Spinodal decomposition in fine grained materials

We have used a phase field model to study spinodal decomposition in polycrystalline materials in which the grain size is of the same order of magnitude as the characteristic decomposition wavelength (Xsu). In the spirit of phase field models, each grain (i) in our model has an order parameter (η _i) associated with it;η _i has a value of unity inside the ith grain, decreases smoothly through the grain boundary region to zero outside the grain. For a symmetric alloy of composition,c = 0–5, our results show that microstructural evolution depends largely on the difference in the grain boundary energies, y_gb, of A-rich (a) and B-rich (β) phases. If Y _gb ^α is lower, we find that the decomposition process is initiated with an a layer being formed at the grain boundary. If the grain size is sufficiently small (about the same as λ_sd), the interior of the grain is filled with the β phase. If the grain size is large (say, about 10λ_SD or greater), the early stage microstructure exhibits an A-rich grain boundary layer followed by a B-rich layer; the grain interior exhibits a spinodally decomposed microstructure, evolving slowly. Further, grain growth is suppressed completely during the decomposition process.     

Force between two parallel screw dislocations and application to linear screw dislocation pileups—Gauge theory results

An analytic expression for the force between two parallel screw dislocations, derived earlier on the basis of the gauge theory of dislocations, has been used to investigate the static distribution of a given numberN of parallel screw dislocations confined between two immobile dislocation obstacles. It is shown that in the limit of a continuous distribution of dislocations the equilibrium condition leads to a Fredholm integral equation of first type which does not admit any nontrivial solution. Implication of this result is discussed. For a finite number of dislocations, the ratio (η) of the obstacle separation to the core radius is an important parameter governing the nature of solution of the discrete equation. It is found that for a givenN, there is a critical valueη _c below which there does not exist any solution.     

Computation of the relaxation and creep functions of elastomers from harmonic shear modulus

The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G ^∗(iν). The experimental data are available in the frequency window ν∈[ν_min,ν_max] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor h( n) = \fracG"( n)G￠(n)\eta( \nu) = \frac{G'( \nu )}{G'(\nu )} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus, G ^∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby, the fractional model is approximated by a generalized Maxwell model and its rheological parameters (G _k ,τ _k ,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic approach, the creep compliance J(t) is computed on inversing the relaxation function G(t).     

A modular integration and multiresolution framework for image interpretation

In this paper, we give a generalized formulation for a vision problem in the framework of modular integration and multiresolution. The developed framework is used to solve the high-level vision problem of scene interpretation. The formulation essentially involves the concept of reductionism and multiresolution, where the given vision taskν is broken down into simpler subtasksν ₁,ν ₂, …,ν _m. Moreover, instead of solving the vision taskν ^Ω =ν at the finest resolution Θ, we solve the synergetically coupled vision subtasks at coarser resolutions (Ω −N) for Θ ≥N>0 and use the results obtained at resolution (Θ −N) to solveν ^{Ω −N+1}, the vision task at resolution (Θ −N+1). Image interpretation is a two-phased analysis problem where some salient features or objects in an image are identified by segmenting the image and the objects in the segmented image are interpreted based on their spatial relationships. We present a solution to the joint segmentation and interpretation problem in the proposed generalized framework. For the interpretation part we exploit the Markov Random Field (MRF) based image interpretation scheme developed by Modestino and Zhang. Experimental results on both indoor and outdoor images are presented to validate the proposed framework.     

Effect of initial microstructure on high velocity and hypervelocity impact cratering and crater-related microstructures in thick copper targets: Part I Soda-lime glass projectiles

Three uniquely different initial microstructure regimes were created in 2.5 cm thick copper targets: an as-received 98 μm grain size containing ∼1010 dislocations/cm2 (Vickers hardness of 0.89 GPa); an annealed 124 μm grain size containing ∼109 dislocations/cm2 (Vickers hardness of 0.69 GPa); and a 763 μm grain size containing ∼109 dislocations/cm2 (Vickers hardness of 0.67 GPa). Each of these target plates was impacted by 3.18 mm diameter soda-lime glass spheres at nominal impact velocities of 2, 4 and 6 km s-1. Grain size was observed to have only a very small or negligible contribution to cratering, while the dislocation density had a controlling influence on both the target hardness and the cratering process. Residual crater hardness profiles were correlated with specific microstructure zones extending from the crater wall into the target, and both hardness profiles and residual microstructures differed for each specific target, and for each different impact velocity. Microbands coincident with traces of {1 1 1} planes were associated with a zone of residual target hardening and increased with increasing grain size and impact velocity. No significant melt-related phenomena were observed, and crater-related target flow occurs by solid-state plastic flow through dynamic recrystallization, forming a narrow, softened zone at the crater wall. This revised version was published online in November 2006 with corrections to the Cover Date.     

Glass transition and fragility of telluro-vanadate glasses containing antimony oxide

The activation energy (ΔH ^*) of the glass transition and the heating-rate dependence of the glass transition temperature (T _g) of V₂O₅–Sb₂O₃–TeO₂ glasses were determined using differential scanning calorimetry technique. Non-isothermal measurements were performed at different heating rates φ (=3, 6, 9, 10, 13 K/min). The heating rate dependence of T _g was used to investigate the applicability of different theoretical models describing the glass transition. The application of Moynihan and Kissinger et al. models to the present data led to different values of (ΔH ^*) at each different heating-rate regions. This behavior was attributed to the strong heating rate dependence of the activation energy of the process. The fragility parameter (m = ΔH ^*/RT _g) were ≲90, suggesting that these glasses may be classified as strong glasses. The viscosity, η, calculated at a few selected temperatures near the glass transition region increased with increasing Sb₂O₃ content at any given temperature, which is also expected. Also the compositional dependence of T _g and ΔH ^* was investigated.     

Diffusion in the CuSn binary system: application to Nb3Sn composites

Non-parabolic growth of intermediate phases in CuSn binary diffusion couples has been observed at 220° C. The deviation from parabolic behaviour may be attributed to grain boundary diffusion. Diffusion coefficients for both the∈-(Cu₃Sn) andη-(Cu₆Sn₅) phases are typically of the order of 2×10⁻¹¹ cm² sec⁻¹, and are in general agreement with other published values.     

Conductometric Study of Some Metal Halides in Glycerol + Water Mixtures

Electrolytic conductivities of potassium halides, KX (X = Cl⁻, Br⁻, I⁻) have been investigated in 10, 20, and 30 mass% glycerol + H₂O mixtures at 298.0, 308.0, and 318.0 K. The conductance data have been analyzed by the Fuoss-conductance–concentration equation in terms of the limiting molar conductance (Λ⁰), the association constant (K _A ), and the distance of closest approach of ion (R). The association constant (K _A ) tends to increase in the order: 10 mass% < 20 mass% < 30 mass% glycerol + water mixtures, while it decreases with temperature. Thermodynamic parameters ΔH ⁰, ΔG ⁰, and ΔS ⁰ are obtained and discussed. Also, Walden products (Λ⁰η) are reported. The results have been interpreted in terms of ion–solvent interactions and structural changes in the mixed solvents.     

Systematic hardness measurements on mixed and doped crystals of rubidium halides

Efforts are made to improve the hardness of rubidium halide crystals by (i) solid solution hardening and (ii) impurity hardening. Systematic microhardness measurements have been made on rubidium halide mixed crystals (RbBr-RbI and KI-RbI) and rubidium halide crystals doped with Sr²⁺ ions. The composition dependence of the hardness of mixed crystals follows the law ΔH _v =K x (1− x),where ΔH _v is the enhancement in hardness,K a constant andx and (1 −x) the concentrations of the first and second component of the mixed crystals, respectively. The hardness of doped crystals increases with the concentrationC of the dopant according to the law, ΔH _v+6 =k C ^m ,wherek andm are constants. The relative efficacy of the two methods of hardening is discussed.     

Ostwald Ripening of precipitates and self similarity of size distributions in reaction controlled growth

We present a mathematical model to describe competitive growth of spherical precipitates in reaction-controlled systems. In this model the flux of solute atoms through the interface depends on the interface migration velocity and on the differences of chemical potential at the interface. The growth-rate obtained is dependent on the precipitate radius, much like in the diffusion-controlled case. Numerical simulations were performed using a modified finite-difference approach where the time-step increase changes during evolution to avoid dissolution of more than one precipitate each step. By using the continuity equation we obtained an analytical function that represents the self-similar shape of the precipitate-size distribution dependent of the growth-parameter ν. The effect of ν on the coarsening evolution was investigated. Our results show that the precipitate size distribution obtained from the numerical simulations agrees well with the analytical solution. As predicted by the theory, we obtained the growth parameter (ν = 4) and the temporal dependence of the mean-radius (t ^1/2) different of the diffusion case, ν = 6.75 and t ^1/3. We also show that the self-similarity of the PSD is independent of the initial PSD. Presented at the V Symposium of the Brazil-MRS. Florianópolis, 8–12 October 2006.     

Acoustic investigations on PbO-Al2O3-B2O3 glasses doped with certain rare earth ions

Elastic moduli (Y, η), Poisson’s ratio (σ), microhardness (H) and some thermodynamical parameters such as Debye temperature (θ_D), diffusion constant (D _i),latent heat of melting (ΔH _m) etc of PbO-Al₂O₃-B₂O₃ glasses doped with rare earth ions viz. Pr³⁺, Nd³⁺, Sm³⁺, Eu³⁺, Tb³⁺, Dy³⁺, Ho³⁺, Er³⁺ and Yb³⁺, are studied as functions of temperatures (in the temperature range 30–200°C) by ultrasonic techniques. All these parameters are found to increase with increasing atomic numberZ of the rare earth ions and found to decrease with increasing temperature of measurement. From these results (together with IR spectra of these glasses), an attempt is made to throw some light on the mechanical strength of these glasses.     

Elastic properties of ZnF2-PbO-TeO2 glasses doped with certain rare earth ions

The elastic moduli (Y, η, σ andH) and some thermodynamical parameters, such as Debye temperatureθ _D, diffusion constantD _i and latent heat of melting ΔH _m, of ZnF₂-PbO-TeO₂ glasses doped with some rare earth (Pr³⁺, Nd³⁺, Eu³⁺ and Tb³⁺) ions are determined as functions of temperature using piezo electric composite oscillator technique. All the parameters are found to decrease with increase in the atomic number Z of the rare earth ions and with increase in the temperature of measurement. The results are explained on the basis of the density of localized bonding defect states within the band gap of the material.     

Influence of grain properties on the Abrikosov vortices interaction with Josephson junction

The problem of the displacement of an Abrikosov vortex is investigated when the magnetic field decreases to H _cl ^G in a grain of a type II superconductor. It is shown that near grain boundaries the vortex line generates an intergranular current which depends on the normalized grain size τ and the anisotropy ratio ν. These parameters strongly influence the conditions of the Josephson vortex generation as a result of the interaction of the Abrikosov vortex with the Josephson junction. We support our theory with calculations of the intergrain critical current taking into account two types of the vortex configuration, triangular and square, for different grain characteristics. The results are of interest for the charge transport in granular superconductors as well as the relaxation process in devices that contain Josephson junctions in micro- and nanoelectronics in magnetic field.     

Transmission electron microscopy on the microstructure of 7050 aluminium alloy in the T74 condition

The microstructure of 7050 aluminium alloy in the T74 condition has been investigated by transmission electron microscopy. It was found that the alloy contains the superlattice Al₃Zr phase, η′ phase and Al₇Cu₂Fe constituent phase. The η′ phase is proposed to have an orthorhombic crystal structure witha=0.492 nm,b=0.852 nm andc=0.701 nm. The orientation relationship between the matrix and η′ phase is [11−2]_m//[100]_η′; [1−]_m//[010]_η′;[−1−1−1]_m//[001]_η′. The phases on the small-angle grain boundary are found to be mainly η′ phase and Cu/Si-rich phase, whereas on the large-angle grain boundary there is only η phase.     

Control of microstructure of Fe-B microcrystalline materials

The correlations between hardness, microstructure and heat-treatment condition of Fe-B microcrystalline materials were systematically investigated. The means of controlling microstructure by adjusting composition and, thus, the type of boride was also explored. It was established that the grain size of the matrix phase was determined by the volume fraction of dispersive boride particles, and their size follows the formula: D _max = 4/3 r/f, and, in turn determines hardness which obeys the Hall-Petch relation: H _V = H _o + kd ^–1/2. It was also found that the size of the boride particles increases exponentially with increasing temperature and linearly with the fourth root of holding time. M₃B₂ has a lower coarsening rate than M₂B; therefore, promoting M₃B₂ and inhibiting M₂B is an effective measure to stabilize the microcrystalline structure under hot exposure.     

Revealing the Anisotropy in MgB<Subscript>2</Subscript> Superconductor and Investigation of Critical Current near Critical Temperature by Using Hall Probe Susceptibility Technique

We report the results of an investigation on critical current measurements in bulk MgB₂ superconductor by using Hall probe ac susceptibility. The temperature versus ac susceptibility has been measured as a function of external ac magnetic field with no dc part and magnitude in the range 240–1200 A/m by using the Hall probe method. The real part of the Hall probe susceptibility showed two-step transitions near critical temperature. We attributed this behavior to the anisotropic nature of the MgB₂ compound. Close to the critical temperature the estimated anisotropy parameter is γ≈2.5, a value that is in fair agreement to the ones reported in the literature for polycrystalline and single crystals MgB₂. We have also analyzed the susceptibility data within the framework of a critical state model (using the real part of the susceptibility) and an anisotropic nature of MgB₂ compound. The inter-grain critical current is found to be 4×10⁶ A/m² at 39.59 K by using the critical state model. The temperature dependence of the critical current density was found to be in the form of J _c (T)∝(1−T/T _c ) ^β , where β was calculated as 2.30 by using critical state model, respectively. Scanning electron microscopy was used for grain size estimation.     

Mechanical response of nanocrystalline steel obtained by mechanical attrition

The mechanical properties of bulk specimens of nanocrystalline 0.55% C steel with a grain size of 30 nm and a relative density higher than 97% have been determined. Samples were obtained by cold compaction and warm sintering at 425 °C of nanocrystalline powders obtained by mechanical attrition in a planetary ball mill. In both processes an Ar protective atmosphere was used in order to avoid oxygen contamination. X-ray diffraction (XRD) and Transmission electron microscopy (TEM) analysis indicated that a volume-averaged grain size of 30 nm is maintained after the warm consolidation processes. TEM studies also showed equiaxed ferrite with no dislocations inside the grains. However, the grain size distribution was no homogeneous as large grains of 100 nm were observed. An average hardness of 8.5 GPa was obtained, in good agreement with other bulk specimens of nanocrystalline Fe or eutectoid carbon steel prepared by other authors. Compression tests of bulk specimens at a strain rate of 10⁻⁴ s⁻¹ showed a compression strength near 2,500 MPa with an absolute lack of ductility. Nanoindentation measurements at room temperature provided a strain rate sensitivity parameter of 0.012, indicating that the deformation mechanism is somehow governed by diffusion mechanisms.     

Formation of nanoscale tungsten oxide structures and colouration characteristics

In this work, pH dependent evolution of tungsten oxide (WO₃) nanostructures is being reported along with physical characteristics. The synthesis was carried out via an inexpensive solvothermal cum chemical reduction route, with sodium tungstate (Na₂WO₄) and cetyl trimethyl ammonium bromide (C₁₉H₄₂NBr) as main reactants. The X-ray diffraction, together with transmission electron microscopic studies have revealed formation of regular polyhedral nanocrystalline structures and fractals as one goes from higher pH (= 5·5) to lower pH (= 2) values. The average crystallite size, as calculated through Williamson–Hall plots, was varied within 2·8–6·8 nm for different pH samples. Fourier transform infrared spectroscopy reveals in-plane bending vibration δ (W–OH), observable at ∼1630 cm^− 1 and strong stretching ν (W–O–W) located at ∼814 cm^− 1. Raman spectroscopy has divulged WO₃ Raman active optical phonon modes positioned at ∼717 and 805 cm^− 1. The thermochromic and photochromic properties of the nanoscale WO₃ sample prepared at pH = 5·5, are also highlighted.     

Microstructure evolution and hardness variation during annealing of equal channel angular pressed ultra-fine grained nickel subjected to 12 passes

The microstructure, thermal stability and hardness of ultra-fine grained (UFG) Ni produced by 12 passes of equal channel angular pressing (ECAP) through the route Bc were studied. Comparing the microstructure and hardness of the as-ECAPed samples with the published data on UFG Ni obtained after 8 passes of ECAP through the route Bc reveals a smaller average grain size (230 nm in the present case compared with 270 nm in 8-pass Ni), significantly lower dislocation density (1.08 × 10¹⁴ m⁻² compared with 9 × 10¹⁴ m⁻² in 8-pass Ni) and lower hardness (2 GPa compared with 2.45 GPa for 8-pass Ni). Study of the thermal stability of the 12-pass UFG Ni revealed that recovery is dominant in the temperature range 150–250°C and recrystallisation occurred at temperatures >250 °C. The UFG microstructure is relatively stable up to about 400 °C. Due to the lower dislocation density and consequently a lower stored energy, the recrystallisation of 12-pass ECAP Ni occurred at a higher temperature (~250 °C) compared with the 8-pass Ni (~200 °C). In the 12-pass Nickel, hardness variation shows that its dependence on grain size is inversely linear rather than the common grain size^−0.5 dependence.