First-principles calculation and experimental study on the effect of rare earth Ce and Nd on the corrosion behavior of Mg alloys

In this study, the influence mechanism of rare earth elements Ce and Nd on the corrosion behavior of Mg alloy was studied by combining experimental characterization with the first-principles calculation. The changes of work function and surface energy of the rare Earth phase and matrix phase in binary rare Earth Mg alloys Mg-0.3%Ce and Mg-0.3%Nd. In addition, the electronic properties of the second rare Earth phase and matrix phase, and the correlation between the interface energy of the second rare Earth phase and matrix and the corrosion behavior of Mg alloys were investigated. The experimental results show that Mg12Ce and Mg12Nd as the second phases of Mg-0.3%Ce and Mg-0.3%Nd, respectively, have not obvious roles in the galvanic corrosion of the alloys. The corrosion morphology of the two alloys is similar, the matrix undergoes filamentary corrosion through the grain to a large area. The results of the first-principles calculation show that the binding energy of the rare Earth phase is higher than that of the matrix phase, this implied the addition of light rare Earth elements Ce and Nd can improve the stability of the second phase. The work function of different surfaces of the second phase is similar to that of the matrix phase, so limited effect of the rare Earth phase on corrosion behavior has been found. In addition, the addition of rare Earth Ce and Nd will decrease the surface stability of Mg matrix, this result reaffirms the higher corrosion rates of Mg-0.3%Ce and Mg-0.3%Nd over that of the pure Mg.


Background
The Mg alloys are widely used in some fields such as aerospace, automotive, and electronics because of their high specific strength and stiffness, low modulus of elasticity, and excellent electromagnetic shielding properties [1]. However, the corrosion resistance of Mg alloys is generally poor, this becomes the 'short board' in the engineering application of Mg alloys [2]. Therefore, the investigation of the corrosion behavior and mechanism of Mg alloys and the development of new Mg alloys with high strength and corrosion resistance have been hot topics in the research.
Currently, the addition of rare Earth to Mg alloys is one of the main methods to improve the corrosion resistance of Mg alloys [3]. Rare Earth elements commonly used to improve the properties of Mg alloys include cerium (Ce), lanthanum (La), yttrium (Y), samarium (Sm), neodymium (Nd), gadolinium (Gd), etc Zhong Liying [4] found that the addition of La or Ce to AZ91 Mg alloy resulted in the refinement of Mg matrix grains, a more uniform distribution of β-Mg 17 Al 12 , and the rare Earth elements inhibited the rate of hydrogen precipitation thus improving the corrosion resistance of Mg alloy. Deng Weilin et al [5] investigated the effect of the content of rare Earth element Nd and solid solution treatment on the corrosion resistance of Mg-4Zn alloy, the results showed that the element Nd increased the content of the second phase in the alloy while refining the Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. alloy grain, the solid solution treatment reduced the content of the second phase in Mg-4Zn-xNd, the corrosion rate of the alloy decreased with the reduction of the content of the second phase, the solid solution treated Mg-4Zn-2Nd showed the best corrosion resistance. Studies have shown that the precipitated phases of AZ series Mg alloys, while giving excellent mechanical properties, also lead to an increased tendency to localized corrosion. For example, Jönsson et al [6] studied the influence of the microstructure of the Mg alloy AZ91on its corrosion behavior using the Kelvin probe technique and found the β-Mg 17 Al 12 and AlMn phases have higher potential relative to the matrix and acted as a cathodic phase to induce corrosion of the matrix. Feng et al [7] concluded that Mg-x Al-(15-x) Zn (x = 12.5, 5.6, 3.3, 1.0 wt%) in Mg alloys with different precipitation phases acted as the cathode of the microcell, promoting the corrosion of the Mg matrix as the anode phase.
Based on the theoretical basis that the electrode potential between the precipitated phase and the Mg matrix determines the location of the corrosion nucleation, any precipitated phase with a higher electrode potential than the matrix has long been considered to have a role in promoting corrosion of the Mg alloy matrix. However, with the development of corrosion detection techniques, researchers have found that the relative potential of the precipitated phase to the matrix in Mg alloys containing rare Earth is not entirely consistent with the corrosion effect predicted by potential values. For example, a study by Buzolina [8] found that a rare-Earth phase in ZK40-2Gd with a relative potential difference of up to 170 mV to the matrix did not significantly contribute to matrix corrosion; whereas a rare-Earth phase in ZK40-2Nd with a relative potential difference of only 35 mV to the matrix contributed to the corrosion of the surrounding matrix. A previous study by the group [9] also found that the addition of (La, Ce) mixed rare Earth to the Mg alloy AZ91 did not significantly induce matrix corrosion despite the high relative potential of the Al 4 (La, Ce) rare Earth phase (relative potential to the matrix was ranged from 390-440mV).
Wen [10] revealed the mechanism of inclusions-induced local corrosion behavior in low alloy steels by combining first-principles calculations with experimental methods. By calculating the work function, surface energy, and density of states of different inclusions, Fe matrix, and Fe 3 C, observing the corrosion morphology, it is found that the magnitude of the work function was consistent with the corrosion resistance tendency of the inclusions, and the larger the work function, the higher the corrosion resistance. Liu [11] calculated the work function of different crystalline surfaces and different atomic terminals of common second phase particles in the Al alloy through the first-principles calculation, used the relationship equation between the work function and Volta potential difference, through the corrosion potential to elucidate the characteristics of the evolution of the micro-galvanic coupling between the different particles and the matrix Al. This work explored a new way to evaluate the environmental factors on the micro-galvanic effect.
In present work, to further understand the related factors on corrosion behavior of the Mg alloy, the results of the theoretical calculation must be combined with the experimental study. The first-principles approach based on density functional theory (DFT) has been applied to determine the factors affecting corrosion behavior of alloys. The surface and interface characteristics that cannot be observed in the experiment can be obtained through the first-principles calculation and then compared with the corrosion behavior observed in the experiment. As such, the main factors affecting the corrosion behavior of a galvanic couple could be determined.

Experimental method
In this study, we used castings smelted at the Baotou Rare Earth Research Institute as the experimental materials. The addition of Ce and Nd is 0.3 wt%, respectively. The pure Mg and master alloy were placed in a mediumfrequency induction furnace with Argon protection. The heating was stopped after the temperature rose to 730°C , which remained warm for 30 min. When the furnace temperature dropped to about 710°C, the melt was poured into the metal mold for natural cooling. The second phases of the Mg alloys were observed and analyzed using environmental scanning electron microscope with an energy dispersive spectroscopy (EDS) (a QUANTA FEG650 field emission) and transmission electron microscopy (TEM, Talos F200X). The preparation of TEM samples is as follows. Grind the samples to a thickness of approximately 1 mm on a grinder, and then grind them to a thickness of approximately 50-80 μm by using sandpaper. Further, cut the thin slices into Φ3 mm discs, and then thin them to tens of nanometers with an ion thinner. As the surface of the Mg alloy easily oxidizes in an argon atmosphere, it must be stored in a TEM sample box. The etched morphology of the sample immersed in 0.1mol l −1 NaCl solution for 30 min was observed through SEM. (Electrochemical Atomic Force Microscope (EC-AFM), MultiMode8, America) in 0.01 mol l −1 NaCl solution. Further, the potential difference between the second and matrix phases was measured by the device module. The PFQNE-AL probe was used for measuring the surface potential, and it works in the tapping mode. The polarization curves and electrochemical impedance spectras of the Mg alloys were measured using the electrochemical workstation (Zennium, German).

Calculation method
In this study, we used the quantum mechanics of the Vienna ab initio simulation package (VASP) for calculations and adopted the periodic boundary conditions. The interaction between the valence electrons and ions is described using the projector-augmented wave (PAW) method. The electron-exchange correlation is generalized using the gradient approximation (GGA) method of Perdew-Burke-Ernzerhof (PBE). The cut-off kinetic energy of the plane-wave basis was set to 350 eV. The k-point mesh of the Brillouin zone was generated using the Monkhorst-Pack method, and the structure was optimized using the conjugate gradient algorithm. When calculating the DOS, the linear tetrahedron method modified by Blöchl [12] was used. When the force acting on all atoms is less than 0.01 eV Å, the optimization is completed. If the energy is stable within 1.0 × 10 -4 eV/atom, the self-consistent calculation of electrons stops and is considered a convergence. By optimizing the structure of the matrix and the second phase, the lattice parameters obtained are as follows:  alloy, either diffusely distributed within the grains or distributed in a discontinuous network at the grain boundaries. To determine the composition, the second phase of the alloys were tested using EDS. The second phase indicated by the arrow in figure (b) (the EDS results are shown in figure (e)), which consists of the elements Mg and Ce with an atomic percentage of approximately 91.5:7.64. According to the Mg-Ce binary phase diagram, the liquid phase on the Mg-rich side will undergo an Mg-0.3 wt% Ce alloy composition is in the range of hypoeutectic, and the organization obtained by equilibrium solidification should consist of the incipient α-Mg and the eutectic phase (α-Mg+Mg 12 Ce). Figure (c) shows the SEM morphology of the Mg-Nd binary alloy, which is dominated by the supersaturated solid solution α-Mg phase, with a small amount of irregularly shaped second phases at the grain boundaries, with a size of about 5 μm. EDS analysis of the second phase indicated by the arrow in figure (d) shows (figure (f)) that the elemental composition and content of the bright white phase corresponds to an atomic ratio of Mg to Nd of 90.65:8.72. Comparing figures (a) and (c), the greater number of second phases in the Mg-Ce alloy than that in the Mg-Nd alloy is due to the fact that the solid solution degree of Ce is smaller than that of Nd. Figure 2 shows a bright field micrograph and electron diffraction spot of the corresponding precipitated phases in the Mg-0.3%Ce and Mg-0.3%Nd. According to the electron diffraction spots in the corresponding selected areas, and the high resolution and Fourier transformed diffraction patterns at the interfaces can be obtained. Figure (

Electrochemical measurement results
Polarization curves of pure Mg, Mg-0.3%Ce and Mg-0.3%Nd in 3.5%NaCl solution are shown in figure 3, the curves are fitted to obtain the corrosion potential (E corr ) and corrosion current density (icorr), the fitting results are shown in table 1. As the contact area of the measured sample and the solution is 1 cm 2 , the corrosion current value is the corrosion current density value, so the larger the value represents the larger the corrosion current per unit area, and the faster the corrosion rate of the alloy. What can be seen from table 1 is that the order of the i corr is as follows: pure Mg < Mg-Ce alloy <Mg-Nd alloy, this implies the Mg corrosion rate is less than Mg alloy with Ce and Nd addition.
The Nyquist diagram (figure 4(a)) shows that the corrosion mechanism is the same before and after the RE addition, and the corrosion rates of different rare Earth Mg alloys are different. The larger the radius of the capacitive arc, the greater the resistance to charge transfer, the lower the corrosion rate and the better the corrosion resistance. Combined with the Bode diagram shown in figure 4(b), the order of corrosion resistance is: pure Mg > Mg-Nd alloy > Mg-Ce alloy, the results show that a small amount of light rare Earth Ce and Nd will reduce the Mg corrosion resistance.

Electronic structure of rare Earth second and matrix phases 3.3.1. Binding energy
In order to clarify the relative stability of the structure of the RE phase and the Mg-matrix of the RE Mg alloys, the binding energy of the bulk phase is calculated separately using the VASP software package, the binding energy (E coh ) is the energy released by the atoms from the free state to form the compound, the greater the negative and absolute value of the binding energy, the more stable the crystal structure of the compound. The binding energy is calculated with equation (1).
E coh is the total energy of the intermetallic compound after structural optimisation, E E and atom A atom B denote the free atomic energies of elements A and B in the solid state, respectively, and N A and N B denote the number of atoms of elements A and B in the intermetallic compound cell structure model, respectively.
The results of the binding energy calculations for the pure Mg, precipitated and matrix phases are shown in figure 5. What can be seen from the figure is that the results of the binding energy calculations are all negative values, indicating that these phases are stable. The structural stability of the above phases can be ranked from the calculation results in the following order: Mg 12 Ce > Mg 12 Nd > Mg-0.3Nd >M g-0.3Ce > α-Mg. The smaller the binding energy, the stronger the interatomic bonding force, and the higher of the resistance to external deformation under the same degree of external forces.

Work function and surface energy of pure Mg
Surface energy is defined as the excess energy at the surface of a material relative to the bulk phase, or the amount of energy required to construct a particular unit area of the surface. Equation (2) can be used for the calculation of surface energy.   where E surf is the surface energy of the material, and E slab n ( ) is the total energy of the lamellar flat structure model, and E bulk is the reference energy of a single atom of the block or the energy of the structural unit. s is the surface area of the lamellar model. Due to the symmetry of the lamellar model, this structural model system contains 2 equal (or symmetrical) crystal surfaces.
The work function is the minimum work or energy done by an electron escaping from the Fermi energy level to reach the vacuum energy level, and reflects the ease with which an electron can escape from the surface of a material. The expression is given in equations (3). The surface work function is largely influenced by the atoms in the surface layers, and the magnitude of the electron work function is usually determined by the atoms in the surface 1-3 layers. In this paper, we have chosen to replace the two Mg atoms in the center of the surface layers on the upper and lower surfaces of several crystalline surfaces of Mg alloys with two rare Earth atoms to establish a symmetric surface doping model. As can be seen from the values of the electron work function in table 3, both the rare Earth elements Ce and Nd can    Figure 6 shows the morphology of the second phase in the rare Earth Mg alloy, the potential distribution and the potential distribution curve of the corresponding area, from the figure (a) can be seen in the bright white Mg 12 Ce phase, figure (b) is the precipitation of the corresponding potential distribution, the two end points of the straight line L were taken from the matrix across the second phase, measured by the figure (c) the potential difference between the location of the two points in the figure is about 200 mV, the second phase of the potential of the second phase is significantly lower than that of the matrix, and there is an uneven distribution of the potential difference. Figure (d) shows the granular Mg 12 Nd phase, Figure (e) shows the potential diagram, and the potential difference distribution curve between the precipitated phase and the matrix area (figure (f)) shows that the potential difference between the two is 300 ∼ 350 mV, through the potential measurement of each phase found that the potential difference between the precipitated phase and the matrix and the difference between the electronic work function of the two phases there is a difference, the main reason may be the actual measurement The main reason for this may be that the second phase and the Mg matrix have different crystalline surfaces or different atomic termination surfaces exposed during the actual measurements.

Results and discussion
In this study, the addition of RE Ce and Nd with a mass fraction of 0.3% respectively reduced the corrosion resistance of the Mg alloy, which can be explained by first-principles calculations.
The results of the binding energy calculations show that the RE second phase is more stable than the matrix phase, with the pure Mg phase being the least stable. It can be seen that the addition of rare Earth Ce and rare Earth Nd may improve the corrosion resistance of the alloy if a higher number of second phases can be formed, due to the high stability of the second phase. Due to the limited additions in this paper (only 0.3 ωt%), the amount of the second phase generated in the alloy is small and the effect of the second phase on the corrosion resistance of the alloy is relatively small.
By calculating the surface energy and the electron work function of the different crystalline surfaces of the Mg matrix and the second phase in pure Mg and rare-Earth Mg alloys before and after the addition of rare Earth, it is found that the more densely arranged the surface atoms of the second phase in Mg alloys, the larger the electron work function. The addition of the rare Earth Ce and Nd decreases the electron work function and increases the surface energy of the Mg matrix. This means that both the rare Earth Ce and Nd will significantly reduce the surface stability of the Mg matrix, with Ce reducing the surface stability more significantly. For the corrosion performance of the alloy, low work function and high surface energy have poor surface corrosion resistance. This also indicates that after adding 0.3 ωt% of rare Earth Ce and Nd, the rare Earth mainly affects the corrosion behavior of the alloy by influencing the surface properties of the Mg alloy matrix, and the influence of the second phase is relatively small.

Conclusion
(1) Calculations of the binding energy of the RE second phase and the matrix phase show that the addition of the light rare Earth elements Ce and Nd can improve the stability of the second phase, but the number of the second phase is small, coupled with the fact that the work functions of the different surfaces of the second phase are similar to those of the matrix phase, so that Mg 12 Ce and Mg 12 Nd have a small effect on the corrosion behavior of the Mg-Ce and Mg-Nd alloys, respectively.
(2) After the addition of rare Earth Ce and Nd, the work function on the surface of the Mg matrix will decrease and the surface energy will increase. This indicates that both RE Ce and Nd will reduce the surface stability of the Mg matrix, Ce decreases more obviously, this is the main contributing factor to the higher corrosion rate of the Mg-Ce alloy over that of the Mg-Nd alloy.