3.1.1. Peritectic Reaction

According to Mg-Zr binary phase diagram, Zr and Mg do not form compounds, and there is a peritectic reaction at 653.5 ◦C. The peritectic reaction leads to Mg nucleation at the primary Zr-rich sites, which plays a very important role in the grain refinement process of Mg by Zr [10,13,39]. The peritectic point of Zr composition was previously found to be 0.6% Zr. However, re-assessment shows that it is substantially lower, at about 0.45% [4]. Thus, it is possible to use a smaller amount of Zr, thus reducing the cost of grain refinement [40].

Table 2 presents a comparison between the crystal structures of Mg and Zr, indicating that both α-Zr and α-Mg have HCP crystal structures, and their lattice parameters are quite similar. Thus, Zr has outstanding potency for acting as a nucleation substrate for Mg phase [41]. The perfect nucleation ability of Zr can be further verified by low undercooling (Δ*Tn* ≈ 0.15 ◦C [42]) equal to that for Al grains nucleating on TiB2 substrates (~0.2 ◦C [43]).

**Table 2.** The crystal structure and lattice parameters of Mg and Zr [41].


Figure 3 shows an example demonstrating that 0.5% Zr content can strongly refine the grains of Mg alloy, where the grain size of WE54 Mg alloy (Mg-5Y-4HRE-0.5Zr, HRE = heavy rare earth elements) was refined from 295 μm to 83 μm [44] under the conditions of pouring at about 780 ◦C into a steel mold preheated to 300 ◦C. This content of Zr is basically in accordance with the peritectic point in the Mg-Zr phase diagram. The simulation work performed by Zhao et al. [45] further showed that the growth velocity of dendrite tip of Mg-4Y alloy can be reduced to be one-sixth (1/6) using 0.5Zr, forming a fine grain size. However, this perspective still requires further evidence.

**Figure 3.** An example showing the powerful effect of grain refinement with Zr on Mg alloy. Electron backscattered diffraction technology (EBSD) image of: (**a**) Zr-free WE54 alloy; (**b**) Zr-containing WE54 alloy. Poured at 780 ◦C into a steel mold (300 ◦C). Reprinted with permission from ref. [44]. Copyright 2013 Elsevier.

In early work, it was thought that only the dissolved Zr was effective for grain refinement, because saturated dissolved Zr content meets the standards of a peritectic composition. However, later work verified that Mg grains can nucleate not only onto Zr particles precipitating from the melt during cooling, but also onto undissolved Zr particles through heterogeneous nucleation [4,31,38,46]. The products of peritectic solidification in the microstructure of Zr-containing Mg alloy are Zr-rich halos or cores, present in most Mg grains, as shown in Figure 4 [26,37]. The Zr-rich halo shows either dendritic or nearly spherical growth, depending on the soluble Zr content. A higher level of soluble Zr (close to the solubility) usually leads to spherical halo, while a lower level of soluble Zr leads to a dendritic halo [38].

**Figure 4.** SEM BSE image of Zr-rich cores in: (**a**) Mg-0.56Zr alloy [37]; Reprinted with permission from ref. [37]. Copyright 2002 Elsevier. (**b**) Mg-5Gd-1.5Y-0.55Zr alloy [26]; Reprinted with permission from ref. [44]. Copyright 2013 Wiley.

#### 3.1.2. HRTEM Observations of Zr Nucleus

To facilitate the understanding of the grain refinement mechanism, the orientation relationships (ORs) between Mg grains and Zr nuclei were observed via high-resolution transmission electron microscopy (HRTEM). Table 3 summarizes some of the reported coherent or semi-coherent ORs in grain-refined Mg alloys [23,47–51]. All the ORs have low misfits, which are responsible for the good nucleating potency of Zr. For example, the misfit of OR 1213 *Mg* 1213 *Zr* + 1212 *Mg* ∧ 1◦ 1212 *Zr*, OR 2110 *Mg* 2110 *Zr* + (0001)*Mg* (0001)*Zr* and OR 0111 *Mg* 0111 *Zr* + 1011 *Mg* 1011 *Zr* is only 0.13% [47], 0.9% [49] and 0.41% [50], respectively. Figure 5 shows a typical example of OR 2110 *Mg* 2110 *Zr* + 0111 *Mg* 0111 *Zr* observed in the sand-cast Mg-8Gd-3Y-0.82Zr alloy [23].



<sup>1</sup> In Table 3, ∧—tilted directions; —parallel directions; IMS—intensive melt shearing; HPDC—high-pressure die casting.

**Figure 5.** TEM showing OR between Mg matrix and Zr nucleus in Mg-8Gd-3Y-0.82Zr alloy: (**a**) bright-field image; (**b**) dark-field image; (**c**) enlarged view of the selected area in (**a**); (**e**) HRTEM image of the interface between Mg matrix and Zr nucleus (beam 2110 *Zr*); (**d**,**f**) fast Fourier transform (FFT) spectrum of α-Zr and α-Mg, respectively; (**g**) EDS analysis of Zr nucleus. Reprinted with permission from ref. [23]. Copyright 2021 Elsevier.

With the analysis of HRTEM and the selected area diffraction pattern (SADP), Saha concluded that Mg grains only nucleate on the "faceted" crystal planes of Zr particles [47,48], e.g., the basal planes {0001} or the prismatic planes 1010 . However, contradicting Saha, Peng et al. [49] found that the interface between the Zr nucleus and the Mg matrix was "curved" rather than "faceted". The curved interface, in combination with coherent ORs, provides perfect lattice matching along various directions and across various planes, benefitting the nucleation of Mg grains on the Zr particle surface.

Although various ORs have been reported, as shown in Table 3, Yang et al. [51] suggested that very strict ORs are not required for Zr nuclei, because Zr particles may be wetted by Mg melt on all exposed crystal planes. This viewpoint was validated by HRTEM observations in Ref. [49], as shown in Figure 6 [51]. Perfect coherent ORs can be observed, among which even the slightly higher index OR 2423 *Mg* 2423 *Zr* + 1010 *Mg* 1010 *Zr* is present, which is similar to that described in Ref. [27]. Thus, α-Mg grains can grow epitaxially on any suitable planes of Zr nuclei. Recently, in-situ neutron diffraction observations have provided further evidence of the grain refinement mechanism of Zr, showing that with the addition of Zr, all of the diffraction intensities of the 1010 , (0002) and 1011 planes of Mg-5Zn-0.7Zr alloy increase at similar rates during the early stages of solidification, leading to the formation of a uniform grain structure [52].

**Figure 6.** HRTEM images showing: (**a**) faceted interface; (**b**–**d**) curved interfaces between α-Mg grains and Zr nuclei in Mg-0.1Zr alloy along four different low-index zone axes. (**e**) Stereographic projection of *HCP* structure showing the various ORs (**a**–**d**) within a 90◦ range [51]. Reprinted with permission from ref. [51]. Copyright 2015 Elsevier.

## *3.2. Constitutional Supercooling (CS) Effect*

Zr can affect both the nucleation and the growth of the dendritic phase in Mg alloy depending on its status in the melt [53]. When the addition of Zr content is higher, grain refinement can be achieved due to the large number of Zr nucleating particles. When the addition of Zr is low, an obvious grain refinement effect can still be observed. This is mainly due to the strong CS effect of solute [4,10,26,43,54–56], since Zr is also a solute element in the Mg-Zr system. The growth restriction factor (*GRF*, *Q*) is defined as follows to reflect the CS effect [4,43,54]:

$$Q = m(k-1)\tag{2}$$

where *m* is the liquidus gradient and *k* is the partition coefficient. The larger the *Q* value is (unit K or ◦C), the stronger the grain refinement effect will be. On the basis of phase diagram analysis, the *Q* value of Zr was calculated to be 38.29, which is much higher than that of most of the alloying elements, such as Al (4.32), Y (1.70), Zn (5.31), etc. [4,11], indicating that soluble Zr produces a strong grain refinement effect [1,4]. Peng et al. [57] proved that the grain refinement of Mg-9Gd-3Y-0.25Zr alloy (low Zr) was mainly contributed by the *GRF* effect, while the grain refinement of Mg-9Gd-3Y-0.51Zr alloy (high Zr) was mainly contributed by the heterogeneous nucleation of Zr particles. The CS effect of Zr was recently verified by Zhang et al. [57]. As shown in Figure 7, remarkable grain refinement (from 74 μm to 3.5 μm) occurred in the melt pool of the laser-surface-remelted (LSR) Mg-3Nd-1Gd-0.5Zr alloy, which was mostly due to the high CS effect of soluble Zr caused by LSR.

**Figure 7.** SEM BSE images of the laser-remelted Mg-3Nd-1Gd-0.5Zr alloy showing the microstructure of: (**a**) the substrate; (**b**) the melt pool, the cross-section EBSD analysis of which is included as an inset in the upper-right corner [58]. Reprinted with permission from ref. [58]. Copyright 2020 Elsevier.

In summary, the nucleation effect combined with the CS effect leads to a high nucleation rate and low undercooling, resulting in the powerful effect of grain refinement with Zr. Such effects are not only of benefit to achieving equiaxed grains during the casting process, they also facilitate the formation of slurries with fine and spherical primary particles during the semi-solid forming process [59,60].

#### **4. Factors Influencing the Grain Refinement Behaviors of Zr**

This section briefly summarizes the effects that influence the Zr alloying efficiency during the melting process.
