Novel heating-and deformation-induced phase transitions and mechanical properties for multicomponent Zr_(50)M_(50),Zr_(50)(M,Ag)_(50)and Zr_(50)(M,Pd)_(50)(M=Fe,Co,Ni,Cu)amorphous alloys

Multicomponent alloys of Zr_(50)M_(50),Zr_(50)(M,Ag)_(50)and Zr_(50)(M,Pd)_(50)(M=Fe,Co,Ni,Cu)can be melt-spun to obtain amorphous ribbons.The maximum thickness for fully amorphous ribbons varies with composition in the range 34-53μm.In contrast,fully amorphous ribbons are not obtainable for binary Zr_(50)Ni_(50)or ternary Zr_(50)(Ni,Cu)_(50)alloys.Heating-induced crystallization occurs through:two stages of amorphous[am]→[~(am')+B2]→[B2+B33]for Zr_(50)M_(50);and[am]→[am'+B2]→[B2+AgZr]for Zr_(50)(M,Ag)_(50);and a single stage of[am]→[B2]for Zr_(50)(M,Pd)_(50),while no B2 phase is formed for the binary and ternary Zr_(50)Q_(50)(Q=Ni or/and Cu)alloys.As-spun amorphous ribbons have good bending plasticity.Remarkably,Zr_(50)M_(50)ribbons in tension show 0.22-0.28%plastic elongation and work-hardening(the yield stress is~820 MPa,the fracture stress is~1200 MPa).When cold-rolled at room temperature to 30%reduction in thickness,Zr_(50)M_(50)ribbons show 10%increase in hardness,while retaining good bending plasticity.Cold-rolling induces precipitation of spheroidal B2 and irregular B33 particles,while deformation in tension induces B2,B33 and also plate-like monoclinic precipitates.The B2 and B33 particles form by polymorphic transformation,and include a high density of internal defects.This novel deformationinduced precipitation has not been recognized for any Zr_(50)Q_(50)binary or ternary alloys.The new multicomponent systems are encouraging for future progress as structural amorphous alloys.

The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions

In this paper we develop an efficient meshless method for solving inhomogeneous elliptic partial differential equations.We first approximate the source function by Chebyshev polynomials.We then focus on how to find a polynomial particular solution when the source function is a polynomial.Through the principle of the method of undetermined coefficients and a proper arrangement of the terms for the polynomial particular solution to be determined,the coefficients of the particular solution satisfy a triangular system of linear algebraic equations.Explicit recursive formulas for the coefficients of the particular solutions are derived for different types of elliptic PDEs.The method is further incorporated into the method of fundamental solutions for solving inhomogeneous elliptic PDEs.Numerical results show that our approach is efficient and accurate.