rock has been revealed. This correlation makes it possible to assume that the anisotropy of magnetic and acoustic characteristics has the same origin, namely, the rock texture. The pronounced triaxial acoustic anisotropy for specimens of polycrystalline rock in the absence of external forces makes it possible to judge the fracturing caused by tectonic loads and the degree of this fracturing. The large body of available experimental data allows the expectation that it will be possible to obtain empirical dependences suitable for estimating the intensity of geological processes based on the values of the magnetic susceptibility anisotropy and elasticity tensor anisotropy.

Thermally activated magnetization reversal in monatomic magnetic chains on surfacesstudied by classical atomistic spin-dynamics simulations

We analyse the spontaneous magnetization reversal of supported monatomic chains of finitelength due to thermal fluctuations via atomistic spin-dynamics simulations. Our approachis based on the integration of the Landau–Lifshitz equation of motion of a classical spinHamiltonian in the presence of stochastic forces. The associated magnetizationlifetime is found to obey an Arrhenius law with an activation barrier equal to thedomain wall energy in the chain. For chains longer than one domain wall width, thereversal is initiated by nucleation of a reversed magnetization domain primarilyat the chain edge followed by a subsequent propagation of the domain wall tothe other edge in a random-walk fashion. This results in a linear dependence ofthe lifetime on the chain length, if the magnetization correlation length is notexceeded. We studied chains of uniaxial and triaxial anisotropy and found that atriaxial anisotropy leads to a reduction of the magnetization lifetime due to ahigher reversal attempt rate, even though the activation barrier is not changed.

Magnetic anisotropy of hematite natural crystals: high field experiments

Hematite is one of the most important carriers of remanent magnetization in natural samples. Its strong magnetocrystalline anisotropy makes it difficult to determine one single value for the magnetic anisotropy constant and other magnetic properties. In particular, the anisotropy of hematite within its basal plane is controversial because an assumed triaxial anisotropy compatible with the crystallographic structure has not always been detected. This study presents a comparative analysis of rock magnetic properties, compositional analysis and determination of the magnetic anisotropy constant. Different models with anisotropy constant within the basal plane ranging from 0 to 13 (J m−3) are considered in the evaluation of the factors that control the presence or absence of a triaxial anisotropy. A linear relationship between saturation magnetization (M s ) and coercitivity (B c ) in measurements at increasing temperatures is observed in samples where anisotropy is either uniaxial or biaxial while those with significant triaxial anisotropies have a power–law relationship between M s and B c .

Magnetic tri-axial orientation in (Y1−xErx)2Ba4Cu7O15−y superconductors

We report the tri-axial grain-orientation effects under a modulated rotation magnetic field for (Y1−xErx)2Ba4Cu7Oy [(Y,Er)247]. The magnetic easy axis at room temperature was drastically changed around x∼0.1; however, the Er-doping levels for the conversion of magnetic easy axes from the c-axis to the ab-direction and from the a- to b-axes were quite different. Tri-axial single-ion magnetic anisotropy of Er3+ was roughly 10 times greater than tri-axial magnetic anisotropy generated by both the superconducting CuO2 plane and the blocking Cu–O chain layer. An appropriate choice of rare-earth (RE) ions in RE-based cuprate superconductors enables the reduction of the required magnetic field for the production of bulks and thick films based on the magnetic orientation technique.

Thermal stresses in two- and three-component anisotropic materials

This paper deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid continuum with uniaxial or triaxial anisotropy. The anisotropic solid continuum consists of anisotropic spherical particles periodically distributed in an anisotropic infinite matrix. The particles are or are not embedded in an anisotropic spherical envelope, and the infinite matrix is imaginarily divided into identical cubic cells with central particles. The thermal stresses are thus investigated within the cubic cell. This multi-particle-(envelope)-matrix system based on the cell model is applicable to two- and three-component materials of precipitate-matrix and precipitate-envelope-matrix types, respectively. Finally, an analysis of the determination of the thermal stresses in the multi-particle-(envelope)-matrix system which consists of isotropic as well as uniaxial- and/or triaxial-anisotropic components is presented. Additionally, the thermal-stress induced elastic energy density for the anisotropic components is also derived. These analytical models which are valid for isotropic, anisotropic and isotropic–anisotropic multi-particle-(envelope)-matrix systems represent the determination of important material characteristics. This analytical determination includes: (1) the determination of a critical particle radius which defines a limit state regarding the crack initiation in an elastic, elastic-plastic and plastic components; (2) the determination of dimensions and a shape of a crack propagated in a ceramic components; (3) the determination of an energy barrier and micro-/macro-strengthening in a component; and (4) analytical–(experimental)–computational methods of the lifetime prediction. The determination of the thermal stresses in the anisotropic components presented in this paper can be used to determine these material characteristics of real two- and three-component materials with anisotropic components or with anisotropic and isotropic components.

Synthesis, structure, and thermal properties of benzene-solvated forms of bis(dimethyldithiocarbamato)piperidinezinc and -copper(II)

Solvated adducts of zinc and copper(II) dimethyldithiocarbamate complexes with piperidine of the general formula [M{NH(CH2)5}{S2CN(CH3)2}2] · C6H6 (M = Zn (I), 63Cu (II)) were isolated on a preparative scale. According to X-ray diffraction data, compound I has a clathrate type structure: the benzene molecules located between the coordinated piperidine rings of neighboring adduct molecules are held by hydrogen bonds. Thermal destruction of I studied by simultaneous thermal analysis includes the desorption steps of benzene solvate molecules and inner-sphere piperidine molecules and thermolysis of the “dithiocarbamate part” of the adduct to give ZnS as the final product. The triaxial anisotropy pattern of EPR parameters of the isotope-substituted magnetically diluted adduct II indicates that the geometry of the copper coordination polyhedron is intermediate between a tetragonal pyramid (TP) and trigonal bipyramid (TBP). It was shown solvation of the adduct [63Cu{NH(CH2)5}{S2CN(CH3)2}2] resulting a considerable increase in the contribution of the TBP component.