Effects of Single Doping and Composite Doping of Yttrium and Antimony on the Structural, Thermodynamic, Mechanical, and Electronic Properties of Mg<sub>2</sub>Si by First Principles

Zhou, Zhonghao; Zhao, Zhen; Li, Zhi

doi:https://doi.org/10.1155/2019/6307163

Journal of Nanomaterials

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Abstract Introduction Results and Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2019 | Article ID 6307163 | https://doi.org/10.1155/2019/6307163

Effects of Single Doping and Composite Doping of Yttrium and Antimony on the Structural, Thermodynamic, Mechanical, and Electronic Properties of Mg₂Si by First Principles

Zhonghao Zhou,¹Zhen Zhao,²and Zhi Li³

Academic Editor: Stefano Bellucci

Received28 May 2018

Accepted15 Oct 2018

Published10 Mar 2019

Abstract

The structural, stability, thermodynamic, mechanical, and electronic properties of Y and Sb doped into Mg₂Si were studied by first principles. The results show that the stable structures are Mg₇Si₄Y, Mg₈Si₄Sb, Mg₆Si₄YSb, and Mg₇Si₄YSb. Mg₈Si₄Sb has the largest ductility among them. Y doping causes strong orbital hybridization between Mg (2p) and Y (4d), while Sb doping causes strong orbital hybridization between Mg (2p), Si (3p), and Sb (5p). However, the thermal conductivity and hardness of Mg₂Si will be reduced by Y and Sb doping. The conductivity of Mg₈Si₄Sb is the best. The anisotropy of the {100}, {010}, and {001} surfaces will increase once doped with Y or Sb. Mg₈Si₄Sb has the highest degree of anisotropy.

1. Introduction

The 6xxx series aluminum alloy is widely used in automobile manufacturing because of its excellent qualities, such as reduced weight and good corrosion resistance [1, 2]. Mg₂Si is the main strengthening phase [3] of the 6xxx series Al alloy, and it possesses a low density and high melting point and impedes grain boundary sliding [4–9]. However, the application of the 6xxx series Al alloy is limited due to its brittleness. This is due to the Mg₂Si phase which is the preferred phase to form coarse Chinese script or dendritic morphology [10–12]. To improve the mechanical properties of Mg₂Si, many alloying elements (such as Bi, As, and Sn [13–20]) are doped. Recently, Y and Sb doping into the Mg₂Si phase was considered. Zhang and Zhang [21] found that the fine modification effect of Y on the primary Mg₂Si phase is better than that of an equal amount of mixed light rare earth, and it can greatly refine the Mg₂Si grains and improve the tensile strength and elongation. Emamy et al. [22] found that the addition of Y increases both the hardness and ultimate tensile strength values of the Al-15%Mg₂Si cast composite. Jiang et al. [23] systematically investigated the modification of in situ-formed Mg₂Si in Mg–Si alloys with yttrium (Y). Ioannou et al. [24] have prepared Sb-doped Mg₂Si compounds through ball milling and a solid-state reaction. Hu et al. [25] found that Sb doping can change the type of Chinese script of Mg₂Si to a fine polygonal shape and decrease the grain sizes. Tani and Kido [26] studied the formation energy and atomic structure of impurities in Mg₂Sn using first-principles plane-wave total energy calculations. The thermoelectric properties of trace Y-doped Mg₂Si crystals have been obtained by experiments, and the total energies of Mg₇Si₄Y, Mg₈Si₃Y, and Mg₈Si₄Y crystals have also been calculated [27]. What are the differences between the single doping and composite doping of Y and Sb? What are the micromechanisms of Y and Sb doping into Mg₂Si? At present, there is no theoretical research on the brittleness of Mg₂Si by Y and Sb codoping as far as we know.

In this work, the structural, thermodynamic, and mechanical properties of Y and Sb doped into Mg₂Si were studied by first principles. It will provide a theoretical reference for further research on Mg₂Si and 6xxx series aluminum alloys.

1.1. Computational Models and Methods

Mg₂Si has an antifluorite (CaF₂) structure [28] (see Figure 1). The atomic coordinates are as follows: Mg (0.25, 0.25, 0.25) and Si (0, 0, 0).

For Y and Sb single doping, the positions of the Mg (or Si) atoms are replaced by Y or Sb, respectively. Despite that both the atom sizes of Y and Sb are larger than those of Mg and Si atoms, to avoid omitting certain configurations, the interpolation Y or Sb atoms into the interval of Mg and Si was considered (see Figure 2).

(a)

(b)

(c)

(d)

(e)

(f)

For the composite doping of Y and Sb, the Mg and (or) Si atoms are replaced by Y and Sb, respectively. Y or Sb enters into the interstitial space of the Mg₂Si cell, and Sb or Y replaces the Mg and (or) Si atoms (see Figure 3).

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

The hypothetical structures of Y- and Sb doping or codoping Mg₂Si configurations must be optimized. The calculations were performed using the CASTEP package based on the density functional theory (DFT) [29]. The exchange-correlation energy functional was adopted by Perdew, Burke, and Ernzerhof (PBE) from the generalized gradient approximation (GGA) [30]. The plane-wave cutoff energy was set to 340 eV. The Brillouin zone was sampled using a Monkhorst-Pack k-point mesh as follows: 4 × 3 × 4 for (j) Mg₈Si₂YSb, (l) Mg₈Si₃YSb, and (m) Mg₈Si₄YSb and the rest are 4 × 4 × 4. To find the lowest energy structures of Y- and Sb-doped Mg₂Si phases, we observe the following convergence thresholds for geometry optimization: total energy convergence tolerance 1.0 × 10⁻⁵ eV/atom steps, 0.03 eV/Å for maximum force, 0.05 GPa for maximum stress components, and 1 × 10⁻³ Å for maximum displacement. After the optimization, the electronic properties are calculated. The density of states (DOS) is computed by means of a scheme developed by Ackland, while the DOS calculation is based on a Mülliken population analysis with the relative contribution of each atom.

2. Results and Discussion

2.1. Structures

The optimized lattice parameters of the pure Mg₂Si phase and Y- and Sb-doped Mg₂Si phases are shown in Table 1. It can be seen that the lattice parameters of Mg₂Si are in agreement with the experimental values [31–33]. Y- and Sb-doped Mg₂Si phases have larger lattice parameters and larger volume than the pure Mg₂Si phase. It is due to the lattice distortion of the Mg₂Si phase by Y and (or) Sb doping which possesses a larger atomic radius.

2.2. Thermodynamic Properties

In order to understand the thermodynamic stability of the doped system, we calculated the formation energy and cohesive energy. The calculated formation energy and cohesive energy of the Mg₂Si phase agree well with the calculated values (−25.92 kJ/mol and −271.15 kJ/mol in [34] and −17.7 kJ/mol and −299.27 kJ/mol in [35]). The process of Y and Sb doping of Mg₂Si is outlined in Table 2.

The corresponding formation energies are shown in Figure 4. It can be seen that the formation energies of (a) Mg₇Si₄Y, (c) Mg₈Si₄Y, (f) Mg₈Si₄Sb, (g) Mg₆Si₄YSb, (i) Mg₇Si₄YSb, (m) Mg₈Si₄YSb, and (n) Mg₇Si₄YSb are negative, indicating that only the structures above are stable. The formation energy is successively (m) < (i) < (n) < (c) < (f) < (g) < (a). It means that (m) Mg₈Si₄YSb is the easiest to form and (a) Mg₇Si₄Y is the most difficult to form. Whether for single doping or composite doping, the formation energies of Y and Sb entered into the interstitial space < the formation energies of Y and Sb replaced the Mg sites < the formation energies of Y and Sb replaced the Si sites (even if it cannot form stable structures). It confirms that Y or Sb is difficult to interpolate into Mg₂Si phases. For the seven stable structures of (a), (c), (f), (g), (i), (m), and (n), the formation energies of composite doping are generally smaller than those of single doping. Only the formation of (g) Mg₆Si₄YSb is greater than those of (c) Mg₈Si₄Y and (f) Mg₈Si₄Sb; this is because Y and Sb in (g) Mg₆Si₄YSb has replaced all the Mg sites to form substitutional solid solutions.

For the stable structures (a), (c), (f), (g), (i), (m), and (n), the calculated cohesive energies are shown in Figure 5. It can be seen that the absolute value of (g) Mg₆Si₄YSb is the largest, indicating that (g) Mg₆Si₄YSb is more stable than the other six structures and (m) Mg₈Si₄YSb has the smallest absolute value and the worst stability. Whether by single doping or composite doping, the structures of Y- or Sb-substituted Mg sites are most stable, while the structures of Y or Sb that entered into the interstitial space are most unstable.

2.3. Mechanical Properties

To satisfy the mechanical stability of the formed structures, the elastic constants of Mg₂Si, (a), (c), (f), (g), (i), (m), and (n) are calculated as shown in Table 3. (a) Mg₇Si₄Y, (c) Mg₈Si₄Y, and (f) Mg₈Si₄Sb are still cubic structures, (g) Mg₆Si₄YSb and (m) Mg₈Si₄YSb are transformed into tetragonal structures, and (i) Mg₇Si₄YSb and (n) Mg₇Si₄YSb are transformed into triclinic structures. The mechanical stability of the phases above can be judged by the criterion for cubic, tetragonal, and triclinic systems in References [36] and [37]. Only Mg₂Si, (a) Mg₇Si₄Y, (f) Mg₈Si₄Sb, (g) Mg₆Si₄YSb, and (i) Mg₇Si₄YSb satisfies the criteria of mechanical stability.

The calculated bulk modulus, shear modulus, and Young’s modulus (51.23 GPa, 51.50 GPa, and 115.85 GPa) of Mg₂Si agree well with the calculated results (57.88 GPa, 48.82 GPa, and 114.32 GPa [38]). Young’s modulus calculated for Mg₂Si, (a) Mg₇Si₄Y, (f) Mg₈Si₄Sb, (g) Mg₆Si₄YSb, and (i) Mg₇Si₄YSb are shown in Figure 6. No matter with what kind of doping, Young’s modulus of pure Mg₂Si will decrease significantly. It means that Mg₂Si has the highest stiffness. In other words, Y and Sb doping will improve the plasticity of Mg₂Si. For single doping, Young’s modulus of doped Sb is lesser than that of doped Y. This shows that the plasticity of (f) Mg₈Si₄Sb is better than that of (a) Mg₇Si₄Y, and the stiffness of (a) Mg₇Si₄Y is larger than that of (f) Mg₈Si₄Sb. For composite doping, Young’s modulus of (g) Mg₆Si₄YSb is less than Young’s modulus of (i) Mg₇Si₄YSb. This shows that the plasticity of (g) Mg₆Si₄YSb is better than that of (i) Mg₇Si₄YSb, and the stiffness of (g) Mg₆Si₄YSb is lesser than that of (i) Mg₇Si₄YSb.

The values of , Poisson’s ratio , , and Debye temperature for Mg₂Si, (a) Mg₇Si₄Y, (f) Mg₈Si₄Sb, (g) Mg₆Si₄YSb, and (i) Mg₇Si₄YSb are shown in Table 4. Poisson’s ratio (0.12) and Debye temperature (600.23 K) calculated for Mg₂Si agree with the results (0.161 and 581.6719 K [38]). From the values of , it can be seen that the values of Mg₂Si and (a) Mg₇Si₄Y are less than the threshold value of 1.75, so Mg₂Si and (a) Mg₇Si₄Y are brittle materials, while (f) Mg₈Si₄Sb, (g) Mg₆Si₄YSb, and (i) Mg₇Si₄YSb are ductile materials. Mg₂Si has minimal and has the worst brittleness, while (f) Mg₈Si₄Sb has maximal and has the greatest ductility. From the values of , it can be seen that (f) Mg₈Si₄Sb has the best plasticity and Mg₂Si has the worst plasticity. The plasticity is successively (f) Mg₈Si₄Sb > (g) Mg₆Si₄YSb > (i) Mg₇Si₄YSb > (a) Mg₇Si₄Y > Mg₂Si. From , it can be seen that the five structures are all anisotropic and Mg₂Si has minimal value, so the degree of anisotropy is minimal. (g) Mg₆Si₄YSb has maximal value, and the degree of anisotropy is the highest. The degree of anisotropy of Mg₂Si will be raised by doped Y and Sb. From the values of , it can be seen that the Debye temperature () of Mg₂Si is the highest, which shows that the thermal conductivity of Mg₂Si is the best, the chemical bonds between the cell’s atoms are the strongest, and the hardness is the greatest. (f) Mg₈Si₄Sb has the lowest Debye temperature (), which shows that the thermal conductivity of (f) Mg₈Si₄Sb is the worst, the chemical bonds between the cell’s atoms are the weakest, and the hardness is the least. Furthermore, no matter with what kind of doping, the Debye temperature () of Mg₂Si will be lowered. It is consistent with the calculated results of Debye temperature () [27].

The shear anisotropic factors , , and are shown in Figure 7. It can be found that the five structures are all anisotropic on the three planes, and the degree of anisotropy on each plane is very similar. (f) Mg₈Si₄Sb has the highest degree of anisotropy, while Mg₂Si has the lowest degree of anisotropy.

2.4. Electronic Properties

To understand the action mechanism, the total density of states (DOS) and the partial density of states (PDOS) should be studied. Figure 8(a) shows the density of states of Mg₇Si₄Y, between −3 eV and the Fermi level, where there exists a very strong orbital hybridization for Mg (2p) and Y (4d) indicating very strong bonding effects. Figure 8(b) shows the density of states of Mg₈Si₄Sb, where there is strong orbital hybridization between the atoms of Mg, Si, and Sb. Figure 8(c) shows the density of states of Mg₆Si₄YSb. The mainly orbital hybridization appears in −6 to 4 eV. The atoms of Mg and Y have strong bonding effects, while the bonding effects of the other atoms are weak. Figure 8(d) shows the density of states of Mg₇Si₄YSb, where all the four atoms show orbital hybridization. In a word, Y doping causes strong orbital hybridization between Mg (2p) and Y (4d), while Sb doping causes strong orbital hybridization between Mg (2p), Si (3p), and Sb (5p). The Fermi surface shifts towards the high-energy region after Y and Sb doping, resulting in an increase in the density of the electron energy states corresponding to the Fermi level. The values are 2 eV (Mg₂Si), 3.05 eV (Mg₇Si₄Y), 5.4 eV (Mg₈Si₄Sb), 3.7 eV (Mg₆Si₄YSb), and 2.9 eV (Mg₇Si₄YSb) in turn, indicating that doping can improve the electrical conductivity of Mg₂Si. This is also consistent with the results which were obtained in Reference [27]. The electrical conductivity of Mg₈Si₄Sb is the best.

(a)

(b)

(c)

(d)

(e)

3. Conclusions

The structural, stability, thermodynamic, and mechanical properties of Y and Sb doped into Mg₂Si are calculated by the GGA-PBE method. The results revealed that the stable structures that can be formed are (a) Mg₇Si₄Y, (f) Mg₈Si₄Sb, (g) Mg₆Si₄YSb, and (i) Mg₇Si₄YSb. (g) Mg₆Si₄YSb is the most stable, while (f) Mg₈Si₄Sb is the least stable. Young’s modulus of Mg₂Si will be reduced by Y and Sb doping, the ductility of Mg₂Si will be improved, and the brittleness of Mg₂Si will be well solved. Among them, the effect of single-doped Sb is better. The Debye temperature () of Mg₂Si will be lowered, and then the thermal conductivity and hardness of Mg₂Si will be reduced by Y and Sb doping. The Debye temperature () of (f) Mg₈Si₄Sb in the five structures is the lowest. Doping with Y and Sb can improve the conductivity of Mg₂Si, and Mg₈Si₄Sb has the best conductivity.

Data Availability

The computational data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Acknowledgments

The authors would like to acknowledge the National Natural Science Foundation of China. This work was also supported by the Key Fund Project (Grant No. 51634004), the Doctoral Scientific Research Foundation of Liaoning Province (Grant No. 20180551213), the Key Laboratory of Chemical Metallurgy Engineering of Liaoning Province, University of Science and Technology Liaoning (Grant No. USTLKFSY201711), and the Fund Project of University of Science and Technology Liaoning (Grant No. 2017YY02).

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Journal of Nanomaterials

Effects of Single Doping and Composite Doping of Yttrium and Antimony on the Structural, Thermodynamic, Mechanical, and Electronic Properties of Mg2Si by First Principles

Abstract

1. Introduction

1.1. Computational Models and Methods

2. Results and Discussion

2.1. Structures

2.2. Thermodynamic Properties

2.3. Mechanical Properties

2.4. Electronic Properties

3. Conclusions

Data Availability

Conflicts of Interest

Acknowledgments

References

Copyright

Effects of Single Doping and Composite Doping of Yttrium and Antimony on the Structural, Thermodynamic, Mechanical, and Electronic Properties of Mg₂Si by First Principles