Investigations on Glass Forming Ability of Hf-Alloys by Mathematical Modeling and Optimizations

Abstract

This paper represents a view at the field of Glass Forming Ability (GFA) of Hf-alloys from positions of the planning of experiment, and by the tools of mathematical modeling and optimization. On the basis of real physical experiments carried out with aim achievement of large GFA, the mathematical models of few chosen characteristics for GFA (Tg, Tx, ΔTx, Tg/Tm, Tg/Tl) are drawn up by Regression analysis with two-rate polynomial. A comparison between modeled results and experimental ones is completed. With aims enlargement of the GFA four two-criteria and three-parametrical optimization tasks are formulated and solved. On the basis of their compromise decisions obtained by searching for maxima of Complex Objective Function following the Method of Deformable Simplex (of Nelder-Mead), the optimal values for Zr xTix-, Gay(Ge2Si)-additions (x = 0-10%, y = 0-3%) and addition of element with maximal atomic radii r at in interval 0.150-0.2013 nm are found depending on the importance of optimization criteria. It is found mathematically that increase of Zr xTix-addition and addition of element with atomic radii approximate to 0.200 nm decrease the supercooled liquid region ΔTx with 30% and increase the ratios Tg/Tl, Tg/Tm with 5.5% and 8.3%, respectively. Addition of GayGe2Si) increases ΔTx and decreases Tg/Tl and Tg/Tm. After comparisons with other conclusions obtained by experimental results the conclusions are drawn that the approach proposed in this paper and obtained modeled results can be used as a basis for formulation and solving of other problems in the field of Bulk Metallic Glass forming.