Morphology and Properties of Mg2Si Phase Modified by Pb in As-Cast Mg-2.5Si-xPb Alloys

Pb plays an important role in determining the morphologies and mechanical properties of the Mg2Si phase in Mg-2.5Si-xPb alloys. As the amount of Pb increases from 0.4 wt.% to 1 wt.%, the primary Mg2Si phase is refined during solidification. Its morphologies transform from equiaxed-dendrite to polygonal and finally to roughly circular. The key reason for morphology evolution is the preferential adsorption of Pb atoms on Mg2Si {100} surfaces to suppress the growth rate along the ⟨100⟩ directions, which is demonstrated by the adsorption model based on first principles. In addition, the hardness of the Mg2Si phase decreases with the increasing solution content of Pb according to the results of the nanoindentation. With the addition of Pb at 1 wt.%, Pb content in the primary Mg2Si phase reaches a maximum of 0.4 wt.%, and the hardness of the primary Mg2Si phase reaches a minimum of 3.64 GPa. This reduction in hardness is attributed to the augmented ionic bond ratio resulting from the solution of Pb, which concurrently enhances the toughness of the Mg2Si phase.


Introduction
Magnesium alloys are commonly utilized as cast components in aerospace and automotive applications [1,2] owing to their advantageous properties, including lightweight, high stiffness, specific strength, and exceptional damping capacity [3,4].However, a significant limitation of traditional magnesium alloys is their reduced strength at temperatures exceeding 400 K, which restricts their broader applicability [5].Consequently, there exists an urgent need to develop cost-effective high-temperature magnesium alloys suitable for use in structural components [6].
To enhance the mechanical properties of magnesium alloys at elevated temperatures, several strategies can be employed.These include incorporating strengthening particles with high thermal stability, reducing the element diffusion rate within the magnesium matrix, and optimizing both the grain-boundary structure and the overall microstructure [7].Mg-Si alloys stand out as an ideal choice for large-scale commercial heat-resistant applications due to their simple production process and low cost.The core heat-resistant strengthening phase of Mg-Si alloys is Mg 2 Si, which exhibits lots of exceptional mechanical properties and thermal stability [8].It can improve mechanical properties and reduce the creep rate of Mg alloy at high temperatures by inhibiting grain-boundary sliding.However, the Mg 2 Si phase in Mg-Si alloys tends to form coarse dendrites in the traditional metallurgical process [9].The presence of coarse and brittle Mg 2 Si particles affects the mechanical properties of Mg-Si alloys, specifically the strength and ductility [10,11].Recently, extensive research has been conducted to control the morphologies and size of the Mg 2 Si phase by adding elements [12][13][14][15] and compounds [16] or employing external highintensity physical energy fields [17].While these approaches have led to improvements in mechanical properties, there remains a significant gap in research aimed at enhancing the brittleness of Mg 2 Si while maintaining its inherent thermal stability.As a result, cracks often initiate within primary Mg 2 Si particles, compromising the structure of Mg alloys [18].Consequently, it is crucial to tackle this issue by enhancing the toughness while controlling the morphology and size of the Mg 2 Si phase in order to fully realize the potential benefits of Mg 2 Si reinforcement.
One promising approach is through the substitution solid solution.For instance, Wang et al. [19] found that the plasticity of Sn-doped Mg 2 Si is superior to that of a pure Mg 2 Si phase.Pb, as a member of the IVA family in the periodic table alongside Si, exhibits the lowest electronegativity among elements within this group [20].The increase in the electronegativity difference between bonded elements enhances the ionic nature of the bond, leading to improved toughness and plasticity of the material [21].Additionally, the intermetallic compound Mg 2 Pb has a lattice structure similar to that of Mg 2 Si, facilitating the good solubility of Pb/Si in Mg 2 Si/Mg 2 Pb [22].The solid solution of Pb atoms could change the bonding characteristics of the Mg 2 Si crystal.The change in the binding properties of these crystals could significantly affect the morphology and mechanical properties of the crystal [23].Consequently, Pb is a potential ideal additive; it is anticipated to enhance the toughness of the Mg 2 Si phase while refining the morphology of Mg 2 Si particles.Furthermore, compared to rare earth elements, Pb is a more economical material.Although Pb vapor has health risks, the addition of a small amount with proper care will not be serious one [24].In order to reveal the effects of Pb on the Mg 2 Si phase and the strengthening potentials of the Mg 2 (Si x Pb 1−x ) phase, first-principles calculations were employed to analyze the modification mechanism of the Mg 2 Si phase.Based on these calculations, further investigations were conducted on the morphologies and mechanical properties of the Mg 2 Si phase.

Theoretical Model, Calculation Method, and Experimental Procedures 2.1. Theoretical Model and Calculation Method
Mg 2 Si and Mg 2 Pb have an anti-fluorite crystal structure, characterized by a space group of Fm3m and a space number of 255.The lattice constants for Mg 2 Si and Mg 2 Pb are 0.6338 nm and 0.6933 nm [25], respectively.The unit cell atom coordinates are precisely as follows: the Mg (8c) position is at (1/4, 1/4, 1/4), while Si/Pb (4a) occupies (0, 0, 0).Based on previous studies [22], the doping of Pb atoms in the Mg 2 Si phase is performed by substituting Si atoms with Pb atoms to form a substantial solid solution Mg 2 (Si x Pb 1−x ).The Mg 2 (Si x Pb 1−x ) phase retains the anti-fluorite crystal structure across varying x values, as shown in Figure 1.
chanical properties, there remains a significant gap in research aimed at enhan brittleness of Mg2Si while maintaining its inherent thermal stability.As a resul often initiate within primary Mg2Si particles, compromising the structure of M [18].Consequently, it is crucial to tackle this issue by enhancing the toughness wh trolling the morphology and size of the Mg2Si phase in order to fully realize the p benefits of Mg2Si reinforcement.
One promising approach is through the substitution solid solution.For i Wang et al. [19] found that the plasticity of Sn-doped Mg2Si is superior to that o Mg2Si phase.Pb, as a member of the IVA family in the periodic table alongside Si, the lowest electronegativity among elements within this group [20].The increas electronegativity difference between bonded elements enhances the ionic natur bond, leading to improved toughness and plasticity of the material [21].Addition intermetallic compound Mg2Pb has a lattice structure similar to that of Mg2Si, fac the good solubility of Pb/Si in Mg2Si/Mg2Pb [22].The solid solution of Pb atom change the bonding characteristics of the Mg2Si crystal.The change in the bindin erties of these crystals could significantly affect the morphology and mechanical ties of the crystal [23].Consequently, Pb is a potential ideal additive; it is antici enhance the toughness of the Mg2Si phase while refining the morphology of Mg2 cles.Furthermore, compared to rare earth elements, Pb is a more economical m Although Pb vapor has health risks, the addition of a small amount with proper c not be serious one [24].In order to reveal the effects of Pb on the Mg2Si phase strengthening potentials of the Mg2(SixPb1−x) phase, first-principles calculations w ployed to analyze the modification mechanism of the Mg2Si phase.Based on thes lations, further investigations were conducted on the morphologies and mechanic erties of the Mg2Si phase.

Theoretical Model and Calculation Method
Mg2Si and Mg2Pb have an anti-fluorite crystal structure, characterized by group of Fm3m and a space number of 255.The lattice constants for Mg2Si and M 0.6338 nm and 0.6933 nm [25], respectively.The unit cell atom coordinates are p as follows: the Mg (8c) position is at (1/4, 1/4, 1/4), while Si/Pb (4a) occupies (0, 0, 0 on previous studies [22], the doping of Pb atoms in the Mg2Si phase is performed stituting Si atoms with Pb atoms to form a substantial solid solution Mg2(SixPb Mg2(SixPb1−x) phase retains the anti-fluorite crystal structure across varying x va shown in Figure 1.Computational analyses were conducted using the plane-wave pseudopotential density functional theory (DFT) method embedded in the CASTEP package (Materials Studio 7.0).The calculations employed an ultra-soft pseudopotential alongside the generalized gradient approximation PBE scheme.The plane-wave cutoff energy was fixed at 400 eV, and the k-point meshes were set to 11 × 11 × 11.First, the cell model of Mg 2 (Si x Pb 1−x ) was geometrically optimized using the BFGS algorithm.Subsequently, self-consistent iterative SCF calculations were performed based on the most stable Mg 2 (Si x Pb 1−x ) crystal structure, with electron relaxation handled via the Pulay density mixing method.Convergence criteria included a self-consistent field tolerance of 1 × 10 −6 eV/atom and a maximum stress limit of 0.05 GPa.The total energy finally converged to less than 5 × 10 −6 eV/atom.The valence states involved comprised Mg 3s 2 2p 6 , Si 3s 2 3p 2 , and Pb 5d 10 6s 2 6p 2 .

Experimental Method
To prepare Mg-2.5%Si-x%Pb (x = 0, 0.4, 0.8, 1; wt.%) alloys, commercial pure Mg (99.7 wt.%) and Mg-10 wt.%Si master alloys were melted at 780 • C in an electric-resistance furnace.A Pb piece was added, with different amounts to the melt.After stirring 3 times with a mean time interval of 15 min, the melt was held for 30 min at 780 • C and then cast into a graphite mold, which was preheated to 400 • C.
For metallographic analysis, specimens underwent mechanical grinding and polishing, followed by a 3 s etch in a Nital solution (4 vol.%HNO 3 , 96 vol.%C 2 H 5 OH).An OLYMPUS optical microscope (OM) (Olympus Corporation, Tokyo, Japan) and a Merlin Compact filed emission scanning electron microscope (SEM) (Carl Zeiss, Oberkochen, Germany) equipped with an Oxford Instruments (Abingdon, UK) energy-dispersive X-ray spectrometer (EDS) were used to examine the microstructures.Transmission electron microscope (TEM) specimens, 3 mm in diameter, were ground to about 60 µm and then, twin-jet electro-polished in a −30 • C solution of 15% nitric acid and 85% methanol.Before TEM observation, the surface oxide film was removed by ion-milling with a Fischoine model 1010 (Fischione Instruments, Cleveland, OH, USA) at 5 kV.TEM and HRTEM observations were conducted on a JEM-2100 microscope (JEOL Ltd., Tokyo, Japan) at 200 kV.TEM and HRTEM observations were carried out in a JEM-2100 microscope operating at 200 kV.Nanomechanical testing was performed on a Hysitron TI-Premier nanoindenter (Bruker, Billerica, MA, USA) equipped with a Berkovich diamond tip of a three-sided pyramid Berkovich probe (Bruker in USA).A trapezoidal loading profile was used to determine the nanomechanical properties of the Mg 2 (Si x Pb 1−x ) phase, which consisted of 5 s of loading, 2 s hold at 1000 µN, and 5 s of unloading.

Structural Stability of the Mg 2 (Si x Pb 1−x ) Phase
The optimized lattice parameters of the Mg 2 (Si x Pb 1−x ) phase are listed in Table 1.The calculated lattice parameters of the optimized Mg 2 Si and Mg 2 Pb are consistent with the experimental data, with an error of about 0.43% and 0.07%, respectively.The lattice constant a of Mg 2 (Si x Pb 1−x ) (x ̸ = 0, 1) falls within the range of the constants of the Mg 2 Si and Mg 2 Pb phases.The structural stability of a crystal is associated with its formation enthalpy per atom (∆H f ) of per atom and cohesive energy (E coh ).The formation enthalpy quantifies the level of difficulty in forming an intermetallic compound by measuring the amount of energy released or absorbed during substance reactions [28].On the other hand, cohesive energy measures the work performed by external forces when a crystal disintegrates into individual atoms [29].The formation enthalpies of per atom (∆H f ) and cohesive (E coh ) were calculated by the following formulae.
where E tot is the total energy of Mg measures the work performed by external forces when a crystal disintegrates into individual atoms [29].The formation enthalpies of per atom (ΔHf) and cohesive (Ecoh) were calculated by the following formulae.
where Etot is the total energy of Mg2(SixPb1−x),  A negative formation enthalpy indicates an exothermic reaction, while a low formation enthalpy signifies robust structural stability [25].The negative formation enthalpy of each Mg2(SixPb1−x) phase suggests that the stability of these phases remains before and after solid solution in the system, thereby indicating their potential for stable formation.Mg2Si exhibits the lowest formation enthalpy, while Mg2Pb possesses a slightly higher formation enthalpy compared to Mg2Si but lower than other Mg2(SixPb1−x) phases (x ≠ 0, 1).It can be inferred that, compared to Mg2Si and Mg2Pb, the formation ability of the Mg2 (SixPb1−x) phase is relatively limited.Furthermore, a low cohesive energy is indicative of elevated structural stability [20].As can be seen in Figure 2, the negative value of the cohesive energy decreases with the increasing Pb content.It indicates that the most stable composition is the Mg2Si phase, and the least is the Mg2Pb phase, in Mg2(SixPb1−x) phases with different compositions.

Elastic Constants and Mechanical Properties of the Mg2(SixPb1−x) Phase
The elastic constant Cij serves as an indicator of a material's resistance to external forces and deformations.It is determined by analyzing the relationship between stress and strain [20].For its cubic symmetry, Mg2(SixPb1−x) have three independent elastic constants: C11, C12, and C44.Combined with the Voigt-Reuss-Hill approximation, the bulk moduli B, shear moduli G, Young's moduli E, and Poisson ratio ν can be deduced by the following formulae, respectively [30]: A negative formation enthalpy indicates an exothermic reaction, while a low formation enthalpy signifies robust structural stability [25].The negative formation enthalpy of each Mg 2 (Si x Pb 1−x ) phase suggests that the stability of these phases remains before and after solid solution in the system, thereby indicating their potential for stable formation.Mg 2 Si exhibits the lowest formation enthalpy, while Mg 2 Pb possesses a slightly higher formation enthalpy compared to Mg 2 Si but lower than other Mg 2 (Si x Pb 1−x ) phases (x ̸ = 0, 1).It can be inferred that, compared to Mg 2 Si and Mg 2 Pb, the formation ability of the Mg 2 (Si x Pb 1−x ) phase is relatively limited.Furthermore, a low cohesive energy is indicative of elevated structural stability [20].As can be seen in Figure 2, the negative value of the cohesive energy decreases with the increasing Pb content.It indicates that the most stable composition is the Mg 2 Si phase, and the least is the Mg 2 Pb phase, in Mg 2 (Si x Pb 1−x ) phases with different compositions.

Elastic Constants and Mechanical Properties of the Mg 2 (Si x Pb 1−x ) Phase
The elastic constant C ij serves as an indicator of a material's resistance to external forces and deformations.It is determined by analyzing the relationship between stress and strain [20].For its cubic symmetry, Mg 2 (Si x Pb 1−x ) have three independent elastic constants: C 11 , C 12, and C 44 .Combined with the Voigt-Reuss-Hill approximation, the bulk moduli B, shear moduli G, Young's moduli E, and Poisson ratio ν can be deduced by the following formulae, respectively [30]: The elastic constants computed for the Mg 2 (Si x Pb 1−x ) phases are presented in Table 2.It was evident that Mg 2 (Si x Pb 1−x ) phases satisfied the mechanical stability requirements specific to cubic crystal systems, including C 44 > 0, C 11 + 2C 12 > 0, and C 11 − C 12 > 0 [31].Among Mg 2 (Si x Pb 1−x ) phases with different Pb contents, the Mg 2 Si phase exhibits the highest Young's modulus of 102.00 GPa, the highest shear modulus of 43.35 GPa, and the lowest Poisson's ratio of 0.1763.As the solid solubility of Pb increases, the Young's and shear moduli for Mg 2 (Si x Pb 1−x ) phases decrease significantly, while the Poisson's ratio increases.Furthermore, the hardness can be predicted through the first-principles calculations utilizing the following formulae [32]: where are the hardness, bond number, bond length, and Phillips ionicity of the x-y bonds, respectively.P is the overlap population of a bond, and Pc is the overlap population of a bond in a hypothetical pure covalent crystal with the same special structure (P c = 0.75).Z x or Z y is the valence electron number.N x or N y is the coordination number of the x or y atom constructing the x-y bond.V is the volume of the calculating unit cell.The calculated bond parameters and Vickers hardness values are shown in Table 3.
Generally, covalent bonds contribute to high strength and hardness, while ionic bonds are associated with high toughness.The ratio of covalent and ionic bonds in the Mg 2 (Si x Pb 1−x ) phase can be determined by Muliken's overlap population P. A value of P = 0 indicates purely ionic bonding, whereas P > 0 suggests an increase in covalent action [33].According to the calculation results, the binding between atoms in the Mg 2 (Si x Pb 1−x ) phase occurred mainly through covalent bonds with a minor presence of ionic bonds.With increasing Pb content, the proportion of covalent bonds decreased while the percentage of ionic bonds increased.Consequently, the trend of hardness aligns with that of the Young's and shear moduli (Table 2), whereby an increase in the solid solubility of Pb in the Mg 2 Si phase led to a decrease in the hardness of the Mg 2 (Si x Pb 1−x ) phase.This change enhances the ductility and toughness and reduces the brittleness of the Mg 2 Si phase.The formation process and final morphology of the primary Mg 2 Si phase are influenced by its inherent crystalline structure as well as external factors, including temperature, pressure, and solvent concentration [34].From a crystallographic perspective, the {111} facets of Mg 2 Si, which exhibit the highest degree of surface packing, manifest the minimum surface energy, while the {100} facets have the lowest degree of packing and the highest surface energy.During crystal growth, the {111} faces expose, and the {100} faces undergo shrinkage [35].The substitution of Si with Pb in Mg 2 Si crystal resulted in a modification of the surface energy, ultimately leading to a morphological transformation.The surface-slab models for the {111} and {100} faces were constructed to study the surface energy and adsorption capacity, respectively, as shown in Figure 3.The surface energy (E surf ) of {111} and {100} faces, as well as the effect of substituting Si atoms with Pb atoms in all slab models, were determined.The corresponding calculation results are shown in Table 4.In pure Mg 2 Si, the surface energy of {111}Mg-I termination was the lowest, with a value of 0.48 eV.Upon substitution of Pb for Si, the surface energy of each termination increased.From the perspective of external growth conditions, the adsorption or bonding of Pb atoms in the liquid phase also exerts an influence on the growth rate of Mg 2 Si crystal faces.To illustrate this phenomenon, an adsorption model was established based on the replacement of Si sites by Pb atoms (as depicted in Figure 3).The adsorption energy E ads of {111} and {100} faces for Pb atoms of all terminations are shown in Figure 4. Generally, a more negative adsorption energy indicates a stronger adsorption [36].Consequently, Pb atoms exhibit a preference for adsorbing onto {100} faces.From the perspective of external growth conditions, the adsorption or bonding of Pb atoms in the liquid phase also exerts an influence on the growth rate of Mg2Si crystal faces.To illustrate this phenomenon, an adsorption model was established based on the replacement of Si sites by Pb atoms (as depicted in Figure 3).The adsorption energy Eads of {111} and {100} faces for Pb atoms of all terminations are shown in Figure 4. Generally, a more negative adsorption energy indicates a stronger adsorption [36].Consequently, Pb atoms exhibit a preference for adsorbing onto {100} faces.

Microstructure of Mg2(SixPb1−x) in Mg-Si-Pb Alloy
The microstructures of as-cast Mg-2.5Si-xPb alloys are shown in Figure 5. Mg-2.5Si-xPb alloys consisted of the Mg2Si phase and α-Mg matrix.In Mg-2.5Si-0.4Pballoy (Figure 5b), the primary Mg2Si phase had a dendritic morphology, similar to that of Mg-2.5Si alloy (Figure 5a).However, there was an increase in the number of primary Mg2Si particles and a decrease in their size.The average particle size decreased from 50.1 µm in Mg-2.5Si alloy  The microstructures of as-cast Mg-2.5Si-xPb alloys are shown in Figure 5. Mg-2.5Si-xPb alloys consisted of the Mg 2 Si phase and α-Mg matrix.In Mg-2.5Si-0.4Pballoy (Figure 5b), the primary Mg 2 Si phase had a dendritic morphology, similar to that of Mg-2.5Si alloy (Figure 5a).However, there was an increase in the number of primary Mg 2 Si particles and a decrease in their size.The average particle size decreased from 50.1 µm in Mg-2.5Si alloy to 34.8 µm in Mg-2.5Si-0.4Pballoy.With the increase of Pb content in the alloy, the morphology and size of the primary Mg 2 Si phase in the Mg-2.5Si-0.8Pballoy changed significantly.As observed in Figure 5c, the morphology of the primary Mg 2 Si phase changed from equiaxed-dendrite to polygonal outlines, and the average particle size further decreased to 18.7 µm.
In Mg-2.5Si-1Pb alloy, the morphology of the primary Mg 2 Si phase exhibited a very special change.There was a significant difference in the size of primary Mg 2 Si particles (Figure 5d).Apart from particles with an average size of 16.9 µm, numerous finer particles with a size ranging from 3 to 6 µm were also present.The distinct characteristic was that while the larger Mg 2 Si particles had been spheroidized, the finer particles retained a polygonal shape.Nonetheless, a rounding effect was evident at the sharp corners of these fine particles, suggesting partial or incomplete spheroidization, as indicated by the arrows in Figure 5d.
Figure 5 shows high-magnification images of the microstructure.There was local energy fluctuation and compositional fluctuation during solidification, so the images seem to show an effect on eutectic Mg 2 Si and α-Mg.Multiple different areas of the alloys were measured to determine the proportion of each phase area, and the results are shown in Table 5.From the proportion of area in each alloy, it can be seen that the change of Pb content has little effect on the eutectic phase and α-Mg.This is due to the low Pb content in the alloy and the high solid solubility of Pb in Mg [22].
(Figure 5d).Apart from particles with an average size of 16.9 µm, numerous finer particles with a size ranging from 3 to 6 µm were also present.The distinct characteristic was that while the larger Mg2Si particles had been spheroidized, the finer particles retained a polygonal shape.Nonetheless, a rounding effect was evident at the sharp corners of these fine particles, suggesting partial or incomplete spheroidization, as indicated by the arrows in Figure 5d.   5. From the proportion of area in each alloy, it can be seen that the change of Pb content has little effect on the eutectic phase and α-Mg.This is due to the low Pb content in the alloy and the high solid solubility of Pb in Mg [22].The distribution of alloying elements and the composition analysis of Mg-2.5Si-xPb alloy were further examined using EDS, as shown in Figure 6.In Mg-2.5Si alloy (Figure 6a), the Si element was mainly distributed within the Mg2Si phase, and the Si content in  The distribution of alloying elements and the composition analysis of Mg-2.5Si-xPb alloy were further examined using EDS, as shown in Figure 6.In Mg-2.5Si alloy (Figure 6a), the Si element was mainly distributed within the Mg 2 Si phase, and the Si content in both primary and eutectic Mg 2 Si phases was similar, with values of 36.5 wt.% and 31.8 wt.%, respectively.In Mg-2.5Si-0.4Pballoy (Figure 6b), Mg 2 Si particles show a prominent Mg K α1,2 peak, a strong Si K α1,2 , and a weak Pb L α1,2 peak.It is evident that the Si element is concentrated in the Mg 2 Si phase.The composition of the primary and eutectic Mg 2 Si phase was about Mg-35.2%Si-0.1% Pb and Mg-30.6%Si-0.2% Pb (wt.%), respectively.The Pb content within the Mg matrix was found to be 0.5 wt.%, which exhibited a significant increase compared to that present in the Mg 2 Si phase.This observation can be attributed to the high solid solubility of Pb in the Mg matrix.
The same analysis was performed on Mg-2.5Si-0.8Pballoy (Figure 6c) and Mg-2.5Si-1Pb alloy (Figure 6d).In the EDS of primary and eutectic Mg 2 Si particles, a minor increase in peak intensity was noted for the Si and Pb elements.In Mg-2.5Si-0.8Pballoy, the Pb content of primary and eutectic Mg 2 Si particles increased to 0.3 wt.%, and 0.5 wt.%, respectively.In Mg-2.5Si-1Pb alloy, the compositions of primary and eutectic Mg 2 Si were about Mg-35.9%Si-0.4%Pb and Mg-32.0%Si-0.7%Pb(wt.%), respectively.The variation in Pb content within the primary Mg 2 Si phase, eutectic Mg 2 Si phase, and α-Mg matrix for Mg-2.5Si-xPb is shown in Figure 7.There was a consistent increase in the proportion of Pb mass within each phase with the increase of Pb content in the alloy.It is noteworthy that the Pb content detected in all phases was slightly smaller than that of the composition of the Mg-2.5Si-xPballoys.The possible reason was that the high density and atomic number of the Pb element make its absorption efficiency of X-ray and gamma-ray higher [37], resulting in a slight decrease in the measured Pb content.In addition, among all components of the alloy, the primary Mg 2 Si phase exhibited the lowest Pb content, and the Pb content in the Mg matrix was close to that in the nominal composition of the alloys.It is reasonable to conclude that the Pb content in the liquid phase had an important effect on the morphology of the primary Mg 2 Si phase.During the analysis of EDS, the influence range of the focused electron beam on the specimen was about 3 µm at 15 kV.Therefore, the content of Pb of the eutectic Mg 2 Si phase is between that in the primary phase and the Mg matrix.
Materials 2024, 17, x FOR PEER REVIEW 9 of 15 both primary and eutectic Mg2Si phases was similar, with values of 36.5 wt.% and 31.8 wt.%, respectively.In Mg-2.5Si-0.4Pballoy (Figure 6b), Mg2Si particles show a prominent Mg Kα1,2 peak, a strong Si Kα1,2, and a weak Pb Lα1,2 peak.It is evident that the Si element is concentrated in the Mg2Si phase.The composition of the primary and eutectic Mg2Si phase was about Mg-35.2%Si-0.1% Pb and Mg-30.6%Si-0.2% Pb (wt.%), respectively.The Pb content within the Mg matrix was found to be 0.5 wt.%, which exhibited a significant increase compared to that present in the Mg2Si phase.This observation can be attributed to the high solid solubility of Pb in the Mg matrix.The same analysis was performed on Mg-2.5Si-0.8Pballoy (Figure 6c) and Mg-2.5Si-1Pb alloy (Figure 6d).In the EDS of primary and eutectic Mg2Si particles, a minor increase in peak intensity was noted for the Si and Pb elements.In Mg-2.5Si-0.8Pballoy, the Pb content of primary and eutectic Mg2Si particles increased to 0.3 wt.%, and 0.5 wt.%, respectively.In Mg-2.5Si-1Pb alloy, the compositions of primary and eutectic Mg2Si were about Mg-35.9%Si-0.4%Pb and Mg-32.0%Si-0.7%Pb(wt.%), respectively.The variation in Pb content within the primary Mg2Si phase, eutectic Mg2Si phase, and α-Mg matrix for Mg-2.5Si-xPb is shown in Figure 7.There was a consistent increase in the proportion of Pb mass within each phase with the increase of Pb content in the alloy.It is noteworthy that the Pb content detected in all phases was slightly smaller than that of the composition of the Mg-2.5Si-xPballoys.The possible reason was that the high density and atomic number of the Pb element make its absorption efficiency of X-ray and gamma-ray higher [37], resulting in a slight decrease in the measured Pb content.In addition, among all components of the alloy, the primary Mg2Si phase exhibited the lowest Pb content, and the Pb content in the Mg matrix was close to that in the nominal composition of the alloys.It is reasonable to conclude that the Pb content in the liquid phase had an important effect on the morphology of the primary Mg2Si phase.During the analysis of EDS, the influence range of the focused electron beam on the specimen was about 3 µm at 15 kV.Therefore, the content of Pb of the eutectic Mg2Si phase is between that in the primary phase and the Mg matrix.Mg-2.5Si-1Pb alloy, which has the highest Pb content, was selected for detailed investigation using TEM and HRTEM.Figure 8 shows TEM micrographs of a primary Mg2Si particle in Mg-2.5Si-1Pb alloy.The interior of the Mg2Si crystal was uniform.However, a distinct banded region with gray-black contrast was observed at the periphery of the Mg2Si particle, as indicated by white arrows.The electron diffraction pattern (DP) obtained from the [001]Mg2Si zone axis of the circular region is shown in Figure 8b.HRTEM was further conducted on the edge region, as shown in Figure 8c.In this image, the gray and white columns correspond to the Si and Mg atomic columns, respectively.The inset highlighted the primary Mg2Si unit cell structure, which is outlined Mg-2.5Si-1Pb alloy, which has the highest Pb content, was selected for detailed investigation using TEM and HRTEM.Figure 8 shows TEM micrographs of a primary Mg 2 Si particle in Mg-2.5Si-1Pb alloy.The interior of the Mg 2 Si crystal was uniform.However, a distinct banded region with gray-black contrast was observed at the periphery of the Mg 2 Si particle, as indicated by white arrows.The electron diffraction pattern (DP) obtained from the [001] Mg2Si zone axis of the circular region is shown in Figure 8b.HRTEM was further conducted on the edge region, as shown in Figure 8c.In this image, the gray and white columns correspond to the Si and Mg atomic columns, respectively.The inset highlighted the primary Mg 2 Si unit cell structure, which is outlined by squares.The measured value of crystal constant a was 0.658 nm and slightly larger than that of pure Mg 2 Si.The enlarged lattice constant can be ascribed to the substitution of Pb for Si.The edge region was thoroughly examined, and no atomic segregation was detected.Therefore, the presence of a gray-black banded area at the edge can be attributed to the thickness fringe due to the spherical morphology of this Mg 2 Si particle.Mg-2.5Si-1Pb alloy, which has the highest Pb content, was selected for detailed investigation using TEM and HRTEM.Figure 8 shows TEM micrographs of a primary Mg2Si particle in Mg-2.5Si-1Pb alloy.The interior of the Mg2Si crystal was uniform.However, a distinct banded region with gray-black contrast was observed at the periphery of the Mg2Si particle, as indicated by white arrows.The electron diffraction pattern (DP) obtained from the [001]Mg2Si zone axis of the circular region is shown in Figure 8b.HRTEM was further conducted on the edge region, as shown in Figure 8c.In this image, the gray and white columns correspond to the Si and Mg atomic columns, respectively.The inset highlighted the primary Mg2Si unit cell structure, which is outlined by squares.The measured value of crystal constant a was 0.658 nm and slightly larger than that of pure Mg2Si.The enlarged lattice constant can be ascribed to the substitution of Pb for Si.The edge region was thoroughly examined, and no atomic segregation was detected.Therefore, the presence of a gray-black banded area at the edge can be attributed to the thickness fringe due to the spherical morphology of this Mg2Si particle.

Nanomechanical Properties of the Mg2(SixPb1−x) Phase
Figure 9 presents the load-displacement curves obtained from in situ nanoindentation tests conducted on the primary Mg2Si phase in Mg-2.5Si-xPb alloys.The maximum indentation depth hmax was 73.9 nm in the Mg-2.5Si-0.4Pballoy and increased to 77.5 nm in Mg-2.5Si-1Pb.The value of plastic depth hf increased from 42.9 nm to 45.8 nm.The nanomechanical properties were calculated using the Oliver-Pharr method [38] based on the unloading segment data, as shown in Table 6.It is evident that the solid solution of Pb in the Mg2Si phase results in the decrease both of elastic modulus E and hardness Hv.Among all compositions, the Mg2Si phase in Mg-2.5Si-1Pb alloy with the highest Pb content exhibits the lowest elastic modulus of 83.4 GPa and hardness of 3.6 The nanomechanical properties were calculated using the Oliver-Pharr method [38] based on the unloading segment data, as shown in Table 6.It is evident that the solid solution of Pb in the Mg 2 Si phase results in the decrease both of elastic modulus E and hardness H v .Among all compositions, the Mg 2 Si phase in Mg-2.5Si-1Pb alloy with the highest Pb content exhibits the lowest elastic modulus of 83.4 GPa and hardness of 3.6 GPa.Compared to the pure Mg 2 Si phase, there is an observed reduction of 11.8% in elastic modulus E and a decrease of 2.0% in hardness H v .

Morphology
In FCC crystals, the preferential growth directions are 〈100〉, and {100} faces have the fastest growth rate [14].Under ideal growth conditions, the {100} faces of Mg 2 Si crystal will gradually shrink during the growth process, ultimately degrading to corners and edges.This leaves the {111} facets exposed, resulting in an octahedral crystal shape [39].The addition of Pb effectively modified the morphology of primary Mg 2 Si crystals in Mg-2.5Si-xPb, primarily due to the changes in thermodynamics and kinetics conditions in front of the solid-liquid interface.
The incorporation of a few Pb atoms into primary Mg 2 Si crystals through substitution at the Si atoms resulted in a change of the surface energy of the {111} and {100} planes (Table 4).According to previous studies, the equilibrium form of an FCC crystal is determined by the proportional surface energies of the {100} and {111} planes [40].With Si sites replaced by Pb atoms, the surface-energy ratio between the {100} Mg termination and {111} Mg-I termination changed from 2.23 to 1.21.Therefore, the morphology of primary Mg 2 Si crystals tended to be a truncated octahedron.Additionally, the calculation results of the adsorption energy of Pb atoms on the Mg 2 Si {111} and {100} planes (Figure 4) show the preferential adsorption of Pb atoms on {100} planes.The growth rates of 〈100〉 directions were inhibited, and the final morphology of the Mg 2 Si crystal was also affected.
Meanwhile, the growth rate was also apparently encouraged by large constitutional undercooling and supersaturation.Once the interface front of the primary Mg 2 Si was unstable, the main stem was formed along the preferential growth direction 〈100〉.Subsequently, secondary branches are aroused in directions perpendicular to the primary dendrite trunk.The rapid generation and growth of these secondary dendrites result in their interconnection or overlapping, as shown in Figure 5a.Due to the low Pb content in Mg-2.5Si-0.4Pballoy, the primary Mg 2 Si phase also tends to form coarse dendrites, similar to those observed in Mg-2.5Si alloy.However, the addition of Pb induced a supercooling effect that significantly enhanced the nucleation capability of Mg 2 Si crystals, consequently leading to an augmentation in the quantity of primary Mg 2 Si particles and a reduction in size.
In Mg-2.5Si-0.8Pballoy, the surface energy of Mg 2 Si crystal change caused by Pb substitution for Si, and the preferential adsorption of Pb atoms on the {100} plane became more obvious.The growth rates of 〈111〉 directions were hindered, resulting in the appearance of truncated octahedral morphologies.The reserved percentage of {100} facets was found to be correlated with the reduction in growth rates along the 〈100〉 directions [9].
The formation of roughly spherical primary Mg 2 Si particles in the Mg-2.5Si-1Pballoy (Figure 5d) was a complex process that requires further analysis.According to Mg-Si and Mg-Pb equilibrium phase diagrams [22], the primary Mg 2 Si crystals first nucleate and grow.However, due to solute trapping under non-equilibrium solidification, some Pb atoms were dissolved into Mg 2 Si, forming a substitution solid solution Mg 2 (Si x Pb 1−x ).According to TEM observations, Pb atoms only replaced Si atoms in Mg 2 Si crystal.In contrast, Sn not only has the capability to replace Si but also exhibits the potential for replacing Mg in Mg 2 Si crystal [41].Therefore, the substitution solution probability of the Pb atom in the Mg 2 Si crystal is less than that of the Sn atom.Furthermore, the calculation results indicated that the Mg 2 Si structure exhibited the highest stability.Under ideal equilibrium conditions, the Mg 2 (Si x Pb 1−x ) phase had a greater tendency to decompose into Mg 2 Si and Pb in order to reduce the energy of the system.The above two reasons significantly restricted the solid solubility of Pb in the Mg 2 Si phase under conventional casting conditions.During the solidification process, the excess Pb atoms were expelled from the primary Mg 2 Si particle and gathered at the solid-liquid interface.At the sharp edge of two meeting growth planes, there was a notable increase in Pb concentration, as shown in Figure 10.Given that Pb has a higher atomic mass compared to Mg and Si [20], the diffusion rate of Pb atoms was considerably slower.The accumulation of Pb atoms at sharp corners hindered the transfer of atoms from the liquid to the solid phase, causing a decrease in growth rate at those locations.This promoted the morphological transformation of truncated octahedral Mg 2 Si particles into roughly spheroidal particles.

Mechanical Properties
According to the principles of general crystal-strengthening theoretical logic, the solubility of Pb in Mg2Si crystal is expected to result in the enhancement of solution strengthening, leading to an increase in the hardness of primary Mg2Si [42].However, the nanomechanical properties data (Table 5) revealed contrary findings.The hardness of the Mg2(SixPb1−x) phase reduced with an increasing Pb solubility.The main reason was that the substitutional solid solution Mg2(SixPb1−x) belongs to a covalent compound.The hardness of the Mg2(SixPb1−x) phase is primarily determined by the energy of covalent bonds localized within electron spin pairs [43].This factor remains unaffected by external influences such as impurities, precipitates, grain boundaries, and other related factors [44].
Examining the bond parameters listed in Table 3, it became evident that the covalent interaction of the Mg-Pb bonds (P = 0.24) was weaker than that of Mg-Si (P = 0.36) in the Mg2(SixPb1−x) crystal.Consequently, as the number of Pb atoms increased in the Mg2(SixPb1−x) crystal, the number of ionic bonds also increased.This led to a decrease in hardness and an increase in the toughness of the Mg2(SixPb1−x) phase.The mechanical properties of Mg2(SixPb1−x) predicted by the first-principles calculation (Tables 2 and 3) aligned well with the experimental values.This agreement can be attributed to the fact that Pb atoms only replace Si atoms in Mg2Si (Figure 8).The formation of the substitution solid solution Mg2(SixPb1−x) was consistent with the crystal model established through first-principles calculations.

Mechanical Properties
According to the principles of general crystal-strengthening theoretical logic, the solubility of Pb in Mg 2 Si crystal is expected to result in the enhancement of solution strengthening, leading to an increase in the hardness of primary Mg 2 Si [42].However, the nanomechanical properties data (Table 5) revealed contrary findings.The hardness of the Mg 2 (Si x Pb 1−x ) phase reduced with an increasing Pb solubility.The main reason was that the substitutional solid solution Mg 2 (Si x Pb 1−x ) belongs to a covalent compound.The hardness of the Mg 2 (Si x Pb 1−x ) phase is primarily determined by the energy of covalent bonds localized within electron spin pairs [43].This factor remains unaffected by external influences such as impurities, precipitates, grain boundaries, and other related factors [44].
Examining the bond parameters listed in Table 3, it became evident that the covalent interaction of the Mg-Pb bonds (P = 0.24) was weaker than that of Mg-Si (P = 0.36) in the Mg 2 (Si x Pb 1−x ) crystal.Consequently, as the number of Pb atoms increased in the Mg 2 (Si x Pb 1−x ) crystal, the number of ionic bonds also increased.This led to a decrease in hardness and an increase in the toughness of the Mg 2 (Si x Pb 1−x ) phase.The mechanical properties of Mg 2 (Si x Pb 1−x ) predicted by the first-principles calculation (Tables 2 and 3) aligned well with the experimental values.This agreement can be attributed to the fact

2 (
Si x Pb 1−x ), E Mg solid , E Si solid , and E Pb solid are the energies per atom of Mg, Si, and Pb, respectively.E Mg atom , E Si atom and E Pb atom are the energies of isolated atoms for each element.n, m, and k are the numbers of Mg, Si, and Pb atoms in a unit cell, respectively.The formation enthalpies (∆H f ) and cohesive (E coh ) of the predicted phase for different compositions (1 − x) are shown in Figure 2. Materials 2024, 17, x FOR PEER REVIEW 4 of 15 of isolated atoms for each element.n, m, and k are the numbers of Mg, Si, and Pb atoms in a unit cell, respectively.The formation enthalpies (ΔHf) and cohesive (Ecoh) of the predicted phase for different compositions (1 − x) are shown in Figure 2.

Figure 5
Figure 5 shows high-magnification images of the microstructure.There was local energy fluctuation and compositional fluctuation during solidification, so the images seem to show an effect on eutectic Mg2Si and α-Mg.Multiple different areas of the alloys were measured to determine the proportion of each phase area, and the results are shown in Table5.From the proportion of area in each alloy, it can be seen that the change of Pb content has little effect on the eutectic phase and α-Mg.This is due to the low Pb content in the alloy and the high solid solubility of Pb in Mg[22].

Figure 7 .
Figure 7. Pb content in each phase of as-cast Mg-2.5Si-xPb.

Figure 7 .
Figure 7. Pb content in each phase of as-cast Mg-2.5Si-xPb.

Figure 7 .
Figure 7. Pb content in each phase of as-cast Mg-2.5Si-xPb.

Figure 8 .Figure 8 .
Figure 8. TEM micrographs of Mg-2.5Si-1Pb alloys.(a) TEM micrograph showing a primary Mg2(SixPb1−x) particle in Mg-2.5Si-1Pb alloy; (b) DP recorded from primary Mg2Si in (a); (c) HRTEM image showing the two-dimensional lattice structure of central region of the Mg2(SixPb1−x) phase in Mg-2.5Si-1Pb alloy and the inset showing the crystal structure of Mg2(SixPb1−x).The circle in panel Figure 8. TEM micrographs of Mg-2.5Si-1Pb alloys.(a) TEM micrograph showing a primary Mg 2 (Si x Pb 1−x ) particle in Mg-2.5Si-1Pb alloy; (b) DP recorded from primary Mg 2 Si in (a); (c) HRTEM image showing the two-dimensional lattice structure of central region of the Mg 2 (Si x Pb 1−x ) phase in Mg-2.5Si-1Pb alloy and the inset showing the crystal structure of Mg 2 (Si x Pb 1−x ).The circle in panel (a) is the acquisition area of electron diffraction.Green balls represent Mg atoms, while yellow balls represent Si atoms in panel (c).

3. 5 .
Figure9presents the load-displacement curves obtained from in situ nanoindentation tests conducted on the primary Mg 2 Si phase in Mg-2.5Si-xPb alloys.The maximum indentation depth h max was 73.9 nm in the Mg-2.5Si-0.4Pballoy and increased to 77.5 nm in Mg-2.5Si-1Pb.The value of plastic depth h f increased from 42.9 nm to 45.8 nm.

Figure 9 .
Figure 9.The load-displacement curves of primary Mg2(SixPb1−x) phase in Mg-2.5Si-xPb alloys.hmax and hf denote the maximum and residual indentation depth, respectively.An applied trapezoidal loading function is depicted in the inset.

Figure 9 .
Figure 9.The load-displacement curves of primary Mg 2 (Si x Pb 1−x ) phase in Mg-2.5Si-xPb alloys.h max and h f denote the maximum and residual indentation depth, respectively.An applied trapezoidal loading function is depicted in the inset.

Figure 10 .
Figure 10.Schematic diagram of atomic distribution at the front edge of the solid-liquid interface of Mg 2 Si crystal (a) Mg-2.5Si-0.8Pballoy; (b) Mg-2.5Si-1Pb alloy.

Table 2 .
Calculated elastic constants and moduli of the Mg 2 (Si x Pb 1− ) phase.

Table 3 .
Calculated bond parameters and hardness of Mg 2 (Si x Pb 1−x ) phase.

Table 4 .
The surface energies of different slab models of the Mg2Si phase.

Table 4 .
The surface energies of different slab models of the Mg 2 Si phase.

Table 4 .
The surface energies of different slab models of the Mg2Si phase.

Table 5 .
The area ratio of each phase of as-cast Mg-2.5Si-xPb alloys.

Table 5 .
The area ratio of each phase of as-cast Mg-2.5Si-xPb alloys.

Table 6 .
The elastic modulus E, hardness H v , maximum indentation depth h max , plastic depth h f , and plastic deformation ratio h f /h max , of two different Mg 2 (Si x Pb 1−x ) phases.