*3.1. Microstructure Characteristic*

Figure 2 reveals the surface morphologies and EDS analyses of the as-cast Mg-RE alloy ingot. It can be seen from Figure 2a that acicular intermetallic compounds crystallize in the Mg-RE alloy ingots. Figure 2b presents the combined EDS results, and the acicular compound crystallization in the red rectangle contains higher contents of Ce elements. Figure 3a presents the microstructure of the Mg-RE alloy sheet at a thickness of ~1.1 mm and a width of ~50 mm obtained at the casting speed of 30 m/min, in which the microstructure of the Mg-RE alloy sheet is characterized by dendrites of fine grains and a closely spaced secondary dendrite axis. Apart from that, as shown by the red rectangular area in Figure 3a, it can be seen that there are portions where no appreciable crystalline features can be observed. Figure 3c shows the XRD patterns of the studied alloys. It can be concluded that the as-cast Mg-RE alloy sheets (Figure 3a) consisted mainly of α-Mg, La-Al and Ce-Al, and it is worth noting that a broad peak appears at the angle of 20◦~30◦, indicating that the sample may contain both crystalline and amorphous phases.

**Figure 2.** SEM morphologies (**a**) and the precipitation by EDS analysis (**b**) of as-cast Mg-RE alloy ingot.

The crystallite size of each detected phase in Figure 3c could be calculated using the Scherrer equation, which is expressed by *Dhkl* = *K*λ/*Bhkl cos*θ [26], where *Dhkl* is the grain size perpendicular to the lattice planes, *hkl* are the Miller index of the planes being analyzed, *K* is a constant numerical factor called the crystallite-shape factor, λ is the wavelengths of the X-rays, *Bhkl* is the width of the X-ray di ffraction peak in radians and θ is the Bragg angle. The calculated results are listed in Table 2. It turns out that the grain sizes of the detected phase are very fine. However, the X-ray tube on the line focus side is unsuitable for analyzing such a specific area without crystals, as shown in Figure 3a, as the line focus range is 0.1~0.2 mm wide and 8~12 mm long [27]. To solve these problems, the structure of the areas without crystals was analyzed by means of micro area X-ray di ffraction. In the current operation, a collimator that was 0.03 mm in diameter was situated at the point focus side of the X-ray tube. Therefore, very small specific areas could be analyzed without reflecting unnecessary regional structural information. Figure 3d displays the μ-XRD of the areas without crystals of the Mg-RE sheet. The amorphous structure was determined by a peak that does not correspond to any sharp crystalline peak. As shown in Figure 3b and Table 2, very fine grains and dendrites with closely spaced secondary dendrite axes can be found around a large amorphous region.

Figure 4 shows the solute element distribution of Mg-RE with TRC. It can be seen that Mg elements are evenly distributed along the matrix, while Al/Ce/La are concentrated in amorphous areas. In addition, Al, Ce, La element segregation exists between crystal phase and the amorphous region. Meanwhile, the grain boundary is prone to segregation, because the relative atomic radius di fference (ARDMg) between Mg and other elements is more than 10% [28], as shown in Table 1. It can also be found that Al, Ce and La elements are enriched in the amorphous phase region, which may be related to the fact that the alloy is prone to producing very stable Al-RE compounds under the solidification condition of low cooling rate. Figure 5 presents the values of enthalpy of mixing (Δ*Hmix* [*AB*]) calculated by Miedma's model for atomic pairs between major elements of Mg-RE sheet samples, in which the enthalpy of mixing between Mg-Al, Mg-La and Mg-Ce are −2 KJ/mol, −7 KJ/mol and −7 KJ/mol, respectively, while the enthalpy of mixing between Al-La and Al-Ce are −38 KJ/mol, which is greater than that between Mg and other major elements [29]. The design of Mg-RE alloy conforms to the three rules summarized by Inoue et al. [30] for the glass forming ability (GFA) of alloys: first, a multi-component system consisting of more than three major elements; second, the difference in atomic size between major elements is large (greater than 10%), and in line with the relationship of large, medium and small; third, the mixed heat between the main elements is a suitable negative value. In other words, Mg-RE alloy has good glass-forming ability.

**Table 2.** Crystallite sizes of the Mg-RE alloy sheet, calculated by Scherrer equation.

**Figure 3.** The SEM micrographs and X-ray diffractometry (XRD) patterns of as-cast Mg-RE sheet: (**<sup>a</sup>**,**<sup>c</sup>**) SEM micrographs and XRD of the Mg-RE sheets. (**b**,**d**) SEM micrograph and μ-XRD of local amorphous region.

**Figure 4.** The major element distribution of the Mg-RE alloy sheet with TRC samples.

**Figure 5.** The values of Δ*Hmix* [*AB*] (KJ/mol) calculated by Miedma's model for atomic pairs between major elements of Mg-RE sheet samples.

To ascertain the amorphous phase structure, many initial specimens were prepared using the FIB technique, and TEM observation was further performed. Figure 6c shows that the first step of TEM sample preparation is to find the amorphous phase on the surface of the sample in the SEM diagram, and then cut the specific phase area with FIB technology which make the cutting area length was 30~60 μm. Figure 6a presents the cross section of the sample is sliced by FIB technique. Since part of the sample was cut with FIB on the surface, it is easy to find the section position to be cut. The sample was cut into steps, originally, and a slice thickness of 0.1 μm was ultimately prepared, as shown in Figure 6b. Figure 6d presents the TEM image and selected area diffraction pattern (SADP) of the amorphous phase, in which amorphous circular halos are not distinctly visible, and a poor crystallinity is shown, although few spots of electron diffraction exist. This may be due to the small size of the amorphous phase in the current TEM sample or the slight oxidation of the Mg-RE alloy sheet after cutting by FIB technology.

**Figure 6.** (**<sup>a</sup>**,**b**) TEM specimen by FIB technique of Mg-RE sheet with TRC; (**c**) SEM and FIB processing area on the Mg-RE sheet surface; (**d**) TEM image and high-resolution morphology.
