Representation surfaces of Young''s modulus and Poisson''s ratio for BCC transition metals

 The general expressions for the compliance , Young's modulus E(h k l) and Poisson's ratio υ(h k l) along an arbitrary direction [h k l] are given for cubic crystals. The representation surfaces, for which the length of the radius vector in the [h k l] direction equals to E(h k l) or υ(h k l), are constructed for seven BCC transition metals Cr, Fe, Mo, Nb, Ta, V and W. Neglecting W, which is isotropic, both representation surfaces of Young's modulus and Poisson's ratio are spherical surfaces. The remaining BCC transition metals may be grouped into two classes. In the first group (Cr, Mo, Nb and V) with negative values of s_A, Young's modulus surface has eight depressed corners and six rounded protuberances at the centers of the faces. In the second group (Fe and Ta) with positive values of s_A, on the contrary, Young's modulus surface has eight rounded protuberance corners and six depressions at the centers of the faces. The contrary conclusions are obtained for Poisson's ratio.     

Atomic simulation of the point defects in three low‐index surfaces of BCC transition metals with the MAEAM

The favorable position of an adatom and the formation energies of a single vacancy and an adatom‐vacancy pair in three low‐index surfaces of body‐centered cubic (BCC) transition metals have been calculated by using the modified analytical embedded atom method (MAEAM). The favorable position of an adatom is at the fourfold and twofold positions above the (100) and (110) surfaces respectively, but it is deviated from the threefold position of the (111) surface. Either the heights of the adatom from the top atomic layer, or the formation energies of a single vacancy, or an adatom‐vacancy pair decrease in sequence of the (110), (100) and (111) surfaces for each metal. Furthermore, the formation energy of an adatom‐vacancy pair is always lower than that of a single vacancy for each low‐index surface of each metal, which shown the formation of adatom‐vacancy pair is more energetically favorable than the vacancy for the BCC transition metals. Copyright © 2007 John Wiley & Sons, Ltd.     

Dependence of stresses on grain orientations in BCC polycrystalline films on substrates

Most thin films have different thermal expansion coefficients from their substrates, thus thermal stresses will be introduced into the films when the temperature is changed during annealing and service. Calculations of these stresses for grains in various crystallographic orientations have been made for seven BCC transition metals Cr, Fe, Mo, Nb, Ta, V and W. Neglecting W, which is isotropic and the stresses are equiaxial and without grain orientation （hkl） dependence, the BCC metals may be grouped into two classes. In the first class （Cr, Mo, Nb and V）, the （100）-oriented grains have the largest stresses, while the stresses σ1 and σ2 in other （hkl）-oriented grains decrease linearly with the increase of the angle between （hkl） and （100）, and with σ1 〈 σ2 except in （100）- and （lll）-oriented grains. In the second class （Fe and Ta）, on the contrary, the （100）-oriented grains have the lowest stresses, and the stresses σ1 and σ2 in other （hkl）-oriented grains increase linearly with the increase of the angle between （hkl） and （100）, and with σ1 〉 σ2 except in （100）- and （111）-oriented grains.     

Behaviors of three BCC metals during non-proportional multi-axial loadings: experiments and modeling

Non-proportional torsion–tension and biaxial-compressive experimental results are presented on tantalum, tantalum alloy with 2.5% tungsten, and AerMet 100 steel. These test results form a comprehensive set of data to show the material behaviors at finite strain and wide strain-rate range. Using the parameter set determined from uniaxial constant strain-rate compressive and tensile tests, the capability of a new constitutive model (Khan, A.S., Liang, R., 1999. Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling. International Journal of Plasticity 15, 1089–1109) is shown to accurately predict complex loading paths of current experimental results. Using von Mises equivalent strain, stress, and strain rate, the constitutive model gives excellent predictions of these non-proportional experimental results.     

PREDICTION OF YIELD FUNCTIONS ON BCC POLYCRYSTALS

By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill's criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs' model, where the volume average of the yield functions of all BCC crystallites in Ω is taken as the macroscopic yield function of the BCC polycrystal. In constructing the formula, we try to find the relationship among the macroscopic yield function, the orientation distribution function (ODF), and the single BCC crystal's plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylor's model in order to compare the expression with that of the macroscopic yield function.     

A note on imposing strong complementary slackness conditions in DEA

A new DEA model has been introduced recently combining the primal and the dual models in order to impose strong complementary slackness conditions. It was claimed that a reference set that contains the maximum number of efficient units can then be determined. The model is very interesting as a theoretical idea. However, not only does the computational burden increase significantly, but it seems also that the basic matrices may be inherently ill-conditioned, leading to erroneous results. Numerical experiments have been carried out on two real datasets of medium size with 163 and 920 units. These experiments, using well known reliable software, show pervasive existence of ill-conditioned matrices leading to obviously wrong estimates of efficiency scores, and units declared as efficient reference units while actually being inefficient.     

Responses and comments to “A comment on “An extended assignment problem considering multiple inputs and outputs””

This note is to response the comments from Jahanshahloo and Afzalinejad for the problem of DEA model formulation in Chen and Lu’s paper [L.H. Chen, H.W. Lu, An extended assignment problem considering multiple inputs and outputs, Appl. Math. Model. 31 (2007) 2239–2248]. The models adopted in that paper are formulated as the output-oriented BCC models, but not input-oriented BCC models stated in Jahanshahloo and Afzalinejad’s comments. Actually, the applied models are adopted in the relevant literature. Four examples, including the example from Jahanshahloo and Afzalinejad, are provided for justifying the responses.     

高容量的Ti-V基BCC相储氢合金

储氢合金是有希望成为燃料电池供氢源的方式之一,在各类储氢合金中,以LaNi5为代表的AB5和以TiMn2为代表的AB5发展已较成熟,但由于其储氢量小于2％(质量百分比)而制约了其应用,Mg基合金具有较大的储氢量(3％左右),但由于其吸放氢条件(温度在473K以上)苛刻难以满足燃料     

Copper-catalyzed one-pot process to construct triazole-linked urea derivatives

A new one-pot synthetic methodology has been developed to construct the triazole-linked urea derivatives. In the same step, triazole forms from azide and alkyne via click reaction and urea forms from addition reaction of amines and isocyanates. The notable features of this work include wide substrate scope, atom economy, environmental friendliness, and easily accessible starting materials. The preliminary biological screening of synthesized compounds show promising cytotoxic activity in basal cell carcinoma (BCC) cell lines.     

Ultraslow dynamics in asymmetric block copolymers with nanospherical domains

Low shear rate and low frequency measurements focused on the extremely slow dynamics of a three-dimensional body-centered cubic (BCC) structure of an asymmetric block copolymer under nanophase-separated conditions. The material studied was poly(styrene-b-ethylene-co-butylene-b-styrene) swollen in a hydrocarbon oil selective for the midblock. Transient viscosities during start-up of shear flow at extremely low shear rates are governed by very long relaxation times and by a modulus that is nearly the same as the plateau modulus obtained from oscillatory shear experiments. Only at extremely low shear rates a zero shear viscosity could be attained. Its very high value is close to the viscosity calculated from stress relaxation experiments. The steady shear viscosity decreases by several orders of magnitude when increasing the shear rate. SAXS experiments on samples sheared even at very low rates indicated loss of the BCC order that was present in the annealed samples before shearing. The SAXS profile recorded on such a sample showed a first-order maximum followed by a broad shoulder indicating a liquid-like short-range order of PS nanospheres in the swollen EB matrix.