Laguerre approximation of random foams

Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam’s cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology.     

Realistic nano-polycrystalline microstructures: beyond the classical Voronoi tessellation

A modified Voronoi tessellation (MVT) is proposed for the computer simulation of realistic microstructures. Compared with standard tessellations, the present algorithm provides the desired grain size distribution in a one-step, non-evolutionary procedure. This is obtained by relaxing the constraints of Voronoi tessellation on position and orientation of the grain boundaries, with the only side effect being the formation of a limited amount of eliminable voids. As an example, it is shown how to directly obtain a distribution of grains of given variance and with a shape statistically close to the lognormal one.     

Grain-boundary sliding in elongated microstructures during diffusion creep

In diffusion creep, the contribution of grain-boundary sliding to the overall strain os can be evaluated in arbitrary polycrystals, if the angular distribution of grain boundaries is known. A os value of 0.5 is obtained for two-dimensional (2D) equiaxed microstructures consisting of regular hexagonal grains, equiaxed grains grown from a Voronoi structure or grains having a circular distribution of grain-boundary angles. The os value is also evaluated for uniaxially deformed 2D microstructures, both diffusionally and uniformly deformed. For the former, the deformed microstructure is obtained by the simulation of microstructural evolution in polycrystals with straight grain boundaries. The os value increases gradually with increasing or decreasing strain and is larger in the diffusionally deformed microstructures than in the uniformly deformed microstructures for a given grain aspect ratio. The os value for three-dimensional (3D) polycrystalline microstructures is also obtained from an ellipsoidal distribution of grain-boundary angles. The resultant os value is 0.60 for 3D equiaxed polycrystals and increases gradually with increasing strain.     

Effect of texture and grain shape on ultrasonic backscattering in polycrystals

An ultrasonic backscattering model is developed for textured polycrystalline materials with orthotropic or trigonal grains of ellipsoidal shape. The model allows us to simulate realistic microstructures and orthotropic macroscopic material textures resulting from thermomechanical processing for a broad variety of material symmetries. The 3-D texture is described by a modified Gaussian orientation distribution function (ODF) of the crystallographic orientation of the grains along the macroscopic texture direction. The preferred texture directions are arbitrary relative to the axes of the ellipsoidal grains. The averaged elastic covariance and the directional anisotropy of the backscattering coefficient are obtained for a wave propagation direction arbitrary relative to the texture and grain elongation directions. One particular application of this analysis is the backscattering solution for cubic crystallites with common textures such as Cube, Goss, Brass and Copper. In our analysis, in the texture-defined coordinates the matrix of elastic constants for cubic crystallites takes the form of orthotropic or trigonal symmetry. Numerical results are presented, discussed and compared to the experimental data available in the literature illustrating the dependence of the backscattering coefficient on texture and grain shape.     

Anisotropic rheology during grain boundary diffusion creep and its relation to grain rotation,grain boundary sliding and superplasticity

The response of periodic microstructures to deformation can be analysed rigorously and this provides guidance in understanding more complex microstructures. When deforming by diffusion creep accompanied by sliding, irregular hexagons are shown to be anisotropic in their rheology. Analytic solutions are derived in which grain rotation is a key aspect of the deformation. If grain boundaries cannot support shear stress, the polycrystal viscosity is extremely anisotropic. There are two orthogonal directions of zero strength: sliding and rotation cooperate to allow strain parallel to these directions to be accomplished without any dissolution or plating. When a linear velocity/shear stress relationship is introduced for grain boundaries, the anisotropy is less extreme, but two weak directions still exist along which polycrystal strength is controlled only by the grain boundary “viscosity”. Irregular hexagons are characterised by four parameters. A particular subset of hexagons defined by two parameters, which includes regular hexagons as well as some elongate shapes, shows singular behaviour. Grain shapes that are close to that of the subset may exhibit large grain rotation rates and have no well-defined rheology unless there is a finite grain boundary viscosity. This new analysis explains why microstructures based on irregular but near equiaxed grains show high rotation rates during diffusion creep and it provides a framework for understanding strength anisotropy during diffusion creep.     

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter (2007 Opt.Lett.32 554) we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family.In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation,which makes the complex continuous wavelet transform theory complete.A new orthogonal property of mother wavelet in parameter space is revealed.     

Crystal plasticity study on stress and strain partitioning in a measured 3D dual phase steel microstructure

Dual phase steels are advanced high strength alloys typically used for structural parts and reinforcements in car bodies. Their good combination of strength and ductility and their lean composition render them an economically competitive option for realizing multiple lightweight design options in automotive engineering. The mechanical response of dual phase steels is the result of the strain and stress partitioning among the ferritic and martensitic phases and the individual crystallographic grains and subgrains of these phases. Therefore, understanding how these microstructural features influence the global and local mechanical properties is of utmost importance for the design of improved dual phase steel grades. While multiple corresponding simulation studies have been dedicated to the investigation of dual phase steel micromechanics, numerical tools and experiment techniques for characterizing and simulating real 3D microstructures of such complex materials have been emerged only recently. Here we present a crystal plasticity simulation study based on a 3D dual phase microstructure which is obtained by EBSD tomography, also referred to as 3D EBSD (EBSD—electron backscatter diffraction). In the present case we utilized a 3D EBSD serial sectioning approach based on mechanical polishing. Moreover, sections of the 3D microstructure are used as 2D models to study the effect of this simplification on the stress and strain distribution. The simulations are conducted using a phenomenological crystal plasticity model and a spectral method approach implemented in the Düsseldorf Advanced Material Simulation Kit (DAMASK).     

CaCu3Ti4O12陶瓷的微观结构和电学性能

利用传统的固相反应工艺，在不同的烧结温度下制备了一系列的CaCu₃Ti₄O₁₂陶瓷样品，考察了其微观结构以及介电和复阻抗方面的电学性质.研究发现这些样品在微观结构方面可分为三种类型，高介电性与微观结构有着密切的关联性.室温下，样品的低频介电常数随陶瓷晶粒尺寸的增大而提高.随着测试温度的升高，不同微观结构类型的样品呈现出不同的电学性质的变化，但其中也存在着一些相同的特征.高温下，介电频谱呈现出一个低频介电响应和两个类Debye型弛豫色散，复阻抗谱呈现出三个Cole-Cole半圆弧.将实验上观测到的电学性质的起因归于陶瓷多晶微结构中的晶畴、晶界和晶粒内的缺陷. 关键词： 3Ti₄O₁₂')" href="#">CaCu₃Ti₄O₁₂ 微观结构 电学性质     

Effect of granularity and inhomogeneity in excess conductivity of YBa2Cu3O7−δ+xBaTiO3 superconductor

Synthesis of polycrystalline YBCO+xBaTiO₃ (x=1.0, 2.5, 5.0) superconductor has been done and the effects of granularity and inhomogeneities due to inclusions of nano-BaTiO₃ in excess conductivity are reported in this work. The phase formation, texture and grain alignments were analyzed through XRD and SEM techniques. SEM results reveal that the grain size is reduced and morphology is improved with the incorporation of nano-BaTiO₃ particles. Superconducting order parameter fluctuation (SCOPF) studies on the electrical conductivity were investigated from the resistivity vs. temperature data in the experimental domain relatively above T_c. Log(Δσ) vs. log(ε) plots show that the 2D to 3D crossover temperature (T_LD) that demarcates dimensional nature of fluctuation inside the grains is influenced by BaTiO₃ incorporation in YBCO matrix. An upward shift of T_LD in the mean field region has been observed as a consequent dominance of 3D region with increase in 1 wt% BaTiO₃ in the composites as compared to higher inclusions. It has been analyzed that microscopic inhomogeneities produced as a result of diffusion of a fraction of Ti ions into the grains affect fluctuations in the excess conductive region. The interplay of microscopic inhomogeneities produced inside the grains and mesoscopic inhomogeneities in the grain boundaries on the excess conductivity has been explained in terms of thermal fluctuations for the composites.     

Investigation of continuous-time quantum walk via spectral distribution associated with adjacency matrix

Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph C_n, complete graph K_n, graph G_n, finite path and some other finite and infinite graphs, where all are connected with orthogonal polynomials such as Hermite, Laguerre, Tchebichef, and other orthogonal polynomials. It is shown that using the spectral distribution, one can obtain the infinite time asymptotic behavior of amplitudes simply by using the method of stationary phase approximation (WKB approximation), where as an example, the method is applied to star, two-dimensional comb lattices, infinite Hermite and Laguerre graphs. Also by using the Gauss quadrature formula one can approximate the infinite graphs with finite ones and vice versa, in order to derive large time asymptotic behavior by WKB method. Likewise, using this method, some new graphs are introduced, where their amplitudes are proportional to the product of amplitudes of some elementary graphs, even though the graphs themselves are not the same as the Cartesian product of their elementary graphs. Finally, by calculating the mean end to end distance of some infinite graphs at large enough times, it is shown that continuous-time quantum walk at different infinite graphs belong to different universality classes which are also different from those of the corresponding classical ones.     

飞秒激光湿法刻蚀微纳制造

飞秒激光微加工作为一种新型微纳制造技术,在复杂三维构型制作方面具有其独特的优势,但激光加工效率问题严重制约了飞秒激光微加工技术走向实际工程应用,提出一种飞秒激光湿法刻蚀微纳制造方法,以提高飞秒激光微加工的效率为突破口,通过调控激光与物质相互作用获得材料的目标靶向改性,进而结合化学湿法刻蚀实现硬质材料上的高效和高精度三维微加工,采用这一方法制作出的微透镜尺寸为80 m,球冠高6.7 m,表面粗糙度小于10 nm。利用这种方法,实现了不同结构与特性的高质量微透镜阵列的超精密制备,在石英内部也实现了螺旋微通道的复杂三维结构,螺旋通道直径为20 m,长径比超过100。     

Ultrasonic backscattering in polycrystals with elongated single phase and duplex microstructures

An analytical solution for a three dimensional integral representation of the backscattering (BS) coefficient in polycrystals with elongated (generally ellipsoidal) grains is obtained; it is a natural generalization of the known explicit result for the BS coefficient in polycrystals with spherical grains. New insights into the dependence of the BS signal on frequency and averaged ellipsoidal grain radii are obtained. In particular it has been shown that the dominant factor for the backscattering is the averaged interaction length of the ellipsoidal grain in the direction of wave propagation, instead of the ellipsoidal cross-section. The theory was applied to a simplified model of Ti alloy duplex microstructure and was compared with experiment. For the experimental data analysis directional backscattering ratios are introduced and shown to be advantageous for characterization of duplex elongated microstructures/microtextures. In addition to the geometrical parameters of the elongated microtextures, the BS directional ratios depend on the newly introduced nondimensional material parameter q. The parameter q exhibits the relative contribution of the second phase (crystallites) to the backscattering signal, the effect of which is measurable and important. Comparison of the model with experiment shows there is a significant advantage in using the directional ratios of backscattering coefficients for data analysis.     

Electronic properties of grains and grain boundaries in graphene grown by chemical vapor deposition

We synthesize hexagonal shaped single-crystal graphene, with edges parallel to the zig-zag orientations, by ambient pressure CVD on polycrystalline Cu foils. We measure the electronic properties of such grains as well as of individual graphene grain boundaries, formed when two grains merged during the growth. The grain boundaries are visualized using Raman mapping of the D band intensity, and we show that individual boundaries between coalesced grains impede electrical transport in graphene and induce prominent weak localization, indicative of intervalley scattering in graphene.     

Bridging simulations and experiments in microstructure evolution

We demonstrate the importance of anisotropic interface properties in microstructure evolution by comparing computed evolved microstructures to final experimental microstructures of 5170 grains in 19 thin aluminum foil samples. This is the first time that a direct experimental validation of simulation has been performed at the level of individual grains. We observe that simulated microstructures using curvature-driven grain boundary motion and anisotropic interface properties agree well with experimentally evolved microstructures, whereas agreement is poor when isotropic properties are used.     

氮气喷射成形FGH4095的组织特征

以氮气为雾化气体采用喷射成形工艺制备了FGH4095高温合金沉积坯, 记录了沉积过程坯体表面温度曲线, 并采用定量金相法、排水法测试了坯体致密度, 观察了坯体晶粒及γ'相的形貌. 结果表明采用氮气作为雾化介质进行喷射成型喷射沉积坯基体致密度可达99%以上, 但也存在着较大的(1—2μm)的气孔, 经热等静压和近等温锻后宏观气孔闭合, 氮以尺寸不超过1 μm的碳氮化物形式存在. 喷射沉积坯以等轴晶组织为主, 坯体内部平均晶粒尺寸约为20—40 μm, 近表面区域晶粒较细, 约为13 μm; 一次γ' 相多数呈尺寸约0.3—0.5 μm不规则块状形貌. 喷射成形坯组织结构的形成与喷射成形过程的降温过程有密切关系.     

Control of grain boundary microstructures in molybdenum polycrystals by thermomechanical processing of single crystals

The formation of grain structures and grain boundary microstructures in polycrystalline molybdenum, produced by thermomechanical processing from cylindrical single crystals with different initial surface normal orientations of ?110?, ?111? and ?112?, were investigated with the objective of controlling grain boundary microstructures. The polycrystalline specimens displayed different microstructures depending on the initial orientation of the single crystal and the deformed microstructure. The recrystallized microstructure was composed of some oriented-grain clusters, in which grains possessing a similar orientation were assembled. The frequency of low-angle boundaries was very high in the oriented-grain clusters. A close relationship also existed between the grain boundary character distribution (GBCD) and the triple junction distribution. Grain boundary microstructures were compared of bcc molybdenum and fcc polycrystalline materials with reference to path-dependent percolation resistance.     

Nd composition dependence of microstructure and magnetic properties for gradient sputtered NdFeB films

NdFeB films with Nd compositions varied from 13.34 to 24.30 at% were deposited by DC gradient sputtering using targets Nd_12.5Fe_71.5B₁₆ and Nd. The hard magnetic properties, grain growth direction and magnetic domain structures were dramatically influenced by Nd composition. The samples with intermediate Nd concentrations exhibited optimal magnetic properties and microstructures, such as large squareness ratio over 0.9, large energy product up to 174 kJ/m³, and vertical domain structure. However, the samples with higher and lower Nd compositions showed almost isotropic loops. (0 0 l) as main X-ray diffraction peaks in the optimal Nd composition region indicated most of Nd₂Fe₁₄B grains with c-axis perpendicular to the film plane, while NdFeB grains in other region are almost random growth. The good magnetic properties can be attributed to the vertical growth of Nd₂Fe₁₄B grains.     

Impedance spectroscopy of Gd-doped BiFeO3 multiferroics

The polycrystalline Bi_1?x Gd _x FeO₃ (BGFO) (x=0.0, 0.05, 0.10, 0.15, 0.20) materials were synthesized by a solid-state reaction (mixed oxide) technique. Preliminary X-ray structural analysis of the compounds confirmed the formation of single-phase polycrystalline samples. Room temperature scanning electron micrographs of the materials revealed the size, type and distribution of grains on the surface of samples. Studies of impedance, electrical modulus and electric conductivity of the materials in a wide frequency (10–1000 kHz) and temperature (30–500 ^°C) range using a complex impedance spectroscopy technique have provided considerable vital information on contribution of grains, grain boundary and interface in these parameters. A strong correlation between these electrical parameters and microstructures (bulk, grain boundary, nature of charge carrier, etc.) of the materials was established. The frequency dependence of electric modulus and impedance of the material shows the presence of non-Debye type of relaxation.