MgCu metallic glass

We generate an amorphous MgCu model using the rapid solidification of the melt through a first-principles molecular dynamics approach within a generalised gradient approximation and reveal, for the first time, its structural features and mechanical properties in details. The liquid and glassy MgCu are found to acquire slightly distinct local structures. Yet in both forms of MgCu, most Cu atoms have a tendency to form the ideal and defective icosahedrons while Mg atoms are arranged in complex configurations. The mean coordination number of Cu and Mg at 300 K is 11.31 and 13.73, respectively. The short-range order of MgCu glass is projected to be different than the known crystalline MgCu and Mg₂Cu phases. The mechanical properties of MgCu glass and the CsCl-type MgCu crystal are computed and compared. On the basis of the enthalpy analyses, a possible pressure-induced crystallisation of the MgCu glass into a CsCl-type structure is proposed to occur at around 11 GPa.     

Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation

A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the deformed configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg–Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a first order correction in the Ginzburg–Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics studies of cubic crystals. In order to consider a fully specified system, a typical sixth order polynomial phase field model is considered. Analytical solutions for the propagating interface and critical nucleus are found, accounting for the influence of the anisotropic gradient energy and elucidating the distribution of components of interface stresses. The orientation-dependence of the nonequilibrium interface energy is first suitably defined and explicitly determined analytically, and the associated width is also found. The developed formalism is applicable to melting/solidification and crystal-amorphous transformation and can be generalized for martensitic and diffusive phase transformations, twinning, fracture, and grain growth, for which interface energy depends on interface orientation of crystals from either side.     

Face-centred cubic to body-centred cubic phase transformation under [1 0 0] tensile loading

Molecular dynamics simulation was used to verify a speculation of the existence of a certain face-centred cubic (FCC) to body-centred cubic (BCC) phase transformation pathway. Four FCC metals, Ni, Cu, Au and Ag, were stretched along the [1?0?0] direction at various strain rates and temperatures. Under high strain rate and low temperature, and beyond the elastic limit, the bifurcation of the FCC phase occurred with sudden contraction along one lateral direction and expansion along the other lateral direction. When the lattice constant along the expansion direction converged with that of the stretched direction, the FCC phase transformed into an unstressed BCC phase. By reducing the strain rate or increasing the temperature, dislocation or ‘momentum-induced melting’ mechanisms began to control the plastic deformation of the FCC metals, respectively.     

Efficient Synthesis of Cyclic Block Copolymers by Rotaxane Protocol by Linear/Cyclic Topology Transformation

High‐yielding synthesis of cyclic block copolymer (CBC) using the rotaxane protocol by linear‐cyclic polymer topology transformation was first demonstrated. Initial complexation of OH‐terminated sec‐ammonium salt and a crown ether was followed by the successive living ring‐opening polymerizations of two lactones to a linear block copolymer having a rotaxane structure by the final capping of the propagation end. CBC was obtained in a high yield by an exploitation of the mechanical linkage through the translational movement of the rotaxane component to transform polymer structure from linear to cyclic. Furthermore, the change of the polymer topology was translated into a macroscopic change in crystallinity of the block copolymer.     

Solid‐state drawing of β‐nucleated polypropylene: Effect of additives on drawability and mechanical properties

Isotactic polypropylene (i‐PP) can crystallize in different crystal modifications. In this article, the effect of sepiolite (one‐dimensional) and carbon black (three‐dimensional) fillers on the solid‐state drawability of i‐PP is discussed. The cross‐hatched structure of thermodynamically most stable α‐crystal phase in i‐PP does not allow for perfect chain alignment during solid‐state drawing. The β‐phase i‐PP, obtained by addition of specific nucleating agents, crystallizes in a non‐cross‐hatched spherulitic structure and allows more easy drawing. Depending on the filler type, β–α transformation takes place at different draw ratios, as was observed by in situ wide‐angle X‐ray diffraction measurements. It was observed that β‐nucleated i‐PP has a lower yield stress and can be drawn further than i‐PP crystallized in the α‐crystal phase. If added in the right amount, both carbon black and sepiolite have a reinforcing effect on PP tapes. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1071–1082     

An improved exponential transformation for nearly singular boundary element integrals in elasticity problems

This paper presents an improved exponential transformation for nearly singular boundary element integrals in elasticity problems. The new transformation is less sensitive to the position of the projection point compared with the original transformation. In our work, the conventional distance function is modified into a new form in the polar coordinate system. Based on the refined distance function, an improved exponential transformation is proposed in the polar coordinate system. Moreover, to perform integrations on irregular elements, an adaptive integration scheme considering both the element shape and the projection point associated with the improved transformation is proposed. Furthermore, when the projection point is located outside the integration element, another nearest point is introduced to subdivide the integration elements into triangular or quadrilateral patches of fine shapes. Numerical examples are presented to verify the proposed method. Results demonstrate the accuracy and efficiency of our method.     

“Painlevé 34” equation: Equivalence test

We give the complete solution of the Equivalence Problem for “Painlevé 34” equation.     

Solitons and Bäcklund transformation for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Bilinear form and Bäcklund transformation are derived by virtue of the Bell polynomials. Besides, the one- and two-soliton solutions are constructed via the Hirota method.