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Composition-Dependent Structural and Electronic Properties of Mg95−xZnxCa5 Metallic Glasses: An Ab Initio Molecular Dynamics Study S. N. Li, J. B. Liu,* J. H. Li, J. Wang, and B. X. Liu Key Laboratory of Advanced Materials (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: Recent progress in the synthesis of Mg-based metallic glasses (MGs) has allowed them to be considered as potential candidates for biodegradable and bioabsorbable implant materials. In this work, we use the Mg−Zn−Ca system as a representative to investigate the effect of composition on the atomic-level structure and local chemical environment in Mg-based MGs from ab initio molecular dynamics simulations. The results suggest that the short-range order of Mg95−xZnxCa5 (x = 21, 25, 29, and 33) MGs is characterized by Zn-centered icosahedral and icosahedral-like clusters, which show an increasing number and a rising tendency to interpenetrate each other with the enrichment of Zn constituents. A considerable degree of charge transfer between Zn and the surrounding Mg/Ca atoms is observed through electronic structure and bonding character analysis. At Zn-rich compositions, a percolated Zn−Zn network extended throughout the entire sample is formed, upon which the accumulated charges around Zn atoms are associated into a continuous conductivity path. Such results may shed light on the improved corrosion resistance of the Zn-rich Mg−Zn−Ca MGs. over their crystalline counterparts,12−14 which makes them eminently suited for use as biodegradable materials. Among the Mg-based MGs, ternary Mg−Zn−Ca alloys are one of the most promising candidates for biodegradable implants,3,14−16 due to their preferable biocompatibility and considerable reduction in corrosion rate. It has been reported that, at compositions above a Zn-alloying threshold, a uniform amorphous layer enriched in Zn and oxygen is formed on the surface after immersion in the simulated body fluid, which would effectively suppress the rapid degradation of the alloy.3,14 The formation of this passivating layer depends on the local chemical environment in Mg−Zn−Ca MGs.7 Consequently, a fundamental understanding of the atomic-level structure of these amorphous alloys would be indispensable for rationalizing the experimental findings and for studying the reaction mechanism.17,18 In recent years, theoretical modeling and experimental observations have shown that the atomic size ratio and multiple chemical interactions in MGs would result in local atomic ordering, which can be intimately correlated to their macroscopic physical and chemical properties.18−24 However, most of these investigations have focused on transition-metalbased systems, such as Cu−Zr19 and Pd−Ni−P,21 while there is only limited information available on Mg−Zn−Ca MGs. Recently, Zhao25 has reported that Zn and Ca in Mg liquid can induce remarkable slowing down of the atoms, thus

I. INTRODUCTION In the field of biomedical application, there is an unrelenting search for desirable temporary implants. Compared with the traditional bioinert materials, biodegradable materials are expected to corrode and completely dissolve in vivo, thus eliminating the need for implant-removal surgery.1,2 As a nontoxic biodegradable and bioabsorbable material with a property profile close or even similar to that of human bone, magnesium (Mg) alloys are attracting intense research interest in the field of degradable bone implants.3−9 However, due to the high reactivity of Mg, the corrosion resistance of current Mg alloys is generally inadequate for implant applications. To improve the corrosion resistance, appropriate composition design is necessary. Numerous publications have already demonstrated that corrosion performance of magnesium can be modulated by suitable alloying elements, e.g., aluminum, manganese, zinc, and rare earth elements, such that Mg-based implants with controlled rates of dissolution are feasible.4−7 However, the full control over the corrosion behavior of Mg alloys is still beyond attainment, given that the solubility of the above elements in crystalline Mg is limited. In recent years, Mg alloys in the form of metallic glass (MG) have captured a great deal of attention owing to their outstanding corrosion resistance. First, they have a greater range of composition over which all the alloying elements can be intimately mixed on the atomic level into a single-phase structure.10 Second, the intrinsic chemical homogeneity and the absence of grain boundaries of MGs could allow for a lower susceptibility to pitting corrosion.11 Because of these intriguing characters, Mgbased MGs typically show improved corrosion performance © XXXX American Chemical Society

Received: January 14, 2015 Revised: February 1, 2015

A

DOI: 10.1021/acs.jpcb.5b00400 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

Figure 1. (a) Total pair-correlation functions (PCFs) and the (b) Mg−Mg, (c) Mg−Zn, (d) Zn−Zn, (e) Mg−Ca, and (f) Zn−Ca partial PCFs of Mg74Zn21Ca5, Mg70Zn25Ca5, Mg66Zn29Ca5, and Mg62Zn33Ca5 at 300 K. The insets display the evolution of partial PCFs of Mg66Zn29Ca5 from 1200 to 300 K. Splitting on the shoulder of the second peak in each of the partial PCF is observed.

method36,37 and the Perdew−Burke−Ernzerhof generalized gradient approximation38 were adopted to describe the interacting valence electrons. The energy cutoff was set to 300 eV and only the Γ-point sampling was used in the AIMD runs, whereas the electronic properties were calculated on the basis of a 3 × 3 × 3 Monkhorst−Pack k-point mesh. All of the simulations were carried out within a canonical NVT (constant number, volume, temperature) ensemble by using a Nosé thermostat for temperature control. To study the dependence of the local structure of Mg−Zn−Ca MGs on the Zn concentration, four compositions, Mg74Zn21Ca5, Mg70Zn25Ca5, Mg66Zn29Ca5, and Mg62Zn33Ca5, were chosen in the present work. For each composition, a cubic cell with periodic boundary conditions and containing 200 atoms was first constructed using a hard-sphere model. In order to eliminate any memory effect from the initial configuration, the system was thermalized at 2000 K for 4000 time steps, with each time step of 3 fs. Then, each alloy was quenched to 1200 K within 12 ps and equilibrated for another 6 ps. After that, the temperature was decreased sequentially to 900, 600, and 300 K with a cooling rate of 3.2 × 1013 K/s, followed by an equilibration time of 4.5 ps at each temperature. The average pressure of the system was tuned to a value close to zero during all the equilibration stages by adjusting the size of the simulation box. Though substantially faster than that used to generate MGs experimentally, the computational cooling rate of this order of magnitude, by using AIMD simulations,20−22,32 has been proven reliable to reproduce the structural models of MGs in agreement with the experimental results. Finally, for each composition at 300 K, an additional 3000 time steps were performed, in which the configurations were collected to study the structural properties of these alloys.

promoting high glass forming ability of Mg−Zn−Ca alloys. Mahjoub26 has investigated the electronic structure and elastic properties of Mg−Zn−Ca MGs, finding a correlation between the elastic constants and the ionicity of chemical bonding in the system. Nonetheless, on the topic of alloy composition and microstructure, it is well-known that a minor addition of alloying elements may have a dramatic influence on the atomiclevel structure and properties.10,27−29 Therefore, a detailed knowledge of the composition-related changes in Mg−Zn−Ca MGs is undoubtedly in need. In the present work, the main idea is to conduct ab initio molecular dynamics (AIMD) simulations to investigate the variations in local structure of Mg−Zn−Ca MGs with respect to different concentrations of Zn. AIMD simulations have been found to be powerful in the research on amorphous structure.20−22,30−32 Although the high computational cost of this approach renders it impossible to use a large simulation box, this disadvantage is offset by the inherent accuracy in this quantum-mechanical method, since no empirical assumption is required and no artificial parameter is relied on. In addition, properties such as electronic structures and bonding nature can be clarified through this approach, which can shed light on the chemical interactions and the corrosion behavior of the alloys. The manuscript is organized as follows. Our theoretical and computational framework is described in section II. General structural properties, such as pair-correlation function and interatomic bond length, are analyzed in section III. Special attention is then devoted to the atomic-level structure as well as to the local chemical environment of the alloys with different concentrations of Zn (section IV). With the aim of providing a preliminary consideration of the chemical properties of Mg− Zn−Ca MGs, a detailed account of the electronic structure is given in terms of electronic density of states, Bader charge analysis, and charge density distribution (section V). Our conclusions are summarized in section VI.

III. GENERAL STRUCTURAL PROPERTIES As a first step, we have considered the pair-correlation function (PCF), which can provide valuable information on the structure of liquid and amorphous alloys thanks to its direct connection with experimental results. It is defined as the spherically averaged distribution of interatomic distances

II. METHODOLOGY AIMD simulations were accomplished by the Vienna Ab initio Simulation Package33−35 within the framework of plane-wavebased density functional theory. The projector augmented wave B


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The Journal of Physical Chemistry B V g (r ) = 2 N ·4πr 2Δr

N

N

neighboring of Mg−Zn and Zn−Ca pairs over the others. As for the effect of alloy composition on the partial PCFs, considerable variation in the shapes of the second and higher order peaks is evident for gZn−Zn(r) and gZn−Ca(r), while the peaks in gMg−Mg(r), gMg−Ca(r), and gMg−Zn(r) remain virtually unchanged as a whole. Hence, it is probable that Zn−Zn and Zn−Ca interactions would play a more important role in determining the local structure of Mg−Zn−Ca MGs with regard to compositional change. To give a quantitative structural description of the Mg−Zn− Ca MGs, the bond lengths estimated from the first maxima of the partial PCFs are compiled in Table 2. The nominal metallic

∑ ∑ δ(r − rij) i

(1)

j≠i

where V is the volume of the simulation box, N is the number of atoms, and Δr refers to the distance interval in the calculation. Partial PCFs can be calculated by restricting the analysis to the specific elements involved. Using the atomic coordinates from the AIMD simulations at 300 K, the total and partial PCFs of the Mg95−xZnxCa5 MGs at the four different compositions are depicted in Figure 1. As can be seen in Figure 1a, the PCF peaks shift to lower r with the enrichment of Zn, implying a decrease in the average interatomic distance of the Mg95−xZnxCa5 alloys. This is consistent with the fact that Zn has a much smaller atomic radius than that of Mg.39 A comparison of the simulated PCF of Mg70Zn25Ca5 with the experimental PCF of Mg72Zn24Ca4 MG26 is also displayed in Figure 1a. Regarding the height of the peaks as well as the overall shape of the curve, the calculated g(r) exhibits an acceptable match with the experimental one, albeit they are not at the same composition. Considering that there is only a slight change in the appearance of the curves with respect to different concentrations of Zn (it is also true of Ca25), the discrepancy in the total g(r) is expected to be small between these two compositions. Therefore, this good fit can be taken as support for the high consistency between the simulation results and the experimental observations, which renders the former to be capable of resolving the amorphous structures for Mg−Zn−Ca MGs. An additional check for the validation of the AIMD configurations is the calculated mass densities, as presented in Table 1. A

Table 2. Interatomic Bond Distances rij (Å) of the Mg95−xZnxCa5 Amorphous Alloys, Which Correspond to the Positions of the First Peaks in the Respective Partial PairCorrelation Functionsa

ρcal

ρexp

(ρcal − ρexp)/ρexp

2.477 2.650 2.824 2.993

2.481 2.646 2.811 2.976

−0.16% 0.15% 0.46% 0.57%

Mg−Mg

Mg−Zn

Zn−Zn

Mg−Ca

Zn−Ca

3.15 3.13 3.14 3.15 3.20 2.82

2.83 2.86 2.85 2.84 2.94 2.63

2.58 2.67 2.60 2.62 2.68 2.44

3.48 3.46 3.47 3.48 3.57 3.17

3.16 3.17 3.17 3.20 3.31 2.98

a

The metallic,40 rm (Å), and covalent,41 rc (Å), bond distances are presented here for comparison.

and covalent bond distances, derived by summating the respective metallic40 and covalent41 atomic radii for all the listed pairs, are also exhibited in Table 2 for comparison. It should be noted that the calculated bond lengths at the four compositions are generally shorter than the metallic bond distances and larger than the covalent counterparts, which indicates a mild densification of atomic packing in the amorphous alloys as compared with the simple mixture of constituent atoms. Similar results have been published for other MG systems in the literature,42−45 which suggest that the negative enthalpy of mixing may account for such bond shortening (−4, −6, and −22 kJ/mol for Mg−Zn, Mg−Ca, and Zn−Ca, respectively46). Phenomenologically, the large negative enthalpy of mixing can greatly enhance the interaction of the components and suppress long-range atomic diffusion,45 thereby promoting chemical short-range order in the amorphous alloys. Nevertheless, enthalpy, as a thermodynamic variable of a uniform system, fails to give an explanation for the compositional dependence of the local structure in MGs. In fact, it has been pointed out that the small-size atoms can possibly squeeze into the interstitial sites between the nearest neighbor atoms and lead to a large variation in bond length at different compositions,47,48 as evidenced by the notable fluctuation of Zn−Zn bond lengths shown in Table 2. In this respect, a careful consideration of the atomic-level structure should be taken into account, as discussed in the following paragraphs.

Table 1. Comparison between the Calculated Mass Density, ρcal (g/cm3), and the Experimental One,26 ρexp (g/cm3), for Mg95−xZnxCa5 Metallic Glasses Mg74Zn21Ca5 Mg70Zn25Ca5 Mg66Zn29Ca5 Mg62Zn33Ca5

rij Mg74Zn21Ca5 Mg70Zn25Ca5 Mg66Zn29Ca5 Mg62Zn33Ca5 rm rc

remarkable agreement is found with the recent experimental values obtained by interpolation of the reported data,26 which further demonstrates the reliability of our AIMD simulation results. For the partial PCFs as shown in Figure 1b−f, all the curves are characterized by a pronounced first peak and a diffuse second peak where splitting on the shoulder is observed. Due to the low abundance of Ca atoms in this ternary alloy system, the Ca−Ca partial PCF falls short of statistical significance and is therefore not considered in the present work. The evolution of the partial PCFs as a function of temperature during the quenching process is also illustrated in the insets using Mg66Zn29Ca5 alloy as a representative. Going from equilibrium liquid with a homogeneous atomic distribution at 1200 K to the amorphous state at the room temperature (300 K), the amplitude of the first peak of each partial PCF grows, whereas a shoulder on the right-hand side of the second peak develops. These observations are indicative of a higher extent of shortrange order when the temperature drops. The first peak of gMg−Zn(r), as well as that of gZn−Ca(r), tends to become much sharper with decreasing temperature as compared with those of gMg−Mg(r), gZn−Zn(r), and gMg−Ca(r), suggesting a preferred

IV. LOCAL STRUCTURAL ANALYSIS In order to seek more detailed information about the local atomic configuration, the geometry of the coordination polyhedra surrounding Mg, Zn, and Ca atoms is obtained from Voronoi tessellation analysis,49,50 through which the coordination number (CN) can be determined unambiguously and reproducibly. In this method, an envelope of a family of C


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Figure 2. Distributions of (a) Mg-, (b) Zn-, and (c) Ca-centered clusters by the total coordination number (CN) derived from the coordination polyhedron in Mg95−xZnxCa5 metallic glasses. (d) The average CN around Mg, Zn, and Ca atoms, aligned from left to right in each group: Mg74Zn21Ca5, Mg70Zn25Ca5, Mg66Zn29Ca5, and Mg62Zn33Ca5. The partial contributions to CN from the three species are also marked.

than the value of its content in the simulation box. This, to some extent, can provide an implication of a preference for Zn atoms to avoid contact with each other. In the following, we further examine the fraction of coordination polyhedra associated with different numbers of Zn atoms at the vertices. The histograms of these clusters are presented in Figure 3. Among the Zn-centered clusters in Mg74Zn21Ca5 glass, those with less than two Zn atoms at the vertices turn out to have higher frequencies than the others, indicating that the isolated and dimerized Zn atoms are prevalent in this alloy, as seen in Figure 3e. This observation can serve as a suitable support for the interpretation of Zn−Zn avoidance. When the concentration of Zn exceeds 25 at. %, we find a dramatic decrease in the population of isolated Zn atoms, with a substantial increase in the interconnecting ones that each have two Zn nearest neighbors and form into a chain-like structure (Figure 3f). An increase of Zn atoms at the nodal points that are connected to three or more atoms of their kind is revealed from Mg70Zn25Ca5 to Mg66Zn29Ca5 (Figure 3g). It is plausible to assume that, with the enrichment of Zn atoms, the Zn-centered clusters would eventually form a percolated network, which interpenetrates in the real space by linking chains and patches throughout the entire sample, and this is what we see in Figure 3h. Such an interpenetrating network can play a decisive role in determining the physical and chemical properties of the bulk materials,54−56 as it may provide potential tunnel routes for electrical conduction and surface segregation of the constituent atoms. Moreover, we examine the volume fraction of Zn atoms in the simulation box by treating them as spheres, and find that the calculated value (15.5%) in the Mg62Zn33Ca5 alloy matches well with the critical volume fraction (≈15%) predicted by Scher and Zallen for

perpendicular bisectors between a central atom and all of its nearby atoms constitutes the surface of a Voronoi polyhedron for the central atom, which can be differentiated by the indices ⟨n3, n4, n5, n6, ...⟩, where ni stands for the number of i-edged faces of the Voronoi polyhedron and ∑i ni is the total CN. Each Voronoi polyhedron is associated with a coordination polyhedron, also denoted by ⟨n3, n4, n5, n6, ...⟩, where ni, instead, would be the number of the vertices common to i polyhedron edges.51 In the present work, Voronoi polyhedral faces with less than 5% of the average face area were neglected to minimize the degeneracy problem and thermal vibration effects.52 The distributions of atomic clusters by the total CN derived from the coordination polyhedron are shown in Figure 2a−c. The CN of Mg-centered clusters dominates in 13−15, while the Zn-centered clusters prefer a lower CN between 10 and 12. A disperse range is observed for the CN of Ca-centered clusters, which mainly varies from 16 to 19. Upon the Zn addition, the Mg- and Zn-centered clusters have seen a noticeable increase in the fraction of the high-CN polyhedra, whereas an inverse trend is displayed by that of the low-CN ones. Such changes are further reflected by the average CN depicted in Figure 2d, where a gradual increase in the total CN of Mg- and Zn-centered clusters from Mg74Zn21Ca5 to Mg62Zn33Ca5 is revealed. This can be understood in terms of the atomic size difference;53 that is, the relatively smaller atomic size of Zn permits the central atoms to accommodate more atoms, especially Zn atoms, in the nearest-neighboring shells and results in a larger CN with increasing concentration of Zn. It is also worth noting that the Zn atoms, as solutes, are predominantly surrounded by Mg and Ca atoms as the nearest neighbors, leaving the fraction of Zn neighbors much lower D


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Statistical results on the coordination number, however, are insufficient to interpret the correlation between the local structure and the composition of MGs. The geometry of coordination polyhedra comes into play. Figure 4 illustrates the

Figure 3. Fraction of coordination polyhedra associated with different numbers of Zn atoms at the vertices: (a) Mg74Zn21Ca5, (b) Mg70Zn25Ca5, (c) Mg66Zn29Ca5, and (d) Mg62Zn33Ca5. Also shown are the snapshots of atomic configurations at the respective compositions: (e) local environment featured by isolated and dimerized Zn atoms in Mg74Zn21Ca5; (f) chain-like structures of Zn atoms in Mg70Zn25Ca5; (g) embryonic form of a continuous network in Mg66Zn29Ca5; (h) a percolated Zn−Zn network extended throughout the simulation box, revealed in Mg62Zn33Ca5 metallic glass. The gray, orange, and green spheres mark the centers of the Mg, Zn, and Ca atoms, respectively.

Figure 4. Occurrences of (a) Mg-, (b) Zn-, and (c) Ca-centered coordination polyhedra in Mg95−xZnxCa5 metallic glasses. Note that only polyhedra with a population of >2% are shown. The atomic structures of the dominant clusters taken from the simulation box are also exhibited.

types and populations of the most abundant coordination polyhedra centered by Mg, Zn, and Ca, respectively. Although there are an incredible variety of coordination polyhedra in these alloys, only several indices appear with high frequencies while many other types are present with fractions lower than 2% of the respective Mg-, Zn-, and Ca-centered clusters. From Figure 4, we can see that the coordination polyhedra in the Mg−Zn−Ca MGs are characterized by the predominance of 5fold vertices n5, which is indicative of the pentagonal-bipyramid arrangement of the atoms, regardless of their kind. The average fraction of pentagonal faces on Voronoi polyhedra is higher than 54% for all the compositions. In other words, over half of the nearest-neighboring pairs are expected to have five common neighbors in a bipyramid structural unit.58 It has been proposed that the stability of amorphous structure in MGs is strongly correlated with this 5-fold geometry.18,59 And it has been further proposed that the full icosahedral cluster ⟨0, 0, 12, 0⟩, which takes the pentagonal-bipyramid motifs as its unique building blocks, can greatly enhance the transition barrier to the crystal phases.45,60 However, since the Mg- and Ca-centered polyhedra with CNs higher than 12 are actually more common

three-dimensional site percolation in a randomly distributed network of spheres.57 This indicates that our analytical results from the AIMD simulations are well supported by the percolation theory. As sort of complementary information to the local chemical environment, the changes in Mg- and Cacentered clusters are also investigated. The number of Zn nearest neighbors for Mg central atoms in Mg62Zn33Ca5 is almost double that in Mg74Zn21Ca5. Ca atoms show similar trends to Mg, but in comparison, the larger number of adjacent Zn atoms for Ca demonstrates a stronger inclination of Ca to be in touch with Zn. This is probably due to the large negative enthalpy of mixing between Zn and Ca as mentioned above. For the Mg66Zn29Ca5 MG, it seems that the spectrum of Mgcentered clusters is more centralized than with other compositions: each Mg atom interacts mostly with 3−5 Zn atoms in its neighborhood. Ca-centered clusters are of the same case. Therefore, a comparatively high extent of local chemical homogeneity could be expected for the Mg66Zn29Ca5 MG, just before the onset of the percolation threshold. E


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Figure 5. Illustration of two common cases in transformation of icosahedral and icosahedral-like clusters: (a) ⟨0, 0, 12, 0⟩ → ⟨0, 2, 8, 2⟩, by switching the four nearby pentagons into two tetragons and two hexagons; (b) ⟨0, 0, 12, 0⟩ → ⟨0, 2, 8, 1⟩, by shifting two adjacent vertex atoms from their ideal positions to the interstitial sites. (c) The bond angle distribution functions of M−Zn−M angles (M = Mg, Zn, Ca) that reflect the icosahedral ordering of Zn-centered clusters. The vertical lines correspond to the peaks of the bond angle distribution function of perfect icosahedra. (d) Distribution of W6 in Mg−Zn−Ca metallic glasses, using Mg66Zn29Ca5 as an example. The dashed line corresponds to the value for perfect icosahedra. The central atoms of the selected clusters (Zn-centered ⟨0, 0, 12, 0⟩, ⟨0, 2, 8, 2⟩, and ⟨0, 2, 8, 1⟩ polyhedra) constitute the main part of the low-W6 ones, which show more pronounced icosahedral ordering than the high-W6 counterparts.

precisely those with the Voronoi types mentioned above, further demonstrating the essential role of our identification of the icosahedral-like polyhedra. Adding up the amount of the icosahedral and icosahedral-like polyhedra around Zn in Mg62Zn33Ca5 gives a total of about 12% of all the Mg-, Zn-, and Ca-centered clusters in the system, while this value is reduced to 9, 8, and 6% for Mg66Zn29Ca5, Mg70Zn25Ca5, and Mg74Zn21Ca5, respectively. As for Ca-centered clusters (Figure 4c), a large variance of their frequencies with respect to the composition is observed. Conceivably, Ca atoms could serve as a modulator by providing more opportunities for structural accommodation of the Mg and Zn atoms, so that they can relax the atomic level stresses63 in their endeavor of filling the entire space. This is different from the Zr46Cu47Al7 MG,45 where Alcentered polyhedra themselves favor the icosahedral shortrange order and can therefore facilitate the 5-fold bond formation in the clusters centered by Cu. In Figure 6, the spatial distributions of icosahedral and icosahedral-like polyhedra around Zn are plotted for the representative structures at different compositions. In the Znpoor glasses, disconnected polyhedra and extended clusters of 2−3 polyhedra connected via edge- or face-sharing are observed (Figure 6a). Vertex-sharing is common, but it is hardly representative of the intercluster correlation.18 With the increase of Zn, volume-sharing appears and the samples feature long chains of mostly face-sharing polyhedra (Figure 6b and c). Here, volume-sharing is referred to as the interconnected linkage of two clusters whose central atoms are adjacent to each other.64 In Mg62Zn33Ca5, volume-sharing is more favorable than other types of connection and becomes dominant, as seen in Figure 6d. The polyhedra in the presented patches are mainly chained in an interpenetrating pattern, which contributes to the formation of large extended clusters constituted by five or more icosahedral and icosahedral-like polyhedra. It has been reported that icosahedral clusters have a strong tendency to aggregate in liquid states.65 Since the icosahedral ordering is salient at Zn-

(Figure 2a and c), the full icosahedra are not dominating in these clusters and can only represent a small population of them. The favored polyhedra in the Mg-centered architecture (Figure 4a) are ⟨0, 1, 10, 2⟩ and ⟨0, 2, 8, 4⟩, each of which accounts for about 6% of all the polyhedra around Mg atoms. The population of both polyhedron types, to some extent, is not sufficiently large as compared with the rest of the Mgcentered group, implying that the preference for a particular type is barely distinguishable in Mg-centered clusters. In contrast, preferred polyhedra with high frequencies appear when Zn is chosen as the central atom (Figure 4b). The leading topological short-range order is the icosahedral and icosahedrallike clusters: ⟨0, 0, 12, 0⟩, ⟨0, 2, 8, 2⟩, and ⟨0, 2, 8, 1⟩. Parts a and b of Figure 5 demonstrate the reason why ⟨0, 2, 8, 2⟩ and ⟨0, 2, 8, 1⟩ are identified as icosahedral-like clusters. Figure 5a shows how ⟨0, 0, 12, 0⟩ could be distorted to be ⟨0, 2, 8, 2⟩ by switching the four nearby pentagons into two tetragons and two hexagons. Figure 5b illustrates that ⟨0, 0, 12, 0⟩ could probably transform into ⟨0, 2, 8, 1⟩ by simply shifting two adjacent vertex atoms from their ideal positions to the interstitial sites over a small distance. Indeed, there are several other polyhedron types that resemble the full icosahedral cluster in the Zn-centered group, such as ⟨0, 3, 6, 3⟩ and ⟨0, 1, 10, 2⟩. Moreover, we analyze the bond angle distribution function with Zn as the central atom, as displayed in Figure 5c. It is found that the calculated distribution shows prominent peaks near θ = 65 and 117°, close to the values given by the perfect icosahedral clusters (63.4 and 116.6°).52,61 Then, it can be inferred that icosahedral ordering should be the preferential structural feature in the Zn-centered clusters, which is well consistent with the results reported by Zhao.25 The bond orientational order parameter62 W6 can be used as a quantitative measure of the icosahedral ordering, because its minimum value (−0.17) is obtained only by a perfect icosahedron. As shown in Figure 5d, the atoms that constitute the majority of the low-W6 (more icosahedral-like) ones are F


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Figure 6. Spatial distributions of icosahedral and icosahedral-like polyhedra around Zn: (a) Mg74Zn21Ca5, (b) Mg70Zn25Ca5, (c) Mg66Zn29Ca5, and (d) Mg62Zn33Ca5. It is seen that the samples at Zn-poor compositions feature disconnected polyhedra or small patches of edge- or face-sharing polyhedra, while at Zn-rich compositions interpenetrating connection (volume-sharing) of clusters is more favorable. The color code for the different atoms is as in Figure 3.

Figure 7. Calculated local density of states (LDOS) for (a) Mg, (b) Zn, and (c) Ca atoms in Mg95−xZnxCa5 MGs. Energies are given relative to the Fermi level (EF). The valence states on Mg and Ca atoms are much lower than that of Zn, indicating the charge transfer from Mg and Ca to Zn atoms.

V. ELECTRONIC STRUCTURE The topologies of the amorphous phases at the four compositions form the basic input for the calculations of their electronic structures. The electronic local density of states (LDOS) averaged over all the atoms of each species in Mg− Zn−Ca alloys is presented in Figure 7. It is known that both Mg and Ca atoms have two valence electrons (3s2 and 4s2,

rich compositions, the interpenetrating clusters with icosahedral-like features would simply develop from this aggregation and retard the crystallization processes upon rapid cooling. However, this does not mean that the Zn-rich glasses would be more stable or easier to be produced than the Zn-poor ones. In reality, factors like bonding nature and electronic structure should be taken into account as well. G


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Figure 8. (a) Bader charges around Mg, Zn, and Ca atoms as a function of composition. The positive (negative) value means electronic charge depletion (accumulation). (b) Distribution of Bader charges for Mg66Zn29Ca5 metallic glass. Each point corresponds to an individual atom in the simulation box.

Figure 9. Three-dimensional isosurfaces with an electron charge density of 0.018 e/Å3 for (a) Mg74Zn21Ca5 and (b) Mg62Zn33Ca5, displayed using the VESTA software.76 For clarity and ease of presentation, only half of the simulation box in the direction perpendicular to the paper is shown. It is seen that the electrons are mainly localized to Zn atoms and form into a continuous network at Zn-rich compositions.

respectively), whereas Zn has a closed shell (3d104s2) electronic configuration in the ground state. As illustrated in Figure 7b, the Zn 3d states are mainly localized at −7.5 eV and make virtually no contribution to bonding. If only the s- and pelectrons are considered, one might expect some resemblance in the LDOS of Mg, Zn, and Ca atoms. However, our calculations show that the valence states on Mg and Ca atoms (Figure 7a and c) are significantly lower than that of Zn (Figure 7b). In consideration of the substantial difference in electronegativity among Mg, Zn, and Ca (Mg 1.31, Zn 1.65, Ca 1.00),66 this finding is evidence for the charge transfer from Mg and Ca to Zn atoms. More specifically, the Zn LDOS shows almost equal occupancy of the s and p states, suggesting that the extra electrons in Zn atoms would go into the 4p orbital and result in Mg−Zn and Ca−Zn bonding having a mixed ionic and metallic character. It is also noted that the d orbital of Ca atoms is overwhelmingly dominant around the Fermi level, similar to the case of Ca−Al MGs.67 The transfer of electrons

from the 4s orbital to the empty 3d orbital of Ca can be due in part to the avoidance of s and p band crossing,68 in the face of an increased occupancy of p states in the alloy system. The values of charge transfer obtained by Bader charge analysis69,70 can enable us to gain further insight into the extent of ionicity. The results are shown in Figure 8, where the positive (negative) values are indicative of electronic charge depletion (accumulation). Figure 8a shows the compositional dependence of average Bader charges around Mg, Zn, and Ca atoms in the alloys. It is seen that an increase of Zn content results in more electrons given away by each Mg atom, while fewer effective charges are received by each of the Zn atoms. Every Ca atom denotes approximately 1.2 electrons and shows a negligible variation with the composition. The observed trends can be further manifested by the LDOS shown in Figure 7, where the occupied states of Mg and Zn undergo noticeable reduction from Mg74Zn21Ca5 to Mg62Zn33Ca5. This indicates a decrease of valence electrons per Mg and Zn atom on average, H


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Moreover, the charge transfer from Mg and Ca to Zn atoms is the key to the water dissociation reaction which governs the corrosion rate of Mg-based alloys. On one hand, Mg and Ca levels near the Fermi energy are largely unoccupied (Figure 7), making them electron acceptors. On the other hand, Zn levels near the Fermi energy are highly occupied, facilitating their roles as electron donors. Accordingly, there would be selective dealloying at the beginning of the degradation, wherein the more active atoms (Mg and Ca) dissolve, leaving behind the more noble Zn atoms on the surface. For Zn-rich MGs, the continuous charge-transfer network provided by the Znnx− superanion results in homogeneous corrosion behavior and promotes the formation of a uniform oxide layer which remarkably improves their corrosion resistance.17 It should be recapitulated that the percolation process within the composition range of 21−33 at. % Zn is accompanied by a distinct drop in the corrosion rate of the Mg−Zn−Ca amorphous alloys.3,14 Such an abrupt change in corrosion behavior is widely observed in microcrystalline alloys, such as Fe−Cr where the threshold in the passivation appears at ∼17 at. % Cr.74,75 All of these phenomena have one thing in common: the solute−solute connection begins to resemble a network at the threshold, which not only alters the electrochemical properties of the alloy but also enables the segregation of solute atoms to the surface. The microscopic analysis would have implications for these alterations in the corrosion behavior, yet further work is still needed to establish the corrosion mechanisms involving water dissociation and hydrogen production on the surface of Mg−Zn−Ca MGs.

which is in correspondence with the excess of positive charges per Mg and the loss of negative charges per Zn. Accounting for all three kinds of atoms in the system, the average charge transfer, defined as Ct = ∑i|ei|/N (ei, the Bader charge for the ith atom; N, the total number of atoms),71 increases from about 0.87 e per atom in Mg74Zn21Ca5 to 1.13 e in Mg62Zn33Ca5. These values are comparable to other alkaline-metal-based MGs, such as Ca50Mg20Cu30 and Mg65Cu25Y10, and appear to surpass most of the transition-metal-based MGs, yet they are still much lower than that of typical ionic materials.71−73 Thanks to the multiplicity of the short-range configurations in MGs, the Bader charges for both Mg and Zn atoms exhibit a broad distribution, as represented by Mg66Zn29Ca5 in Figure 8b. Some of the Mg atoms are negatively charged, while the accumulated charges around Zn atoms show an even wider scatter from 0.8 e to 3.0 e. However, the charges around Ca atoms do not vary with local environment, even for different compositions of the MGs. This feature might have its origin in the high propensity of Ca atoms to denote electrons to the neighboring species, which demonstrates an ionicity-dominated bonding behavior between Ca and Zn atoms. The spatial distributions of charge density are plotted in Figure 9 for the Zn-poor Mg 74 Zn 21 Ca 5 and Zn-rich Mg62Zn33Ca5 alloys. The partial charge density in the energy range below −7 eV (relative to the Fermi level) is not included in the calculation, so that we can eliminate the effect of Zn 3d states. The charge distribution for Mg74Zn21Ca5 shows that electrons are mainly localized to Zn atoms and only a moderate degree of covalency is displayed in the Zn dimers (Figure 9a). Instead, charge density in the middle of adjacent Zn atoms is prominent in Mg62Zn33Ca5 (Figure 9b), which joins into a continuous network along the Zn−Zn bond structure. Then, it is deduced that the Zn atoms in Mg62Zn33Ca5 MG would behave as a Ζnx− n superanion with both metallic and covalent boding characters. The partial covalent bonding between Zn atoms is probably attributed to the overlap of electron wave functions of the accumulated charges. In this case, the valence electrons are predominantly distributed throughout the Zn network, which serves as a continuous conductivity path for charge carriers and facilitates the homogeneous corrosion on the surface. This corresponds to the observation that the larger amount of Zn atoms embedded in the Mg matrix is capable of generating more ordered corrosion morphologies on Mg−Zn− Ca MGs.14 Since there is a considerable degree of charge transfer between Zn and the surrounding Mg/Ca atoms, the stability of Zn-centered polyhedra can benefit a lot from the additional ionic bonding with Mg and Ca atoms. It further justifies our focus on Zn-centered clusters as the key motifs in Mg−Zn−Ca MGs. In contrast, Zn atoms in the nearest-neighboring shell of another Zn are likely to be unfavored in this context, similar to the cases of the metalloid atoms in metal−metalloid MGs.21 Then, it can be anticipated that a competition between the geometrical factors (more icosahedral-like Zn-centered clusters) and the chemical effects (stronger Zn−Zn electrostatic interactions) during the increase of Zn would play an essential role in determining the stability of the Mg95−xZnxCa5 MGs. A compromise between them is reached at the locally optimal composition for MG formation. This presumably is responsible for the experimental results10 that a local maximum of glass forming ability resides in the vicinity of Mg66Zn29Ca5, near the percolation of the interconnected Zn atoms (Figure 3).

VI. CONCLUSIONS The extended solubility of Zn in the amorphous structure of the Mg−Zn−Ca MGs gives them potential advantages over their crystalline counterparts for applications in biodegradable implants. Further optimization of their relative stability and corrosion performance requires a better understanding of the structural and electronic properties. In this work, ab initio molecular dynamics is used to build the realistic models of the Mg95−xZnxCa5 MGs. The calculated pair-correlation functions display an obvious splitting on the second peak, indicating that strong short-range ordering is formed in these amorphous alloys. The Zn-centered coordination polyhedra are dominated by icosahedral and icosahedral-like clusters which show an increasing number with the enrichment of Zn; in contrast, Mg and Ca atoms favor larger coordination number and experience more flexible local environments. Geometric ordering, characterized by interpenetrating Zn-centered clusters with icosahedral-like features, rises significantly from Mg74Zn21Ca5 to Mg62Zn33Ca5. From the analysis of the electronic structures, we find a considerable degree of ionic bonding between Zn and the surrounding Mg/Ca atoms, which on the one hand enhances the bond strength between atoms of different kinds and on the other hand destabilizes the Zn−Zn bonding by electrostatic repulsion. A competition between the geometrical factors and the chemical effects would probably dictate the stability of Mg−Zn−Ca MGs. Additionally, we provide evidence for a percolation process within the composition range of 21−33 at. % Zn, as the Zn atoms change from isolated to interconnected states. By linking the adjacent Zn atoms (or interpenetrating Zn-centered clusters), a continuous network is observed for the Mg62Zn33Ca5 sample. Furthermore, the accumulated charges on Zn atoms are extended throughout the percolated network, I


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which is likely to promote a homogeneous corrosion behavior on the alloy surface. These observations may provide some atomic-level insight into the improved corrosion resistance of the Zn-rich Mg−Zn−Ca MGs and present a rational foundation for further investigation of the corrosion mechanisms.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +86-10-62772619. Fax: +86-10-62771160. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for the financial support from the National Natural Science Foundation of China (51131003), the Ministry of Science and Technology of China (973 Program 2011CB606301, 2012CB825700), and the Administration of Key Laboratory of Advanced Materials in Tsinghua University.

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REFERENCES

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