Characterisation of precipitate phases in magnesium alloys using electron microdiffraction

Recent results of the characterisation of the structure, morphology and orientation of fine-scale, strengthening precipitate phases in selected magnesium alloys using transmission electron microscopy and microdiffraction are reviewed. The strengthening precipitate phases in Mg–Y–Nd alloys, aged to maximum hardness at 250°C, have been found to include two metastable precipitate phases β′ and β₁, and the equilibrium precipitate β. The β′ phase has a globular form, a base-centred orthorhombic structure (potential point group of mmm), and an orientation relationship such that (100)_β′//(1 10)_α, [001]_β′//[0001]_α. The β₁ phase has an f.c.c. structure (space group and an orientation relationship that may be described by (100)_β1//[0001]_α, and forms as plates parallel to The β phase has an f.c.c. structure (space group ) and also forms as plates on with an orientation relationship with the matrix phase that is identical to that observed for β₁ phase. Precipitates in Mg–Al alloys, aged isothermally at 200°C, invariably have the b.c.c. structure of the equilibrium precipitate phase β (Mg₁₇Al₁₂). Three orientation relationships have been observed between β and the matrix phase. Most precipitates have an irrational orientation relationship that approximates to the Burger's relationship, (001)_β//(0001)_α, and a faceted lath morphology with habit plane parallel to (0001)_α. A minor fraction of precipitates posses an orientation relationship that is of the form

Full-size image

and have a prismatic rod morphology. The long axes of these rods are parallel to [0001]_α, and their faceted surfaces are parallel to A few precipitates are observed to have an orientation relationship such that

Full-size image

and a rod shape, with their long axes apparently inclined with respect to [0001]_α.     

In response to the article by Ivan Kausz: A discriminant and an upper bound for w 2 for hyperelliptic arithmetic surfaces

We define a natural discriminant for a hyperelliptic curve X of genus g over a field K as a canonical element of the (8g+4)th tensor power of the maximal exterior product of the vectorspace of global differential forms on X. If v is a discrete valuation on K and X has semistable reduction at v, we compute the order of vanishing of the discriminant at v in terms of the geometry of the reduction of X over v. As an application, we find an upper bound for the Arakelov self-intersection of the relative dualizing sheaf on a semistable hyperelliptic arithmetic surface.     

反向Chrystal不等式

利用控制不等式理论建立了三个反向Chrysta l不等式,并给出了若干应用.     

Stochastic Order and Generalized Weighted Mean Invariance

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.     

On molecular topological properties of hex‐derived networks

Topological indices are numerical parameters of a molecular graph, which characterize its topology and are usually graph invariant. In quantitative structure–activity relationship/quantitative structure–property relationship study, physico‐chemical properties and topological indices such as Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study hex‐derived networks HDN1(n) and HDN2(n), which are generated by hexagonal network of dimension n and derive analytical closed results of general Randić index R_α(G) for different values of α, for these networks of dimension n. We also compute the general first Zagreb, ABC, GA, ABC₄, and GA₅ indices for these hex‐derived networks for the first time and give closed formulae of these degree‐based indices for hex‐derived networks. Copyright © 2016 John Wiley & Sons, Ltd.     

Porous polycrystals built up by uniformly and axisymmetrically oriented needles: homogenization of elastic propertiesPolycristaux poreux constitués d'aiguilles orientées de façon uniforme ou axisymétrique : homogénéisation des propriétés élastiques

Porous polycrystal-type microstructures built up of needle-like platelets or sheets are characteristic for a number of biological and man-made materials. Herein, we consider (i) uniform, (ii) axisymmetrical orientation distribution of linear elastic, isotropic as well as anisotropic needles. Axisymmetrical needle orientation requires derivation of the Hill tensor for arbitrarily oriented ellipsoidal inclusions with one axis tending towards infinity, embedded in a transversely isotropic matrix; therefore, Laws' integral expression of the Hill tensor is evaluated employing the theory of rational functions. For a porosity lower 0.4, the elastic properties of the polycrystal with uniformly oriented needles are quasi-identical to those of a polycrystal with solid spheres. However, as opposed to the sphere-based model, the needle-based model does not predict a percolation threshold. As regards axisymmetrical orientation distribution of needles, two effects are remarkable: Firstly, the sharper the cone of orientations the higher the anisotropy of the polycrystal. Secondly, for a given cone, the anisotropy increases with the porosity. Estimates for the polycrystal stiffness are hardly influenced by the anisotropy of the bone mineral needles. Our results also confirm the very high degree of orientation randomness of crystals building up mineral foams in bone tissues. To cite this article: A. Fritsch et al., C. R. Mecanique 334 (2006).     

Characterizing texture in polycrystalline materials by ultrasonic waves

A method for characterizing texture from measurements of ultrasonic wave velocities is proposed. In polycrystalline aggregates, ultrasonic wave velocities are strongly affected by orientation distribution coefficients (ODCs), which are usually used to describe the degree of preferred grain orientation in textured materials. In this work, velocities of longitudinal and transverse waves propagating into aluminum alloy 6061 were measured under pure shear, simple shear and uniaxial tension. From the measured ultrasonic wave velocities, the ODCs W₄₀₀ and W₄₂₀ were calculated to infer the deformation-induced texture. The predicted pole figures, obtained using ultrasonic velocities, were in good qualitative agreement with the finite element polycrystal model analyzed pole figures.     

Rotating bunsen flames as solutions of the Kuramoto-Sivashinsky equation

Steadily rotating solutions of the Kuramoto-Sivashinsky equationu _t + ² u++¦u¦ ² =c ² are studied. These solutions bifurcate from the steady radial solution of the above equation. For large values ofc and angular velocities such thatN¦¦<2c<(N+1)¦¦, we show that there exists a 2N-1 family of bifurcating solutions. The proof is based on a certain generic transversality assumption. A computer-assisted proof of this assumption is given for 1N10.     

聚对苯二甲酰对苯二胺纤维的热老化行为与机理研究

在250～400℃空气中对自由状态下对位芳纶进行等温热老化处理,采用万能材料试验机、红外光谱法、广角X射线衍射法、声速法和特性黏数法表征了老化过程中力学性能和结构的变化.结果表明,在老化初期,由于分子链的解取向,强度随时间快速下降;随后的热分解使强度随老化时间继续降低,符合二级反应动力学模型,其热老化表观活化能为32.4kJ/mol.老化样品的强度随温度升高显著下降,但高于350℃时热交联反应变得明显,同时结晶度增大和结晶结构完善,使强度的损失速率减小.老化样品的模量随老化温度的升高而增大,低于350℃时,非晶态分子链的解取向占优,模量较未热老化样品低;升高至350℃时,结晶结构完善占优,表现在第二类晶格畸变参数降低、表观微晶尺寸增大,特别是微晶横向融合使a,b轴方向尺寸显著增大,模量明显高于未老化样品.