Nanoscale precipitates strengthened lanthanum-bearing Mg-3Sn-1Mn alloys through continuous rheo-rolling

We elucidate the effect of lanthanum (La) on the microstructure and mechanical properties of Mg-3Sn-1Mn-xLa (wt.%) alloy plates processed through continuous rheo-rolling for the first time. At x = 0.2 wt.%, La dissolved completely in the α-Mg matrix. As the La content was increased to 0.6 wt.%, a new plate-shaped three-phase compound composed of La5Sn3, Mg2Sn and Mg17La2 phases was formed with an average length of 380 ± 10 nm and an average width of 110 ± 5 nm. This compound had a pinning effect on the α-Mg grain boundary and on dislocations. With further increase in La-content to 1.0 wt.%, the length of the plate-shaped compound increased to an average length of 560 ± 10 nm, while the width was reduced to 90 ± 5 nm. The particle size of Mg2Sn decreased from 100 nm to 50 nm with increase in La-content from 0.2 to 1.4 wt.%. At La content of 1.0 wt.%, the tensile strength and elongation of the alloy was maximum, with 29% and 32% increase, respectively, compared to the Mg-3Sn-1Mn (wt.%) alloy, and 37% and 89% increase, in comparison to the Mg-3Sn-1Mn-0.87 Ce (wt.%) alloy.

Magnesium (Mg) is abundant in natural reserves and its alloys have a number of attractive properties 1,2 . Specifically, Mg-alloys have high specific strength and specific stiffness, good damping and shock absorbing capacity, high thermal conductivity, and strong electromagnetic shielding ability 1,2 . Thus, Mg alloys are widely used for automotive, aerospace, and packaging applications. However, cold processing of Mg alloys is challenging because Mg has a hexagonal close-packed (HCP) lattice with limited slip systems, making their deformation at low temperature difficult. Another limiting factor that restricts the use of Mg alloys is their low thermal stability leading to deterioration in mechanical properties at high temperatures. The melting temperature of Mg 17 Al 12 phase in currently used Mg alloys (AZ and AM series) is ~735 K. In a number of structural applications, it is desirable to have high strength and superior corrosion resistance.
Microalloying has been actively pursued to enhance the mechanical properties of Mg-alloys. Certain microalloying elements form strengthening phases in the α -Mg matrix or at the grain boundaries, resulting in solid-solution strengthening and/or precipitation strengthening. These secondary strengthening phases, formed through microalloying, can assist in retaining a high dislocation density in the alloy by promoting the multiplication of dislocations and by pinning them, thereby improving the mechanical properties of Mg-alloys 3,4 . Previous research has shown that the addition of Si or Sn in magnesium alloys led to the formation of thermally stable and high-hardness Mg 2 Si or Mg 2 Sn phases, and thus improved the mechanical properties of Mg alloys at room and high temperatures [5][6][7][8] . We selected Sn instead of Si as one of the alloying elements considering the advantages of Mg 2 Sn phase and disadvantages of Mg 2 Si phase. The Mg 2 Sn phase has a high melting temperature of 1051 K, which is significantly higher than 735 K of Mg 17 Al 12 phase in the currently used AZ series of Mg alloys. Additionally, the Mg 2 Sn phase has a high hardness of 119 HV. The high melting temperature and high hardness of Mg 2 Sn phase makes it an excellent strengthening phase for enhancing mechanical properties and thermal stability [9][10][11][12] . In contrast, the Mg 2 Si phase has a strong tendency to coarsen grains in as-cast Mg-alloys, thereby decreasing strength, reducing casting ability of the alloys, and increasing their brittleness at room temperature. In addition to Sn, Mn is also a beneficial element from the perspective of solid solution strengthening and grain refinement 13,14 . Moreover, Bursik et al. demonstrated good creep resistance of Mg-xSn-1Mn (x = 3 and 5 wt.%) alloys 15 . Shi and Huang et al. reported new relationship between the Mg 2 Sn phase and the α -Mg matrix in the Mg-Sn-Mn alloy 16,17 .
Rare earth elements play an important role in governing the ultimate properties of Mg alloys. For example, Wei et al. studied the creep properties of Mg-Sn-La alloys at high temperatures and observed that Mg-xSn-2La (x = 5, 6.5 and 8.5 wt.%) exhibits superior creep properties at high temperatures than Mg-5Sn (wt.%) alloy at 473 K and 25-35 MPa. The main reason for this observation was the presence of rare-earth strengthening phase observed in Mg-xSn-2La (x = 5, 6.5 and 8.5 wt.%) alloy 11 . Although La is a beneficial alloying element, the influence of La on the microstructure and mechanical properties of Mg 2 Sn and other phases in Mg-3Sn-1Mn-xLa (wt.%) alloy, and strengthening mechanisms remain largely unexplored.
Considering that cold processing of Mg alloys is difficult, we explored a novel semi-solid processing, specifically, continuous rheo-rolling, to produce Mg-3Sn-1Mn-xLa (wt.%) alloy and improve the ability of the alloy to deform. Semi-solid processing has recently attracted significant attention to process magnesium-based alloys 18 . However, extensive studies are required to translate this novel process to industrial applications. Continuous rheo-rolling is a highly efficient semi-solid processing method in which a semi-solid metal composed of a liquid phase and a spherical solid phase is directly rolled following melting. In rheo-rolling, multiple traditional solid processing steps, including ingot casting, solidification, re-heating, and rolling, are integrated into one process, which makes it cost-effective and energy-efficient process. Moreover, rheo-rolling has a higher processing speed for non-ferrous metals than liquid metal roll casting. Using continuous rheo-rolling, Haga (Osaka Institute of Technology, Japan) produced A356 aluminum (Al) alloy plates with superior mechanical properties (tensile strength of 270 MPa) compared to A5052-H34, A6063-T4 and T6 19 . Continuous rheo-rolling effectively addresses the problem of poor deformability of Mg-alloys at room temperature. In this study, rheo-rolling processing with a novel shearing/vibration device for semi-solid metals was used to produce Mg-3Sn-1Mn (wt.%) alloy plates to improve the microstructure and properties of the alloy 20 .
The objective of the study described here is to process Mg-3Sn-1Mn-xLa (wt.%) alloy plates with La concentration in the range of 0.2 to 1.4 wt.% using continuous rheo-rolling process, and elucidate the effect of La on the microstructure and mechanical properties of Mg-3Sn-1Mn-xLa (wt.%) alloy plates that has not been previously explored.

Experimental Procedure
A self-designed continuous rheo-rolling experimental apparatus was used to conduct the experiments 20 . The roller diameter was 400 mm, the cross-sectional area of the prepared alloy plates was 4 mm × 160 mm, and the maximum processing rate was 22 m/min. Figure 1 shows a schematic configuration of the equipment used in this study 20 . A molten alloy was cast onto the vibrating slope plate to form a high-quality semi-solid metal slurry via flow shear and vibration effects. This semi-solid metal slurry entered directly into the bottom of the width-restricted roll for rheo-rolling. The process has two main advantages: (i) the temperature of the semisolid slurry is significantly lower than the melt in conventional roll casting, resulting in short solidification time and consequently very high rolling speed for the semi-solid alloy; and (ii) the process is expected to be developed as a high-speed semi-solid roll-casting technique. Thus, using this approach, the mechanical properties of the strip can be improved through tailoring of the microstructure.
The Mg-3Sn-1Mn-xLa (x = 0.2, 0.6, 1.0 and 1.4 wt.%) alloys used in this study were prepared using 99.95 wt.% pure Mg, 99.95 wt.% pure Sn, Mg-25La (wt.%) alloy, and Mg-4.38Mn wt.% alloy. The nominal chemical composition (in wt.%) of the alloy was Mg-3% Sn-1% Mn-(0.2, 0.6, 1.0, 1.4%) La, with traces of 0.01% Si, 0.05% Cu, 0.01% Ni, and 0.01% Fe. A resistance furnace (3 kW, SG2-3-9, Shenyang General Furnace Manufacturing Co., Ltd, China) was used to melt Mg alloys. The Ar gas was pumped into the resistance furnace when the temperature of the furnace approached 673-773 K at a pressure of 1.5 MPa and flow rate of 5 l/min. After replacement of air with argon inside the furnace, the magnesium ingots were placed inside the furnace and the temperature was increased to 973-1003 K. Preheated and dried Sn metal, Mg-25La (wt.%) alloy, and Mn were added to the molten mixture, and the temperature was increased and held at 1023 K for 20 min. Hexachloroethane was then used for degassing and skimming of slag. Finally, Mg-3Sn-1Mn-xLa (x = 0.2, 0.6, 1.0 and 1.4 wt.%) alloy plates were prepared by casting under Ar-shielded atmosphere by continuous rheo-rolling at 943 K with a roller speed of 0.052 m·s −1 , and a flow rate of 15 l/min for cooling water 20 .
Samples of Mg-3Sn-1Mn-xLa (x = 0.2, 0.6, 1.0 and 1.4 wt.%) alloys of dimensions of 15 mm × 15 mm × 10 mm and polished using standard metallographic procedure. X-ray diffraction (XRD; X'Pert, PANalytical B.V., Almelo, Holland) was used to analyze precipitates in the Mg-3Sn-1Mn-xLa (x = 0.2, 0.6, 1.0 and 1.4 wt.%) alloys. Samples with different La concentrations were first polished and etched using a solution consisting of 13 vol.% HCl, 47 vol.% C 2 H 5 OH, and 40 vol.% H 2 O at room temperature for 0.2 s, followed by scanning electron microscopy (SEM; SSX-550, Shimadzu, Kyoto, Japan) to study the distribution of each element in the matrix. Samples with different La concentrations were processed into Φ 3 mm × 0.5 mm discs using a spark-cutting machine (DK7740, Precision Machinery Co., Ltd, China); the discs were then ground to a thickness of 80 μm and further thinned using a precision ion polishing System (Gatan 691, USA). The microstructure and precipitate phase in the alloy was analyzed using high-resolution transmission electron microscopy (HRTEM, Tecnai G 2 F20, FEI, Oregon, USA). Uniaxial tensile tests were performed on a MTS 810 mechanical properties testing system (MTS, USA) at a constant strain rate of 5 × 10 −3 s −1 at room temperature. A MTS LX300 laser extensometer was used to calibrate and measure the sample strain on tensile loading. For each condition, three tests were performed to obtain the average mechanical property data. After tensile tests, the alloy with the best mechanical properties was selected to study the deformed microstructure by HRTEM. The optimal Mg-3Sn-1Mn-xLa (wt.%) alloy plate was deformed to 2% elongation, and specimens were cut from the gage of the deformed samples, to fundamentally understand the impact of precipitate phase on dislocation movement via HRTEM. Figure 2 shows the effect of La concentration on precipitate formation in Mg-3Sn-1Mn-xLa (wt.%) alloy plates as studied by X-ray diffraction for different La concentrations. It can be seen that α -Mg and Mg 2 Sn were the two main phases in Mg-3Sn-1Mn-0.2La (wt.%) alloy (curve (b)). However, the diffraction peaks of Mg 2 Sn phase at (111), (200), (222) and (513) were weaker than those observed in Mg-3Sn-1Mn (wt.%) alloy. As shown in curve (c) in Fig. 2, when the La concentration was increased to 0.6 wt.%, diffraction peak intensities associated with the Mg 2 Sn phase at (111), (200), (222) and (513) were further decreased. The Mg 17 La 2 phase emerged at (312) and (116) and the La 5 Sn 3 phase emerged at (330). The diffraction peaks corresponding to La 5 Sn 3 phase at (111) and (930) overlapped with the α -Mg phase at (100) and (201), respectively, while the diffraction peak at (642) overlapped with the diffraction peaks of Mg 2 Sn phase at (513). As the La concentration was increased to 1.0 wt.% (curve (d)), the diffraction peak intensities corresponding to Mg 2 Sn phase at (111), (200), (222) and (513) was further decreased. A new diffraction peak emerged at (412) position and was identified as Mg 17 La 2 phase, suggesting a gradual increase in the volume fraction of Mg 17 La 2 phase. Meanwhile, the diffraction peak intensity at (330) was also increased for the La 5 Sn 3 phase. As the La concentration was increased to 1.4 wt.%, the diffraction peak intensities of the Mg 2 Sn phase at (200), (222) and (513) were very weak as shown in curve (e) in Fig. 2. The intensities were increased for Mg 17 La 2 phase ((312) and (116) peaks) and La 5 Sn 3 phase ((330) peak). New diffraction peaks emerged at (500) and (006) were identified as Mg 17 La 2 phase. Figure 3a-c are SEM micrographs and the associated results of energy dispersive X-ray spectrometer (EDS) analysis of α -Mg grain boundaries, labeled as 1-3 in Table 1. These results indicate that in Mg-3Sn-1Mn-0.2La (wt.%) alloy, the compounds formed at the grain boundaries were primarily composed of Mg and Sn with a ratio of ~2:1, based on atomic %. Based on XRD and EDS analyses, the compound formed at α -Mg grain boundaries was determined to be Mg 2 Sn phase, which was confirmed by TEM studies (Fig. 4a-c). The associated results of energy dispersive X-ray spectrometer (EDS) analysis at the α -Mg grain boundaries are labeled as 4-6 ( Table 1). Only a short, rod-like Mg 2 Sn phase was observed, with an average length of 100 ± 5 nm and an average width of 45 ± 2 nm. XRD and EDS results indicated that no La-containing phase precipitated in the Mg-3Sn-1Mn-0.2La (wt.%) alloy, and majority of La was present in solid solution in the α -Mg matrix.

Microstructure of Mg-3Sn-1Mn-xLa alloys.
EDS analysis revealed that the chemical composition was 56.5Mg-26.5Sn-17.0La (wt.%) for the plate-shaped compound at the α -Mg grain boundary of Mg-3Sn-1Mn-0.6La alloy (No. 3 in Table 1). The TEM observations, suggested that this new phase was present as plate-like at α -Mg grain boundary, with an average length of 380 ± 10 nm and an average width of 110 ± 5 nm (Fig. 5a). This plate-shaped compound had a Mg:Sn:La ratio of ~66:26:7 (at.%), as determined from EDS analysis (No. 7 in Table 1). As shown in Fig. 5b, the average length of the plate-shaped compound at the α -Mg grain boundary of Mg-3Sn-1Mn-1.0La (wt.%) plates approached ~560 ± 20 nm and an average width of 90 ± 5 nm, indicating a significant increase in volume fraction, and the  Table 1.
compound appeared to be evenly distributed at the α -Mg grain boundary. The related EDS analysis is listed in Table 1 (labeled as 8). This plate-shaped compound grew perpendicular to the α -Mg grain boundary and extended toward the inside of the matrix, preventing the α -Mg grain boundary from sliding (Figs 5 and 6), and thereby potentially increases the strength of the alloy. In addition, the refinement of the Mg 2 Sn phase was beneficial in improving the mechanical properties of Mg-Sn-Mn alloy 17 . This aspect is supported by the observation that a spherodized Mg 2 Sn phase of ~50 ± 2 nm in diameter was formed and evenly distributed between the plate-shaped compounds (the inset in Fig. 5b). The volume fraction of compound increased in comparison to the other two alloys ( Fig. 3 and No. 3 in Table 1). The Mg 2 Sn phase continued to be intragranular precipitate, and variation in morphology and distribution were not significant, as shown in Fig. 4c. However, the quantity of the plate-shaped compounds at the α -Mg grain boundary was increased. The average length increased to 2300 ± 50 nm, whilst the average width decreased to 70 ± 5 nm (Fig. 5c). Figure 6a,b are the morphologies of the plate-shaped compound observed along the zonal direction of [10,11] Mg , and Fig. 6c,d show the diffraction patterns of these plate-shaped compounds that overlapped with the surrounding α -Mg matrix. Two systems of periodic spots can be seen in Fig. 6c. One set of spots indicated by red lines reveal R 11 = 3.5, R 12 = 7.4, along with an angle of 74° between R 11 and R 12 . Therefore, these spots are indexed as La 5 (Fig. 6c). Moreover, another set of relatively regular spots were observed in Fig. 6d, showing R 31 = 1.6, R 32 = 2.1 as well as an angle of 106° between R 31 and R 32 . These spots are indexed as Mg 2 Sn (face-centered cubic, FCC, a = b = c = 0.6759 nm) phase according to the [433] Mg2Sn zone axis. Thus, it was confirmed that this plate-shaped compound was composed of La 5 Sn 3 , Mg 2 Sn and Mg 17 La 2 phases, which is consistent with the XRD analysis presented in Fig. 2. This new-type of composite structure was first observed in this study and has not been previously reported [8][9][10][11][12][13] .
With increasing La concentration in the range of 0.2-1.4 wt.%, the intragranular Mg 2 Sn phase was gradually refined, spherodized, and uniformly distributed. The average length of the plate-shaped compound (La 5 Sn 3 and Mg 17 La 2 phases) was gradually increased, accompanied by decreasing width and average length of Mg 2 Sn phase (Fig. 7).
Mechanical properties of Mg-3Sn-1Mn-xLa alloys. Engineering stress-strain plots of Mg-3Sn-1Mn-xLa (x = 0.2, 0.6, 1.0 and 1.4 wt.%) alloys tested at room temperature are presented in Fig. 8a. The Mg-3Sn-1Mn (wt.%) alloy showed no yield plateau during tensile straining. However, on the addition of La, yield plateau was observed for Mg-3Sn-1Mn-xLa (wt.%) alloys during tensile tests, which is different from the deformation characteristics of the reported Mg-alloys 4 . Figure 8b summaries the influence of La concentration on tensile stress and elongation of Mg-3Sn-1Mn-xLa (wt.%) alloys. With increased La concentration, the tensile strength and

Table 1. Chemical compositions of different regions in the Mg-3Sn-1Mn-xLa alloys obtained by EDS analysis. Numbers represent the different positions in Figs 3, 4 and 5, respectively.
elongation of the alloys was first increased and then decreased, the peak values were achieved at 1.0 wt.% La. The Mg-3Sn-1Mn-1.0La (wt.%) alloy plate exhibited a tensile strength of 230 ± 10 MPa and elongation of 7.5 ± 0.2%. These values are 29% and 32% higher than the tensile strength (175 ± 5 MPa) and elongation (5.6 ± 0.1%) of Mg-3Sn-1Mn (wt.%) alloy, and are respectively 37% and 89% higher than the tensile strength and elongation of Mg-3Sn-1Mn-0.87Ce (wt.%) alloy 13 . The small but consistently observe improvement in elongation of ~2% is encouraging because Mg element is an intrinsic brittle metal. The symmetry of the hexagonal close-packed (HCP) crystal structure has limited number of independent slip systems, resulting in poor ductility at room temperature 21 . Moreover, the melting points of precipitates are higher than pure Mg. For example, La 5 Sn 3 such has a melting point of 1500 °C, whilst that of Mg 17 La 2 is 672 °C. Thus, the stability of mechanical properties can be improved by the addition of La to Mg alloys.

Discussion
Mechanism of microstructure formation. The difference in electronegativity of alloying elements determines their ability to form compounds. The greater the difference in electronegativity, the larger the binding force  Table 1.
between these elements, thus making them more likely to form a compound 13,22 . Table 2 summarizes the electronegativity difference between Mg, Sn, La and Mn. The maximum difference in electronegativity is between La and Sn, followed by Mg and Sn 13,22 . The solid solubility of La in the α -Mg matrix is 0.14 wt.% 23 , and thus, majority of La is dissolved within the α -Mg matrix, when 0.2 wt.% La was added to the alloy. In the Mg-3Sn-1Mn-0.2La (wt.%) alloy, La-containing phases did not form because of the fast cooling rate of the vibration plate during continuous rheo-rolling and the rapid solidification rate of the alloy 20 25 .
In addition to the microalloying ability, La can also facilitate the nucleation of Sn-containing phases 25 . Thus, with increase in La concentration, a significant amount of La was homogeneously distributed within the matrix,  Table 1.
Scientific RepoRts | 6:23154 | DOI: 10.1038/srep23154 as indicated by SEM observations, which facilitates an uniform distribution of Sn phase near the grain boundaries and the nucleation of Mg 2 Sn phase (Fig. 9a-c). During the growth of Mg 2 Sn phase, the surrounding La atoms segregate on the surface of initial Mg 2 Sn phase, thus increasing the surface energy and making it very difficult for surface atoms to continuously diffuse into the inner Mg 2 Sn phase, which hinders further growth of Mg 2 Sn phase, resulting in the gradual refinement and spherodization of Mg 2 Sn phase. As a result, the Mg 2 Sn phase becomes smaller and the aspect ratio is close to 1 with increase in La concentration (Fig. 4).
During the solidification of the alloy, as the solute concentration was high to form intermetallic compounds, the phase with the highest melting point will be the first to form. Then, as the temperature of the molten alloy decreases, eutectic reactions occur among the remaining alloying elements and phases with low melting point start to form 26 . Because of the large electronegativity difference between La and Sn (Table 2), and higher melting point of La 5 Sn 3 phase (1773 K) than Mg 2 Sn (1043 K) and Mg 17 La 2 phases (945 K), La 5 Sn 3 phase first nucleated and grew at the α -Mg grain boundary, when the La concentration was 0.6 wt.% (Fig. 10a,b). Idbenali et al. showed that  La 5 Sn 3 phase was stable at room temperature 27 . The La 5 Sn 3 phase contained few Sn atoms and no Mg atoms and grew perpendicular to the α -Mg grain boundary, resulting from eutectic transformation during the final solidification. Thus, during the formation of La 5 Sn 3 phase at the α -Mg grain boundary, Mg and Sn atoms were constantly expelled and accumulated at the solidification interface, such that the nucleation of Mg 2 Sn phase occurred. The formation of La 5 Sn 3 phase provided a site for the formation of Mg 2 Sn phase (Fig. 10c). As the Mg 2 Sn phase adhered to the surface of the La 5 Sn 3 phase and nucleation started, its surface energy was decreased; therefore, nucleation occurred at lower degree of undercooling (Fig. 10d). Additionally, since the electronegativity difference between Mg and Sn is greater than between Mg and La, and the melting point of the Mg 2 Sn phase is higher than Mg 17 La 2 phase, thus, the Mg 2 Sn phase nucleated on La 5 Sn 3 phase, prior to the nucleation of Mg 17 La 2 phase. With nucleation and growth of Mg 2 Sn phase, Mg and La atoms were expelled and accumulated at the liquid-solid interface, providing constituents for the formation of the Mg 17 La 2 phase, as well as the adherent points for nucleation of the Mg 17 La 2 phase, thus facilitating the formation of the Mg 17 La 2 phase (Fig. 10e). Therefore, at the α -Mg grain boundary, La 5 Sn 3 , Mg 2 Sn and Mg 17 La 2 phases nucleated and grew alternately, forming a plate-shaped compound comprising of three phases, confirmed by HRTEM (Fig. 10) and XRD and EDS analyses ( Fig. 2 and Table 1).
As the La concentration increased, more La 5 Sn 3 and Mg 17 La 2 were gradually formed and plate-shaped compounds comprising of La 5 Sn 3 , Mg 2 Sn, and Mg 17 La 2 phases at the α -Mg grain boundary. In Mg-La alloys, higher concentration of La increases the cohesive energy of Mg-La compound and α -Mg grain stability, which is favorable for increasing the stability of La-containing phases 28 . Thus, the stability of La 5 Sn 3 and Mg 17 La 2 phases Effects of microstructure on mechanical properties of alloys. It can be seen from Fig. 8 that after the addition of La, the Mg-3Sn-1Mn-xLa alloy showed a yield plateau during stretching, which is seldom observed in Mg alloys 4 . The yield plateau is mainly due to the pinning effect of the precipitates such as La 5 Sn 3 , Mg 2 Sn, and Mg 17 La 2 on dislocations. As dislocations are pinned by the precipitates, higher stress is required for dislocations to escape the blockage of the precipitates and move, thus generating the upper yield point. Once dislocations eventually overcome the pinning force, they move and the stress decreases, generating the lower yield point. Several studies have shown that rare earth atoms can effectively impede dislocation movement 4,29,30 . After deformation to a strain of 2%, a high density of dislocations can be observed around the Mg 2 Sn phase in the Mg-3Sn-1Mn-1.0La alloy (Fig. 11), suggesting that the Mg 2 Sn phase had a pinning effect on the movement of dislocations. In fact, it is reported that the Mg 2 Sn phase is a hard phase in Mg-3Sn-1Mn-xLa (x = 0.2, 0.6, 1.0 and 1.4 wt.%) alloys with a microhardness of 1.19 GPa 7-9 . When the dislocations move to the region near the Mg 2 Sn particles, they indicated a tendency to bypass the Mg 2 Sn phase (Fig. 12a), leading to Orowan strengthening 35 . A similar scenario has been reported by Sasaki et al. 36 . On the other hand, the Mg 2 Sn phase was gradually refined, spherodized, and more uniformly distributed with increased La concentration (Figs 4 and 7), leading to increase in the pinning effect of Mg 2 Sn phase on dislocations slip 17 . For example, the length of Mg 2 Sn phase decreased from 100 nm to 50 nm with increased La addition from 0.2% to 1.4%, exhibiting equiaxial morphology.
Based on the well-known Orowan mechanism, the strength increment due to precipitation strengthening, σ prec. , is given by equation (2) 35 : .

8 (2)
prec where M is the Taylor factor, G is the shear modulus, b is the Burgers vector and λ is the average spacing between neighboring particles. Apparently, a decrease in both particle size and the spacing of adjacent precipitates not only increases the stress required for dislocation movement, but also dislocation density, leading to increased strength of the studied alloys. With increase in La concentration to 1.0 wt.%, a plate-shaped compound composed of La 5 Sn 3 , Mg 2 Sn and Mg 17 La 2 phases formed at the α -Mg grain boundary of the Mg-3Sn-1Mn-1.0La (wt.%) alloy. Despite increased average length to 560 ± 10 nm, the width of the plate compounds reduced to 90 ± 5 nm, accompanied by a decrease in length of Mg 2 Sn particles to 50 nm. Following equation (2), the strength associated with precipitation strengthening should increase because of reduced spacings between plate-shaped compounds and spherical Mg 2 Sn particles. This deduction was supported by tensile tests, as indicated in Fig. 8. Grain boundary sliding plays a significant role during the plastic deformation of the alloy, therefore, the morphology of the precipitates at α -Mg grain boundary and the energy of α -Mg grain boundary are important factors in governing the strain of the alloy 37 . The plate-shaped composite was characterized by HRTEM (Figs 10 and 11) and the degree of mismatch was 4.6% according to equation (1). This value means that the interface has a lower strain energy and this kind of interface is more stable, less likely to initiate nucleation and growth of microcracks during deformation. Moreover, this plate-shaped compound is formed near the α -Mg grain boundary and grows perpendicular to the boundary and toward inside of the α -Mg matrix, by pinning the α -Mg grain boundary and impede the sliding of α -Mg grain boundary (Figs 5, 6, 10 and 11). As the dislocations move to a nearby location in the vicinity of the plate-shaped compound, they pile up because of impeding effect of the compound (Fig. 12), leading to an increase in the strength of the alloy. As the La concentration approached 1.4 wt.%, more plate-shaped compounds were formed and gradually became thinner, with average thickness of 70 ± 5 nm and significantly increased average length of 2300 ± 50 nm. According to equation (2), the stress increment derived from precipitation strengthening should increase because the thickness of plate-shaped compounds decreased (Figs 5c and 6). However, Fig. 8 shows that both tensile strength and strain decreased with increasing La content from 1.0% to 1.4%. The main reason must be related to the high degree of segregation of the plate compounds (Figs 3c and 5c), though the size of Mg 2 Sn particles still remained constant as small as ~50 nm, in comparison to that of Mg-3Sn-1Mn-1.0La (wt.%) alloy. As a result, the total pinning effect of the precipitates on the α -Mg grain boundary was decreased due to the high degree of segregation of plate-shaped compounds, despite similar dimension of Mg 2 Sn particles, leading to a relatively weak hardening effect compared to the alloy containing 1.0 wt.% La.
A power-law hardening equation can be used to describe the flow strength of metal materials, as follows 38 : 1 2 where σ is the flow stress, ɛ is the strain, n is the work hardening exponent, K 1 represents the initial yield strength of the materials and K 2 represents the increment in strength due to work hardening. According to equation (3), instability necking is activated, when ɛ u = n (uniform elongation) during uniaxial tension of sheet specimens. Referring to Fig. 8a, it is evident that the Mg-3Sn-1Mn-1La alloy had the highest n value among all the five alloys.