Ying Tng,Yongsheng Li,Weimin Zho,Irin Roslykov,Lijun Zhng

a School of Materials Science and Engineering,Hebei University of Technology,Tianjin 300130,PR China

b ICAMS,Ruhr-Universit?t Bochum,Universit?tsstrasse150,44801 Bochum,Germany

c State Key Laboratory of Powder Metallurgy,Central South University,Changsha 410083,PR China

Received 29 June 2019;received in revised form 4 March 2020;accepted 8 March 2020 Available online 30 June 2020

Abstract 16 Mg–Al–Zn–Bi quaternary alloys were utilized to measure the phase equilibria and transformation temperatures in the Mg-rich Mg–Al–Zn–Bi quaternary system by means of the X-ray diffraction,electron probe micro-analysis and differential scanning calorimetry techniques.The isothermal section at 400 °C and three vertical sections along Mg–8wt%Al–0.75wt%Zn–xBi,Mg–3.4wt%Al–0.5wt%Zn–xBi and Mg–6.9wt%Al–2.3wt%Zn–xBi in the Mg–Al–Zn–Bi quaternary system were constructed.Based on the literature data,the ternary Mg–Al–Bi and Mg–Bi–Zn systems were re-assessed using the CALculaiton of PHAse Diagram(CALPHAD)approach.The calculated phase equilibria agree well with the measured data.By directly extrapolating the constituent sub-ternary systems,the thermodynamic database for the Mg–Al–Zn–Bi quaternary system was developed.The remarkable consistency between the predicted phase equilibria and the presently measured data in Mg–Al–Zn–Bi quaternary system further demonstrated the accuracy and reliability of the established thermodynamic database.After that,by using the newly developed thermodynamic database,the growth restrict factors and the solidification curves in Bi-containing AZ series magnesium alloys were calculated and analyzed.It was confirmed that the grain size of AZ alloys can be refined with the addition of Bi,and the component Al had larger grain refinement effect than Bi.Besides,the amount of Bi had also noticeable effect on the solidification sequence of the AZ alloys.

Keywords:Mg–Al–Zn–Bi quaternary system;Phase equilibira;CALPHAD;Thermodynamics;Solidification behavior.

1.Introduction

The usage of magnesium alloys has been increasing dramatically because of their low density,rather good mechanical properties and metallic behavior[1–3].In the past decade numerous research activities and development projects have been carried out on casting magnesium alloys mainly for automotive applications[4].Among different types of magnesium alloys,the AZ(Mg–Al–Zn)series alloys have been becoming one of the most widely used ones by reasons of the excellent casting behavior[5–7].However,the applications of AZ series magnesium alloys are restricted to the temperatures below 120 °C[6,8]owing to the dramatic reduction of the strength and creep properties as a result of softening of the precipitateγ-Al12Mg17phase at higher temperatures.To increase the operating temperature of AZ series alloys,the alloying elements such as Sn,Sb and Bi are usually introduced[9–11].For example,a small number of Bi additions would refine the as-cast structure of AZ alloys and form a new D52-type intermetallic phaseα-Mg3Bi2[10,11].Indeed,the as-formedα-Mg3Bi2(with a melting point of 823 °C)is more stable than the naturally discontinuousγ-Al12Mg17precipitated phase in the traditional AZ system at elevated temperature.Thus,the extra-introduced Bi can greatly improve the creep resistance of the AZ series alloys at high temperatures.Although more and more attentions have been attracted on the Bi-additional AZ series alloys in recent years,it is still the truth that how to improve the mechanical properties of the casting Mg-Al-Zn based alloys with the introduction of Bi has not been systematically illustrated yet.At present,the traditional,costly and time-consuming trial-and-error approach has been employed to find the optimal addition amount of Bi in AZ alloys[10,11],but it seems very difficult to achieve the optimal one based on the trial-and-error approach.

The mechanical properties of the as-cast alloys are strongly influenced by the microstructure forming during the solidification process.However,the systematical knowledge about the as-cast microstructures and solidification behavior in Mg–Al–Zn–Bi system is absent.It is believed that quantitative descriptions of the solidification behavior in Mg–Al–Zn–Bi alloys will be helpful for efficiently design the novel Biadditional AZ series casting alloys.It is worth mentioning that the accurate phase equilirbia and thermodynamic data can help to understand the effect of the alloy chemistry on the solidification behavior,and thus serves as one of the key stones for the novel alloy design[12,13].Nevertheless,the phase equilibira data for Mg–Al–Zn–Bi quaternary system available in the literature are very limited so far.

Consequently,the main tasks of this study include(i)to perform new experiments for determination of the phase relations and transition temperatures in the Mg-rich corner of the quaternary Mg–Al–Zn–Bi system,(ii)to establish a selfconsistent set of thermodynamic descriptions for Mg–Al–Zn–Bi quaternary system by using the CALculaiton of PHAse Diagram(CALPHAD)approach,and(iii)to predict and analyze the growth restrict factor and solidification sequence of a series of Bi-containing AZ series alloys based on the presently established Mg–Al–Zn–Bi thermodynamic database,from which the hints for design of novel Bi-additional AZ series casting alloys are pointed out.

2.Experimental procedure

16 Mg–Al–Zn–Bi quaternary alloys were prepared by melting the high-purity Mg(99.95wt% purity),Al(99.7wt%purity),Zn(99.99wt% purity)and Bi(99.95wt% purity)with an inductive furnace under a gas mixture of CO2and SF6in a graphite crucible.The melt was stabilized at 720°C for 30min,followed by pouring into a cylindrical steel mold preheated to 200°C.Specimens were taken in the middle of the as-cast ingot.The as-casted samples were subjected to the inductively coupled plasma(ICP)analysis for further identification of the actual chemical compositions.Then,the samples were sealed into quartz tube and annealed at 400°C for 35 days.The annealed samples were then quenched in cold water.

Phase identification of all the alloys was analyzed by Xray diffraction(XRD)diffractometer(Rigaku D-max/2550 VB+,with Cu-Kαradiation at 40kV and 300mA).The microstructure observation was performed by using a JSMIT500 scanning electron microscope(SEM)with an energy dispersive X-ray spectroscopy(EDS)system.Then,the phase compositions of the samples were analyzed using the electron probe micro-analysis(EPMA;JXA-8100,JEOL,Japan)with wavelength dispersive X-ray spectrometry(WDS)technique.Four points in different areas of the target phase were measured by using EPMA/WDS to get the average phase composition.After that,the phase transition temperatures of all the annealed alloys were examined by differential scanning calorimetry(DSC;DSC449C,Netzsch,Germany)with a Pt-Pt/Rh thermocouple.The measurements were performed at heating and cooling rates of 5°C/min under Ar flow atmosphere.

3.Thermodynamics modeling

3.1.Binary and ternary systems in the literature

The Mg–Al–Zn–Bi quaternary system contains 6 binary systems(i.e.Mg–Al,Al–Bi,Al–Zn,Mg–Bi,Bi–Zn and Mg–Zn)and 4 ternary systems(i.e.Mg–Al–Zn,Mg–Al–Bi,Mg–Bi–Zn and Al–Bi–Zn).The thermodynamic descriptions for all the sub-binary and sub-ternary systems are available in the literature,which are briefly reviewed in the following.

There are several literature reports on thermodynamic assessments for binary Mg–Al[14-18]and Mg–Zn[18-20]systems.Based on a detailed experimental investigation,the Mg–Al and Mg–Zn systems were thermodynamically re-optimized by Liang et al.[18]in their assessment of Mg–Al–Zn system.Most of experimental data in Mg–Al and Mg–Zn binary systems can be well reproduced by using the thermodynamic descriptions in Ref.[18].Besides,the thermodynamic modeling for Al–Zn binary system from Mey[21]was adopted by Liang et al.[18].Thus,the thermodynamic descriptions for Al–Mg[18],Mg–Zn[18]and Al–Zn[21]binaries are employed in the present work.

Both Al–Bi and Bi–Zn binary systems exhibit a stable liquid miscibility gap.McAlister[22]reviewed all reported experimental data in the Al–Bi system,and proposed a set of interaction parameters to describe the liquid miscibility gap.Later,Mirkovi′c et al.[23]re-assessed the Al–Bi system to achieve a better agreement with the measured data.Thus,the thermodynamic descriptions from Mirkovi′c et al.[23]were adopted.As for the Bi–Zn binary system,its thermodynamic descriptions were assessed for several times[24–26].In addition,the thermodynamic parameters proposed by Malakhov[24]were adopted to obtain the thermodynamic descriptions for several Bi–Zn related ternary systems[27–29].The thermodynamic parameters of Bi–Zn system from Malakhov[24]were used to establish the Al–Bi–Zn ternary thermodynamic database by Gr?bner et al.[27],and thus were directly adopted here to keep the consistency of thermodynamic description.

The Mg–Bi binary system was thermodynamically modeled by four research groups[30–33].The liquid phase was modeled as the ionic liquid by Oh et al.[30]and the modified Quasi-chemical Models(MQM)by Paliwal and Jung[31].In order to describe the high-order systems conveniently,the substitutional solution model is preferred for the liquid phase.Moreover,the polynomiala+bT+cTlnTwas employed to model the Gibbs energies of compounds(α-Mg3Bi2andβ-Mg3Bi2)but without the sufficient experimental support[30,32].Subsequently,this binary was updated by Zhang et al.[33].Because very good agreement with all the experimental phase equilibria and thermodynamic properties can be achieved,the thermodynamic description from Zhang et al.[33]was adopted in the present work.

The phase relation in the Al–Mg–Zn ternary system is very complex.Thermodynamic optimizations of this ternary system were performed by three groups[18,20,34]based on a variety of experimental data.Later,the reliability of the descriptions by Liang et al.[18]was experimentally validated by Ohno et al.[35].Therefore,the descriptions by Liang et al.[18]were directly used here.The phase equilibria of Al–Bi–Zn system were experimentally investigated and thermodynamically assessed by Gr?bner et al.[27],in which the good agreement between the calculations and the experimental data was obtained.Thus,the thermodynamic parameters from Gr?bner et al.[27]were adopted.In the very recent,Niu and Li[36,37]performed a thermodynamic optimization for Mg–Al–Bi and Mg–Bi–Zn ternary systems by adopting their previously reported Mg-Bi thermodynamic description[32].Since the thermodynamic parameters of binary Mg–Bi system provided by Zhang et al.[33]will be adopted in the present work,the thermodynamic parameters in the Mg–Al–Bi and Mg–Bi–Zn ternary systems will be slightly modified by adopting all the reported data in the literature.

3.2.Thermodynamic models

The quaternary Mg–Al–Zn–Bi system includes 17 phases(liquid,(Al),(Mg),(Zn),(Bi),γ-Al12Mg17,ε-Al30Mg23,β-Al140Mg89,MgZn2,Mg2Zn,MgZn,Mg2Zn11,Mg2Zn3,α-Mg3Bi2,β-Mg3Bi2,τandφ).The liquid and terminal solid solution phases(i.e.,(Mg),(Zn),(Al)and(Bi))were described by using the substitutional model.Since the liquid phase of the Mg–Bi system,which is with the short-range ordering behavior,was described using the associated model by Zhang et al.[33],the liquid phase thus consists of five species(i.e.,Mg,Al,Bi,Mg3Bi2and Zn),in which Mg3Bi2is the associated cluster.

The sublattice model was applied to describe all the intermetallic compounds in Mg–Al–Zn–Bi system.Since there are no experimental information on the solubility of Bi inγ-Al12Mg17,ε-Al30Mg23,β-Al140Mg89,Mg2Zn,MgZn2,MgZn,Mg2Zn11,Mg2Zn3,τandφphases in the literature,the Gibbs energies model of these compounds are treated as the same as those in the Mg-Al-Zn system,as listed in Table 2.According to the EPMA results in Table 1,both Al and Zn have solubilities in the binary compoundα-Mg3Bi2,and thus the ternary solubilities were considered in this study.With the similar consideration,Bi and Mg are also considered to be easily substituted by Al and Zn inβ-Mg3Bi2phase.Thus,theα-Mg3Bi2andβ-Mg3Bi2phases are described with the sublattice model(Al,Mg,Zn)3(Al,Bi,Zn,Va)2.The detail expression of molar Gibbs energy for the above intermetallic compounds can be referred to Ref.[38].

4.Results and discussion

4.1.Experimental results

The compositions of Mg–Al–Zn–Bi alloys analyzed by ICP were summarized in Table 1.As listed in Table 1,the contents of Al and Zn in Alloys 1–7 are close to the commercial magnesium alloy AZ80,of which the composition is with 7.6–8.4wt% Al and 0.35–0.65wt% Zn.Moreover,Alloys 8,9 and Alloys 10–16 can be considered as Bi-additional AZ63(with 5.3–6.7wt% Al and 2.5–3.5wt% Zn)and AZ31(2.5–3.5wt%Al and 0.6–1.4wt%Zn)alloys,respectively.Fig.1(a)gives the XRD patterns for four selected alloys(Alloys 1,7,9 and 15)annealed at 400 °C for 35 days.As shown in Fig.1(a),Alloy 1,which is an Mg–Al–Zn alloy without Bi addition,only consists of the(Mg)phase at 400 °C.There are two phases((Mg)andα-Mg3Bi2)in the Alloys 7,9 and 15,which have the similar contents of Bi.The XRD results of all the annealed alloys were summarized in Table 1.The XRD results indicate that Alloys 1,2,3,and 10 are in the single(Mg)phase region,while other alloys consist of(Mg)andα-Mg3Bi2phases.The present results indicate inexistence of ternary or quaternary compounds in these alloys.Fig.1(b)gives the typical SEM misconstrues of Alloy 13.It shows that Alloy 13 consists of two phases,i.e.,the dark gray phase was(Mg),and the light gray one wasα-Mg3Bi2phase.Those alloys with two phases were then subjected to the EPMA determination.As listed in Table 1,both elements Al and Zn have solubilities inα-Mg3Bi2phase.The maximal solubilities of Al and Zn inα-Mg3Bi2phase are measured to be 0.5wt%and 0.72wt%,respectively.Based on the above measured data together with the phase equilibria on the boundary Mg–Al–Zn,Mg–Al–Bi,Mg–Bi–Zn ternary systems,the isothermal section at 400 °C in the Mg-rich corner of Mg–Al–Zn–Bi quaternary system can be then constructed.

Table 1List of the actual alloy compositions and EPMA phase compositions in the present Mg–Al–Zn–Bi system.

Table 2Summary of the transition temperatures observed from DSC heating and cooling curves of the annealed Mg–Al–Zn–Bi alloys.

The phase transition temperatures of all the annealed Mg–Al–Zn–Bi alloys between 400 °C and 650 °C were measured by DSC.Fig.2 shows the DSC curves of Alloy 9 during the heating and cooling process.There are two endothermic and exothermic peaks in the DSC curves.Obviously,Peak 1a and Peak 1b correspond to the melting point of Alloy 9.The transition temperatures of Peak 2a and Peak 2b are 526 °C and 516 °C respectively,indicating that they may have the same phase transition.The detected peak temperatures observed during the heating and cooling process of all the alloys are summarized in Table 2.As listed in Table 2,the melting points of all the alloys during the heating and cooling processes have been detected.Moreover,the melting points of all the alloys observed on heating and cooling show a slight deviation less than 7 °C.The second transition temperatures of most alloys corresponding to the solidus have been observed except for Alloy 4.The absence of the second transition temperature in Alloy 4 may be due to the very weak endothermic and exothermic peaks,which are difficult to be detected.

Fig.2.DSC heating and cooling curves of Alloy 9 after annealing at 400°C for 35 days.

4.2.Thermodynamic description

4.2.1.Thermodynamic re-assessment for the Mg–Al–Bi and Mg–Bi–Zn systems

The thermodynamic parameters were evaluated by the optimization module PARROT[39]incorporated in the Thermo-Calc software package.Taking the Mg–Al–Bi system for example,the optimization process is as follows:the ternary parameters in the liquid phase were firstly introduced to reproduce the reported liquidus temperatures.Then,the parameters in(Mg)phase were optimized by fitting the solidus temperatures.After that,the ternary parameters inα-Mg3Bi2andβ-Mg3Bi2phases were optimized to reproduce the solubility data.Finally,all the thermodynamic parameter were optimized together to achieve the self-consistent thermodynamic description.The analogous assessment process was carried out in Mg–Bi–Zn ternary system.The updated thermodynamic parameters in Mg–Al–Bi and Mg–Bi–Zn ternary systems are listed in Table 3.

Fig.3.Calculated vertical sections in ternary Mg–Al–Bi system along(a)20wt% Bi,(b)10wt% Al,(c)60 at% Mg,and(d)Mg–Al-50wt% Bi,compared with the experimental data[40,41].

Table 3Summary of the finally obtained thermodynamic parameters for the Mg–Al–Zn–Bi quaternary system.

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Table 3(continued)

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Table 3(continued)

Fig.4.Calculated vertical sections in ternary Mg–Bi–Zn system along(a)MgZn–Mg3Bi2,(b)20wt% Bi and(c)20wt% Zn,compared with experimental data[42].

Fig.3(a)–(c)presents three calculated vertical sections of the Mg–Al–Bi system according to the presently updated thermodynamic descriptions,at 20wt% Bi,10wt% Al and 60 at% Mg,respectively.The presently calculated vertical sections exhibit excellent consistency with the measured ones[40,41].The calculations of the Mg～Al-50wt%Bi section were also carried out,which show a good consistency between the calculations and the measured data[40,41],as shown in Fig.3(d).Fig.4(a)shows the calculated vertical section through the MgZn–Mg3Bi2in the Mg–Bi–Zn ternary system.Most of experimental data[42]can be well reproduced.Moreover,the calculated vertical sections along 20wt.% Bi and 20wt.% Zn are displayed in Fig.4(b)and(c),and yield the reasonable agreement with the measured data[39].

Fig.5 gives the liquidus projections in the Mg–Al–Bi and Mg–Bi–Zn systems on the basis of the updated thermodynamic descriptions.The measured data from Refs.[40–42]are also appended in Fig.5 for a comparison.It shows that the presently calculated results can agree nicely with most of the measured data[40–42].As shown in Fig.5,the stable liquid miscibility gap,which is common in the ternary alloys[43],exists in both Mg–Al–Bi and Mg–Bi–Zn ternary systems.The present calculations predicate the existence of three monotectic four-phase reactions(i.e.β-Mg3Bi2→L1+L2+α-Mg3Bi2(M1),L1+β-Mg3Bi2→L2+α-Mg3Bi2(M2)and L1+L2→α-Mg3Bi2+(Al)(M3))in the Mg–Al–Bi system.Similarly,two monotectic reactions L1+β-Mg3Bi2→L2+α-Mg3Bi2(M1)and L1+L2→α-Mg3Bi2+(Zn)(M2)also exist in the Mg–Bi–Zn system.Moreover,the present calculations indicate such stable miscibility gaps in the Mg–Al–Bi and Mg–Bi–Zn systems are extended from the Al–Bi and Bi–Zn boundary binaries,respectively.

4.2.2.Thermodynamic database for the Mg–Al–Zn–Bi quaternary system and its experimental validation

Since there is no reported quaternary compound in Mg-rich corner of the Mg–Al–Zn–Bi quaternary system,the thermodynamic database of the Mg–Al–Zn–Bi quaternary system can be established by directly extrapolating from the four boundary ternaries.Based on the thermodynamic descriptions of the Mg–Al–Zn[18]and Al–Bi–Zn[27]in the literature,together with those of the Mg–Al–Bi and Mg–Bi–Zn systems assessed in this work,the thermodynamic database for Mg–Al–Zn–Bi quaternary system was established.In order to validate the reliability of this quaternary database,calculations were carried out to compare with the presently obtained experimental data.

Fig.5.Calculated liquidus projections in ternary(a)Mg–Al–Bi and(b)Mg–Bi–Zn systems,compared with experimental data[40–42].

Fig.6(a)shows the calculated isothermal section in the Mg-rich corner of Mg–Al–Zn–Bi quaternary system at 400°C with different contents of Al,i.e.from 3.4wt% to 7.52wt%.In order for a direct comparison,the contents of Al used in the calculation are the same as those of Alloys 3–5,8,9,11–16(as listed in Table 2).The presently obtained experimental data are also appended in Fig.6(a).It shows that the present calculations agree well with most of the experimental data except for Alloy 4.The calculation indicates that Alloy 4 locates in the two-phase region of(Mg)+α-Mg3Bi2,while the experimental measurement indicate that it only contains(Mg)phase.Moreover,the phase regions of(Mg)and(Mg)+α-Mg3Bi2shrink as the Al contents increase,as shown in Fig.6(a).Fig.6(b)presents the calculated isothermal section of Mg–Al–Zn–Bi system along 8.67wt% Al at 400 °C.According to the calculations,both Alloys 6 and 7 locate in the two-phase region of(Mg)+α-Mg3Bi2at 400 °C,which agrees well with the experimental measurements,as shown in Fig.6(b).Specially,the three-phase region of(Mg)+α-Mg3Bi2+γ-Al12Mg17and four-phase region of L+(Mg)+α-Mg3Bi2+γ-Al12Mg17are expected to exist according to the phase rules from Fig.6(a).Fig.7 illustrates an integrated isothermal section at 400 °C of four sub-ternary systems in the Mg–Al–Zn–Bi quaternary system.

Fig.6.Calculated isothermal section of quaternary Mg–Al–Zn–Bi system at 400°C(a)over the region of 3.4–7.52wt% Al,and(b)at 8.67wt% Al,compared with the presently experimental data.

Fig.7.Combination of the isothermal sections of four sub-ternary systems at 400 °C in the Mg–Al–Zn–Bi quaternary system.

Fig.8.Calculated vertical sections of quaternary Mg–Al–Zn–Bi system along(a)Mg–8wt%Al–0.75wt%Zn–xBi,(b)Mg–3.4wt%Al–0.5wt%Zn–xBi,and(c)Mg–6.9wt%Al–2.3wt%Zn–xBi,compared with the presently experimental data.

Fig.8 presents the calculated vertical sections in Mg–Al–Zn–Bi quaternary system according to the established Mg–Al–Zn–Bi quaternary thermodynamic database.Fig.8(a)shows the calculated vertical section along 8wt% Al and 0.75wt% Zn.The compositions of Al and Zn in this vertical section are fixed to be the average values of Alloys 1–7,respectively.It should be noted that the calculated phase transition temperatures of the alloys Mg–8Al–0.75Zn–xBi(here,xis the concentration of Bi in Alloys 1–7)show small deviations(i.e.,that the liquidus temperatures are within 5°C while the other phase transition temperatures are within 10 °C)from those using the real compositions of Alloys 1–7,respectively.Thus,it is reasonable to append the DSC data of Alloys 1–7 in Fig.8(a)for a comparison.As shown in Fig.8(a),very good agreements can be observed between the experimental data and the calculations.Fig.8(b)gives the calculated vertical section along 3.4wt% Al and 0.5wt% Zn,which also show an excellent agreement with the presently obtained experimental data of Alloys 8 and 9.Similarly,the calculated vertical section with the average Al and Zn contents(with 6.9wt% Al and 2.3wt% Zn)in Alloys 10–16 is presented in Fig.8(c).These calculations match well with most of the experimental results,which indicate a high reliability of the established Mg–Al–Zn–Bi quaternary thermodynamic database.

4.3.Solidification behavior of Bi-containing AZ series magnesium alloys

The effects of the addition of Bi on the as-cast microstructures and solidification behavior of the Mg–Al–Zn alloys were experimentally investigated by four research groups[11,44–46].The previous researches[11,44]demonstrated the grain refinement of Bi on as-cast AZ alloys.Wang et al.[11]reported that the average grain size of as-cast AZ80 alloys was 408μm,and decreased to 348μm,339μm and 331μm with the addition of 0.5wt%,1wt% and 2wt% Bi,respectively.Later,Joshi and Babu[44]pointed that the average grain size of AZ31 alloy was 405μm,which decreased to 185μm with 0.2wt% Bi.In a very recent publication by the present authors[45],the average grain size of three series Bi-additional AZ as-cast alloys were measured.It shows that the average grain size of Mg–8.52Al–2.31Zn,Mg–8.67Al–0.66Zn and Mg–3.02Al–0.7Zn as-cast alloys were measured to be 65.00,57.64 and 94.06μm,but decreased to 52.33,52.04 and 54.17μm when 10.93,11.01 and 9.84wt% Bi additions were added in the respective alloys.Moreover,Wang et al.[46]reported that the small addition of Bi can change the solidification sequence of AZ80 alloys.In this section,the solidification behavior of the Bi-containing AZ series magnesium alloys will be calculated and analyzed by using the above established Mg–Al–Zn–Bi thermodynamic database.

The growth restriction factor(Q),which describes the initial slope in the development of constitutional supercooling with phase fraction of the growing solid phase,is one of the important parameters to quantitatively assess the solutal effect on grain growth and grain refinement of the alloys[47–49].Experimental observations from different sources[50,51]indicated an approximate linear relationship between the actual average grain size of the primary phase and the reciprocal of growth restriction factor Q.Such correlation has also been theoretically discussed by Qian et al.[52].Moreover,it has been proved that the values of Q in multicomponent alloys can be evaluated from the thermodynamic description of the alloy phase equilibria[53,54].The definition of Q is given as follows:

in which,is the constitutional supercooling(the difference between the liquidus temperature(TL)and the real solidification temperature(T),=TL?T)andfsis the phase fraction of the growing phase,respectively.The values ofTLcan be calculated from the equilibrium solidification by using the presently obtained thermodynamic database.The relationship betweenTandfsfor an alloy can be obtained from both equilibrium solidification and Scheil-Gulliver solidification simulations.Since the same values forTandfsunder these two conditions would be obtained whenfs→0,Tandfsare also calculated from equilibrium calculations for simplification.The initial slope is obtained from a parabolic fit(=a+b?fs+c?fs2)to about 5–10 closely spaced sampling points at very small values 0

Fig.9.Calculated(a)growth restriction factor Q and(b)growth restriction sensitivity QAl and QBi in quaternary alloys of AZ91+xBi,AZ61+xBi and AZ31+xBi.

The growth restriction factors of three commercial AZ series alloys(i.e.,AZ31(Mg–3wt%Al–1wt%Zn),AZ61(Mg–6wt%Al–1wt%Zn)and AZ91(Mg–9wt%Al–1wt%Zn))with the addition of Bi were evaluated based on the presently established Mg–Al–Zn–Bi quaternary thermodynamic database.According to the calculated vertical sections of these three series alloys,the primary crystallization of all these alloys is(Mg).As shown Fig.9(a),as the Bi content increases,the values of Q in these three series alloys show a steady increase.The present calculation indicates that the grain size of AZ alloys would be refined with the addition of Bi,which agrees reasonably with the reported experimental data[11,44,45].Moreover,with the increase of the amount of Bi,the grain refinement will be enhanced.

As shown in Fig.9(a),the present calculations show that the refining ability of AZ91+xBi alloys is larger than that of AZ61+xBi and AZ31+xBi alloys with the same Bi addition.In order to describe the impact of individual components on the growth restriction factor,the growth restriction sensitivity was introduced by Schmid-Fetzer and Kozlov[54].The growth restriction sensitivity of componentiis presented as:

Fig.10.Scheil solidification curves for AZ series alloys with the different additions of Bi:(a)AZ31+xBi,(b)AZ61+xBi and(c)AZ91+xBi,x=0,0.2wt%,0.5wt% and 1wt%,respectively according to the presently established thermodynamic database of the Mg–Al–Zn–Bi quaternary system.M is a constant used to separate the results for different alloys.

whereciis the composition of the componenti.The values of Qiare obtained by fitting at least three neighboring Q points with a parabolic equation(Q=A+B?ci+C?ci2)and evaluating the slope of each parabola according to Eq.(2).By applying the above definition,the growth restriction sensitivity of Al(QAl)and Bi(QBi)in Bi-containing AZ31,AZ61 and AZ91 alloys were calculated.As shown in Fig.9(b),the value of QAlis significantly larger than QBi.It may indicate the grain refining ability of element Al is stronger than Bi in AZ alloys.That is,the grain refinement in the Bi-additional AZ alloys is mostly effected by element Al but not the element Bi according to the present calculation.Further experimental verification for this predication is to be performed in our next work.

Different solidification sequences can cause different microstructure characteristics,and then affect the mechanical properties of alloys.To study the effect of Bi addition on the solidification sequences of Mg–Al–Zn alloys,the solidification processes of 12 Bi-containing AZ alloys(AZ31+xBi,AZ61+xBi and AZ91+xBi withx=0,0.2,0.5 and 1wt%)were simulatedviathe Scheil–Gulliver solidification mode.In the Scheil solidification mode,it is assumed that the liquid phase is with the fast diffusion while there is no diffusion in the solid phase.In general,the Scheil solidification is much closer to the real casting process comparing with the equilibrium solidification.

Fig.10(a),(b)and(c)gives the model-predicted solidification curves of AZ31+xBi,AZ61+xBi and AZ91+xBi alloys from the Scheil solidification simulation,respectively.According to simulated results,the solidification sequences of AZ31,AZ61 and AZ91 alloys are:L→(Mg)and L→(Mg)+γ-Al12Mg17.As shown in Fig.10,with the addition of Bi,the intermetallic phaseα-Mg3Bi2will precipitate during the solidification process in all the AZ magnesium alloys.As discussed in Section 1,theα-Mg3Bi2phase is very stable at high temperatures,which can enhance the high-temperature mechanical properties of the AZ alloys.The present simulations show that the solidification sequences of AZ61+0.2Bi,AZ91+0.2Bi and AZ91+0.5Bi alloys are:L→(Mg),L→(Mg)+γ-Al12Mg17and L→(Mg)+α-Mg3Bi2+γ-Al12Mg17,while those for the other Bi-additional AZ alloys are:L→(Mg),L→(Mg)+α-Mg3Bi2and L→(Mg)+α-Mg3Bi2+γ-Al12Mg17.As listed above,a ternary eutectic reaction(L→(Mg)+α-Mg3Bi2+γ-Al12Mg17)occurs in all the Bi-additional AZ alloys.Moreover,the binary eutectic reaction will change from L→(Mg)+γ-Al12Mg17to L→(Mg)+α-Mg3Bi2when the Bi contents is larger than a critical value(i.e.,0.174 in AZ31,0.475 in AZ61 and 0.826 in AZ91 alloys,respectively).Upon the critical Bi content,theα-Mg3Bi2phase can directly form from the primary(Mg)phase during the solidification process.In this case,the solidification microstructure of the AZ alloys will be changed,leading to the change of the mechanical performance of the alloys.Besides,the present simulation results also show that different AZ series alloys have different critical Bi contents.For instance,the critical Bi content in AZ31 alloy is smaller than those in AZ61 and AZ91 alloys,which indicates that the solidification sequences of AZ31 alloy is very sensitive to Bi.

5.Conclusion

?16 Mg–Al–Zn–Bi quaternary alloys were prepared to determine the phase equilibria and phase transformation temperatures by using the XRD,EPMA and DSC methods.The isothermal section at 400 °C and 3 vertical sections(Mg–8wt%Al–0.75wt%Zn–xBi,Mg–3.4wt%Al–0.5wt%Zn–xBi and Mg–6.9wt%Al–2.3wt%Zn–xBi)in the Mg-rich corner of Mg–Al–Zn–Bi system were constructed.

?The Mg–Al–Bi and Mg–Bi–Zn ternary systems were reassessed based on the reported experimental data.Most of the experimental data can be well reproduced by using the presently obtained ternary thermodynamic parameters.The thermodynamic database for Mg–Al–Zn–Bi quaternary system was established based on the presently assessed ternary systems as well as those reported ones.The reliability of the quaternary thermodynamic database was then validated by the present experimental measurements.

?The effects of the alloying element Bi on the grain refinement for the AZ31,AZ61 and AZ91 alloys were analyzed by using the calculated growth restrict factor Q and growth restriction sensitivity QAland QBi.The grain size of AZ series alloys can be refined with the addition of Bi,which was nicely validated by the present calculations.Moreover,the present calculation also indicated that it is the element Al but not Bi contributed majorly to the grain size refinement in AZ alloys.Furthermore,the solidification processes of Bi addition to AZ series Mg-alloys were predicted by the Gulliver–Scheil simulation.The amount of Bi-addition has great effect on the solidification sequence of AZ alloys.It is believed that the presently established Mg–Al–Zn–Bi thermodynamic database can be widely used to design the novel Bi-additional AZ series casting alloys.

Declaration of Competing Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The financial support from Hebei Provincial Science and Technology Program of China(Grant no.E2019202234)and Research Foundation from Education Department of Hebei Province(Grant no.BJ2018026)-Outstanding Young Talents Plan is acknowledged.Y.Tang acknowledges the financial support from Yuanguang fellowship released by Hebei University of Technology.