Atomic Interaction Mechanism of Heterogeneous Nucleation in Mg-Al Alloys Achieved by Carbon Inoculation

Abstract

Theoretical calculations were performed to explore the heterogeneous nucleation mechanism of an Mg-Al alloy inoculated by a carbon-containing substance. The valence electron structure and cohesive energy of Al₄C₃ and Al₂C₂Mg crystals were calculated using the empirical electron theory of solids and molecules (EET). The binding energy of Al1-C2 bonds in Al₄C₃ is about 140.6 kJ/mol with a lower number of equivalent bonds. Correspondingly, the binding energy of Al2-C2 bonds is about 129.6 kJ/mol, and the number of equivalent bonds is high. The weak combination of the Al1 and C2 atomic layers might lead to the breaking of Al₄C₃, and then the remaining strong skeleton of the Al2-C2 structure will facilitate the formation of Al₂C₂Mg. Based on the calculating results, the atomic interaction mechanism to account for the heterogeneous nucleation of α-Mg by C inoculation is elaborated, which also provides insights into the essence of the overheating process and the influence of Al and Mn elements on the refinement efficiency of Al₂C₂Mg.

1. Introduction

Mg-Al alloy is one of the most widely used magnesium alloys; its conventional as-cast microstructure is coarse and its mechanical properties are relatively low. Thus, it is a necessary method for causing the heterogeneous nucleation of α-Mg by adding a refining agent into the Mg-Al melt, which eventually contributes to refining the matrix grain size and improving the mechanical properties of Mg-Al alloys [1,2,3]. However, unlike aluminum alloys or magnesium alloys without the Al element, due to a lack of in-depth understanding of heterogeneous nucleation mechanisms, a reliable, efficient, and environment-friendly commercial refining agent for Mg-Al serial alloys has not yet been successfully developed [4,5,6].

As early as 1945, Davis originally found that carbon-containing substances have a significant refining effect on Mg-Al alloys [7], and since then, considerable efforts had been performed on this topic to reveal the grain refinement mechanisms of the carbon-refining method for nearly a hundred years. Compared to the segregation mechanism of the C element at α-Mg grain boundaries [8], the heterogeneous nucleation mechanism of carbide for α-Mg is more accepted, and the reason for this heterogeneous nucleation hypothesis supported by many investigators is because of the similarity of crystallographic characteristics between Al₄C₃ and α-Mg [9,10,11,12]. However, it seems no Al₄C₃ substance was found in the center of α-Mg and eventually in the Mg-Al alloy [13]. In addition to Al₄C₃, Huang [14] determinately found another carbide, i.e., ternary carbide Al₂C₂Mg, in the center of α-Mg when the Mg-Al alloy was inoculated by SiC, of which the lattice constant is smaller in comparison with that of α-Mg. Therefore, to date, there is still significant controversy regarding whether the heterogeneous nucleus of α-Mg is Al₄C₃ or not.

In addition, whether C-containing substances can refine the grain size of Mg-Al alloys is also related to the alloy composition and refining process conditions. As expected, aluminum as the main alloying element has an obvious effect on the refining efficiency of carbon inoculation. Mg-Al alloy with a small amount of Al content, can be well refined by a carbon agent, but the Mg-Al alloy with high Al content cannot be refined [15]. As to the influence of the Mn element on the refining efficiency of carbide, adding a small amount of Mn not only has no negative effect on the grain refinement results but also can solve the problem and facilitate the refining effect of the carbon agent for Mg-Al alloys with high Al contents [16]. However, when the Mn content exceeds a certain value, adding Mn will deteriorate the refining ability of carbide [17]. Kim [18] proposed that Al₈Mn₅ formed on the surface of Al₄C₃ can become a heterogeneous core of α-Mg; thus, the grain-refining mechanism of Mn-containing Mg-Al alloys by carbon inoculation can be characterized as duplex nucleation (Al-containing carbides→Al₈Mn₅→α-Mg). On the contrary, many researchers insist that the formation of Al₈Mn₅ will interfere with the grain-refining efficiency of Al₄C₃ particles [19,20]. This is clearly a contradictory explanation that accounts for both the coarsening and refining of Al₈Mn₅, which cannot simply lead to a conclusion regarding whether Al₈Mn₅ is a heterogeneous core of α-Mg instead of Al₄C₃. The influence mechanism of Mn on carbide efficiency should be analyzed in depth at the atomic level based on the refinement mechanism of carbon inoculation. Although the influence mechanisms of Al and Mn element contents have not yet been reasonably explained, from which we can at least indicate the similarity of the atomic arrangement structure between Mg and carbide, it seems to not be the only and sufficient criterion for the heterogeneous nucleation of α-Mg.

It is worth noting that compounds such as TiC, TiB₂, and AlB₂ are also disabled for refining most aluminum alloys [21,22,23] in spite of satisfying the condition of an atomic arrangement misfit. Therefore, it seems that there are other key factors that affect and determine whether heterogeneous nucleation can eventually proceed or not. At present, all the mechanisms of heterogeneous nucleation only focus on the geometric conditions of nucleation [24]; few have considered the initial process of heterogeneous nucleation, i.e., the atomic interactions between C-containing particles and Mg–Al liquid at the atomic level, especially the influence of melting temperature and composition on the heterogeneous nucleation process.

This study used the empirical electron theory (EET) of solids and molecules to calculate the valence electron structure and cohesive energy of Al₂C₂Mg and Al₄C₃. Based on the analysis of calculation results, a new atomic interaction mechanism of heterogeneous nucleation during the solidification of Mg-Al melt was proposed to insightfully clarify the essence of heterogeneous nucleation by paying specific attention to the atomic interactions between the liquid phase and the heterogeneous particle. Moreover, the affecting mechanisms of alloying components and refining processes on the refining efficiency of carbide particles were further elaborated.

2. Calculation Method

2.1. Calculations of Valence Electron Structure (VES) of Al₂C₂Mg and Al₄C₃

The VES in EET generally includes the covalent bonds formed by different atoms, the electron distribution on covalent bonds, and the atomic states, and the VES analysis models of Al₂C₂Mg and Al₄C₃ are shown in Figure 1.

The VES parameters of Al₂C₂Mg and Al₄C₃ can be calculated with the bond length difference (BLD) method [25,26] in EET. In this paper, we take the Al₂C₂Mg structure unit as an example, and the detailed calculation steps of the VES of Al₂C₂Mg are given as follows.

Al₂C₂Mg has a non-close packed hexagonal lattice similarly to Mg and Al₄C₃; its lattice constants are a = b = 0.3377 nm, c = 0.5817 nm; each unit cell contains 1 magnesium atom, 2 carbon atoms and 2 aluminum atoms, and the other calculation parameters of Al₂C₂Mg and Al₄C₃ are both listed in

Table 1. Inputted parameters for the VES calculation of Al₂C₂Mg and Al₄C₃ compound.

Chemical Formula	Space Group	Lattice Constants /nm	Atomic Parameters
			Atoms	Wyckoff Sites	x/a	y/b	z/c
Al2C2Mg	$R\overline{3}m1$ (164)	a = 0.3377 c = 0.5817	Mg	1a	0	0	0
			Al	2d	1/3	2/3	0.3773
			C	2d	1/3	2/3	0.7346
Al4C3	$R\overline{3}m$ (166)	a = 0.3335 c = 2.4967	Al1	6c	0	0	0.29422
			Al2	6c	0	0	0.12967
			C1	3a	0	0	0
			C2	6c	0	0	0.2168

.

In order to calculate the VES, the hybridization states and single-bond radius (SBR) of the Al, C, Mg three atoms need to be calculated first. This calculation process and results can be referred to in reference [24]. There are nine kinds of covalent bonds in the Al₂C₂Mg structure unit. The covalent bond name (CBN, $B_{\alpha }^{u-v}$, here, u and v, respectively, denote the atoms forming α covalent bonds), experimental bond length (EBL, $D_{n\alpha }^{u-v}$), and equivalent bond number (EBN, $I_{\alpha }$) are shown and calculated as follows.

$$\begin{array}{c}{B}_{n1}^{Mg-C}, D_{n1}^{Mg-C}=0.24862\mathrm{nm}, I_1={\displaystyle \frac{1}{5}}\times 2\times 6=2.4\\ B_{n2}^{Mg-Al}, D_{n2}^{Al2-C2}=0.29357\mathrm{nm}, I_2={\displaystyle \frac{1}{5}}\times 2\times 6=2.4\\ B_{n3}^{Mg-Mg}, D_{n3}^{C1-Al1}=0.3377\mathrm{nm}, I_3={\displaystyle \frac{1}{5}}\times 6\times 1=1.2\\ B_{n4}^{Al-\mathrm{C}}, D_{n4}^{C2-Al2}=0.20555\mathrm{nm}, I_4={\displaystyle \frac{2}{5}}\times 2\times 3=2.4\\ B_{n5}^{Al-\mathrm{C}}, D_{n5}^{Al2-Al2}=0.20784\mathrm{nm}, I_5={\displaystyle \frac{2}{5}}\times 2\times 1=0.8\\ B_{n6}^{Al-Al}, D_{n6}^{Al1-Al1}=0.24164\mathrm{nm}, I_6={\displaystyle \frac{2}{5}}\times 3\times 1=1.2\\ B_{n7}^{Al-Al}, D_{n7}^{Al2-Al1}=0.3377\mathrm{nm}, I_7={\displaystyle \frac{2}{5}}\times 1\times 6=2.4\\ B_{n8}^{C-C}, D_{n8}^{C2-C2}=0.33542\mathrm{nm}, I_8={\displaystyle \frac{2}{5}}\times 1\times 3=1.2\\ B_{n9}^{C-C}, D_{n9}^{C-\mathrm{C}}=0.3377\mathrm{nm}, I_9={\displaystyle \frac{2}{5}}\times 1\times 6=2.4\end{array}$$

Here, the $I_{\alpha }=I_{\mathrm{M}}\cdot I_{\mathrm{S}}\cdot I_{\mathrm{K}}$ formula is used to calculate EBN parameters, and the meaning of $I_{\mathrm{M}}$, $I_{\mathrm{S}}$ and $I_{\mathrm{K}}$ can be found in Ref. [26].

In EET, every covalent bond should follow the bond length equation, i.e.,

$$D_{n\alpha }^{u-v}=R_u(I)+R_v(I)-\beta \lg n_{\alpha }$$

(1)

where $R(I)$ represents the single-bond radius (SBR) of atoms; $n_{\alpha }$ is the shared electron pair number of the α covalent bond; β is a constant and its value represents the interaction potential between electrons.

According to the above bond length equation shown in Equation (1), the special bond length equations of the Al₂C₂Mg crystal structure can be expressed as follows.

$$\begin{array}{c}{D}_{n1}^{Mg-C}=R_C\left(I\right)+R_{Mg}\left(I\right)-\beta \lg n_1\\ D_{n2}^{Mg-Al}=R_{Al}\left(I\right)+R_{Mg}\left(I\right)-\beta \lg n_2\\ D_{n3}^{Mg-Mg}=R_{Mg}\left(I\right)+R_{Mg}\left(I\right)-\beta \lg n_3\\ D_{n4}^{Al-C}=R_C\left(I\right)+R_{Al}\left(I\right)-\beta \lg n_4\\ D_{n5}^{Al-C}=R_C\left(I\right)+R_{Al}\left(I\right)-\beta \lg n_5\\ D_{n6}^{Al-Al}=R_{Al}\left(I\right)+R_{Al}\left(I\right)-\beta \lg n_6\\ D_{n7}^{Al-Al}=R_{Al}\left(I\right)+R_{Al}\left(I\right)-\beta \lg n_7\\ D_{n8}^{C-C}=R_C\left(I\right)+R_C\left(I\right)-\beta \lg n_8\\ D_{n9}^{C-C}=R_C\left(I\right)+R_C\left(I\right)-\beta \lg n_9\end{array}$$

Subtracting the first length equation separately from the remaining eight length equations, the (N − 1) related equations can be obtained as below,

$$\begin{array}{c}\lg {\gamma }_2=\lg {\displaystyle \frac{n_2}{n_1}}=\left[D_{n1}^{Mg-C}-D_{n2}^{Mg-Al}+R_{Al}\left(I\right)-R_C\left(I\right)\right]/\beta \\ \lg {\gamma }_3=\lg {\displaystyle \frac{n_3}{n_1}}=\left[D_{n1}^{Mg-C}-D_{n3}^{Mg-Mg}+R_{Mg}\left(I\right)-R_C\left(I\right)\right]/\beta \\ \lg {\gamma }_4=\lg {\displaystyle \frac{n_4}{n_1}}=\left[D_{n1}^{Mg-C}-D_{n4}^{Al-C}+R_{Al}\left(I\right)-R_{Mg}\left(I\right)\right]/\beta \\ \lg {\gamma }_5=\lg {\displaystyle \frac{n_5}{n_1}}=\left[D_{n1}^{Mg-C}-D_{n5}^{Al-C}+R_{Al}\left(I\right)-R_{Mg}\left(I\right)\right]/\beta \\ \lg {\gamma }_6=\lg {\displaystyle \frac{n_6}{n_1}}=\left[D_{n1}^{Mg-C}-D_{n6}^{Al-Al}+2R_{Al}\left(I\right)-R_C\left(I\right)-R_{Mg}\left(I\right)\right]/\beta \\ \lg {\gamma }_7=\lg {\displaystyle \frac{n_7}{n_1}}=\left[D_{n1}^{Mg-C}-D_{n7}^{Al-Al}+2R_{Al}\left(I\right)-R_C\left(I\right)-R_{Mg}\left(I\right)\right]/\beta \\ \lg {\gamma }_8=\lg {\displaystyle \frac{n_8}{n_1}}=\left[D_{n1}^{Mg-C}-D_{n8}^{Al-Al}+R_C\left(I\right)-R_{Mg}\left(I\right)\right]/\beta \\ \lg {\gamma }_9=\lg {\displaystyle \frac{n_9}{n_1}}=\left[D_{n1}^{Mg-C}-D_{n9}^{Al-Al}+R_C\left(I\right)-R_{Mg}\left(I\right)\right]/\beta \end{array}$$

At present, eight groups of the ratio of the covalent electron distribution on bonds have been obtained by subjecting the SBR and the EBL into the above correlation equations: here, ${\gamma }_1={\displaystyle \frac{n_1}{n_1}}=1$. Furthermore, in order to solve the above equations, the electron conservation equation (ECE) is also needed, i.e.,

$${\displaystyle \sum n_{\mathrm{C}}}=n_{\mathrm{A}}{\displaystyle \sum I_{\alpha }{r}_{\alpha }}$$

(2)

where ${\displaystyle \sum n_{\mathrm{C}}}$ represents the total covalent electron number of the calculated structure unit, $n_{\mathrm{A}}{\displaystyle \sum I_{\alpha }{r}_{\alpha }}$ represents the total number of electrons distributed on all covalent bonds; and n_A represents the covalent electron pair number of the strongest covalent bonds. The ${\displaystyle \sum n_{\mathrm{C}}}$ under each hybridization state in the calculated structure unit can be obtained from the hybridization table of EET. Thus, both n_A and n_α (n_α = n_A⋅γ_α) can be calculated out. The ECE of the Al₂C₂Mg crystal structure can be illustrated as follows.

$$n_A={\displaystyle \frac{{\displaystyle \sum n_C}}{{\displaystyle \sum I_{\alpha }{\gamma }_{\alpha }}}}={\displaystyle \frac{\frac{2}{5}{n}_C^{Al}+\frac{2}{5}{n}_C^C+\frac{1}{5}{n}_C^{Mg}}{{\displaystyle \sum I_{\alpha }{\gamma }_{\alpha }}}}$$

(3)

Although the VES of the Al₂C₂Mg crystal structure has been obtained, the accuracy of the calculated results still needs to be verified by comparing the D-value between the calculated results and the reality results under the discriminant of EET, i.e.,

$$\Delta D_{n\alpha }=\left|D_{\alpha }-{\overline{D}}_{\alpha }\right|<0.005\mathrm{nm}$$

(4)

where ${\overline{D}}_{n_{\alpha }}^{u-v}$ represents the theoretical bond length which can be obtained by substituting n_α into Equation (1). If the discriminant is satisfied, the calculated VES parameters of the structure unit are acceptable. However, there might be a group number of solutions meeting the discriminant of EET, which is referred to as multi-solutions of EET.

Generally, it is quite difficult to select the optimal solution from many groups of solutions. Therefore, in order to deal with the problem of multi-solutions in EET, another equation is also introduced [27], i.e.,

$$X_{\alpha }^{\prime }={\displaystyle \sum _{i=1}^{{\sigma }_{\mathrm{N}}}{X}_{\alpha i}}\cdot c_i$$

(5)

where $X_{\alpha }^{\prime }$ represents the statistical value of the characteristic parameter $X_{\alpha }$ (e.g., the shared electron pair number $n_{\alpha }$ and bond energy $E_{\alpha }$) of the covalent bond; $X_{\alpha i}$ represents the characteristic parameter of the α covalent bond under the i electron configuration state for the crystal structure cell; $c_i$ represents the probability for the i electron configuration state to be present, i.e., $c_i=1/{\sigma }_n$.

All of the above calculation equations comprise the main body of the bond length difference (BLD) in EET, and inputting these calculated parameters and the measured lattice constants into the calculation software of BLD methods, we can obtain the VES parameters of the Al₂C₂Mg crystal structure; the calculated results are shown in

Table 2. Calculated VES parameters, bond energies and cohesive energies for Al₄C₃.

Crystals	CBN	EBN	EBL (nm)	n′α	E′α (kJ/mol)
Al2C2Mg	$B_{n1}^{Mg-C}$	2.4	0.24862	0.164619	17.37550
	$B_{n2}^{Mg-Al}$	2.4	0.29357	0.150971	14.58221
	$B_{n3}^{Mg-Mg}$	1.2	0.3377	0.036500	2.729387
	$B_{n4}^{Al-\mathrm{C}}$	2.4	0.20555	0.654524	89.18834
	$B_{n5}^{Al-\mathrm{C}}$	0.8	0.20784	0.599381	80.77451
	$B_{n6}^{Al-Al}$	1.2	0.24164	0.843422	106.5203
	$B_{n7}^{Al-Al}$	2.4	0.3377	0.021138	1.910899
	$B_{n8}^{C-C}$	1.2	0.33542	8.705 × 10−4	0.065904
	$B_{n9}^{C-C}$	2.4	0.3377	7.975 × 10−5	0.599728
	${\overline{E}}_C=341.1013$

. According to the same BLD method and calculation steps, we can also calculate the VES of the A₄C₃ crystal structure, and the results are shown in

Table 3. Calculated VES parameters and bond energies for Al₂C₂Mg.

Crystals	CBN	EBN	EBL (nm)	n ′α	E ′α (kJ/mol)
Al4C3	$B_{n1}^{Al1-C2}$	0.57143	0.19329	0.901025	140.6895
	$B_{n2}^{Al1-C1}$	1.71429	0.21589	0.404659	56.7197
	$B_{n3}^{Al1-Al1}$	0.85714	0.35307	0.014245	1.3669
	$B_{n4}^{Al1-Al2}$	1.71429	0.29698	0.103878	11.8197
	$B_{n5}^{Al1-Al1}$	1.71429	0.33350	0.028487	2.8916
	$B_{n6}^{Al1-C2}$	3.42857	0.38547	9.969 × 10−4	0.07896
	$B_{n7}^{Al2-C2}$	1.71429	0.19532	0.838577	129.6129
	$B_{n8}^{Al2-C2}$	0.57143	0.21754	0.381740	53.1114
	$\begin{array}{l}{B}_{n9}^{Al2-Al2}\end{array}$	0.85714	0.26683	0.302200	38.1997
	$B_{n10}^{Al2-C1}$	0.57143	0.32375	8.867 × 10−3	0.8350
	$\begin{array}{l}{B}_{n11}^{Al2-Al2}\end{array}$	1.71429	0.33350	0.028487	2.8916
	$B_{n12}^{Al2-C2}$	1.71429	0.38649	9.605 × 10−4	0.07596
	$B_{n13}^{C1-C1}$	0.85714	0.33350	1.383 × 10−3	0.11253
	$B_{n14}^{C1-C2}$	1.71429	0.34889	8.019 × 10−4	0.06241
	$B_{n15}^{C2-C2}$	0.85714	0.31583	2.586 × 10−3	0.22205
	$B_{n16}^{C2-C2}$	1.71429	0.33350	1.383 × 10−3	0.11253
${\overline{E}}_C=495.7274$

.

2.2. Calculation of Bond Energy and Cohesive Energy of Al₂C₂Mg

The bond energies of covalent bonds and the cohesive energy of the Al₂C₂Mg crystals structure can also be calculated on the basic of the calculation results of the VES, and the main calculation equations for bond energies (E′_α) in Al₂C₂Mg are shown as

$$\left.\begin{array}{l}{E}_{\alpha }^{\prime }=b{\displaystyle \sum \frac{I\alpha n\alpha }{\overline{D}n\alpha }}f\\ b={\displaystyle \frac{31.395}{n-0.36\delta }}\\ f=\sqrt{\alpha s}+\sqrt{3\beta p}+g\sqrt{5\gamma d}\end{array}\right\}$$

(6)

where the meaning of the calculation parameters in Equation (6) can be found in Ref. [26].

The used calculation equations of cohesive energy ${\overline{E}}_C$ can be expressed as

$${\overline{E}}_{\mathrm{C}}=b\left\{{\displaystyle \sum _{\alpha }\frac{I_{\alpha }{n}_{\alpha }}{{\overline{D}}_{n\alpha }}f}+{\displaystyle \frac{n_f}{\overline{D}}}{f}^{\prime }+k{m}^{3d}-CW\right\}$$

(7)

where the meaning and solving of the above calculation parameters can also be found in ref. [26].

Similarly, considering the issue of the multi-solutions of EET, the statistical value of the cohesive energy of the Al₂C₂Mg structure units also needs to be calculated using the following formula according to Refs. [28,29], i.e.,

$${\overline{E}}_{\mathrm{C}}^{\prime }={\displaystyle \sum _{i=1}^{{\sigma }_{\mathrm{N}}}{\overline{E}}_{\mathrm{C}i}}\cdot c_i$$

(8)

where the meaning of the above calculation parameters has been given in Ref. [26]. Based on Equations (6)–(8), we can finally calculate the bond energies and cohesive energy of the Al₂C₂Mg structure. The calculated results of bond energies and cohesive energy are also listed in Table 2 and Table 3.

3. Results and Discussion

3.1. Elaborate Analysis of Al₄C₃ and Al₂C₂Mg Based on VES and Bond Energy

Figure 2 presents the distribution of predominant bonds in the Al₂C₂Mg unit cell based on the calculated VES parameters and the bond energy analysis of Al₂C₂Mg. According to the calculation results listed in Table 2 and Figure 2, it is obviously can be seen that the primary bonds in Al₂C₂Mg are Al-C and Al-Al bonds. In contrast, Al-Mg and C-Mg bonds exhibit significantly weaker bonding strengths. This structural configuration suggests that the four-layer atomic structure Al-C-Al-C, where the Al-C and C-Al tetrahedra structures connect sequentially in a head-to-tail fashion, forms the fundamental framework of Al₂C₂Mg. Consequently, the Al/C structure architecture emerges as the critical determinant for Al₂C₂Mg formation. The proposed formation sequence of Al₂C₂Mg involves the initial development of a C-Al-Al-C double tetrahedral core structure, which is followed by the epitaxial growth of a two-layer hexagonal Mg atomic layer on its upper and lower surface. When the Al element concentration in Mg-Al melt remains low, a large amount of liquid Mg atoms dilute the system, reducing C-Al interaction probabilities and limiting the Al:C ratio to ≤1:1. Thus, at this point, these conditions inhibit Al₄C₃ formation in Mg-Al melt while permitting Al₂C₂Mg crystallization.

Figure 3 illustrates the bonding network and structural units within an Al₄C₃ unit cell derived from the calculated VES parameters and the bond energies of Al₄C₃. Table 3 and Figure 3 identify four primary bond types in Al₄C₃: Al1-C2, Al2-C2 (dual configurations), Al1-C1, and Al2-Al2 bonds. Notably, Al₄C₃ contains a C-Al-Al-C double tetrahedral structure similar to Al₂C₂Mg along with an additional Al1-C1 tetrahedral unit. Two Al2-C2 tetrahedra form head-to-tail connections via Al2-C2 (~53.1 kJ/mol) and Al2-Al2 (~38.2 kJ/mol) bonds, while two Al1-C1 tetrahedra share a central carbon atom in a head-to-head configuration. Finally, the two different double tetrahedral structural units interconnect exclusively through Al1-C2 bonds. Comparing with all the bond energies, it can be seen that although the individual Al2-C2 and Al1-C1 bond energies in a double tetrahedral structure are lower than those of Al1-C2, their equivalent bond numbers are threefold higher, which enhances the overall stability. The Al2-C2 dimer receives additional stabilization from adjacent Al-Al bonds and secondary Al2-C2 interactions, indicating superior stability compared to Al1-C2 configurations.

In general, the complex Al₄C₃ structure essentially combines two basic stable Al-C structural units, but the connection between the two is relatively weak. In addition, it is worth pointing out that the atomic arrangement structure of Al₄C₃ is one layer of Al adjacent to one layer of C atoms with only an Al2 atomic layer inserted between the C2-Al2-C2 atom layers, which also explains why Al₄C₃ has more Al atoms than Al₂C₂Mg.

As mentioned above, by comparative analysis of the atomic structures between Al₄C₃ and Al₂C₂Mg, it can be found that except for the similar crystal structure and lattice constant, the excess Al atoms in Al₄C₃ are specifically used to form the C2-Al2-Al2-C2 structure similar to that in Al₂C₂Mg. In other words, their main atomic skeletons are all composed of Al-C double tetrahedra with the same structure and lattice constant. Therefore, it can be inferred that under specific conditions, there might being a potential mutual transformation between Al₄C₃ and Al₂C₂Mg. According to the calculation results, the cohesive energy of Al₄C₃ is higher than that of Al₂C₂Mg. Hence, in general, Al₄C₃ should generally be formed preferentially over Al₂C₂Mg when the ratio of Al and C atoms is greater than 1:1 in a Mg-Al melt [30]. Conversely, when the ratio of Al/C is less than 1, it is more conducive to the formation of Al₂C₂Mg. Additionally, the Mg-Al cluster size in different temperatures further influences the final Al-C product selection. Elevated temperatures reduce cluster sizes (Figure 4), effectively decreasing local aluminum concentrations and promoting Al₂C₂Mg formation during solidification.

3.2. Effect Mechanism of Overheating on the Refinement Efficiency of Carbon Inoculation

Surface termination determines Al₄C₃’s nucleation capability. Generally, whether Al₄C₃ was externally added or in situ formed in aluminum melt, it usually terminated with an Al-Al atomic layer on its outermost surface, which cannot achieve a grain refinement effect especially for high Al bearing Mg-Al alloy because of the weak interaction between the Al₄C₃ surface and liquid Mg atoms. However, only when Al₄C₃ terminates with C2 atoms as the outermost surface layer can the liquid Mg atoms in the melt be easily attracted by the C2-Al2-Al2-C2 double tetrahedral structure and become a stable single solid-phase structure of Al₂C₂Mg. That is to say, the breakage of Al1-C2 bonds in Al₄C₃ is the key factor in whether it can be transformed into Al₂C₂Mg and finally become an effective heterogeneous nucleus for α-Mg, which is also responsible for the atomic mechanism of Al₄C₃ heterogeneous nucleation for Mg-Al alloy. During the whole melting and solidification process of Mg-Al, the alloy composition and melt temperature jointly regulate the stability of Al1-C2 bonds on the Al₄C₃ surface.

Based on the discussion of the valence electrons structure and mutual conversion relationship between Al₄C₃ and Al₂C₂Mg, a simple atomic interaction model can be proposed to elaborate the overheating mechanism of Mg-Al alloy inoculated by carbon in terms of atomic level, of which a schematic diagram, i.e., the transformation process from Al₄C₃ to Al₂C₂Mg under the condition of overheating and cooling, is shown in Figure 4. At conventional melting temperatures, the preferred carbide formed is the relatively more stable Al₄C₃, of which the outermost surface must be terminated by an Al-Al atomic layer (as illustrated in Figure 4a). However, under an overheating process, the Al1-C2 bonds of Al₄C₃ will quickly disconnect and cause the decomposition of Al₄C₃. The released Al2-C2 double tetrahedral structure rapidly and uniformly disperses into Mg-Al melt (as illustrated in Figure 4b), which subsequently leads to the formation of Al₂C₂Mg during the rapid quenching process as follows (as illustrated in Figure 4c).

It should be emphasized that without rapid cooling during solidification, the Al-C tetrahedral structure will aggregate again and recrystallize into Al₄C₃ instead of Al₂C₂Mg due to its 18.6% higher cohesive energy. In contrast, during the rapid cooling process, the Al-C tetrahedral structure does not have enough time to recombine but preferentially forms Al₂C₂Mg with sufficient liquid Mg atoms in the Mg-Al melt at lower temperature. Due to high melting temperature, the more broken nanoscale Al-C tetrahedral structure is relatively dispersed uniformly in the melt. Therefore, the size of Al₂C₂Mg generated during the subsequent rapid cooling process should also be nanoscale, which can obviously enhance its refinement efficiency compared to micron-scale Al₄C₃, but it makes it difficult to be detected by SEM inside of α-Mg grain [13].

In addition, compared with the overheating mechanism proposed by Cao [31] (AlMn layer covering the surface of Al₄C₃, which can be removed when the melt is overheated, and rapid cooling will not cause the AlMn layer to reform), the overheating mechanism proposed in this paper can further better explain the refinement mechanism of Al₄C₃ without the participation of Mn, and it can also reveal the atomic mechanism of Al and Mn alloying elements on the grain-refining efficiency of Al₄C₃.

3.3. Effects Mechanism of Al and Mn Element on Nucleating Efficiency of Carbide

The atomic interaction model mentioned above can also explain the experimental phenomenon through which Al and Mn contents negatively influence the heterogeneous nucleation of the Al₄C₃ substrate for α-Mg. Regarding the Al element, the literature suggests that the grain size of Mg-Al alloy might not be well refined by a carbon agent when the aluminum concentration exceeds 3 wt.% [15]. First, high aluminum content promotes Al₄C₃ formation, whereasAl₂C₂Mg only forms under low-aluminum conditions. Second, for externally added Al₄C₃ particles, according to the atomic interaction model mentioned above, the transition from Al₄C₃ to Al₂C₂Mg remains critical for enabling Al₄C₃ to become an effective heterogeneous core of α-Mg. The fracture of the Al1-C2 bond is positively correlated with the chemical potential of Al in the melt (i.e., the Al content in the melt). As shown in Figure 5a, the high Al content in Mg-Al melts elevates the chemical potential of Al in the Mg-Al melt, which does not favor the fracture of Al1-C2 bonds on the surface of Al₄C₃. Conversely, in low-Al melts (as shown in Figure 5b) including few Al atoms, the reduced chemical potential facilitates Al-C bond breaking, exposing the C2-Al2-Al2-C2 to direct contact with liquid Mg atoms. This enables complete or partial Al₄C₃-to-Al₂C₂Mg transformation, allowing Al₄C₃ to serve as a direct effective heterogeneous nucleus for α-Mg.

The addition of minor Mn amounts can restore the refinement effect of carbon agents in high-Al-content Mg-Al alloys, which is a phenomenon unexplained by traditional overheating mechanisms [32]. Mn’s influence mechanism on the refinement efficiency of carbon parallels that of Al, which can also be analyzed based on the overheating-induced atomic interaction mechanism. Figure 6 schematically illustrates the effecting mechanism of Mn atoms on the refining efficiency of Al₄C₃ in Mg-9Al alloy. When a small amount of Mn is added into the melt, Mn atoms should form Mg-Al-Mn atomic clusters with primary Mg-Al atoms clusters in the Mg-Al melt, which acts as a restraint on Al atoms among liquid Mg atoms [33]. Concurrently, the reduction of relative free Al in the melt can effectively reduce the chemical potential of Al in the Mg-Al melt, which can further lead to an easier break of the Al1-C2 bonds on the Al₄C₃ surface and create necessary conditions for the subsequent heterogeneous nucleation of α-Mg (the atomic mechanism can be seen in Figure 6a). However, exceeding critical Mn levels, according to the Mg-Al-Mn phase diagram, promotes preferential Al-Mn phase formation over α-Mg [33]. In this scenario, Al₄C₃ becomes the heterogeneous core of Al-Mn, i.e., the Al-Mn phase formed on the surface of Al₄C₃ (as shown in Figure 6b), which undoubtedly can prevent Al1-C2 bond breakage and cause Al₄C₃ to lose its refining effect on α-Mg.

4. Conclusions

In this study, the heterogeneous nucleation mechanism of Mg-Al alloy was investigated by the calculation results of Al₂C₂Mg and Al₄C₃, and the investigated results are as follows.

1.

Under certain conditions, the broken Al1-C2 bonds in Al₄C₃ lead Al₄C₃ to decompose into an atomic cluster level with an Al-C tetrahedral skeleton in the Mg-Al melt, which has a strong force on Mg atoms in the liquid phase and finally forms Al₂C₂Mg as the heterogeneous core of α-Mg;

2.

A higher melt temperature is beneficial for the fracture of Al1-C2 bonds and produces more nano-Al₂C₂Mg under the following rapid cooling process, which is responsible for the refinement mechanism of overheating treatment in Mg-Al alloy;

3.

The changes in Al and Mn content both affect the fracture of Al1-C2 bonds and the formation of Al₂C₂Mg, which in turn affects whether a carbon agent can become an effective heterogeneous core for α-Mg.