Effects of Strontium incorporation to Mg-Zn-Ca biodegradable bulk metallic glass investigated by molecular dynamics simulation and density functional theory calculation

Abstract

Molecular dynamics (MD) simulation and density functional theory (DFT) calculations were used to predict the material properties and explore the improvement on the surface corrosion resistance for the Mg₆₆Zn₃₀Ca₃Sr₁ bulk metallic glass (BMG). The Mg₆₆Zn₃₀Ca₄ BMG was also investigated to realize the influence of the addition of Sr element on the material behaviors of Mg₆₆Zn₃₀Ca₄. The Mg-Zn-Ca-Sr parameters of the next nearest-neighbor modified embedded atom method (2NN MEAM) potential were first determined by the guaranteed convergence particle swarm optimization (GCPSO) method based on the reference data from the density functional theory (DFT) calculation. Besides, using the 2NN MEAM parameters of the Mg-Zn-Ca-Sr system, the structures of Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁ were predicted by the simulated-annealing basin-hopping (SABH) method. The local atomic arrangements of the predicted BMG structures are almost the same as those measured in some related experiments from a comparison with the calculated and experimental X-ray diffraction (XRD) profiles. Furthermore, the HA index analysis shows that the fractions of icosahedra-like local structures are about 72.20% and 72.73% for Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁, respectively, indicating that these two BMG structures are entirely amorphous. The uniaxial tensile MD simulation was conducted to obtain the stress-strain relationship as well as the related mechanical properties of Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁. Consequently, the predicted Young's moduli of both BMGs are about 46.4 GPa, which are very close to the experimental values of 48.8 ± 0.2 and 49.1 ± 0.1 GPa for Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁, respectively. However, the predicted strengths of Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁ are about 850 and 900 MPa, both are slightly higher than the measured experimental values about 747 ± 22 and 848 ± 21 MPa for Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁. Regarding the thermal properties, the predicted melting temperature of Mg₆₆Zn₃₀Ca₃Sr₁ by the square displacement (SD) profile is about 620 K, which is very close to the experimental melting temperature of about 613 K. The self-diffusion coefficients of Mg, Zn, Ca, and Sr elements were also calculated for temperatures near their melting points by means of the Einstein equation. The methodology can determine the diffusion barriers for different elements by utilizing these diffusion coefficients resulting in a fact that the diffusion barriers of Ca and Sr elements of Mg₆₆Zn₃₀Ca₃Sr₁ are relatively high. For the electronic properties predicted by the DFT calculation, the projected density of states (PDOS) profiles of surface Mg, Zn, Ca, and Sr elements clearly show that the addition of Sr into Mg₆₆Zn₃₀Ca₄ effectively reduces the s and p orbital states of surface Mg and Zn elements near the Fermi level, particularly the p orbits, which suppresses the electron transfer as well as increases the surface corrosion resistance of Mg₆₆Zn₃₀Ca₄. Consequently, this study has provided excellent 2NN MEAM parameters for the Mg, Zn, Ca, and Sr system by the GCPSO method to predict real BMG structures as well as by means of the DFT calculation to explore the electronic properties. Eventually, through our developed numerical processes the material properties of BMGs with different compositions can be predicted accurately for the new BMG design.

Figure 1

(a) The unit cell of Mg₆₆Zn₃₀Ca₃Sr₁ used for simulating by the SABH method; (b) The 3 × 2 × 2 supercell for the tensile simulation.

Figure 2

The XRD profiles of Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁.

Figure 3

(a) The radial distribution function (RDF) profiles for Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁; (b) the partial radial distribution function (PRDF) profile for Mg₆₆Zn₃₀Ca₃Sr₁. The first peaks of HCP Mg and Zn are indicated with vertical dashed lines for comparison.

Figure 4

(a) Schematic diagrams corresponding to several characteristic HA indexes; HA indexes for different pairs in (b) Mg₆₆Zn₃₀Ca₄ and (c) Mg₆₆Zn₃₀Ca₃Sr₁.

Figure 5

The stress-strain curves of Mg₆₆Zn₃₀Ca₄ and Mg₆₆Zn₃₀Ca₃Sr₁.

Figure 6

The shear band and local shear transition zone evolution within Mg66Zn30Ca3Sr1 at strains of (a) 0, (b) 0.062, (c) 0.089, and (d) 0.127.

Figure 7

Average system square displacement (SD) as a function of temperature for Mg₆₆Zn₃₀Ca₃Sr₁ during the heating process.

Figure 8

Mean-square displacement profiles (MSD) for Mg₆₆Zn₃₀Ca₃Sr₁ at different temperatures close to the melting point in the range from about 600 K to 900 K.

Figure 9

The diffusion coefficient of logarithm profiles as a function of the inverse of temperature for Mg₆₆Zn₃₀Ca₃Sr₁, Mg, Zn, Ca, and Sr, respectively.

Figure 10

Projected density of states (PDOS) for (a) Mg, (b) Zn, and (c) Ca atoms on the surface of Mg66Zn30Ca4 and Mg₆₆Zn₃₀Ca₃Sr₁, and PDOS profile for (d) Sr atoms on the surface of Mg₆₆Zn₃₀Ca₃Sr₁ BMG. The energy is given relative to the Fermi level (E_F).