Thermodynamic Modeling and Mechanical Properties of Mg-Zn-{Y, Ce} Alloys: Review

: Magnesium alloys are a strong candidate for various applications in automobile and aerospace industries due to their low density and speciﬁc strength. Micro-alloying magnesium with zinc, yttrium, and cerium enhances mechanical properties of magnesium through grain reﬁnement and precipitation hardening. In this work, a critical review of magnesium-based binary systems including Mg-Zn, Mg-Y, Mg-Ce, Zn-Y, and Zn-Ce is presented. Based on the CALPHAD approach and ﬁrst-principles calculations, thermodynamic modeling of Mg-Zn-Y and Mg-Zn-Ce ternary phase diagrams have been summarized. The inﬂuence of micro-alloying (yttrium and cerium) on the mechanical properties of magnesium is discussed. A comparison between mechanical properties of magnesium commercial alloys and magnesium–zinc–{yttrium and cerium} have been summarized in tables.

To better understand phase stability, phase relation, and the effect of precipitation on age hardening, knowledge of binary and ternary phase diagrams is essential.Additionally, accurate prediction of phase diagram plays an important role in materials development and alloy design.Phase diagram is a tool used to predict the equilibrium phase(s) and phase(s) percentage at certain temperatures for specified alloys and simulate the phase consistency and solidification process of individual alloys.Moreover, the percentage of the predicted phase(s) that exist in the microstructure can be calculated.This will enable us to track particular alloys during solidification and subsequent heat treatment by predicting phase composition and distribution.Therefore, binary sub-systems of Mg-Zn-{Y, Ce} including Mg-Zn, Mg-Y, Mg-Ce, Zn-Y, and Zn-Ce phase diagram have been critically reviewed.In addition, ternary phase diagrams of Mg-Zn-Ce and Mg-Zn-Y have been assessed.A comparison between mechanical properties of commercial Mg-based alloys and Mg-Zn-{Ce,Y} alloys has been reported.
The CALPHAD approach is a well-known method to predict phase equilibria in a multi-component system based on Gibbs free energy of the phases [89][90][91].Solid solutions were modeled using compound energy formalism with sublattice [92].The modified quasi-chemical (MQC) solution model precisely describes short-range ordering in the liquid phase; therefore, liquid phase was optimized using MQC to treat configurational entropy [93].The main novelty of the current work is to critically review phase equilibria of Mg-Zn-{Y, Zn} systems and mechanical properties based on the experimental investigations reported in the literature.

Zinc-Yttrium Phase Diagram
Chiotti et al. [94] largely examined phase diagram and thermodynamic data of Zn-Y phase diagram using DTA, metallographic, and XRD.Mason and Chiotti [95] subsequently reviewed the work of [94] and measured phase relation and thermodynamic properties of the intermetallic compounds using eight samples.In the work of [94,95], tantalum containers were unsuccessful because of the penetration of Y-Zn liquid at high zinc contents.Mason and Chiotti [95] reported three intermetallic compounds that melt congruently: YZn, YZn 2 , and Y 2 Zn 17 (YZn 8.5 ) at 1105, 1080, and 890 • C, respectively.Thermodynamic modeling of Y-Zn binary phase diagram in the work of [96][97][98] presented a polymorphic transformation in the YZn 2 at 750 • C, which is in accord with [95,99].Mason and Chiotti [95] found five intermetallic compounds that decompose peritectically: YZn 3 , Y 3 Zn 11 (YZn 3.67 ), Y 13 Zn 58 (YZn 4.46 ), YZn 6 , and YZn 12 at 905, 896, 882, 872, and 685 • C, respectively.Mason and Chiotti [95] determined the thermodynamic properties of the intermetallic compounds using dewpoint method.The large number of intermetallic compounds found in the RE-Zn system was similar and related to RE-coordination number [100].Crystal structure data of Y-Zn compounds were determined by [100][101][102][103]. Gibbs energy of formation of the intermediate compounds in the Y-Zn system was investigated by [104][105][106][107][108]. The most accurate description of Y-Zn binary phase diagram was established by Zhu and Pelton [109] based on experimental data [94,95] as shown in Figures 1 and 2. The optimized Y-Zn phase diagram presented by Zhu and Pelton [109] presented some amendment to the work of Spencer et al. [98].The calculated enthalpy and Gibbs energies of formation of the intermetallic compound presented in the work of [98] are in good agreement with the experimental data of [95,104,105,108].

Zinc-Cerium Phase Diagram
The A detailed investigation on the crystallographic data of intermetallic phases was presented in [114].These intermediate compounds were included in the thermodynamic modeling of Zn-Ce phase diagram in the work of Wang et al. [115], Spencer et al. [98], and Zhu and Pelton [109].The work of Chiotti and Mason [116] was the only experimental phase diagram data that could be found in the literature.Chiotti and Mason [116] inves-tigated Zn-Ce phase diagram using metallography, differential thermal analysis (DTA), X-ray diffraction, and vapor pressure measurements.Johnson and Yonco [117] reported the standard Gibbs free energy of formation of the CeZn 11 phase, which was in accord with [116].Chiotti and Mason [116] used dewpoint method to derive standard Gibbs free energy of formation for the intermetallic compounds.Johnson and Yonco [118] used the equation of standard Gibbs free energy to derive enthalpy of formation of the intermediate compounds.
Spencer et al. [98] and Zhu and Pelton [109] used modified quasi-chemical model to optimize liquid phase.Zn-Ce phase diagram published by [109] was an improvement to the work of Zhu and Pelton [109].Zn-Ce phase diagram presented by Zhu and Pelton [109] is shown in Figure 3. experimental phase diagram data that could be found in the literature.Chiotti and Mason [116] investigated Zn-Ce phase diagram using metallography, differential thermal analysis (DTA), X-ray diffraction, and vapor pressure measurements.Johnson and Yonco [117] reported the standard Gibbs free energy of formation of the CeZn11 phase, which was in accord with [116].Chiotti and Mason [116] used dewpoint method to derive standard Gibbs free energy of formation for the intermetallic compounds.Johnson and Yonco [118] used the equation of standard Gibbs free energy to derive enthalpy of formation of the intermediate compounds.
Spencer et al. [98] and Zhu and Pelton [109] used modified quasi-chemical model to optimize liquid phase.Zn-Ce phase diagram published by [109] was an improvement to the work of Zhu and Pelton [109].Zn-Ce phase diagram presented by Zhu and Pelton [109] is shown in Figure 3.

Mg-Zn, Mg-Y, and Mg-Ce Phase Diagrams
Based on the literature, many researchers modeled liquid phase using a random solution model.This model is only anticipated at a very high temperature when the entropy term overwhelms any tendency for ordering or clustering of atoms.Therefore, the configurational entropy of mixing should vary with temperature.The modified quasi-chemical solution model has a better treatment of configurational entropy that accounts for a nonrandom distribution of atoms.Therefore, no model based on the random mixing can properly describe the influence of short-range ordering, because they do not solve the problem of the configurational entropy.The description of short-range ordering can be taken into account with bond energy models by considering the interactions between atoms that extend beyond the nearest neighbor's approximation.This problem has been treated using the modified quasi-chemical model.Liquid phase in the work of [77] was optimized using the modified quasi-chemical model (MQM).This model has been used to describe the liquid phase as this is the only scientific model that accounts for the presence of short-range ordering.Therefore, the reported phase diagrams in the work of [77] adequately describe thermodynamic properties of these systems.Islam et al. [77] critically reviewed and assessed thermodynamic data and phase diagrams of Mg-Zn, Mg-Y, and Mg-Ce systems.Figures 4-6 presented the most accurate calculated binary phase diagrams for these systems [77].It is worth mentioning that the liquid phase was optimized using a modified quasi-chemical model to accurately describe short range ordering in the liquid.

Mg-Zn, Mg-Y, and Mg-Ce Phase Diagrams
Based on the literature, many researchers modeled liquid phase using a random solution model.This model is only anticipated at a very high temperature when the entropy term overwhelms any tendency for ordering or clustering of atoms.Therefore, the configurational entropy of mixing should vary with temperature.The modified quasichemical solution model has a better treatment of configurational entropy that accounts for a non-random distribution of atoms.Therefore, no model based on the random mixing can properly describe the influence of short-range ordering, because they do not solve the problem of the configurational entropy.The description of short-range ordering can be taken into account with bond energy models by considering the interactions between atoms that extend beyond the nearest neighbor's approximation.This problem has been treated using the modified quasi-chemical model.Liquid phase in the work of [77] was optimized using the modified quasi-chemical model (MQM).This model has been used to describe the liquid phase as this is the only scientific model that accounts for the presence of short-range ordering.Therefore, the reported phase diagrams in the work of [77] adequately describe thermodynamic properties of these systems.Islam et al. [77] critically reviewed and assessed thermodynamic data and phase diagrams of Mg-Zn, Mg-Y, and Mg-Ce systems.Figures 4-6 presented the most accurate calculated binary phase diagrams for these systems [77].It is worth mentioning that the liquid phase was optimized using a modified quasi-chemical model to accurately describe short range ordering in the liquid.[97] in comparison to [120] showed in dotted line [77].Figure 6.Mg-Y phase diagram solid lines [97] in comparison to [120] showed in dotted line [77].Figure 6.Mg-Y phase diagram solid lines [97] in comparison to [120] showed in dotted line [77].Figure 6.Mg-Y phase diagram solid lines [97] in comparison to [120] showed in dotted line [77].

Magnesium-Zinc-Yttrium Ternary Phase Diagram
Gröbner et al. [121] investigated the Mg-Zn-Y ternary system using ten ternary alloys by DSC, SEM/EDXS, and TEM.Based on their experimental results and assessment to the stoichiometric of ternary phases reported in the literature [96,122-140], Gröbner et al. [121] calculated liquidus projections and isothermal sections at 400, 500, and 600 • C. In 2015, Zhu and Pelton [140] calculated liquidus projection and isothermal sections at 400, 500, and 600 • C. Zhu and Pelton [140] defined ternary phase diagrams of Mg-Zn-RE systems using the Kohler model to estimate ternary properties of Mg-Zn-RE systems.It is worth mentioning that liquidus projections of Zhu and Pelton [140] and Gröbner et al. [121] are the only works that could be found in the literature.Gröbner et al. [121] modelled five ternary compounds: 18R, 14H, W, I, and Z, and one ternary solid solution (H).However, Zhu and Pelton [140] reported four ternary compounds (τ 5 , H, X, and I phases) and three ternary solid solutions (Y(Mg,Zn), Y 2 (Mg,Zn) 17 , and τ 3 (YMg(Mg,Zn) 2 ).
Chemical compositions and notations of the ternary phases were confusing as described in the literature [96, [121][122][123][124][125][126][127][128][129][130][131][132][133][134][135][136][137][138][139][140].Many of the ternary phases reported in the literature were considered as metastable phases according to the work of Zhu and Pelton [140].The slow kinetics of transformation of ternary phase, long-period stacking ordered (LPSO), has been described in the literature with different notations and chemical compositions [32][33][34][35][36]39,40,52,67,69,70,112,126,127,138].This ternary phase exists in many Mg-Zn-RE systems which corresponds to Mg 12 ZnY 2 [40,140] and was designated in the literature as X-phase with simplified composition Mg 12 YZn [96,127,140].Ternary phase with notation of I-phase was reported by Tsai et al. [124] as Mg 30 Zn 60 Y 10 and later simplified as Mg 3 Zn 6 Y [138] and adopted in thermodynamic modeling in the work of [96,121,140].Moreover, W-phase was reported in the work of [96] with composition of Mg 3 Zn 3 Y 2 and Mg 25 Zn 60 Y 14 [128], while Zhu and Pelton [140] and Gröbner et al. [121] described this phase as a ternary solid solution of yttrium in (MgZn) binary phase where yttrium may substitute magnesium and zinc element in the sublattice.Ternary phase designated as H-phase and composition of Mg 15 Zn 70 Y 15 [124] was accepted in the work of Zhu and Pelton [140].Similarly to other Mg-Zn-RE ternary systems, this phase has been modeled as stoichiometric ternary compound.However, Gröbner et al. [121] describe this phase as ternary solid solubility of Mg in (YZn 5 ): Y(Mg, Zn) 1.5 Zn 3.5 using the experimental data of [138].Zhu and Pelton [140] treated H-phase differently because the crystallographic data (lattice constants) significantly differ from those of YZn 5 phase.Ternary solid solubility of Mg in Zn 17 Y 2 binary phase, reported in the work of Zhu and Pelton- [140], was not observed in the liquidus projections of Gröbner et al. [121].Based on the above confusion of the chemistry of ternary compounds, as well as ternary solid solutions in the Mg-Y-Zn system, further experimental investigation is required to resolve the discrepancies in the literature.Liquidus projections of the ternary Mg-Zn-Y phase diagram reported by Gröbner et al. [121] and Zhu and Pelton [140] are shown in Figure 7a,b, respectively.

Magnesium-Zinc-Cerium Ternary Phase Diagram
Experimental investigation and thermodynamic modeling of the Mg-Zn-Ce received considerable attention by many researchers [141][142][143][144][145][146][147][148][149][150][151][152][153].However, the reported ternary phases and ternary solid solutions were confusing.Table 1 summarizes the reported ternary phases in the Mg-Zn-Ce system [151].Ternary solid solution designated by Mg 3 Ce was reported by [149,152] where zinc atom substitutes magnesium atom in the binary Mg 3 Ce phase.The solubility of zinc in Mg 3 Ce and crystallographic data are shown in Table 2. Recently, this phase was verified in the work of Shi et al. [153].Ternary solid solution, denoted as τ 3 in the work of [152,153], was reported by [144,150] with a prototype of AlMnCu 2 .The percentage of zinc in this phase was 38 to 50 at.%[150], whereas Kevorkov and Pekguleryuz [148] reported this percentage as 45 to 50 at.%.Moreover, Mel'nik et al. [144] and Chiu et al. [149] reported that this phase contained 35 to 45, and 0 to 48 at.%Zn, respectively.It is worth noting that Chiu et al. [149] reported Mg 3 Ce solid solution with two different prototypes, namely BiF 3 and AlMnCu 2 .Whereas Shi et al. [153] verified the existence of τ 3 and indicated the difficulty to distinguish between τ 3 and Mg 3 Ce because of the structural similarity.The authors of [153] declared the difficulty of detecting the difference using XRD.According to the BSE image in the work of [153], Mg 3 Ce showed diamond shape whereas τ 3 exhibited irregular shape.Meanwhile, τ 3 exists in equilibrium with Mg 3 Ce in accord with [152,153].Reported comparisons between the crystallographic data and solid solubility for other ternary phases were summarized in the work of Chiu et al. [149] and Zhu et al. [152].
Liquidus projections of the Mg-Zn-Ce ternary phase diagram were calculated by [148][149][150][151][152][153].The calculated ternary phase diagram by Chiu et al. [149] proposed that τ 3 and Mg 3 Ce were similar phase, which contradicts the findings in [152,153].Moreover, ternary phase diagram presented by Zhu et al. [152] was an amendment to the work of Mostafa and Medraj [151].Primary crystallization regions of ternary phases could not be found in the liquidus projection of Shi et al. [153].Liquidus projections of Mg-Zn-Ce calculated by Zhu et al. [152] and Shi et al. [153] are shown in Figure 8a,b, respectively.Ternary solid solution, denoted as τ3 in the work of [153,154], was reported by [145,151] with a prototype of AlMnCu2.The percentage of zinc in this phase was 38 to 50 at.%[151], whereas Kevorkov and Pekguleryuz [149] reported this percentage as 45 to 50 at.%.Moreover, Mel'nik et al. [145] and Chiu et al. [150] reported that this phase contained 35 to 45, and 0 to 48 at.%Zn, respectively.It is worth noting that Chiu et al. [150] reported Mg3Ce solid solution with two different prototypes, namely BiF3 and AlMnCu2.Whereas Shi et al. [154] verified the existence of τ3 and indicated the difficulty to distinguish between τ3 and Mg3Ce because of the structural similarity.The authors of [154] declared the difficulty of detecting the difference using XRD.According to the BSE image in the work of [154], Mg3Ce showed diamond shape whereas τ3 exhibited irregular shape.Meanwhile, τ3 exists in equilibrium with Mg3Ce in accord with [153,154].Reported comparisons between the crystallographic data and solid solubility for other ternary phases were summarized in the work of Chiu et al. [150] and Zhu et al. [153].
Liquidus projections of the Mg-Zn-Ce ternary phase diagram were calculated by [149][150][151][152][153][154].The calculated ternary phase diagram by Chiu et al. [150] proposed that τ3 and Mg3Ce were similar phase, which contradicts the findings in [153,154].Moreover, ternary phase diagram presented by Zhu et al. [153] was an amendment to the work of Mostafa and Medraj [152].Primary crystallization regions of ternary phases could not be found in the liquidus projection of Shi et al. [154].Liquidus projections of Mg-Zn-Ce calculated by Zhu et al. [153] and Shi et al. [154] are shown in Figure 8a,b, respectively.

Mechanical Properties of Mg-Zn-{Ce, Y} Alloys
Alloying Mg-Zn with rare earth elements is promising in modifying magnesium texture.Among rare-earth element, many researchers reported that micro-alloying Mg-Zn with yttrium or cerium exhibited a comparable ductility and formability with commercial

Mechanical Properties of Mg-Zn-{Ce, Y} Alloys
Alloying Mg-Zn with rare earth elements is promising in modifying magnesium texture.Among rare-earth element, many researchers reported that micro-alloying Mg-Zn with yttrium or cerium exhibited a comparable ductility and formability with commercial magnesium alloys.Tables 3 and 4 summarize the mechanical properties of the published alloys in Mg-Zn-Y [154][155][156][157] and Mg-Zn-Ce [48,71,81,85,[156][157][158], respectively.The addition of yttrium to Mg-Zn alloys enhances the formation of magnesium solid solution in ternary systems due to high solid solubility of yttrium in magnesium.Meanwhile, precipitation of nano-scale ternary phases as a result enhances mechanical properties.It is worth noting that the ratio of Zn/Y and heat treatment conditions play a significant role in mechanical properties as can be seen in Table 3. Unlike yttrium, the micro-addition of cerium to Mg-Zn reduces magnesium solid solution and precipitates a binary Mg12Ce phase as well as ternary nano-scale phases.Maximum solid solubility of cerium in magnesium is 0.5 wt.% at 590 • C and Mg12Ce precipitate up to 32.4 wt.% Ce.The existence of cerium and zinc in magnesium resulted in weakening structure and therefore enhanced ductility of magnesium alloys.Meanwhile, the percentage of cerium magnesium alloys must be in small amounts to hinder precipitation of high intensity of Mg12Ce phase; besides, heat treatment conditions and weight fraction of cerium play a remarkable role in mechanical properties of Mg-Zn alloys as shown in Table 4.

Conclusions
To reduce oil consumption in the automobile industry, designers are interested in lightweight alternative materials.Among lightweight materials is magnesium, and products of Mg-Zn alloys used in the automobile industry include transmission housings, heads, and engine blocks.In the current work, thermodynamic modeling of yttrium-zinc and yttrium-cerium phase diagrams were critically assessed, and the most appropriate phase diagrams were presented.Crystallographic data and solid solubilities of ternary phases in Mg-Zn-Y and Mg-Zn-Ce systems were evaluated.Lack of experimental data on ternary Mg-Zn-Y required further experimental investigations.Based on the recent findings, liquidus projections of the Mg-Zn-Y and Mg-Zn-Ce ternary phase diagrams were given.Ternary intermetallic phases and ternary solid solution reported in the literature were confusing, and additional key experiments are needed to resolve the discrepancies on the existence and chemical compositions of these phases.Mechanical properties reported in the literature of the two ternary systems were summarized.

Table 1 .
Reported ternary phases in the Mg-Zn-Ce system in comparison with literature.

Table 2 .
Crystallographic data and Zn solubility in Mg 3 Ce.

Table 2 .
Crystallographic data and Zn solubility in Mg3Ce.

Table 3 .
Mechanical properties of Mg-Zn-Y alloys.