Phase Formation of Mg-Zn-Gd Alloys on the Mg-rich Corner

The phase constitutions of as-cast magnesium (Mg)-Zn-Gd alloys (Zn/Gd = 0.25~60, Zn 0~10 at.%, Gd 0~2 at.%, 48 samples) were investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The Mg-Zn-Gd phase diagram focused on the Mg-rich corner (with up to 20 at.% Zn, 10 at.% Gd) has been set up. Five regions can be classified as follows: (I) α-Mg+W-phase+(binary compounds), (II) α-Mg+W-phase+I-phase(+binary compounds), (III) α-Mg+I-phase(+binary compounds), (IV) α-Mg+binary compounds, and (V) α-Mg. The phase diagram has been verified by solidification behaviors observation using differential thermal analysis (DTA). Moreover, the structures of I-phase and W-phase in the alloy were explored in details. In terms of the Hume-Rothery rules, I-phase is confirmed as FK-type quasicrystalline with a chemical stoichiometry as Mg30±1Zn62Gd8±1 (at.%). The composition and lattice parameter a W-phase (fcc structure, m3¯m) are affected by the composition of Mg-Zn-Gd alloys, especially by the Zn/Gd ratio of alloys. This work would be instructive for the design of Mg-Zn-Gd alloys to obtain the phase components, and then selected the strengthening ways, which could adjust its mechanical properties.


Introduction
Magnesium (Mg) alloys are very attractive for automobile applications because of their light weight, energy saving, and beneficial properties for environment [1]. Among them, the Mg-Zn-Gd system seems particularly promising in that it offers a unique opportunity to produce both prismatic and basal precipitate planes [2], the combination of which can lead to a maximum impediment to propagating dislocations and twins, and hence exceptional mechanical properties. But, there is very limited information on the phase formation in this system. Such information is critically needed not only for designing alloys with further improvement in strength, but also for any insightful understanding of the texture weakening effect of Gd in dilute Mg-Zn-Gd alloys and the effects of intermetallic phases, such as quasicrystalline on mechanical properties in more concentrated Mg-Zn-Gd extrusion alloy [3].

Material and Methods
In total, 48 ternary Mg-Zn-Gd samples were prepared (with up to 2 at.% Gd, 10 at.% Zn, 0.25~60 Zn/Gd atomic ratio). The sample compositions are shown in Table 1, together with analytical methods. All of the samples were produced from high purity Mg (99.9 wt %), Zn (99.99 wt %), and Gd (99.99 wt %) by high-frequency induction melting in the graphite crucible and then casting into a steel mold under an argon atmosphere. Typical weight of these samples was 50 g. In order to prevent the vaporization of Mg and Zn, the graphite crucibles containing the weighted raw materials were sealed into quartz tubes under a rarified argon atmosphere. The sketch map of the melting device was shown in Figure 1. Mg-Zn-Ho [18,19]. During the hot deformation process (i.e., hot rolling, extrusion, equal channel angular extrusion (ECAE), and severe hot rolling), I-phase particles are claimed to be stable against coarsening, and can retain strength at high temperatures due to strong interface bonding strength [5][6][7][8]. In addition, the alloys containing LPSO structures, a thickness of a single unit cell height and having an extraordinarily large aspect ratio structure, exhibit superior mechanical properties. After rapidly solidified powder metallurgy (RS P/M), Mg-1Zn-2Y (at.%) [20,21], and Mg-Zn-(Y, Dy, Ho, Er) [22][23][24][25] alloys would obtain LPSO structures. Mg-Zn-Gd alloy could both form this staking from the supersaturated solid solution phase within elevated temperature, as reported by M. Yamasaki et al. [26,27]. W-phase ( 3 Fm m , Mg3 RE2Zn3) in Mg-Zn-RE alloy system was first reported by Padezhnova et al. [28], which could be easily formed in the solidification of alloy. W-phase basically has no strengthening effect on Mg alloy [29] because of its limited structural symmetry and weak adhesive strength with the Mg matrix [30]. A research of Xu [31] reveals that a small volume fraction of W phase (below 13.8%) is beneficial to the ductility of Mg-Zn-Y-Zr alloy. Thus, the precipitation of the W-phase in Mg-Zn-RE alloys is still worthy to be investigated.
In this paper, X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were employed to study the typical microstructures and the phase constitutions of Mg-Zn-Gd alloys in as-cast. The phase formation regions could be explored and validated by samples with up to 10 at.% Gd and 20 at.%Zn. The DTA experimental observation was used to verify the phase constitution results. Moreover, the intermetallic phase structures in the as-cast alloy, such as I-phase and W-phase, were discussed in detail.

Material and Methods
In total, 48 ternary Mg-Zn-Gd samples were prepared (with up to 2 at.% Gd, 10 at.%Zn, 0.25~60 Zn/Gd atomic ratio). The sample compositions are shown in Table 1, together with analytical methods. All of the samples were produced from high purity Mg (99.9 wt %), Zn (99.99 wt %), and Gd (99.99 wt %) by high-frequency induction melting in the graphite crucible and then casting into a steel mold under an argon atmosphere. Typical weight of these samples was 50 g. In order to prevent the vaporization of Mg and Zn, the graphite crucibles containing the weighted raw materials were sealed into quartz tubes under a rarified argon atmosphere. The sketch map of the melting device was shown in Figure 1.   The phase constitutions for all of the alloys were examined by X-ray diffraction (XRD, D8 Advance-Bruker, Karlsruhe, Germany) at 40 kV and 40 mA with the Cu-Kα radiation. For the typical alloys, the microstructures were characterized by scanning electron microscopy (SEM, JEM-6460, JEOL, Tokyo, Japan or FEI Sirion-200, Hillsboro, OR, USA), equipped with an energy-dispersal X-ray spectroscopy (EDS, Oxford X-maxn, Oxford, UK). In special alloys, some phases were further characterized by transmission electron microscopy (TEM, JEM-2010 equipped with Oxford inca EDS system) (JEOL, Tokyo, Japan) to determine the crystal structure. For TEM examinations, the discs of 3 mm diameter and 0.1 mm thickness were prepared from the bulk sample by electric spark machining cutting, and then mechanical thinning, twin-jet elector-polishing to 0.1 mm, followed by ion milling using a Gatan precision ion polishing system (PIPS). The typical alloys were also investigated by differential thermal analysis (DTA) (MDSC2910, Perkin Elmer, Waltham, MA, USA) at a heating/cooling rate of 0.17 K/s. Helium at a 2 L/h flow rate was applied as the analysis chamber gas. The overall uncertainty of DTA measurements for temperature determination was less than 3 K.

Phase Formation of Mg-Zn-Gd Alloy on the Mg-rich Corner
The phase identification in this work was based mainly by XRD, but SEM/EDS/TEM were also conducted on selected alloys to confirm the phase identification. The phases identified in all 48 alloys are given in Table 1 (first sort by the Zn descending, then sort by Gd descending). Some experimental findings that were reported in the literature [32][33][34] were also given for comparison. Figure 2 has summarized the phase formation information for Mg-Zn-Gd system focusing on the Mg-rich corner with up to 10 at.% Gd and 20 at.% Zn. During the casting process, the melt was poured into a permanent mold with a comparatively faster cooling rate, which resulted in unequilibrium phase formation. The intermetallic phases that were observed in as-cast samples were mainly I-phase, W-phase, and binary Mg-Zn, Mg-Gd compound, but without any Zn-Gd compound or LSPO structures. So, the phase formation would be a little different from the equilibrium Mg-Gd-Zn ternary phase diagram, as presented by J. Grobner [34] or H.Y. Qi [35]. Five regions can be classified as follows: (i) α-Mg+W-phase(+binary compounds), (ii) α-Mg+W-phase+I-phase(+binary compounds), (iii) α-Mg+I-phase(+binary compounds), (iv) α-Mg+binary compounds, and (v) α-Mg.
The region division is mainly according to the X-ray diffraction results for not all of the alloys have been further characterized by TEM/SEM/EDS. Some binary compounds in certain alloys may not be detected for XRD analysis sensitivity.

The Typical Microstructures and Phase Structures
With the typical alloys (Samples as 35, 39, 10, and 14), the microstructures were investigated by SEM. From the second electronic image (SEI, Figure 3), Gd content effect on the microstructure of Mg-Zn-Gd alloys could be seen. With a higher Gd content, a larger amount of dendritic phase and more closed network microstructure would exist in alloys. While, with a lower Gd content, a dispersed and granular microstructure would exhibit. The microstructures of Mg-Zn-Gd alloys are coherent with our previous work [11][12][13][14][15] and literature [32,33]. To further identify the phase stoichiometry, EDS was carried out and listed in Table 2. For the Mg-1Zn-2Gd alloy (Sample 35, Figure 3a), the particle and dendritic phases have the similar Zn/Gd ratio and verified as W-phase (Mg90.85±1.0Zn3.95±1.0Gd5.2±1.0, at.%, confirmed by XRD analysis later). The matrix behaves as a supersaturated solid solution phase of α/-Mg. One lamellar phase, with 14H-phase, would appear from this matrix in by heat treatment, and it exhibits thermodynamic equilibrium and thermal stability [26,27]. The same stacking sequence was observed in annealed rapidly solidified (RS) Mg-1Zn-2Y alloys [23]. For Mg-1Zn-0.333Gd alloy (Sample 39, Figure 3b), there exists some granular phase verified as Mg5Gd and dendritic phase verified as W-phase (Zn/Gd ≈ 2, confirmed by TEM analysis later). For Mg-5Zn-0.278Gd alloy (Sample 10, Figure 3c), it reveals a larger amount of dendritic phase ascertained as I-phase with a composition of Mg56.1±1.0Zn40±1.0Gd3.9±1.0 (at.%, Zn/Gd = 10.2, confirmed by TEM analysis later). Mg2Zn3 with finely size of about 0.6 μm could also be founded in this alloy. For the Mg-5Zn-0.083Gd alloy (Sample 14, Figure 3d), it mainly contained Mg2Zn3 besides a small amount of W-phase (confirmed by XRD analysis later).

The Typical Microstructures and Phase Structures
With the typical alloys (Samples as 35, 39, 10, and 14), the microstructures were investigated by SEM. From the second electronic image (SEI, Figure 3), Gd content effect on the microstructure of Mg-Zn-Gd alloys could be seen. With a higher Gd content, a larger amount of dendritic phase and more closed network microstructure would exist in alloys. While, with a lower Gd content, a dispersed and granular microstructure would exhibit. The microstructures of Mg-Zn-Gd alloys are coherent with our previous work [11][12][13][14][15] and literature [32,33]. To further identify the phase stoichiometry, EDS was carried out and listed in Table 2. For the Mg-1Zn-2Gd alloy (Sample 35, Figure 3a), the particle and dendritic phases have the similar Zn/Gd ratio and verified as W-phase (Mg 90.85±1.0 Zn 3.95±1.0 Gd 5.2±1.0 , at.%, confirmed by XRD analysis later). The matrix behaves as a supersaturated solid solution phase of α/-Mg. One lamellar phase, with 14H-phase, would appear from this matrix in by heat treatment, and it exhibits thermodynamic equilibrium and thermal stability [26,27]. The same stacking sequence was observed in annealed rapidly solidified (RS) Mg-1Zn-2Y alloys [23]. For Mg-1Zn-0.333Gd alloy (Sample 39, Figure 3b), there exists some granular phase verified as Mg 5 Gd and dendritic phase verified as W-phase (Zn/Gd ≈ 2, confirmed by TEM analysis later). For Mg-5Zn-0.278Gd alloy (Sample 10, Figure 3c), it reveals a larger amount of dendritic phase ascertained as I-phase with a composition of Mg 56.1±1.0 Zn 40±1.0 Gd 3.9±1.0 (at.%, Zn/Gd = 10.2, confirmed by TEM analysis later). Mg 2 Zn 3 with finely size of about 0.6 µm could also be founded in this alloy. For the Mg-5Zn-0.083Gd alloy (Sample 14, Figure 3d), it mainly contained Mg 2 Zn 3 besides a small amount of W-phase (confirmed by XRD analysis later).   Phases in special alloys were further characterized by TEM. For Mg-5Zn-0.278Gd alloy (Sample 10, Zn/Gd = 18, represented for region (III)), the dendritic phase is identified as I-phase ( Figure 4a). A slight lattice deviation from the ideal icosaheral symmetric positions is pointed out with the white arrow in the corresponding selected area electron diffraction (SAED)patterns (Figure 4b), owing to linear phason strains coming from its anisotropic growth during solidification [36]. Through the analysis of EDS, a composition of Mg30±1Zn62Gd8±1 (at.%) is adopted for I-phase. One another phase with triangular shape has also been observed ( Figure 4c) and identified as W / -phase by SAED patterns (Figure 4d). It has a composition of approximate Mg94±1Zn5.47±0.5Gd0.53±0.1 (at.%) and a face centered cubic (fcc) structure with a lattice parameter of a = 2.3529 nm. The lattice parameter of the W / -phase is triple as one of W-phase [13]. There is a cube-to-cube orientation relationship existing between W-phase and W / -phase, as (  Table 2. Energy-dispersal X-ray spectroscopy (EDS) analysis of the compounds in Mg-Zn-Gd alloys along with scanning electron microscopy (SEM) (D-Dendritic, P-Particle, M-Matrix). Phases in special alloys were further characterized by TEM. For Mg-5Zn-0.278Gd alloy (Sample 10, Zn/Gd = 18, represented for region (III)), the dendritic phase is identified as I-phase ( Figure 4a). A slight lattice deviation from the ideal icosaheral symmetric positions is pointed out with the white arrow in the corresponding selected area electron diffraction (SAED) patterns (Figure 4b), owing to linear phason strains coming from its anisotropic growth during solidification [36]. Through the analysis of EDS, a composition of Mg 30±1 Zn 62 Gd 8±1 (at.%) is adopted for I-phase. One another phase with triangular shape has also been observed ( Figure 4c) and identified as W -phase by SAED patterns (Figure 4d). It has a composition of approximate Mg 94±1 Zn 5.47±0.5 Gd 0.53±0.1 (at.%) and a face centered cubic (fcc) structure with a lattice parameter of a = 2.3529 nm. The lattice parameter of the W -phase is triple as one of W-phase [13]. There is a cube-to-cube orientation relationship existing between W-phase and W -phase, as ((100) W //(100) W , (010) W //(010) W , (001) W //(001) W ), which has been reported in our previous work [13] and by Luo [37]. W -phase is usually considered as 2/1 crystalline approximate to I-phase. For Mg-1Zn-0.333Gd alloy (Sample 39, Zn/Gd = 3, for region (II)), the skeleton morphology phase is W-phase (Figure 5a) Figure 5b-d, respectively. The W-phase has a composition of approximate Mg 31 Zn 45 Gd 24 (Zn/Gd = 1.9, at.%) and it is identified to have a face centered cubic (fcc) structure with a lattice parameter of a = 0.6927 nm. The lattice parameter of W-phase in Mg-1Zn-0.333Gd alloy (a = 0.6927 nm) is slightly larger than that in Mg-Zn-Y system (a = 0.6848 nm) [37]. Meanwhile, I-phase with particle shape is founded ( Figure 6). By the extrapolation technique described by Lorimer et al. [38], a composition of Mg 27.5±3.5 Zn 63.5±1.5 Gd 10±3 (at.%) is adopted to I-phase. For the Mg-1Zn-1Gd alloy (Sample 36, Zn/Gd = 1, represented for region (I)), two kinds of W-phase with dendritic or twist-like shape have been identified in Figure 7a For W-phase with the cubic structure ( Figures 5 and 7), a lower Zn/Gd ratio would result in a larger lattice parameter. W-phase has the similar face-centered cubic structure to Mg 3 Gd (m3m, a = 0.700 nm), and once been considered as Mg 3 Gd [39]. which has been reported in our previous work [13] and by Luo [37]. W / -phase is usually considered as 2/1 crystalline approximate to I-phase. For Mg-1Zn-0.333Gd alloy (Sample 39, Zn/Gd = 3, for region (II)), the skeleton morphology phase is W-phase ( Figure 5a) Figure 5b-d, respectively. The W-phase has a composition of approximate Mg31Zn45Gd24 (Zn/Gd = 1.9, at.%) and it is identified to have a face centered cubic (fcc) structure with a lattice parameter of a = 0.6927 nm. The lattice parameter of W-phase in Mg-1Zn-0.333Gd alloy (a = 0.6927 nm) is slightly larger than that in Mg-Zn-Y system (a = 0.6848 nm) [37]. Meanwhile, I-phase with particle shape is founded ( Figure 6). By the extrapolation technique described by Lorimer et al. [38], a composition of Mg27.5±3.5Zn63.5±1.5Gd10±3 (at.%) is adopted to I-phase. For the Mg-1Zn-1Gd alloy (Sample 36, Zn/Gd = 1, represented for region (I)), two kinds of W-phase with dendritic or twist-like shape have been identified in Figure 7a

The Effect of Zn/Gd Ratio on the Phase Formation
The effect of Zn/Gd ratio on the phase formation could directly obtained from the Figure 2 and Table 1. The phase formation regions in Mg-rich section are mainly decided by Zn/Gd ratio. When Zn/Gd = 0.25~1.5, the alloys mainly consist of α-Mg and W-phase In the Zn/Gd ratio range of 1.5~6, I-phase is detected as another main phase besides the α-Mg and W-phase. The quasi lattice parameter of the I-phase could be determined as approximately 0.520 nm by the Elser's method [39], with I-phase indexing from [40]. When Zn/Gd = 6~40, only α-Mg and I-phase exist. I-phase could not be founded in alloys with the Zn/Gd ratio up to 60. Moreover, Mg-5Zn binary alloy (Sample 15) is analyzed for comparison, it contains Mg2Zn3 and Mg7Zn3.
When Zn/Gd ratio of the alloys is between 0.25~6, the W-phase would form, but be of a different composition and with a changed lattice parameter. The Zn/Gd ratio in W-phase is ascribed with the one in alloy (Figure 8), which indicates that extra solute has occurred by the substitute or interstitial mode when W-phase precipitating. The cubic lattice parameter of W-phase could be deduced with the Bragg's law for the cubic crystal lattice [41]: where 2θ represents the degree of X-ray peak, λ represents the wavelength of Cu-Kα radiation, a represents the lattice parameter, and (hkl) represent crystal plane for 2θ. The mean a values of

The Effect of Zn/Gd Ratio on the Phase Formation
The effect of Zn/Gd ratio on the phase formation could directly obtained from the Figure 2 and Table 1. The phase formation regions in Mg-rich section are mainly decided by Zn/Gd ratio. When Zn/Gd = 0.25~1.5, the alloys mainly consist of α-Mg and W-phase In the Zn/Gd ratio range of 1.5~6, I-phase is detected as another main phase besides the α-Mg and W-phase. The quasi lattice parameter of the I-phase could be determined as approximately 0.520 nm by the Elser's method [39], with I-phase indexing from [40]. When Zn/Gd = 6~40, only α-Mg and I-phase exist. I-phase could not be founded in alloys with the Zn/Gd ratio up to 60. Moreover, Mg-5Zn binary alloy (Sample 15) is analyzed for comparison, it contains Mg 2 Zn 3 and Mg 7 Zn 3 .
When Zn/Gd ratio of the alloys is between 0.25~6, the W-phase would form, but be of a different composition and with a changed lattice parameter. The Zn/Gd ratio in W-phase is ascribed with the one in alloy (Figure 8), which indicates that extra solute has occurred by the substitute or interstitial mode when W-phase precipitating. The cubic lattice parameter of W-phase could be deduced with the Bragg's law for the cubic crystal lattice [41]: where 2θ represents the degree of X-ray peak, λ represents the wavelength of Cu-Kα radiation, a represents the lattice parameter, and (hkl) represent crystal plane for 2θ. The mean a values of W-phase in alloys have been calculated by six individual X-ray diffraction peaks (corresponding to (111), (200), (220), (311), (400), and (422), Table 3). The lattice parameter a W-phase deviates with the Zn/Gd ratio in W-phase is shown in Figure 9. It can be concluded that a W-phase could be a good index for the Zn/Gd ratio of alloys, with more sensitive in low Zn/Gd ratio range (from 0.25 to 1.5) than in the higher Zn/Gd ratio range (from 2 to 6).  Table 3). The lattice parameter aW-phase deviates with the Zn/Gd ratio in W-phase is shown in Figure 9. It can be concluded that aW-phase could be a good index for the Zn/Gd ratio of alloys, with more sensitive in low Zn/Gd ratio range (from 0.25 to 1.5) than in the higher Zn/Gd ratio range (from 2 to 6).    I-phase forms when Zn/Gd ratio in alloys is between 1.5~40, but Zn/Gd ratio in I-phase composition can be faintly effected by it. For example, eight points of I-phase in Mg-1Zn-0.33Gd alloy (Sample 39, Zn/Gd = 3) have confirmed by EDS analysis along with TEM ( Figure 10). Although Mg content ranges from 24 to 31, the Zn/Gd ratio is still close to 6, suggesting a standard stoichiometry of Mg 30 (Zn 6 Gd 1 ) 70 . Moreover, the composition of I-phase in other alloys, such as Mg-5Zn-0.278Gd (Sample 10, Zn/Gd = 18) or Mg-3Zn-0.3Gd (Sample 23, Zn/Gd = 10), is also quite approximate to the standard stoichiometry. In the other way, some alloys have the same Zn/Gd ratio (Table 4), but with different Zn/Gd ratio in I-phase. I-phase forms when Zn/Gd ratio in alloys is between 1.5~40, but Zn/Gd ratio in I-phase composition can be faintly effected by it. For example, eight points of I-phase in Mg-1Zn-0.33Gd alloy (Sample 39, Zn/Gd = 3) have confirmed by EDS analysis along with TEM ( Figure 10). Although Mg content ranges from 24 to 31, the Zn/Gd ratio is still close to 6, suggesting a standard stoichiometry of Mg30(Zn6Gd1)70. Moreover, the composition of I-phase in other alloys, such as Mg-5Zn-0.278Gd (Sample 10, Zn/Gd = 18) or Mg-3Zn-0.3Gd (Sample 23, Zn/Gd = 10), is also quite approximate to the standard stoichiometry. In the other way, some alloys have the same Zn/Gd ratio (Table 4), but with different Zn/Gd ratio in I-phase.  Figure 9. The lattice parameter a W-phase plotted as a function of Zn/Gd ratio in W-phase (Zn/Gd ratio in alloys range from 0.25 to 6, sample 45,35,28,21,18,5,6). Table 4. EDS analysis of I-phase in Mg-Zn-Gd alloys by using SEM.  The influence of Zn/Gd ratio on phase formation has been demonstrated above. Furthermore, the alloying element content in alloys plays indispensable roles, as shown in Figure 11. The higher content of alloying elements, under the same Zn/Gd ratio (Figure 11b-e) Zn/Gd = 10), would incline

The Effect of Alloying Element Content on the Phase Formation
The influence of Zn/Gd ratio on phase formation has been demonstrated above. Furthermore, the alloying element content in alloys plays indispensable roles, as shown in Figure 11. The higher content of alloying elements, under the same Zn/Gd ratio (Figure 11b-e) Zn/Gd = 10), would incline to form more I-phase, together with more binary compounds. This can be mainly associated with the tendency of segregation of residual liquid during solidification.

The DTA of Mg-Zn-Gd Alloys on the Mg-Rich Corner
The DTA analysis was carried out for Mg-Zn-Gd alloys. The DTA analysis of Mg-5Zn alloy (Sample 15) is also given as a comparison benchmark. The liquidus temperature for Mg-5Zn alloy was 613 °C, which agrees with that (610 °C) in the Mg-Zn binary phase diagram [39]. It indicates that there exists little loss of Mg and Zn elements in the melting process, which would just lead to a minor affection to the equilibrium temperature of alloys designed in this work.
The characterized temperatures were summarized in Table 5. TP, Tie, TW, and TL, represent the Mg-Zn-Gd alloy contain is less than 5%. The Gd content effect on microstructure could be gotten from Figure 3 (Sample 35, 29, 10, 24) and Figure 11 (Sample 45, 40, 23, 7, 1, 2). With a higher Gd content, a larger amount of dendritic phase and more closed network microstructure would exist in alloys. While, with a lower Gd content, a dispersed and granular microstructure would exhibit. Gd element is indispensable for I-phase formation. Although the alloy of different composition (Sample 23, 7, 1 with Zn/Gd = 10, and Sample 24, 11, 2 with Zn/Gd = 25), Gd content in these I-phase is approximate to 3 at.% (Table 4).
Since the high Zn content would result in fluidity decreasing, hot tear, and shrinkage porosity, commercial Mg-Zn-Gd alloy contain is less than 10 at.%. The SEI images of Mg-Zn-Gd alloys, in Zn content ascending, are shown in Figure 11. EDS was also carried out. For Mg-0.5Zn-2Gd alloy (Sample 45, Figure 11a), dendritic and strip shaped W-phases (Mg 87.4 Zn 8 Gd 4.6 , at.%, Zn/Gd = 1.74) are found, while the granular particles are confirmed to be Mg 3 Gd. For Mg-1Zn-0.1Gd alloy (Sample 40, Figure 11b), the MgZn particle and gray strip W-phase, in a small amount (not detected by XRD sensitivity), exist besides the I-phase. For Mg-3Zn-0.3Gd alloy (Sample 23, Figure 11c), the dendritic phase is confirmed as I-phase (Mg 75 Zn 21.5 Gd 3.5 , Zn/Gd = 6.14, at.%), while the particle phase in a small amount is verified as MgZn compound (not detected by XRD sensitivity). For Mg-5Zn-0.5Gd alloy (Sample 7, Figure 11d), I-phase exhibits dendritic and lamellar shape morphology having a composition of Mg 67.8-74.7 Zn 22.6-28.6 Gd 2.7-3.6 (at.%, Zn/Gd = 7.95~8.5). In addition, there exist W-phase particles having a composition of Mg 79.5 Zn 9.6 Gd 10.9 (at.%). For Mg-10Zn-1Gd alloy (Sample 1, Figure 11e), it contains MgZn and MgGd compounds other than I-phase. For the Mg-10Zn-0.4Gd alloy (Sample 2, Figure 11f), I-phase exhibits block or lamellar shape, having a composition of Mg 55.1 Zn 42.1 Gd 2.8 (Zn/Gd = 15, at.%). The BSE image of I-phase inset in Figure 11f shows the same contrast, which gives direct evidence for the homogeneity in chemical stoichiometry. The strip MgZn compound appears, as pointed with arrow in Figure 11f.

The DTA of Mg-Zn-Gd Alloys on the Mg-Rich Corner
The DTA analysis was carried out for Mg-Zn-Gd alloys. The DTA analysis of Mg-5Zn alloy (Sample 15) is also given as a comparison benchmark. The liquidus temperature for Mg-5Zn alloy was 613 • C, which agrees with that (610 • C) in the Mg-Zn binary phase diagram [39]. It indicates that there exists little loss of Mg and Zn elements in the melting process, which would just lead to a minor affection to the equilibrium temperature of alloys designed in this work.
The characterized temperatures were summarized in Table 5. T P , T ie , T W , and T L , represent the reaction of binary compound, I-phase, W-phase, and liquidus temperature of alloys, respectively. It should be noted that T ie and T W do not vary with the alloy composition change. However, T L would be quite different. The temperature interval between T L and T ie expressed as ∆T Li = T L − T ie , defined as equilibrium melting range. ∆T Li would largely affect the I-phase formability. The T L changing along with the alloy composition would be investigated in details, as follow: Figure 12 shows the heat trace of Mg-Zn-Gd alloys with different Zn/Gd ratio (Sample 45, 35, 5, 6, 7, 14, 15). As Zn/Gd ≤ 0.5, the Mg-Zn-Gd alloys exhibit similar melting behavior. Two major endothermic peaks are detected at 519 • C (T w ) and 655 • C (T L ). As Zn/Gd = 3, a new endothermic peak at 431 • C (T ie ) emerges other than those for T L (635 • C) and T w (519 • C). As Zn/Gd = 6, only endothermic peaks that were associated with T L (611 • C) and T is (431 • C) exist. When Zn/Gd = 10, besides endothermic peaks for T ie (431 • C) and T L (595 • C), one another endothermic peak at 341 • C (T p ) associated with binary compound emerges. When Zn/Gd = 60, there are only T p (366 • C) and T L (588 • C). It could be seen in Figure 12 that T L decreases as Zn/Gd ratio increasing. endothermic peaks are detected at 519 °C (Tw) and 655 °C (TL). As Zn/Gd = 3, a new endothermic peak at 431 °C (Tie) emerges other than those for TL (635 °C) and Tw (519 °C). As Zn/Gd = 6, only endothermic peaks that were associated with TL (611 °C) and Tis (431 °C) exist. When Zn/Gd = 10, besides endothermic peaks for Tie (431 °C) and TL (595 °C), one another endothermic peak at 341 °C (Tp) associated with binary compound emerges. When Zn/Gd = 60, there are only Tp (366 °C) and TL (588 °C). It could be seen in Figure 12 that TL decreases as Zn/Gd ratio increasing.   Figure 13 shows the heat trace of alloys with different alloying element content with Zn/Gd = 10 (Sample 1, 7, 48,). Mg-0.5Zn-0.05Gd alloy (Sample 48) only shows one endothermic peak at 655 • C corresponding to T L . For Mg-5Zn-0.5Gd (Sample 7) alloy and Mg-10Zn-1Gd (Sample 1) alloy two more endothermic peaks are identified, corresponding to T p (Mg 7 Zn 3 ) and T is , respectively. The endothermic peaks for Mg-10Zn-1Gd alloy are wider than the ones for the Mg-5Zn-0.5Gd alloy. T L (595 • C) of the former one is higher than T L (567 • C) of the later one. It could be seen in Figure 13 that T L decreases as the alloying element content increasing. The same phenomenon could also been found in the alloys with Zn/Gd = 5 in Table 5.
corresponding to TL. For Mg-5Zn-0.5Gd (Sample 7) alloy and Mg-10Zn-1Gd (Sample 1) alloy two more endothermic peaks are identified, corresponding to Tp (Mg7Zn3) and Tis, respectively. The endothermic peaks for Mg-10Zn-1Gd alloy are wider than the ones for the Mg-5Zn-0.5Gd alloy. TL (595 °C) of the former one is higher than TL (567 °C) of the later one. It could be seen in Figure 13 that TL decreases as the alloying element content increasing. The same phenomenon could also been found in the alloys with Zn/Gd = 5 in Table 5.  Table 5. Characteristic temperatures for Mg-Zn-Gd alloys in the differential thermal analysis (DTA) curves.

The Structure and Composition of I-Phase
The formation range of I-phase in Mg-Zn-Y system has been reported about in the Zn/Y ratio of 2.7~9.5 (at.%) [42]. While for Mg-Zn-Gd system in present study, the I-phase can be formed in the Zn/Gd ratio range of 1.5~40. It indicates that the Mg-Zn-Gd system has higher formability of I-phase as compared with Mg-Zn-Y system under the conventional cast condition. Furthermore, higher volume fraction of I-phase was formed in alloys that were containing higher alloying element  Table 5. Characteristic temperatures for Mg-Zn-Gd alloys in the differential thermal analysis (DTA) curves.

The Structure and Composition of I-Phase
The formation range of I-phase in Mg-Zn-Y system has been reported about in the Zn/Y ratio of 2.7~9.5 (at.%) [42]. While for Mg-Zn-Gd system in present study, the I-phase can be formed in the Zn/Gd ratio range of 1.5~40. It indicates that the Mg-Zn-Gd system has higher formability of I-phase as compared with Mg-Zn-Y system under the conventional cast condition. Furthermore, higher volume fraction of I-phase was formed in alloys that were containing higher alloying element content under same Zn/Gd ratio. As reported previously, the volume fraction of I-phase plays an important role in the properties of alloys, such as Mg-Zn-Y [43] and Mg-Zn-Ho [44]. Singh et al. [19] has dominated strengthening mechanism when I-phase content varied. Meanwhile, our previous results also indicated that the mechanical properties of Mg-Zn-Gd alloys varied with its phase constitutions, such as the I-phase and Laves phase [44]. Therefore, the anticipated mechanical properties of Mg-Zn-Gd alloy can be obtained by adjusted the fraction of I-phase and phase constitution with the help of the diagram, as demonstrated in Figure 2.
Tsai et al. [45] has investigated I-phase in Mg-Zn-RE (RE=Gd, Tb, Dy, Ho, Er) systems using XRD and TEM. The structure type of I-phase in Mg-Zn-RE systems has been classified in the view of quasi lattice parameter and valence electron concentration (e/a). The as-cast alloy with the nominal composition of Mg 42 Zn 50 Gd 8 (at.%) has been proved to be a single I-phase by Tsai et al., but the real stoichiometry of I-phase has still not been detected. The I-phase in Mg-Zn-Gd alloys exhibits a stoichiometry of Mg 30±1 Zn 62 Gd 8±1 (at.%) in present work, and the average composition (at least three points) of I-phase in each sample was determined by EDS along with TEM or SEM. The icosahedral quasi crystals are generally classified into two groups, depending on the cluster structures [46]. Mackay-icosahedral clusters (MI-type) has a lattice parament of a = 4.6 Å and the e/a about 1.75. The rhombic-triacontahedron clusters (FK-type) is the other one, having a quasi lattice of a = 5.2 Å and the e/a about 2.1. Table 6 lists the data about e/a, atomic radii, and element electronegativity of I-phase. Zn and Mg element have the same value of e/a about 2, while the Gd element has the value of e/a about 3. Therefore, the content of Gd element plays a significant role in the value of e/a of I-phase. When the content of Gd of I-phase exhibits a relatively settled range of 8 ± 1 at.%, it would result in the e/a value between 2.06 to 2.1, which was nearly matching with the FK-type. In the view of atomic size, the value of δ (δ = (r A − r B )/r A ) for Zn/Mg is about 16.8%, which exceeded the limits of the solubility. The literature [44] has reported that the 5 at.% Zn replacement by Mg in Mg-Zn-Y quasicrystalline phase would induce an expansion of the lattice, which confirmed the dissolution of Zn in the quasicrystalline phase. This means that the replacement between Mg and Zn in I-phase has been restricted. In the aspect of electronegativity, Zn, Mg, and Gd is about 1.65, 1.31, and 1.1, respectively. The large difference in electronegativity among Mg, Zn, and Gd, gives an indirect evidence of the high stability of I-phase. Since the configuration of I-phase can be elucidated with valence electron concentration, atomic size, and electronegativity, the formation and stability of I-phase could be understood within the frame work of the Hume-Rothery rules. However, it is still unclear that why the chemical stoichiometry of I-phase would be different, i.e., formed during casting processing (Mg 30±1 Zn 62 Gd 8±1 , at.%), nano-size formed during hot extrusion (Mg 40 Zn 52 Gd 8, at.%) [13]. The equilibrium solidification range ∆T Li changes with the composition of alloying (Table 5), and ∆T Li would largely affect the I-phase formability. J. Grobner, et al. [34] also pointed out that the formation of I-phase should largely depend on the composition range of alloys with certain thermodynamic conditions. However the nucleate kinetics of I-phase still needs to be studied further.

The Structure and Composition of W-Phase
The W-phase with fcc structure in Mg-Zn-Gd system can be formed in the Zn/Gd ratio range of 0.25-6. This kind of W-phase was firstly determined by E. M. Padezhnova et al. [28] by X-ray diffraction in the Mg-Zn-Y system. It possesses a partially ordered AlMgCu 2 -type fcc structure: a = 0.6848 nm and its space group is m3m [37]. The crystal structure of the W-phase in the Mg-Zn-Y system was shown in Figure 14. It can be found that four Y atoms occupy the 4A positions, four Mg atoms occupy the 4B positions, and eight (Mg+Zn) atoms, with the ratio of 1:3, occupy the 8C positions. When Gd atom instead of Y atom, the W-phase exhibits a larger lattice value due to the larger atomic size (r Gd = 0.181 nm, r Y = 0.178 nm). Meanwhile, the lattice parameter a of the W-phase is very sensitive to the composition of Mg-Zn-Gd alloys, especially when affected by the Zn/Gd ratio of alloys. The Gd solution would induce the lattice expansion. W-phase would transform into another compound under certain condition by the diffusion and rearrangement. This has been verified by its disappearance and transformation to the 14H phase during the heat-treatment at 773 K, as reported by M. Yamasaki [26]. The similar phenomenon occurred in the Mg-Zn-Y system [23,28]. The X-phase with 18R-type structure, in as-cast Mg-Zn-RE-Zr alloy with low content of Zn and high content of RE, transformed into the 14H LPSO structure through certain heat treatment procedure [47]. In addition, the occurrence of W-phase in Mg-Zn-Gd alloy indirectly reveals that W-phase would transform under some condition. 0.6848 nm and its space group is m m 3 [37]. The crystal structure of the W-phase in the Mg-Zn-Y system was shown in Figure 14. It can be found that four Y atoms occupy the 4A positions, four Mg atoms occupy the 4B positions, and eight (Mg+Zn) atoms, with the ratio of 1:3, occupy the 8C positions. When Gd atom instead of Y atom, the W-phase exhibits a larger lattice value due to the larger atomic size (rGd = 0.181 nm, rY = 0.178 nm). Meanwhile, the lattice parameter a of the W-phase is very sensitive to the composition of Mg-Zn-Gd alloys, especially when affected by the Zn/Gd ratio of alloys. The Gd solution would induce the lattice expansion. W-phase would transform into another compound under certain condition by the diffusion and rearrangement. This has been verified by its disappearance and transformation to the 14H phase during the heat-treatment at 773 K, as reported by M. Yamasaki [26]. The similar phenomenon occurred in the Mg-Zn-Y system [23,28]. The X-phase with 18R-type structure, in as-cast Mg-Zn-RE-Zr alloy with low content of Zn and high content of RE, transformed into the 14H LPSO structure through certain heat treatment procedure [47]. In addition, the occurrence of W-phase in Mg-Zn-Gd alloy indirectly reveals that W-phase would transform under some condition.  The study of Mg-Zn-Y alloys [48][49][50][51] indicated that the existence of W-phase was unfavorable to the mechanical properties of as-extruded alloys. Thus, the formation range of the W-phase should be avoided during the design of I-phase strengthening Mg-Zn-Gd as-extruded alloys.

Conclusions
The formation range of I-phase and W-phase of Mg-Zn-Gd alloy in the Mg-rich section has been explored. The effect of Zn/Gd ratio and the alloying element content on phase constituents has been systematically elucidated. Results that were obtained in the present work can be summarized, as follows: (1) Five regions can be classified in this Mg-rich section: (I)α-Mg+W-phase(+binary compounds), (II)α-Mg+W-phase+I-phase(+binary compounds), (III)α-Mg+I-phase (+binary compounds), (IV)α-Mg+binary compounds, and (V)α-Mg. This diagram of phase constitution would give a guideline for the design of Mg-Zn-Gd alloys to match the expecting properties by obtaining the desired phase components. (2) The I-phase in Mg-Zn-Gd alloys has a composition of Mg 30±1 Zn 62 Gd 8±1 (at.%), belonging to FK-type quasicrystalline phase in terms of the Hume-Rothery rules. I-phase can be formed in Zn/Gd ratio range of 1.5~40. The equilibrium solidification range of ∆T Li is boarded when Zn/Gd ratio or alloying element content decrease, and it would largely influence the formability of the I-phase. (3) The W-phase in Mg-Zn-Gd alloy has fcc structure with the space group m3m. It can be formed only in the Zn/Gd ratio range of 0.25~6. The composition of the W-phase is very sensitive to the composition of Mg-Zn-Gd alloys.