Thermodynamic re-assessment of the Mg-Gd-Y ternary system coupling with the driving forces for phase precipitations during aging process

Based on the available experimental phase equilibrium relations and aging precipitation sequences,the Mg–Gd–Y ternary system has been thermodynamically re-assessed by means of CALPHAD technique.To simulate the experimentally reported aging precipitation sequence,α(Mg)_(SS)(supersaturated)→GP zones(D019-type,metastable)→β’-Mg_(7)Gd(c-bco,metastable)→β_(1)-Mg_(3)Gd(fcc,metastable)→β-Mg_(5)Gd(fcc,stable)near the Mg–Gd side,andα(Mg)SS(supersaturated)→β’-Mg_(7)Y(c-bco,metastable)→β-Mg_(24)Y_(5)(bcc,stable)near the Mg–Y side,the effective nucleation driving forces obtained by deducting the nucleation resistances from the thermodynamic driving forces are calculated and analyzed.Two metastable components,GP zones(D019-type)andβ’(c-bco)ordered fromα(Mg)_(SS),do not exist in the stable equilibrium phase diagram but appear in the annealing process of typical alloys.The Redlich–Kister equations are adopted to describe three solution phases,Liquid,HCP_A3 and BCC_A2.The intermediate compounds Mg_(2)Y,Mg_(24)Y_(5),Mg_(2)Gd,Mg_(3)Gd and Mg_(5)Gd are expressed by the formulas of(Mg,Y)_(2/3)(Gd,Mg,Y)_(1/3),Mg_(24/29)(Gd,Mg,Y)_(4/29)Y1/29,(Gd,Mg)_(2/3)(Gd,Mg,Y)_(1/3),(Gd,Mg)_(3/4)(Gd,Mg,Y)_(1/4)and Mg_(5/6)(Gd,Mg,Y)_(1/6),respectively.In particular,the two-sublattice models(Gd,Mg,Y)_(1/2)(Gd,Mg,Y)_(1/2),(Gd,Mg,Y)_(3/4)(Gd,Mg,Y)_(1/4)and(Gd,Mg,Y)_(7/8)(Gd,Mg,Y)_(1/8)have been respectively used to describe the stable Mg(Gd,Y)(BCC_B2)alloy compound as well as the metastable GP zones(D019-type)andβ’(c-bco)phase,in order to cope with the order-disorder transitions.A set of self-consistent thermodynamic parameters has been obtained to ensure the thermodynamic calculations well consistent with the reported experimental data,containing not only the stable equilibrium phase diagram but also the aging precipitation sequence.

Stable and metastable phase equilibria in binary Mg-Gd system: A comprehensive understanding aided by CALPHAD modeling

In this paper,a comprehensive understanding of stable and metastable phase equilibria in binary Mg-Gd system was conducted with an aid of the CALculation of PHAse Diagram(CALPHAD)modeling.Firstly,thermodynamic descriptions of all the stable phases in the Mg-Gd system were re-assessed by considering all the experimental data in the literature.The discrepancy between the phase equilibria and thermochemical properties existing in the previous assessments was eliminated,and the better agreement with the experimental data was achieved in the present assessment.Secondly,the Gibbs energies for metastable β"-Mg3Gd and β"-Mg7Gd were constructed based on the first-principles and CALPHAD computed results as well as their correlation,and then incorporated into the CALPHAD descriptions.The model-predicted solvuses of(Mg)in equilibrium with the metastable β"-Mg7Gd and β'-Mg7Gd compounds showed very good agreement with the limited experimental data.Finally,the presently obtained thermodynamic descriptions of both stable and metastable phases in the binary Mg-Gd system were further validated by realizing the quantitative Scheil-Gulliver solidification simulations of 5 as-cast Mg-Gd alloys,and the successful prediction of the precipitation sequences in Mg-15Gd and Mg-12Gd alloys during the aging process.

Theory and Application of Natural-Based Wavelet Method

Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the results vary greatly. To overcome this problem and to improve the accuracy and efficiency, a new method denoted by Natural-based Wavelet Method is introduced and extended. It can be proved that the proposed method in fact is a special class of discrete wavelet. At first, two numerical examples are designed to show the capacity of the novel method. Second, this method is applied to a precipitation series. According to wavelet analysis and short-range precipitation prediction, this precipitation exists a faintly increasing trend. Through the analysis, the studied precipitation has two major periods: 11 and 41 years. The results validate that the Natural-based Wavelet Method used in application of multi-complicated observed data is suitable. It is easy to write the source code of the proposed method. When new information appears, new information can be easily added into the original sequence, this is another advantage of the proposed method.