**1. Introduction**

The need for weight reduction in automobile and aerospace industries makes magnesium alloys attractive due to their low density and high strength-to-weight ratio [1–3]. However, the use of magnesium alloys in structural parts is limited because of their poor mechanical properties at elevated temperatures [4–16]. Many researchers investigated the effect of micro-alloying on magnesium to enhance its mechanical performance [17–76]. The addition of rare-earth (RE) elements are attractive and receive increasing attention because of their excellent properties such as better creep resistance, grain refinement, improved ductility, enhanced formability, and strength [40,43–45,54,55,60,61,67–72,76].

Micro-alloying magnesium with RE such as zinc and yttrium resulted in promising mechanical properties [27,31,35,40,44,46,55,58,60]. RE elements enhance mechanical properties due to precipitation hardening through precipitation of nanoparticles of ternary phases [27–71]. These phases have an ability to inhibit the growth of deformation twins [18–23]. Furthermore, the addition of RE elements to Mg-Zn promote activation of prismatic slip and increase the stacking fault energy, therefore weakening the texture of magnesium alloys [35–40,44,51,61,66,72]. Micro-alloying magnesium with zinc increases its fluidity in casting [77], whereas yttrium addition has a remarkable effect on aging precipitation and high solid solution strengthening [78–80]. Moreover, cerium tends to precipitate a thermally high stable compound (Mg2Ce) in magnesium rich region, which improve microstructure stability at elevated temperatures. Diluting zinc in Mg-Ce alloy significantly improves stretch formability by modifying the basal plane texture through solid solution hardening mechanism [81–85]. Moreover, the highest zinc in Mg-Ce alloy improves yield strength and ultimate tensile strength through precipitation of intermetallic

**Citation:** Aljarrah, M.; Alnahas, J.; Alhartomi, M. Thermodynamic Modeling and Mechanical Properties of Mg-Zn-{Y, Ce} Alloys: Review. *Crystals* **2021**, *11*, 1592. https:// doi.org/10.3390/cryst11121592

Academic Editor: Wojciech Polkowski

Received: 8 December 2021 Accepted: 15 December 2021 Published: 20 December 2021

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compounds. Whereas the ratio of Ce/Zn increases, grain refinements and loss of formability occurs [71,81–88]. Mg-Zn-Y alloys display promising mechanical properties because of precipitates of thermally stable ternary compounds (W-Mg3Y solid solution, I-Mg3YZn6, and LPSO-phase Mg12ZnY) as well as high solubility of yttrium in magnesium.

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 [89–91]. 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.

#### **2. 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, YZn2, and Y2Zn17 (YZn8.5) at 1105, 1080, and 890 ◦C, respectively. Thermodynamic modeling of Y-Zn binary phase diagram in the work of [96–98] presented a polymorphic transformation in the YZn2 at 750 ◦C, which is in accord with [95,99]. Mason and Chiotti [95] found five intermetallic compounds that decompose peritectically: YZn3, Y3Zn11 (YZn3.67), Y13Zn58 (YZn4.46), YZn6, and YZn12 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 [100–103]. Gibbs energy of formation of the intermediate compounds in the Y-Zn system was investigated by [104–108]. 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].

**Figure 1.** Yttrium–zinc phase diagram [109].

**Figure 2.** Yttrium–zinc phase diagram in Zn-rich region [109].

## **3. Zinc–Cerium Phase Diagram**

The first Zn-Ce phase diagram was published by Hansen and Anderko [110]. Subsequently, Veleckis et al. [111] reported eight intermediate phases; CeZn11, Ce2Zn17, CeZn, CeZn8.8-6.2, CeZn2, CeZn7, Ce2Zn, and Ce4Zn. Okamoto and Hiroaki [112] suggested the existence of nine intermediate phases, namely CeZn, CeZn2, CeZn3, CeZn3.67, CeZn4.5, CeZn5.25, CeZn7, Ce2Zn17, and CeZn11. The discrepancies in the stoichiometry and phase boundary reported by [110–112] were because of the delayed nucleation of these phases. Investigating the phase boundary and similarity of the Zn-Ce system to another Zn-RE phase diagram (such as Zn-Pr, Zn-Nd, Zn-Y, and Zn-Pm), nine intermetallic compounds were suggested [101,112–114]: CeZn, CeZn2, CeZn3, Ce3Zn11, Ce13Zn58, CeZn5, Ce3Zn22, Ce2Zn17, and CeZn11. 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 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.

**Figure 3.** Zinc–cerium phase diagram calculated by [109].

#### **4. 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.

**Figure 4.** Mg-Zn phase diagram [119].

**Figure 5.** Mg-Ce phase diagram [77].

**Figure 6.** Mg-Y phase diagram solid lines [97] in comparison to [120] showed in dotted line [77].

#### **5. 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 (τ5, H, X, and I phases) and three ternary solid solutions (Y(Mg,Zn), Y2(Mg,Zn)17, and τ<sup>3</sup> (YMg(Mg,Zn)2).

Chemical compositions and notations of the ternary phases were confusing as described in the literature [96,121–140]. 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– 36,39,40,52,67,69,70,112,126,127,138]. This ternary phase exists in many Mg-Zn-RE systems which corresponds to Mg12ZnY2 [40,140] and was designated in the literature as X-phase with simplified composition Mg12YZn [96,127,140]. Ternary phase with notation of I-phase was reported by Tsai et al. [124] as Mg30Zn60Y10 and later simplified as Mg3Zn6Y [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 Mg3Zn3Y2 and Mg25Zn60Y14 [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 Mg15Zn70Y15 [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 (YZn5): Y(Mg, Zn)1.5Zn3.5 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 YZn5 phase. Ternary solid solubility of Mg in Zn17Y2 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.

**Figure 7.** Liquidus projections of the ternary Mg-Zn-Y phase diagram; (**a**) Gröbner et al. [121] and (**b**) Zhu and Pelton [140].
