Synergistic refining mechanism of Mg-3%Al alloy refining by carbon inoculation combining with Ca addition

Chengbo Li,Shuqing Yang,Jun Du,HengBin Liao,Gan Luo

Department of Metallic Materials,School of Materials Science and Engineering,South China University of Technology,Wu Shan Road 381,Tianhe District,Guangzhou 510640,China

Received 29 June 2019;received in revised form 9 September 2019;accepted 14 December 2019 Available online 30 June 2020

Abstract Mg-3%Al alloy was refined by carbon inoculation combining with 0.2%Ca addition.High grain refining efficiency was obtained and the synergistic refining mechanism was deeply discussed in the present study.Al–C–O particles,actually Al4C3 particles,were formed in the carbon-inoculated Mg-3%Al alloy acting as nuclei forα-Mg grains.Ca addition had no obvious effect on size distribution of the nucleating particles.Ca segregation was proved on Al4C3 particles,which should reduce the interfacial energy of nuclei/Mg.The constitutional undercooling in front of nucleus/liquid was increased from 0.12°C to 0.15°C induced by 0.2%Ca addition.The synergistic grain refining efficiency can be attributed to the higher constitutional undercooling and lower the interface energy of nucleus/Mg induced by Ca addition.More nucleating particles with small size could be activated acting as potent nuclei ofα-Mg grains.Consequently,Mg-3%Al alloy could be effectively refined due to the synergistic effect induced by carbon inoculation combining with Ca.

Keywords:Mg-Al alloys;Grain refinement;Carbon inoculation;Synergistic refinement.

1.Introduction

Mg alloys are the lightest metallic structural material in practical metals.They have some key advantages of favorable heat dissipation,better damping and electromagnetic shielding performance[1].However,wider applications of Mg alloys in industries are restricted due to their low absolute strength.It is well known that grain refinement has been widely paid attention since it is successfully applied in improving mechanical properties of Mg alloys[2,3].As for the commercial Mg-Al-based alloys,many grain refining routes based on melt treatment have been developed,such as carbon inoculation[4–6],alloying elements addition[7–9]and superheating[10,11].Among them,inoculation is considered as a successful melt treatment approach.The grain refinement by inoculation can be attributed to the introduction of the potent nucleating particles into melt[12].While the solute elements can effectively refineα-Mg grain through restricting the grain growth,such as Ca[13,14],Sr[15,16],Si[17],etc.

To date,there still exist some major problems in grain refinement for Mg-Al-based alloys although some great progresses have been made.There are no dependable and commercial grain refiners in grain refinement of Al-bearing Mg alloys.No sufficient direct evidence can disclose the refining mechanisms.The developed grain refinement models cannot comprehensively explain the phenomenon of grain refinement in Mg alloy systems.The dominant role of solutes or nucleated particles in the refining process is still controversial.Therefore,the currently theories to explain the refining mechanism can be divided into two groups.One group focused on the crystal structure and scale of nucleated particles.The other group,focuses on the constitutional undercooling produced by solute element.

In recent years,the research progress about nucleation model are edge-to-edge model(E2EM)and free growth model[18–22].The E2EM proposes that the potent nuclei should be well matched with the matrix due to low interfacial energy.In addition,the effect of heterogeneous nucleation can be significantly influenced by the size of nucleating particles.The free growth model points out that the size of potent nucleant should be larger than a critical threshold,otherwise,heterogeneous nucleation cannot occur.

Many researchers believe that not only the nucleation event is the most dominant,but also the solute element plays a major role in the grain refinement process.To evaluate growth inhibition resulting from solute elements,Johnson put forward growth restriction model(GRF orQ)[23].The model considers that solute elements tend to segregate in front of the solid-liquid interface during solidification,resulting in constitutional undercooling and grain growth restriction.

These theories have been widely accepted due to its success in explaining many grain refinement behaviours.However,none of these theories can explain all phenomena perfectly.The growth restriction model has successfully explained that a small amount of Ca(about 0.2%)can significantly inhibit the grain growth of Mg alloys[13,24,25].Unfortunately,this model cannot explain that the grain refinement improve marginally with the further addition of Ca(up to 0.4%)[13].The maximum reduction of Mg-Al alloys was reached at 0.2% Ca addition.In addition,the grain size calculated by the GRF value of Ca was much larger than the actual grain size when the content of Ca exceeded 0.2%[13].So far,there are still some arguments on the grain refining mechanism,such as carbon inoculated Mg-Al alloy.Jin[26]suggests that the grain refinement of carbon inoculation can be attribute to the constitutional undercooling produce by solute segregation rather than the commonly accepted Al4C3hypothesis.Cao[27]apparently opposed this view and did research to respond.The result is shown that carbon inoculation has no effect on magnesium alloys that do not contain aluminium.The Al-C particle is the most reasonable mechanism for the grain refinement of Mg-Al alloy by carbon inoculation.

In order to integrate the effects of nucleants and solutes,Easton and St John proposed the interdependence theory model to explain the synergistic effect of nucleation particles and solutes in the melt on the as-cast grain size[28].In the interdependent theory,the nucleation events are triggered by the constitutional undercooling.Once the nucleation occurs,the constitutional undercooling region will reach extra undercooling produce by the solutes released into the liquid phase.The extra undercooling will promote subsequent nucleation.The interdependence theory was applied to describe the grain refinement of Mg-3%Al in Hu’s research[29].The phenomenon of grain coarsening and refining by Sm was reasonably explained.The theory was also successfully used to clarify the mechanism of as-cast zinc alloy refining by Mg inoculation[30].In accordance with the experimental validation[29–32],the interdependence theory clearly elucidates mechanisms of grain refinement.

In our previous studies,we found that Mg-3%Al alloys could be significantly refined by carbon inoculation combining with Ca addition[25,33,34].Furthermore,Ca addition could effectively avoid grain-coarsening induced by trace Fe impurity in the carbon-inoculated Mg-Al alloy[33].However,the relationship between carbon inoculation and Ca element on grain refinement is still unclear.Meanwhile,the dominant factors to determine the grain refining efficiency need further research.In addition,their synergetic refining mechanism also needs to be discussed deeply.Therefore,this study was designed to reveal the refining mechanism of Mg-3%Al alloy refined by carbon inoculation combining with Ca addition and provided new insights on the relationship between nucleation particles and solute elements.The synergetic refining behavior of carbon inoculation and Ca addition is revealed by the latest interdependence theory model.

2.Experimental procedure

The raw materials used in the present study were high purity Mg ingot(99.98%,mass ratio,same as below),high purity Al ingot(99.99%)and Mg-10%Ca master alloy.About 350g Mg-3%Al alloy were melted at 760°C in the high-purity MgO crucible by electric resistance furnace.The mixed gas of 98vol.%N2and 2vol.%SF6was used to protect molten melt from being oxidized during the smelting process.The graphite,Mg and Al powders with mass ratio of 1:4:5 were mixed and then prepared into cylindrical pellets under the pressure of 150MPa for 2min.The Mg-10%Ca master alloy was added into the Mg-3%Al melt and the Ca content was controlled about 0.2%.The Mg-3%Al-0.2%Ca melt was inoculated by carbon as the following processes.The pellets containing graphite were plunged into the melt.The addition amount of carbon was about 0.2% of the melt weight.The melt containing graphite was manually stirred with MgO ceramic rod for about 1min to ensure that graphite powders were uniformly dispersed in the melt.The carbon-inoculated melt was held for about 20min and then was poured into a cone steel mold(22×20×30mm)preheated at 500°C.

The as-cast sample was horizontally cut into two parts at 15mm away from the bottom.One part was treated with solid solution at 400°C for 8h for the grain microstructure observation.The heat-treated specimens were polished and subsequently chemically etched.The etchant consists of picric acid(4.2g),glacial acetic acid(10ml),ethyl alcohol(70ml)and distilled water(10ml).The as-cast samples were etched by 2vol.% nitride acid ethanol solution and subsequently observed by electron probe microanalyzer(EPMA-1600,Shimadzu company)equipped with energy dispersive X-Ray spectroscopy(EDAX)and wavelength dispersion spectrometer(WDS).The size of nucleation particles was calculated by Image-Pro Plus software.

According to the free growth model[21],the nucleation undercooling is inversely proportional to the size of nucleating particles.Each nucleating particle size corresponds to a specific nucleation undercooling.Therefore,the average spacing between the particles with the same size can be used to calculate the grain size.This study provided a measurement program executed by MATLAB software to evaluate the spacing between two particles with a certain size(xsd).The schematic diagram of the measurement is shown in Fig.1.In the EPMA image,a nucleated particle is used as the center of the circle to search for the particles with the same radius around them and measure their average spacing,as Fig.1 shown.The average spacing of each particle size is automatically measured by this program.It should be noted that the particle size is not equal to the center of the particle should be ignored.

Fig.1.Schematic diagram of average particle spacing measurement(xsd).

Limited by experimental,first-principles calculation is used to evaluate the adsorption and interfacial energies between the heterogeneous nucleus and Mg matrix.

3.Results

3.1.Grain refining efficiency

Fig.2 shows the grain morphologies of the Mg-3%Al alloy treated with different processes.As for the Mg-3%Al alloy without any treatment,its grains were very coarse with average size of 623±21μm,as shown in Fig.2a.The grain size was reduced to 582±13μm for the Mg-3%Al alloy with 0.2%Ca addition,as shown in Fig.2b.Carbon inoculation could effectively refine the grains of Mg-3%Al alloy and the average grain size was about 185±7μm,as shown in Fig.2c.As expected,higher refining efficiency was obtained for the Mg-3%Al alloy refining by carbon inoculation combining with Ca addition.The average grain size was 117±3μm,as shown in Fig.2d.

Fig.2.Grain morphologies of the Mg-3%Al alloy treated by different processes(a.without any treatment,b.0.2%Ca addition,c.carbon inoculation,d.carbon inoculation combining with 0.2%Ca addition).

3.2.Investigation of nucleating particles

In the initial nucleation stage,the size and distribution of heterogeneous nucleation particles are the important factors to determine grain refining efficiency.Fig.3 illustrates the EPMA-BSE micrographs of the Mg-3%Al alloy refined by carbon inoculation(a)and combining with Ca addition(b).There were many black particles with different sizes in the two samples.In addition,there are some white particles containing Ca,as shown in the red region of Fig.3b.In order to analyze the compositions of two typical particles,the sample inoculated by carbon combining Ca addition was observed by the point analysis,as shown in the yellow region of Fig.4a.The compositions of the black,white particles and Mg matrix are listed in Table 1.The black particle mainly consisted of Al,C,and O elements measured by EPMA point analysis.The contents of Al,C and O elements are obviously higher than those in the area of Mg matrix.Based on the chemical analyses,the black particle existed in Fig.4a are Al-C particle.However,the Al–C–O particles were always observed in the carbon-inoculated Mg-Al-based alloys due to hydrolyze during sample preparation.The chemical reaction equation is proposed as Al4C3(s)+12H2O(l)→4Al(OH)3(s)+CH4(g)↑[35].These particles are actually Al4C3particles.Similar Al–C–O particles are easily observed in other researches about the Mg-Al alloys inoculated by carbon[12,36,37].

Fig.3.EPMA-BSE micrographs of the Mg-3%Al alloy refined by carbon inoculation(a)and carbon inoculation combining with 0.2%Ca addition(b).

Table 1 The compositions of the typical particles in the sample refined carbon inoculation combining with Ca addition.

In comparison with the black particles,the white particles only exist in the samples of carbon inoculation combining with Ca addition.Compared with the matrix,high contents of Al and Ca were detected in the white particle.Therefore,the white particles should be Al-Ca particles.Specially,the Ca content in the Al-C-rich particles is seven times higher than that of in the matrix.

Fig.4 shows the distribution of elements C,Ca and O in the sample of the Mg-3%Al alloy refined by carbon inoculation combining with Ca addition by EPMA-WDS map analysis.It can be seen from the images that the black particles contain C and O elements.In addition,the distribution of C and O elements is overlapped.It should be noted that the element of Ca is segregated around the black particle in the area denoted by the elliptical line.

More than 10 pictures were taken to analyze the size distribution of the Al-C particles by using Image-Pro Plus and MATLAB software.Fig.5 presents the statistical data of the Al-C particles size distribution in the samples refined by carbon inoculation(a)and combining with Ca addition(b).Similar size distribution of Al-C-rich particles was observed in these two simples.These results suggest that Ca addition did not affect the size distribution of the Al-C particles.The Al-C particle sizes were distributed in the range from 1.25 to 9.75μm and mainly located in the size between 3.75 and 5.75μm.It should be noted that the maximum particle size is about 9.75μm.Meanwhile,these particles are less than 1%of the total particle number.

It can be seen from Fig.5c that the average spacing of nucleation particles is decreased with the particle size increased when the particle size is less than 4μm in the sample refined by carbon inoculation.There is a clear trend of the average spacing of nucleation particles increase with the particle size increasing when the particle size is larger than 4μm.Similar phenomena occurred in the sample refined by carbon inoculation combining with 0.2%Ca addition,as shown in Fig.5d.

4.Discussion

4.1.The role of nucleation

The nucleation on Al-C-rich particle formed in the carboninoculated Mg-Al melt is considered to be the refining mechanism[36–38].Many researches have shown that Al-C-rich compound should be Al4C3due to its high melting point(2200°C)and low misfit withα-Mg phase[39].In the present study,the grain size of Mg-3%Al inoculated by carbon decreased significantly,as shown in Fig.2c and d.However,the grain size of Mg-3%Al decreased slightly by Ca addition,as shown in Fig.2b.These results indicate that in-situ Al4C3particles are the dominant factor to determine the grain refining efficiency.Even so,the addition of Ca can further decrease the grain size refined by carbon inoculation.This finding provided the evidence that carbon inoculation combining with Ca had good synergistic grain refinement on Mg-3%Al alloy.

Fig.4.EPMA-WDS map analysis results of the elements of C,Ca and O for the Mg-3%Al refined by carbon inoculation combining with Ca addition.

Greer et al.put forward a model establishing the relationship between nucleation particle size and nucleation undercooling[21],as shown in Eq.(1):

whereσSLis the solid-liquid interface energy,is the entropy of fusion per unit volume anddpis the diameter of the particle.The relationship between nucleation undercooling and nucleation particle size can be obtained by taking the nucleation particle parameters measured in Fig.5a and b into Eq.(1),as shown in Fig.6a and b.

Table 2List of related parameters used in the present study.

The parameters required in Eq.(1)are given in Table 2.It can be seen from Fig.6a and b that the lager particle size is,the smaller nucleation undercoolingis required.Large particles have higher potency to act as heterogeneous nucleation sites.Therefore,the heterogeneous nucleation would start from the largest particle and promote the subsequent nucleation.

Fig.5.Statistical size distributions and the average spacings of the Al-C nucleation particles in Mg-3%Al alloy refined by carbon inoculation(a,c)and carbon inoculation combining with 0.2%Ca addition(b,d).

The relationship between nucleation undercooling and particle spacing can be obtained by particle size distribution(Fig.5a and b)and spacing(Fig.5c and d),as shown in Fig.6c and d.The smallest nucleation undercooling is appeared on the average particle spacing of 80–140μm.

In the present study,Ca was added into the melt in the form of Mg-10%Ca master alloy,which is mainly composed by Mg2Ca andα-Mg phases judged from the Mg-Ca binary phase diagram[40].The melting point of Mg2Ca phase is only 715°C,which is less than the melting temperature of 760°C.Therefore,Mg2Ca should be completely dissolved into Mg-3%Al melt as solute since the solubility of Ca in Mg melt is about 0.8% at 760°C[41].According to the amount of element addition,the sequences of phase formation during solidification were calculated by thermodynamic software,as Fig.7 shown.Al and C elements react in the melt to form Al4C3in the initial stage of carbon inoculation.It is worth noting that the AlCaMg phase is formed afterα-Mg formation.This result indicates that the Al-Ca particles observed in EPMA images(Figs.3b and 4)were not possible to be the potent nucleating particles ofα-Mg grains.Furthermore,this result also proves that Ca exists as a solute during the carbon inoculation process.

4.2.The role of solute

During the solidification process,the concentrations of solutes are usually higher in front of solid-liquid interface due to solute redistribution.The theoretical solidification temperature is lower than the actual temperature.As a result,constitutional undercooling is induced in front of the liquid-solid interface.The maximum constitutional undercooling,,can be calculated using:

Wheremlis the slope of the liquidus line,c0is the original composition of alloy andcsis the composition of the solid at the interface of solid-liquid.The constitutional undercoolings with and without Ca element can be obtained by introducing the relevant parameters of Al and Ca elements(listed in Table 1).Calculation results show that the constitutional undercooling increased from 0.12°C to 0.15°C after 0.2%Ca addition.According to the free growth model discussion above,particle nucleation requires undercooling and the smaller the particle is,the more undercooling is required.Therefore,the constitutional undercooling increases by Ca addition can activate more potent nucleating particles.

Fig.6.The relationship of nucleation undercooling and the nucleation particle size:(a)carbon inoculation,(b)carbon inoculation combining with 0.2%Ca addition;the relationship of nucleation undercooling and the average particle spacing:(c)carbon inoculation,(d)carbon inoculation combining with 0.2%Ca addition.

Fig.7.Thermodynamic calculation of phase formation sequence in solidification process.

It can be seen from Fig.4c that there are a lot of Ca-rich particles around the Al-C particles.Ca is apt to segregate in front of the solid-liquid interface since it is a surface active element[42].There is a hypothesis that no diffusion occurs in the solid state and the local equilibrium is achieved at the liquid/solid interface.The Scheil equation can be established:

WherefSis the solid mass fraction andfLis the liquid mass fraction.Eq.(4)can be defined by integrating Eq.(3):

Fig.8.The constitutional undercoolingTcs during the initial stage of solidification.

wherep=1-k.By introducing Eq.(4)into Eq.(2),the relationship between constitutional undercooling and solid phase mass fractionfScan be obtained:

According to Eq.(5),the functional relationship between constitutional undercoolingand solidification mass fractionfScan be calculated,as shown in Fig.8.It is obviously that the addition of Ca can improve the constitutional undercooling at the solid-liquid interface.The minimum nucleation undercooling required for heterogeneous nucleation is 0.049°C calculated by Eq.(1),which is based on the maximum nucleation particle size is about 9.75μm.Heterogeneous nucleation occurs earlier after Ca addition due to the nucleation undercooling can be satisfied earlier at the solid-liquid interface,as Fig.8 shown.

Furthermore,the slope of the function can be obtained in Eq.(6),which is deduced from Eq.(5):

At the beginning of solidification,the solid fraction is approaching zero:fs→0.Thus,Eq.(7)can be obtained by deriving Eq.(6):

The increase rate of constitutional undercooling calculated by Eq.(7)is about 0.49 and 0.13 with/without Ca addition,respectively.The result shows that Ca element can quickly establish the constitutional undercooling zone ahead of the growing dendrite/grain and higher possibility to produce smaller grains.

4.3.The mechanism of synergistic effect

According to the interdependence theory,the heterogeneous nucleation is triggered by the constitutional undercooling in the initial stage of solidification.Nucleation first occurs on the largest particles due to the minimum constitutional undercooling required.Subsequently,the heterogeneous nucleation occurs from large particles to small particles.Each nucleation event sets off the next available particle nucleation when the sufficient constitutional undercooling is produced.Therefore,the pre-nucleation provides a extra constitutional undercooling for the subsequent potent particles,which can promote the small particles to nucleate.

Fig.9.The schematic diagram of nucleation process.

The schematic diagram of nucleation process is shown in Fig.9.Assume that a nucleus is formed in the melt at the beginning of solidification.With the growth of the nucleus,the excess solute element enters to the liquid phase,which provides a constitutional undercooled zone()and facilitates the nucleation.Once the criterion condition:=is met,the nucleation phenomenon set off.At the moment,the new grains were formed.However,there is a region where the constitutional undercooling produced by the solute segregation is insufficient to meet the critical nucleation undercooling.The region is so-called the Nucleation Free Zone(xNFZ).There is no heterogeneous nucleation occurs in the Nucleation Free Zone only the nucleus grows.It is worth nothing that the black particles can be as the heterogeneous site while the gray particles cannot work.No heterogeneous nucleation phenomenon occurs on the gray particles since its nucleation undercooling is too large to nucleate,even if some gray particles are outside the nucleation free zone.Therefore,the grain size is equal to the nucleation free zone plus(xNFZ)the average particle spacing(xsd),as Fig.9 shown.

The grain size can be calculated by the interdependence theory[28]:

WhereDis the diffusion rate in the liquid,vis the growth velocity,clis the composition of the liquid in front of the solid–liquid interface,is the undercooling for nucleation,Z·is related to the temperature gradient within the melt andQis the growth restriction factor.The final theoretical grain size can be calculated by taking the relevant parameters(Table 1 and Fig.6c and d)into Eq.(9).The grain sizes of the carbon-inoculated Mg-3%Al alloy without or with Ca addition are shown in the Fig.10.

Fig.10.The grain sizes of Mg-3%Al alloy refined by carbon inoculation(a)and combining with 0.2%Ca addition(b)calculated by the interdependency theory.

As shown in Fig.10a,the calculated grain size of the Ca-free carbon-inoculated Mg-3%Al alloys is about 161μm which is smaller than the actual grain size(185±7μm).The number of the large particles which were activated by the constitutional undercooling were not enough.After 0.2%Ca addition,the theoretical value of grain size is 125μm which is very close to the actual value 117±3μm.The addition of Ca reduces the distance of nucleation free zone from 53μm to 48μm.However,the theoretical grain size reduces from 161μm to 125μm.This result indicates that the inhibition of grain growth by Ca adding only is limited.The metallographic photo in Fig.2b also supports this result.According to Eq.(9),it can be seen that the addition of Ca only affects the distance of nucleation free zone.Unfortunately,the nucleation free zone is limited.This result was also confirmed in Ravi’s research that the Ca addition is up to 0.4%[13].The maximum reduction in grain size has been observed at 0.2% Ca addition in Mg-Al alloys.Furthermore,the theoretical value of grain size calculated byQvalue is larger than the experimental grain size.From the discussion above,it can be inferred that the nucleate particles play a dominant role in the grain refinement process.

Fig.11.The relationship of the grain size and nucleating particle size.

Interestingly,the nucleation free zone only decrease 5μm and the theoretical grain size and actual grain size decrease about 36μm,after Ca addition.As Fig.10b shown,the addition of Ca produces extra constitutional undercooling in front of the solid-liquid interface.This extra constitutional undercooling can promote more nucleate particles nucleation.The relationship of the grain size and nucleating particle size are shown in Fig.11.The effective nucleate particle size is 9.75μm without Ca addition.After Ca addition,the other small particles can be activated to be the heterogeneous nucleating particles,due to the extra of the constitutional undercooling produce by Ca.Actually,the actual activated particles are extended to 7.75μm after Ca addition.

The effect of Ca on nucleating particles in refining process is shown in schematic diagram Fig.12.Without Ca addition,the constitutional undercooling at the solid-liquid interface is only enough to nucleate on the largest particles.After Ca addition the constitutional undercooling at the solid-liquid interface is sufficient to set off the next available smaller particles.This pattern is repeated towards to the thermal center of the casting until the constitutional undercooling is not enough to active the smaller particles.

Fig.13 provides an overview of the calculation results by first-principles.Fig.13a is the 2×2×1 supercell of Al4C3slab.The adsorption energies of different Ca adsorbed on Al4C3surface(adsorption coverage range from 0.25 to 1 ML)are shown in Fig.13b to e.Fig.13f to i are the adsorption energies of different Mg adsorbed on Al4C3surface(adsorption coverage range from 0.25 to 1ML),respectively.Fig.13j is the adsorption energy of Mg adsorbed on Al4C3surface in the presence of Ca.As shown in Fig.13,Ca has a strong adsorption capacity on Al4C3surface.The EPMA-WDS in Fig.4 also confirm these results.It can be observed from Fig.13 that the adsorption energy of Ca is higher than Mg.These results suggest that Ca is easier adsorbed to the Al4C3surface than Mg.In the presence of Ca,the adsorption energy of Mg adsorbed to Al4C3surface increased from 1.055eV to 2.015eV.These results provide important insights on Ca atoms promote the adsorption of Mg on Al4C3surface.

Fig.12.The effect of Ca on nucleating particles in refining process.

Fig.13.(a)is the Al4C3 2×2×1 surface slab;(b to e)are the adsorption energy of different Ca adsorption on Al4C3 surface(adsorption coverage range from 0.25 to 1ML),respectively;(f to i)are the adsorption energy of different Mg adsorption on Al4C3 surface(adsorption coverage range from 0.25 to 1ML),respectively;(j)is the adsorption energy of Mg on Al4C3 surface in the presence of Ca.Ead represents adsorption energy,Ead(Mg)represents the adsorption energy of Mg when co-adsorbed with Ca atom.

Moreover,the interfacial energy between nuclei and matrix interface is a key factor to determine the grain refining efficiency.The interfacial energies of Al4C3/Mg interface with and without Ca addition were calculated by first-principles,as Table 3 shown.The energy of clean interface between Al4C3/Mg is 0.802J/m2.As Table 3 shows,there is a clear trend of decreasing interfacial energy of Al4C3/Mg interface by Ca atoms dope to the interface.

Table 3The interfacial energies of Al4C3/Mg interface and Ca-doped Al4C3/Mg interface.

The relationship between the constitutional undercooling,interface energy and the nucleation particle size can be expressed by the equation:

Whereis the constitutional undercooling,γAl4C3/Mgis the interface energy of Al4C3/Mg,dpis the diameter of the particle,Tmis the melt pointing,Lvis the latent heat of phase change.According to Eq.(10),the decrease of interface energy of Al4C3/Mg would lead to the diameter of the particle decrease at a certain constitutional undercooling.Therefore,the active particles will be increased by the nucleation particle size expand to small particle size.

5.Conclusions

(1)Mg-3%Al alloy could be refined by carbon inoculation.0.2%Ca addition could further improve the grain refining efficiency.Carbon inoculation combining with Ca had good synergistic grain refinement on Mg-3%Al alloy.

(2)Al–C–O particles were always observed in the carboninoculated Mg-3%Al alloy with/without 0.2%Ca addition.These particles should be actually Al4C3particles acting as nuclei forα-Mg grains.0.2%Ca addition had no obvious effect on size distribution of the Al-C particles.Ca segregation was proved on Al4C3particles with higher content.

(3)The effect of Ca re-distribution in front of nucleus/liquid was theoretically discussed.Calculated results indicated the increase rate of constitutional undercooling and constitutional undercooling were increased from 0.13 and 0.12°C to 0.49 and 0.15°C after 0.2%Ca addition,respectively.

(4)The theoretical grain size of carbon-inoculated Mg-3%A alloy was less than the experimental value since no enough Al4C3particles were activated.After Ca addition,the other small particles can be activated to be the heterogeneous nucleating particles,due to the extra of the constitutional undercooling produce by Ca.Actually,the actual activated particles are extended to 7.75μm after Ca addition.5.The synergistic grain refining efficiency can be attributed to the higher constitutional undercooling and lower the interface energy of nucleus/Mg induced by Ca addition.More nucleating particles with small size could be activated acting as potent nuclei ofα-Mg grains.

Declaration of Competing Interest

None.

Acknowledgments

This work was supported by the National Natural Science Foundation of China(51574127)and Natural Science Foundation of Guangdong Province(2014A030313221).