The relative atomic mass values of the alloying elements, including Al,Zn, Cu, Ca, Gd, Nd, Ce, Ag, Ni, Y and C¹² were obtained from the periodic table of elements. The absolute atomic mass values of the alloying elements were calculated via the following formula: Absolute   tomic   mass = Relative   atomic   mass   of    alloying   elements Relative   atomic   mass of   C 12 × 1.9927 × 10 − 26 K g (1)

The results were shown in Table 1.

The crystal structure and parameters of the common precipitated phases in the magnesium alloys, including Mg₁₇Al₁₂, MgZn₂, MgCu₂, Mg₂Ca, Mg₃ Gd, Mg₁₂Nd, Mg₁₂Ce, MgAg, MgNi₂ and Mg₂₄Y₅ were obtained by the phase diagram.

The atom number in a single unit cell of the precipitated phases Mg_AX_B was calculated via the crystal structure. For example, the crystal structure of Mg₂₄Y₅ is body-centered cubic (BCC), so there are two Mg₂₄Y₅ intermetallics in each unit cell. The total atom number in a single Mg₂₄Y₅ unit cell is 2 × (24Mg+5Y) = 48Mg + 10Y. The absolute mass of a single Mg₂₄Y₅ unit cell (the sum of 48Mg atoms and 10 Y atoms) was obtained as following: 48 × 4.0303×10⁻²³ g + 10 × 14.7425 × 10⁻²³ g = 340.8794 × 10⁻²³ g. The absolute mass of other single precipitated phases Mg_AX_B was calculated via the same method with results shown in Table 2.

The volume of a single unit cell was calculated according to the crystal structure and parameters obtained from the XRD card. The density of a single unit cell was calculated via the following formula: Density   of   a    single   unit   cell = Absolute   mass   of   a   single   unit   cell Volume   of   a   single   unit   cell (2)

The Mg₂₄Y₅ unit cell is body-centered cubic (BCC) structure, and the lattice parameters is a = 1.1257 × 10⁻⁷ cm. So the Volume of a single unit cell is a³ = (1.1257 × 10⁻⁷ cm)³ = 1.4265 × 10⁻²¹ cm³, the density of a single Mg₂₄Y₅ unit cell is 340.8794 × 10 − 23 g 1.4265 × 10 − 21 cm 3 = 2.3896 / c m 3 , according to Eq. 2. The densities of single unit cells of the other precipitated phases were obtained via the same method. The density of a single Mg₂₄Y₅ unit cell is the density of the Mg₂₄Y₅ intermetallics.

The molar volume of precipitated phases Mg_AX_B in magnesium alloys was calculated via the formula as follow: Molar   volume   of   precipituated   phases =   Molar mass of precipitated phases Density of a single MgAXB unit cell (3)

For example, the molar volume of M g 24 X 5   1027.845 2.3896 = 430.132   c m 3 . All the calculated results are shown in Table 2.

According to the formation Gibbs energies of the metal’s oxides (James 2005), the preferential metal atom of the precipitated phases Mg_AX_B in magnesium alloys during oxidation reaction in the atmospheric environment were:

1) Δ_fG°Al₂O₃ = −38.5 kJ/mol＞Δ_fG°MgO = −135.27 kJ/mol; Mg₁₇Al₁₂→Mg→MgO

If there is one type of precipitated phase A_UB_V in magnesium alloy, the preferentially oxidized element is B-content in the A_UB_V single unit cell. Because the preferentially oxidized B-content is derived from A_UB_V, which is a solid solution structure. Therefore, the volume of B-content can be obtained from the volume of A_UB_V single unit cell subtracted the volume of unoxidized A-content (Xu and Gao, 2000), as shown by the following formula, Volume   of   x B = Volume   of   [ ( X / V ) AuBv ] − Volume   of   [ ( u x / v ) A ] (4)

For example, the molar volume of Y atom in Mg₂₄Y₅ unit cell was calculated via: 1 / 5 [ V M g 24 Y 5 − 24 V Mg ] = 1 / 5 × [ 430.132 − 24 × 13.9845 ] c m 3 = 18.9008   c m 3 . In consideration of x in Eq. 6 (2 for Y₂O₃), the volume of 2 mol of Y in alloy is calculated by 2 × 18.9008 cm³ = 37.8016 cm³.

Then, the density and molar mass of oxide product can be obtained via periodic table of elements. Thus, the molar volume of oxidized product can be calculated via the formula: Molar volume of oxide =   Molar mass of oxide product Density of oxide product (5)

For example, the molar volume of oxide product Y₂O₃ from the oxidation of precipitated phases Mg₂₄Y₅ was calculated as follow: M Y 2 O 3 D Y 2 O 3 = 225.81   g / mol 5.01   g / c m 3   = 45.0719 .

The PBR value of oxidation films formed from the precipitated phases in magnesium alloys was calculated via the formula: PBR precipitated phases Volume of one mole of B x O y Volume   of   x   moles   of   B   in   alloy (6)

All the results were shown in Table 3.

Commercially pure Mg (99.9 wt. %), Mg- 3Y wt.%, Mg- 5Y wt.% and Mg- 7Y wt.% were used to characterize the oxide film on the surface of magnesium alloys. The samples with dimensions of 1 cm × 1 cm×1 cm were heated in the dry air at 400°C for 36 h. These samples were used to analyze the microstructure of oxide films, including the morphologies, thicknesses and compositions by scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS). The samples with dimensions of 2 cm × 2 cm × 0.5 cm were also heated in dry air at 400°C for 36 h, which were used to test the open circuit potential (OCP) using the electrochemical workstation. Three parallel samples were used to ensure the accuracy of the test results. All the samples were polished with 1,000, 3,000 and 5,000# SiC papers and then cleaned with absolute ethanol.

Due to the affinity of oxygen to magnesium alloys, samples are oxidized rapidly at a high temperature in dry air. The rate of oxidation increases first linearly, then exponentially with the extension of oxidation time (Zhou et al., 2013; Yu et al., 2016). Below 400–450°C, the magnesium alloys have certain oxidation resistance, with a parabolic oxidation kinetics and intact oxide film (Yu et al., 2018). Once the temperature exceedes 400°C, the oxidation reaction kinetics will change from parabolic to linear. The acceleration of oxidation reaction leads to the formation of film cracks on the surface. Therefore, in order to study the microstructure of the dense oxide films on Mg-Y alloys, the oxidation temperature of 400°C was chosen. The thermo gravimetric analysis (TGA) was used to measure the weight increment of different samples. The heating rate was 10°C/min in the air environment from room temperature to 500°C.

As shown in Figure 1, the morphologies of oxide films formed on Mg-xY (x = 0, 3, 5, 7 wt.%) samples are quite different. Many MgO particles and pores existed on the surface of pure Mg, indicating a poor corrosion resistance of the oxide film. With the addition of 3 wt.% Y, the surface tended to be smooth and compact, and the pores were also disappeared. However, there were still a small amount of MgO particles on the sample surface. With the increasing of Y-content, MgO particles disappeared completely, whereas the squama-like oxides formed on the surface of Mg-5Y alloys. As the Y content increased to 7 wt.%, the size of the squama-like oxides becomes larger, and the boundary of oxides turned clearly.

The EDS results of oxides on the surface of Mg-xY (x = 0, 3, 5, 7 wt.%) samples are shown in Table 4. The Y-contents in the oxides are more than the matrix. Both the O-content and Y-content increased with the addition of Y element, whereas the Mg-content decreased. This phenomenon because that the activity of Y element is higher than Mg element. With the extension of oxidation time, the thickness of oxides increased. The oxidation rate of all the samples was reduced by the oxides barrier, which inhibited the inward diffusion of O₂ and the outward diffusion of Mg²⁺. According to the calculation in Table 3, the PBR of Y₂O₃ formed from the Mg₂₄Y₅ unit cell was 1.1923, which indicated that the Y₂O₃ oxidation film was compact. Moreover, the chemical property of Y₂O₃ was relatively stable. Therefore, when Mg-Y alloys were exposed in the high temperature environment, the dense MgO/Y₂O₃ composite oxide layers were formed on the sample surfaces. The composite oxide layer acted as a physical barrier to hinder the oxidation reaction, thus the oxidation of magnesium alloys was slowed down (Wang et al., 2008).

The TGA result was shown in Figure 2. From the trends of the curves in the figure, all samples had a fast oxidation rate at the initial stage. The oxidation reaction rate decreased with the prolong of oxidation reaction time and the rising of temperature. The Mg-5Y alloys had the faster oxide reaction rate than the pure Mg, Mg-3Y and Mg-7Y samples at the initial stage of oxidation. Then, the thin, smooth and dense oxide films were formed on the surface of samples, the oxidation rates were all reduced. At the maximum temperature, the weight improvement ratio of pure Mg, Mg-3Y, Mg-5Y and Mg-7Y was 0.80, 0.82, 0.85 and 0.91%, respectively. This phenomenon indicated that Y element had the higher activity to bind with oxygen than Mg.

According to the mapping results in Figure 3, the difference of Y-content in Mg-xY (x = 3, 5, 7 wt.%) alloys led to the different elementary composition in the oxidation products.

As shown in Table 5, mapping analysis on the surface of pure magnesium showed that the O content was only 2.5%. This phenomenon proved that the oxide film on the surface was very thin, so that the electron beam can penetrate the oxide film and reach the Mg matrix. The oxidation films of Mg-3Y samples were composed of MgO as the major constituent and minor Y₂O₃. When Y-content was 3 wt.%, the average content of oxygen element in the surface mapping analysis was about 13.8 wt.%, and the Y element was about 21.1 wt.%, which indicated that a large number of Y₂O₃ were formed in the oxide film. The content of Y element was larger than that of in the alloy matrix without oxidation. With the increase of Y-content to 7 wt.%, the O element on the surface film increased to 16.1 wt.%, while the Y content increased to 26.9 wt.%.

The average thicknesses of oxidation films for different samples were measured by backscattered electrons scanning spectroscopy, as shown in Figure 3. And the elemental composition at different cross-section locations was also analyzed by EDS, with results summarized in Table 6. In Figure 4 the average thickness of oxidation films on the surface of pure Mg was about 0.4 μm. With the addition of Y-content, the oxidation film thickness increased from 0.5 μm (Mg-3Y) to more than 1.5 μm (Mg-7Y). This phenomenon was attributed to the high activity of Y element, which preferentially combines with oxygen to form oxide films (Wang et al., 2009).

As shown in Table 6, all the oxidation films were consisted of Y₂O₃ and MgO. For both pure Mg and Mg-xY (x = 3, 5, 7 wt.%) alloys, the major content of the oxidation film is MgO. However, the closer to the top surface of the oxide film, the larger amount of Y₂O₃-content. In general, the protection performance of oxidation products to α-Mg matrix was related the PBR of films covered on the samples, which determine the diffusion rate of metal atoms from metal/oxide interface to oxide/air interface, and the diffusion rate of oxygen atoms from oxide/air interface to metal/oxide interface (Zhao et al., 2018). The inward diffusion of oxygen atoms and the outward diffusion of Mg atoms through the oxide films was suppressed due to the compact microstructure of Y₂O₃-content.

Figure 5 shows the open circuit potential of pure Mg and Mg-xY alloys covered with oxidation films in 3.5% NaCl solution. As time increased, all the ocp values decreased, due to the desquamation of oxidation films covered on the surface of samples (Jiang, et al., 2021). The OCP value of Mg-7Y alloy was the most positive, indicating the most alleviated local corrosion of Mg-7Y alloy among the samples. In addition, with the extension of immersion time, the OCP of Mg-Y alloys tended to be stable, indicating a stabilized surface state. The electrochemical activity of the samples decreased in the order of Mg-7Y > Mg-5Y > Mg-3Y > pure Mg. The corrosion tendency of Mg-7Y was the lowest in the exposure of 3.5% NaCl for 1200s, due to the protection of the thick and compact oxidation film.

The Tafel slopes of pure Mg and Mg-xY alloys covered with oxidation films measured in 3.5% NaCl solution was shown in Figure 6. The corrosion reactions were identical according to the similarity of all the Tafel curves. As shown in Figure 6, the characteristic anode branches were generally sharp formation, which represented the dissolution of α-Mg. The cathodic hydrogen evolution was the main reaction, which determined the reaction rate of the electrochemical corrosion. When the potential was more negative than the pitting potential, the cathodic branch showed up linear Tafel characteristics. Therefore, the corrosion current density of pure Mg and Mg-xY alloys was calculated by the tangent of linear cathode branch. The results of corrosion current density were shown in the table of Figure 6. Due to the different resistance of oxides films to the corrosion reaction, the pure Mg showed a largest I _corr, whereas the Mg-7Y alloy showed the smallest. The results depended on thickness and density of oxides films, which indicated that the oxides films formed in the surface of Mg-7Y alloy showed a best corrosion barrier effect.

The electrochemical impedance spectra curves of pure Mg and Mg-xY alloys covered with oxidation films measured in 3.5% NaCl solution was shown in Figure 7. The largest electrochemical impedance spectra of Mg-7Y alloy samples indicated that hydrogen evolution of the α-Mg matrix reaction had the largest energy barrier. According to the results in Figure 6, the corrosion resistance can be ranked as follows: pure Mg＜Mg-3Y＜Mg-5Y＜Mg-7Y, which demonstrated that the tendency was consistent with the preceding data in this study. The electrochemical impedance spectra curves of different samples were different, which represented distinctive dynamic corrosion process. The larger of the PBR of oxides films, the stronger of the barrier effect on the ion diffusion of corrosion reaction. Therefore, the alloy with the most Y-content showed the best corrosion resistance.

PBR is the ratio of oxide volume generated from the combination of metal and oxygen on the metal surface to the volume of consumed metal atoms, which reflects the stress condition in the oxide film. The corrosion tendency of magnesium alloy is closely related to the conditions of oxide layer during oxidation. The PBR of Y₂O₃ films generated from Mg₂₄Y₅ was about 1.1923, which indicated the Y₂O₃ films were continuous and compact (Okamoto, 1992). Therefore, the content of Y-content increased, the corrosion tendency of Mg-Y alloys decreased. When PBR is less than 1 or more than 2, tensile stress or excessive compressive stress exists in the oxide film, and the film is prone to rupture. The PBR value of MgO/Mg was 0.81, which indicated that the MgO layer had a large internal tensile stress, and the film structure was loose (Lin, et al., 2010; Qin, et al., 2016; Lee, et al., 2017). As a result, the pure Mg had the largest corrosion tendency than Mg-Y alloys.

As shown in Figure 8, the oxidation mechanism of pure Mg and Mg-Y alloys in this study. With the increasing of Y-content, the amount and volume fraction of precipitated phases on grain boundary of Mg-Y binary alloys became larger before heat treatment. After the heat treatment, pure Mg reacted with O atom to form a loose porous oxide film in Figure 7A. For Mg-Y binary alloys, the Y atom bonded to the O atom preferentially, and then the Mg atom bonded to the O atom at the high temperatures. The Y₂O₃ and MgO products formed in the surface of different Mg-Y binary alloys. With the increasing of Y-content, the ratio of Y₂O₃ formed in the oxides became larger. Moreover, the volume and dimensions of Y₂O₃ also showed a large improvement. As the oxidation reaction processed, the equilibrium state of the interface between the alloy and the oxidation environment changed (You, et al., 2014). At the initial stage of oxidation, the equilibrium state of the alloy interface was alloy-oxidation environment. With the formation of oxidation films, the equilibrium state of the interface changed to alloy/oxidation products/oxidation environment. During the oxidation reaction, the PBR value of MgO products was only about 0.8, which could not protect the α-Mg matrix from the further corrosion reaction effectively. However, the PBR value of Y₂O₃ was larger than 1, which improved the overall density of mixed oxide in the surface to a certain extent. Therefore, the protective effect of mixed oxide on the matrix was improved. This phenomenon indicated that the more of Y-content, the stronger the protective effect of oxide film on the α-Mg matrix.

On the other hand, precipitated phases in the magnesium alloys often act as the cathode of microelectrochemical coupling reaction, accelerating the corrosion of α-Mg matrix. With the alloying element increased gradually, more and more Y-content reacted with α-Mg matrix, the number of precipitated phases also increased tremendously. However, In the heating process, the precipitated phases containing rare earths were easier to oxidize than the magnesium matrix. And then the Y₂O₃ formed have a better protection effect on the α-Mg matrix. The more precipitated phases contained rare earth were, the more Y₂O₃ is oxidized, which resulted a improvement to the corrosion resistance of α-Mg matrix.

In fact, different types of precipitated phases may exist in the same magnesium alloy. Moreover, one alloying element also may form different kinds of precipitated phases in the magnesium alloys with the changes of the alloying element content. In this work, the PBR values of the oxide film formed from the common precipitated phases in magnesium alloys were calculated. In the actual oxidation process of magnesium alloys, it is possible that multiple oxidation reactions occur simultaneously. This research is expected to provide guidance in the development of heat-resistant magnesium alloys by adjusting the types of alloying elements and film formation from the precipitated phases.