Inclusion Geometry Research Articles

Absorption of light by soot particles in micro-droplets of water

Absorption cross section of carbon soot clusters inside water microdroplets is calculated. Fractal geometry of carbon inclusions is considered with the fractal dimension D in the interval 1≤D≤3, which includes the trivial geometry (D=3) as a limiting case. It is found that the absorption cross section of a soot cluster inside a water droplet is increased, compared to that in vacuum, by the factor of ≈16 for the practically important case of D=1.8. This result is obtained by averaging of the enhancement factor over the diffraction parameter of the microdroplets x=ka ( k=2 π/λ) a is the radius of the microdroplet) with a fine resolution. It is shown that the narrow resonances in the enhancement factor as a function of x play important role and should be taken into account for the purpose of averaging over x. The absorption enhancement factor increases, on average, when D decreases, and reaches the value of ≈22 for D=1.

Non-rotation of garnet porphyroblasts and 3-D inclusion trail data: an example from the Imjingang belt, South Korea

We describe non-rotation of garnet porphyroblasts in non-coaxially deformed metapelites of the Imjingang orogenic belt in the middle Korean Peninsula. The three-dimensional geometry of inclusion trails within 1–2 mm garnet porphyroblasts was analyzed by serial polishing and reflected-light microscopy. Most of the garnet porphyroblasts have straight inclusion trails of quartz and some plagioclase (S i) oblique to an external foliation (S e). Serial polishing of two samples normal to mineral/elongation lineation (A plane), and normal to S e and parallel to the lineation (B plane), with twenty intervals of about 0.1 mm, reveals that the straight S i is a planar structure. Measurement of the angles between S i and S e on both planes from samples of sixteen outcrops shows that S i orientation of individual garnets is fairly constant in each sample. The attitude of S i in geographic space, determined by using its pitch angles on the A and B planes, is more or less constant throughout the area (over 6.5 km traversing normal to the strike of regional foliation). The sense of asymmetry of strain shadows at the margin of garnet porphyroblasts and the S i/S e relationship indicate rotation of S e rather than garnet porphyroblasts with respect to the geographic reference frame. Rotation of S e is also supported by a sense of shear inferred from other shear criteria, all indicating a top-up-to-the-south shearing.

Variational methods, bounds and size effects for two-phase composites with coupled heat and mass transport processes at the two-phase interface

New variational principles are developed for the effective heat conductivity tensor of anisotropic two-phase composites in the presence of coupled mass and heat transport processes at the two-phase interface. We focus on physical situations where an imposed temperature gradient causes impurities or lattice defects to concentrate on the two-phase interface and diffuse along it. This is accompanied by the release and absorption of heat as the impurities, respectively, enter or leave the interface. We investigate the effect of the inclusion geometry on the overall thermal conductivity. For randomly distributed inclusions new size effects are given in terms of the inclusion size distribution and nearest neighbor distribution function for the included phase.

Influence of the alkyl chain length on the fluorescence properties of N-alkyl-2,3-naphthalimides included in β-cyclodextrin

Absorption spectra of N-alkyl-2,3-naphthalimides (1, R=CH3; 2,: R=n–C6H13; 3, R=n–C12H25; 4, R=n–C18H37) show absorption maximum independent of the alkyl chain length but dependent on the nature of the solvent. In the polar aprotic solvent acetonitrile N-alkyl-2,3-naphthalimides 1–4 exhibit a vibrationally resolved fluorescence emission, while in polar protic solvents (methanol or water) their fluorescence is broad and shows a bathochromic shift when compared to the one in acetonitrile. This behaviour is in agreement with previously reported data on N-methyl-2,3-naphthalimide. By the addition of aqueous solutions of β-cyclodextrin (β-CD) (concentration ranging from 1×10−3 to 1×10−2 M) to an aqueous solution of the probe, a hypsochromic shift and a strong increase of the fluorescence intensity were observed for short, i.e. 1, and long alkyl chains, i.e. 2–4. From these data we can conclude that an inclusion complex between 1–4 and β-CD is formed. The inclusion geometry for these complexes is dramatically affected by the alkyl chain length. Thus, for the short chain N-alkyl-2,3-naphthalimide, 1, a broad emission is revealed, whereas for long chains, 2–4, a vibrationally structured emission was observed. This indicates a tighter geometry for the latter case, which is a consequence of the inclusion of both the naphthalimide moiety and the alkyl group into the β-CD cavity.

A generalized self-consistent method for solids containing randomly oriented spheroidal inclusions

In this paper, a generalized self-consistent method is proposed to predict the effective moduli of a material containing single-phase and randomly oriented spheroidal inclusions, with same aspect ratios. This is achieved by using an energy equivalence framework, associated with a generalization of the classical three phase model to spheroidal inclusions. The localization problem (spheroidal duplex inclusion problem) is formulated with the Papkovitch-Neuber approach; this requires expansion formulae for the spheroidal potentials, which are derived in the Appendix. Finally, the determination of the effective moduli is equivalent to solving a system of nonlinear equations. Effective moduli are presented for various types of inclusions, and comparisons are made with the estimations obtained from the self-consistent and Mori-Tanaka methods. Moreover, the effects of inclusion geometry and spatial distribution of inclusions on the effective moduli are investigated and compared to each other.

NMR Investigations of the Inclusion of Thyroxine and Derivatives in Natural Cyclodextrins

Thyroxine T4 and its derivatives (T3, T2) are very sparingly soluble in aqueous solutions even in the form of salts. In the presence of β or γ-cyclodextrins and in buffered basic solution, their solubilities are increased by inclusion in the cavity. The inclusion of these hormones in cyclodextrins was investigated by 1H-NMR in order to derive the influence of the number and position of the iodine atoms, and of the ionization state of the phenol group on the inclusion geometries.

On the absorption and emission properties of three newnon‐steroidal anti‐inflammatory drugs‐β‐cyclodextrinhost‐guest inclusion complexes: differentiatedsensitivity to the microenvironmentupon light excitation

The effects of β‐cyclodextrin (β‐CD) complexation on the absorption and emission properties of the non‐steroidal anti‐inflammatory drugs tolmetin (TM), diflunisal (DF), and fenbufen (FB) have been investigated. The absorption spectra of all these compounds are only slightly affected by the addition of β‐CD. In contrast, the emission properties were markedly influenced by CD complexation and in a different manner for the three compounds due to a differentiated sensitivity of the excited drugs to the microenvironment. The complexes are all characterised by a 1: 1 stoichiometry and two different inclusion geometries for TM‐ β‐CD complexes have been observed. Induced circular dichroism (icd) is observed due to the interaction of the compounds with the CD chiral cavity. The icd spectra are characterized by maxima well corresponding to those of the absorption spectra. A nonlinear analysis of the dependence of the icd signal magnitude on the CD concentration provided association constants values Kass = 1400 ± 100M−1, and 2600 ± 150M−1 for TM, DF, and FB respectively.

Fundamental magnetization processes in nanoscaled composite permanent magnets

Excellent candidates for high remanent permanent magnets are nanoscaled composite materials consisting of soft magnetic $\ensuremath{\alpha}$-Fe grains embedded into a hard magnetic ${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$ environment. The magnetic properties of such permanent magnets sensitively depend on the prepared grain structure. This can be understood by computational micromagnetism, which reveals the relation between details of the grain structure and intergranular interaction mechanisms like the short-range exchange and the long-range stray field. The main problem of composite materials is to preserve a sufficiently high coercivity. This can be only guaranteed if the soft magnetic inclusions are smaller than twice the domain-wall width ${\ensuremath{\delta}}_{\mathrm{B}}^{\mathrm{hard}}=\ensuremath{\pi}\sqrt{{A/K}_{1}}$ of the hard magnetic environment with the exchange constant $A$ and the first magnetocrystalline anisotropy constant ${K}_{1}.$ Otherwise we obtain a strong decrease of the coercivity following a ${D}_{\mathrm{soft}}^{\mathrm{\ensuremath{-}}\mathrm{const}}$ law, where ${D}_{\mathrm{soft}}$ is the diameter of the soft magnetic inclusion. According to analytical and numerical investigations, the const varies between -2 and -0.5 depending on the dimension and the geometry of the soft magnetic inclusion.

A1H NMR study of cyclodextrin - hydrocarbon surfactant inclusion complexes in aqueous solutions

A1H NMR chemical shift ( delta ) study of a homologous series of hydrocarbon (hc) (CxH2x+ 1CO2Na, x = 5, 7, 9, 11, 13) surfactants (S) has been carried out in water and in binary solvent (D2O + cyclodextrin (CD)) systems at 22°C. Complementary1H NMR chemical shift ( delta ) data of the cyclodextrins in binary (D2O + S) systems containing hc surfactants have also been obtained. Complex induced shift (CIS) values for selected host or guest protons were found to increase as the alkyl chain (Cx) length of the surfactant increased. The CIS values are found to depend on the following factors: (i) the magnitude of the binding constant (Ki, i = 1:1, 2:1), (ii) the chain length of the surfactant, (iii) the mole ratio of the host to guest species, (iv) the host-guest stoichiometry, and (v) the host-guest inclusion geometry. The CIS values of the CD-S systems have been analyzed using equilibrium models in which 1:1 complexes, 1:1 plus 2:1 complexes, and uncomplexed species are present. Differences in the binding affinity, stoichiometry, and inclusion geometry of the complexes formed between a given hc surfactant and the various cyclodextrins were observed.Key words: cyclodextrin, surfactant, NMR, chemical shift, complex, binding constant.

Absorption correction procedures for quantitative analysis of fluid inclusions using synchrotron radiation X-ray fluorescence

The main limiting factor associated with individual fluid inclusion analysis using synchrotron radiation X-ray fluorescence (SRXRF) is the quantification of absorption of the incident and fluorescent radiation by the fluid and the host material. Theoretically, the measured ( K α/ K β) z intensity ratio from a given element Z in solution is directly proportional to the thickness of material traversed and therefore could be used as a reliable term for the absorption correction. In order to constrain experimentally the relationship between ( K α/ K β) z, host material thickness and fluid inclusion size and salinity, a three-step protocol has been developed using the LURE (Orsay, France) photon microprobe installed on line D15. These are: (1) interception of the X-ray fluorescent beam emerging from pure-metal targets (Mn, Fe, Ni, Cu, Zn) using thin plates of aluminium and quartz of known thicknesses; (2) feasibility tests on silica-glass capillaries containing known concentrations (∼5000 ppm) of various metals (Mn, Ni, Zn) and salts (0 and 15 wt.% NaCl); (3) confirmation tests on synthetic fluid inclusions containing known metal contents (∼1000 ppm Ni and Zn) hosted in halite crystals. The results of experiment 1 indicate that the evolution of the ( K α/ K β) z ratio as a function of host material thickness is in perfect agreement with theoretical predictions and is independent of the local analytical environment (reproducibility of the measurements). For experiments 2 and 3, the ( K α/ K β) z ratio of a reference element in solution (Zn), was used to estimate the thickness of host material traversed. Establishing that the X-ray peak intensity of Zn corresponds to a given concentration allowed the concentration of other trace metals in solution to be determined. In both experiments, the precision is high with standard deviations (1 σ) from 1 to 8% of the mean, but the accuracy can be relatively poor with mean values ranging from 3–11% (capillary tests) to as high as 17% (inclusion tests) of the known concentrations. Tight ranges of calculated metal concentrations at values higher than the known concentrations strongly suggests that the Zn concentration used to calibrate the Zn X-ray peaks may be different from that effectively measured using SRXRF. A knowledge of Mn, Ni and Zn chloride and silica speciation during SRXRF measurements is required to evaluate better this potential source of error. Despite this, results are commonly better than 20% (experiment 2) and 32% (experiment 3) relative to the known concentrations. This implies that elemental concentrations in individual fluid inclusions can be quantitatively determined using the SXRF technique without precise knowledge of the inclusion depth and geometry.

An Eshelby inclusion based model for the study of stresses and plastic strain localization in metal matrix composites II. Fiber reinforcement and lamellar inclusions

The extended Eshelby model developed in Part I of the current paper is applied to inclusions with different aspect ratios and the localization of plastic strain is calculated. Its influence on concentration factors is studied for a variety of field variables. The inclusions are considered linear elastic and plastically rigid while the matrix flows when it reaches an isotropic yield stress. Matrix plastic relaxation is found to be a mechanism for composite strengthening by stress homogenization. Fiber-like inclusions provoke the highest reduction of concentration factors with no reduction of its reinforcing ability by a load transferring mechanism. The development of hydrostatic stresses is studied both before and after plastic relaxation of the matrix. New insights are obtained to explain the macroscopic behavior of metal matrix composites and its dependence on inclusion geometry.

Steady-state creep rate of a composite: Two-dimensional analysis

A new method is proposed for calculating the steady-state creep rate of a composite, when the inclusion geometry and the matrix creep law are known. The method is demonstrated in a simple two-dimensional problem. During steady-state creep, an increment in plastic strain in the matrix causes a jump in displacement on the interface between the matrix and an individual elastic inclusion. The jump is counterbalanced by that due to diffusion and sliding on the interface. The rate of diffusion is determined by a normal force distributed on the interface and that of sliding by a tangential force. From these forces, the average stress in the inclusions is calculated; it is proportional to the steadystate creep rate. From the condition that an external stress is a volumetric average of the stress in the inclusions and that in the matrix, the constitutive equation of stationary creep of the composite is formulated.

The effect of an elliptical inclusion on a crack

The interaction between an elliptical inclusion and a crack is analyzed by body force method. The investigated stress field is simulated by superposing the fundamental solutions for a point force applied at a point in an infinite plate containing an elliptical inclusion. Based on numerical results, effects of the inclusion shape on the crack tip stress intensity factor are discussed. It is found that for small cracks emanating from a stress-higher point on the inclusion interface the stress intensity factors are mainly determined by the stresses, occurring at the crack starting point before the crack initiation, and the inclusion root radius, besides the crack length. However, for the cracks occurring in a stress-lower region around the inclusion, it is difficult to characterize the effect of the inclusion geometry on the stress intensity factors of small cracks by the inclusion root radius alone.

On a Signorini problem for inclusions in shells

We consider an equilibrium problem for a thin inclusion in a shell. The faces of the inclusion are assumed to satisfy a non-penetration condition, which is an inequality imposed on the tangential shell displacements. The properties of the solution are studied, in particular, the smoothness of the stress field in the vicinity of the inclusion. The tangential displacements are proved to belong to the space H2 near the internal points of the inclusion. The character of the contact between the inclusion faces is described in terms of a suitable non-negative measure. The stability of the solution is investigated for small perturbations to the inclusion geometry.

Stress intensity factors for an interface crack along an elliptical inclusion

The problem of a crack along the interface of an elliptical elastic inclusion embedded in an infinite plate subjected to uniform stresses at infinity is analyzed by the body force method. The crack tip stress intensity factors are calculated for various inclusion geometries and material combinations. Based on numerical results, the effect of the inclusion geometry on the stress intensity factors is investigated. It is found that for small interface cracks the stress intensity factors are mainly determined by the stresses, occurring at the crack center point before the crack initiation, and interface curvature radius alone.

Determination of the Inclusion Geometry for the β-Cyclodextrin/Benzoic Acid Complex by NMR and Molecular Modeling

Determination of the Inclusion Geometry for the β-Cyclodextrin/Benzoic Acid Complex by NMR and Molecular Modeling

Assessment of the uncertainties and limitations of quantitative elemental analysis of individual fluid inclusions using synchrotron X-ray fluorescence (SXRF)

Synchrotron X-ray Fluorescence (SXRF) analysis is a nondestructive analytical technique that provides compositional information from single fluid inclusions. A protocol for conducting quantitative analyses of metal concentrations in individual fluid inclusions has been developed. This has led to an understanding of the accuracy, precision, and detection limits of this technique, as well as the optimal shapes, sizes, and geometries required for reliable fluid inclusion analysis. Aqueous fluid inclusions containing known concentrations of SrCl 2 were synthesized for the development and the standardization of this technique. Strontium chloride was selected because it is highly soluble, its freezing-point depression is well known (allowing us to confirm the inclusion composition using microthermometric analyses), and the energetic Sr X-rays are only mildly attenuated by quartz. To confirm the composition of the synthetic standards, solutions were measured before and after each hydrothermal run using Atomic Absorption Spectroscopy (AAS), and the freezing-point depression for each fluid inclusion was measured. SXRF analyses were performed on beam line X26A of the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory using an 8 × 12 μm white X-ray beam. The analytical volume was calculated based on known beam dimensions and fluid inclusion geometry determined using a modified spindle stage. Elemental concentrations were determined by ratioing the Sr counts from an inclusion to the counts obtained from capillaries of known diameter containing similar solutions. Numerous inclusions from five samples, each with a different Sr concentration, were analyzed. Within a single population the mean is very close to the known concentration, but the precision is poor, with standard deviations (lσ) from 10–39% of the mean. Errors in determining the inclusion geometry are the main contributor to the poor precision. The poor precision requires that numerous inclusions within one population be analyzed and averaged to accurately estimate the metal concentration for that population. Selection of flat-lying, equant, regularly-shaped inclusions for analysis minimizes errors resulting from inclusion geometry if quantitative results are sought. The detection limit for Sr in synthetic fluid inclusions (typically 4–15 μm thick, and 5–100 pm below the upper polished surface) is approximately 2,000 ppm Sr.

Bounds on the complex permittivity of sea ice

An analytic method for obtaining bounds on effective properties of composites is applied to the complex permittivity ∈* of sea ice. The sea ice is assumed to be a two‐component random medium consisting of pure ice of permittivity ∈1 and brine of permittivity ∈2. The method exploits the properties of ∈* as an analytic function of the ratio ∈1/∈2. Two types of bounds on ∈* are obtained. The first bound R1 is a region in the complex ∈* plane which assumes only that the relative volume fractions p1 and p2 = 1 ‐ p1 of the ice and brine are known. The region R1 is bounded by circular arcs and ∈* for any microgeometry with the given volume fractions must lie inside it. In addition to the volume fractions, the second bound R2 assumes that the sea ice is statistically isotropic within the horizontal plane. The region R2 is again bounded by circular arcs and lies inside R1. Built into the method is a systematic way of obtaining tighter bounds on ∈* by incorporating information about the correlation functions of the brine inclusions. The bounding method developed here, which does not assume any specific geometry for the brine inclusions, offers an alternative to the classical mixing formula approach adopted previously in the study of sea ice. In these mixing formulas, specific assumptions are made about the inclusion geometry, which are simply not satisfied by the sea ice under many conditions. The bounds R1 and R2 are compared with experimental data obtained from artificially grown sea ice at the frequencies 4.8 and 9.5 GHz. Excellent agreement with the data is achieved.

Estimation of effective elastic moduli for composites

The linearly elastic deformation of a composite material with matrix outer boundary is shown to be governed by the matrix deformation, inclusion deformation and deformation due to a change in the relative inclusion geometry. The latter deformation can be shown to be independent of the inclusion material property. If the effective elastic moduli of a composite are known, then we can estimate the effective elastic moduli of other composites with the same inclusion geometry and matrix material, but with different inclusion materials. This is true for any inclusion geometry and any inclusion volume fraction as long as the outer boundary of the sample consists of matrix material.

Weak polar host–guest interactions stabilizing a molecular cluster in a cyclodextrin cavity: C–H ⋯ O and C–H ⋯π contacts in β-cyclodextrin–but-2-yne-1, 4-diol heptahydratet

In the crystalline title complex, the guest molecules are ordered and the inclusion geometry is stabilized by a system of host–guest O–H ⋯ O, C–H ⋯ O and C–H ⋯π contacts; this is an example of weak but crucial polar interactions between the surface of a cyclodextrin cavity and a cluster of polar guest molecules.