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Sluggish mobility and strong icosahedral ordering in Mg–Zn–Ca liquid and glassy alloys
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ScienceDirect Acta Materialia 67 (2014) 266–277 www.elsevier.com/locate/actamat
Sluggish mobility and strong icosahedral ordering in Mg–Zn–Ca liquid and glassy alloys Y.F. Zhao a, D.Y. Lin a, X.H. Chen a, Z.K. Liu b, X.D. Hui a,⇑ a
State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China b Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA Received 24 June 2013; received in revised form 22 December 2013; accepted 26 December 2013 Available online 1 February 2014
Abstract The dynamic properties and atomic configuration of Mg, Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu liquid and solid systems were comprehensively studied using ab initio molecular dynamics calculation. The viscosities of an Mg–Zn–Ca alloy were measured from 700 K to 960 K. It was found that Zn and Ca in Mg liquid induce remarkable slowing down of atoms, but Cu acted as a stimulus to the diffusion. Icosahedral short-range orders are most dominant in Mg–Zn–Ca alloys in view of the existence of a majority of 1551 type of bond pairs, h0, 0, 12, 0i type of Voronoi polyhedra. Icosahedral medium-range orders can be formed in Mg–Zn–Ca alloys by the perfect icosahedra via the linkage of vertex-, edge-, face- and intercross-shared atoms. It is suggested that the high glass forming ability of Mg–Zn–Ca alloys is essentially related to the sluggish mobility and strong icosahedral short- and medium-range ordering in the undercooled liquid. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Mg–Zn–Ca; Dynamic properties; Atomic structure; Ab initio molecular dynamics; Icosahedral medium-range orders
1. Introduction Bio-absorbable implants have been widely employed in orthopedic surgery and have become an important materials field today. Of the miscellaneous metallic implants developed, Mg-enriched crystalline material showed a Young’s modulus similar to that of bone (E = 3–20 GPa), favorable compatibility with bone cell and tissue growth, and antibacterial properties [1–3]. However, their wide application has been limited by their rapid corrosion rate accompanied by hydrogen evolution in vivo [2]. In recent years, Mg-based bulk metallic glasses (BMG) have attracted significant attention as potential bio-absorbable implant materials, owing to their higher strength and better corrosion resistance than traditional magnesium crystalline materials. The earliest BMG were developed in 1988 in the Mg– TM–RE (TM, transition metal; RE, rare-earth element) ⇑ Corresponding author. Tel.: +86 10 62333066; fax: +86 10 62333447.
E-mail address: [email protected] (X.D. Hui).
system [4]. This type of BMG exhibits a wide supercooled liquid region, high glass-forming ability (GFA) and high tensile strength. Based on this ternary system, many multicomponent Mg-based BMG have been prepared [5–9]. Unfortunately, RE-containing Mg-based BMG exhibit bad biocompatibility for biomedical materials. Recently, great progress has been achieved in the synthesis and properties of RE-free Mg-based BMG by adding a few per cent of Ca element to the Mg–Zn binary system. New Mg–Zn– Ca BMG with a critical diameter of 4 mm were prepared using conventional casting techniques [10–14]. Their feasibility as biodegradable metallic materials was evaluated by investigating their mechanical, corrosion and cytotoxicity properties. The experimental results show that these BMG are of higher cell viability than that of as-rolled pure Mg. Through animal experiments, Zberg et al. [10] revealed that the Mg–Zn–Ca BMG exhibit a great reduction in hydrogen evolution, as the content of Zn is below a threshold value of 28 at.%, and the same good tissue compatibility as observed in crystalline Mg implants. Wang et al. [11] synthesized Fe particle reinforced Mg69Zn27Ca4 BMG
1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.12.037
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composites by copper mold injection casting with industrial raw materials. It was shown that the corrosion resistance of this type of BMG-based composite has been remarkably improved in 3.5 wt.% NaCl solution compared with that of AZ31 and pure Mg. The reliability of the compressive fracture strength of Mg96xZnxCa4 (x = 30, 25) BMG has also been investigated [12]. It was found that the compressive fracture strength of Mg–Zn–Ca BMG exhibit surprisingly high uniformity. In the present work, as shown in Supplementary Fig. 1, it was found that the addition of Cu increases the corrosion potential and decreases the corrosion current density of Mg–Zn–Ca metallic glasses in PBS solution, thus delaying the biodegradability of this type of metallic glass alloy. The compressive fracture strength of Mg–Zn–Ca BMG is enhanced by addition of Cu. However, it was also found that the glass-forming ability of Mg–Zn–Ca BMG is reduced by the appropriate addition of Cu. Crystalline phases are precipitated, as the content of Cu is >3 at.%. The large GFA, good biocompatibility, low cost and easy recycling ability of Mg–Zn–Ca BMG make them promising for structural engineering or biomedical application. To make the most of the advantage of BMG, it is essential to thoroughly understand their dynamics properties and structural mechanism. In recent years, experimental investigations and theoretical modeling have been performed on Zr-, Pd-, Mg- and La-based BMG alloys using X-ray diffraction (XRD), extended X-ray absorption fine structure (EXAFS), anomalous X-ray scattering and neutron diffraction, molecular dynamics (MD) and ab initio molecular dynamics (AIMD). Theoretically, cluster dense packing [15] and quasi-equivalent cluster models [16] have been developed besides the structural theories, such as dense random packing of the hard sphere [17], the trigonal prism model [18] and the chemical twinning model [19]. To understand the ultrahigh strength of Co–Fe–Ta–B BMG, Inoue et al. [20] investigated the precipitates from the BMG and deduced that the ultrahigh strength of Co-based BMG results from the formation of local atomic ordering. Hui et al. [21] proved that the short-range order in Co–Fe–Ta– B BMG is of a (Co, Fe)2B-like but not (Co, Fe)23B6-like crystallographic structure. Yao et al. [22] found that the high strength in Fe–Nb–B BMG is associated with the formation of a network-like structure. Gerold et al. [23] conducted EXAFS studies on the nature of atomic correlations of Zr41.2Ti13.8Cu12.5Ni10Be22.5 (vit1) BMG alloy in the as-quenched state, and found that the atoms tend to form a dense packing. Using the AIMD calculation, Hui et al. [24] revealed that the icosahedral short- and medium-range orders (ISRO and IMRO) are most dominant in vit1 BMG in view of the presence of a majority of bond pairs (BP) and Voronoi polyhedral (VP). Short-range ordering (SRO) was found by Mattern et al. [25] in Zr–Ti–Al–Cu– Ni BMG in terms of the pair correlation function (PCF). A high degree of dense random packed structures has also been confirmed from the XRD profiles in ternary La–Al– Ni [16,26] and Mg–Cu–La [17,27] BMG alloys. Cheng
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et al. [28,29] investigated the influence of local structure on the dynamics in the Cu–Zr and Cu46Zr47Al7 systems by MD simulation using EAM potentials, and found that the local icosahedral clusters are responsible for the viscosity of the supercooled liquid. Jiang et al. [30] measured the general PCF and structure factor (SF) of the Cu46Zr46Al8 glass alloy using synchrotron radiation XRD. ISRO, of which Al atoms are caged in the center of icosahedra with Cu and Zr atoms are the vertices, have been evidenced in the Cu46Zr46Al8 BMG by AIMD simulation [31]. In spite of such great progress in the structural characterization of BMG, the dynamic properties and structural characterization of Mg–Zn–Ca glassy alloys during the glass formation process are still less understood. In particular, the mobility and short-to-medium-range order in the atomic packing of this type of BMG have not been reported. In the present work, a comprehensive study of the evolution of the dynamic properties and atomic configuration of Mg, Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu alloys from liquid to solid state was performed using AIMD calculation. The mean square displacement (MSD), PCF, SF, BP, coordination numbers (CN) and VP were analyzed for these metals and alloys with different components. The short-to-medium-range ordering was investigated in these metallic glasses. Based on these results, the nature of glass transition and the relation of GFA to the atomic structure for this type of MG are discussed. This work has implication for providing guideline for the optimization of the composition and properties of BMG alloys, especially for the alkaline–earth metal base BMG. 2. Methodology and experiments 2.1. Methodology Mg, Mg70Zn30, Mg66.25Zn28.75Ca5, Mg65Zn27.5Ca7.5 and (Mg66.25Zn28.75Ca5)97Cu3 were chosen for this work (for convenience, these four subjects are named Mg, MZ, MZC5, MZC7 and MZCC in the following context). The reason for investigating MZC5 and MZC7 is that these two BMG exhibit relatively large GFA, with critical diameters of 5 and 2 mm, respectively. And with the addition of Cu atoms, the GFA of the alloy is decreased compared with those of MZC5 and MZC7, as shown in Supplementary Fig. 1. The AIMD calculation was implemented by employing the Vienna ab initio simulation package. The electron– ion interactions and the exchange and correlation function of electrons are described by the ultra-soft pseudopotential and the generalized gradient approximation, respectively [32,33]. A canonical NVT (constant number, volume and temperature) ensemble was used. The sampling of k-mesh is on C point only. The time step used in the AIMD simulation is equal to 5 fs. The AIMD calculations were performed with a cubic supercell containing 240 atoms. These four types of atoms were distributed randomly in the supercell with the initial density obtained by the average atomic volume.
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The quenching schemes for Mg and the alloys of interest in the simulation were designed as follows. For Mg, the system was first equilibrated for 3000 steps at 1300 K to obtain a dynamic equilibrating configuration to avoid the impact of initial configuration. For the other four MG alloys, the start temperature for simulation was 1500 K. Then the system was quenched to 1100 K within 2000 time steps, and then kept at this temperature for 1000 time steps. At this temperature, the supercell volume was adjusted corresponding to zero external pressure, which is also named the “zero external pressure” method. In this process, the relative position of atoms was fixed. After that, the liquid was sequentially quenched to 900 K, 700 K, 500 K and 300 K with same cooling rate. Finally, the system was held at 300 K for 3000 time steps. The whole simulation process was run for 100 ps. The average cooling rate of Mg and the Mg-based MG alloys was 2 1013 K s1 and 2.4 1013 K s1, respectively. 2.2. Experiments To verify the calculated dynamic properties, the viscosities of MZC7 melt in the temperature range from 700 K to 960 K were measured in this work using Japanese production of a rotary vibration-type liquid viscometer in a graphite crucible. The sample of MZC7 alloys sealed in a vacuum of 103 torr was first overheated to 960 K and held at this temperature for 1 h. Then the sample was cooled to the predetermined temperature before the viscosity measurement was performed using a torsional oscillation viscometer for high temperature melts. Next, the crucible was placed in a vessel hung by a torsional suspension, and the vessel was set in oscillation about a vertical axis. The resulting motion was gradually damped on account of frictional energy absorption and dissipation within the melt. 3. Results and discussion 3.1. Dynamic properties For a time shorter than 0.1 ps, the MSD is proportional to the square of time and independent of temperature, as expected for ballistic motion and vibration [34]. For a longer time, the MSD increases with temperature, which is characteristic of a thermally activated process such as long-range diffusion. From the Einstein correlation, the diffusivity Di can be calculated via [35] PN i 2 h j¼1 jRj ðt þ t0 Þ Rj ðt0 Þj i hR2i ðtÞi Di ¼ lim ¼ lim ð1Þ t!1 t!1 6t 6N i t where hR2i ðtÞi is the mean-square displacement of atom i, Ni is the number of atom i, Rj is theP coordinates of the jth atom i i, t0 is the origin of time, and h Nj¼1 jRj ðt þ t0 Þ Rj ðt0 Þj2 i is the ensemble average of the square displacement of atom i. In this work, the self-diffusion coefficient for the liquid Mg at 1300 K was calculated as D = 5.78 108 m2 s1,
which is of the same order of magnitude as the previously reported value of D = 1.22 108 m2 s1 at 1223 K [36]. This result illustrates that the present AIMD calculation method for dynamic properties is valid. To further verify the calculated mobility of the elements, the calculated viscosities were compared with the measured data for MZC7 alloy. For a simple liquid system, the dynamic relax time of a simple particle is comparable with that of the whole group. In this case, the viscosity of the liquid can be related to the diffusivity using the Stokes–Einstein relation gSE ¼
kBT npRD
ð2Þ
where kB is the Boltzmann constant, R is the effective diameter of diffusive particles, D is the self-diffusion coefficient, n is a constant related to the ratio of diffusion particles to the medium particles, in this work n = 3. According to this scheme, the calculated viscosities for MZC7 alloy are shown in Fig. 1. It is seen that the calculated the values of viscosities for the liquid MZC7 alloy vary from g = 1.57 103 Pa s to 3.23 103 Pa s as the temperature is decreased from 1000 K to 700 K. The tested viscosities are in the range from g = 2.30 103 Pa s at 960 K to g = 3.24 103 Pa s at 700 K. Therefore, one can employ these calculated dynamics parameters for the analysis of glass transition and GFA of the Mg-based BMG. The MSD of Mg, Zn and Ca atoms in Mg, MZ, MZC5 and MZCC alloys are shown in Fig. 2. The slope of MSD curves as a function of time reflects the diffusion ability of atoms. Fig. 2 shows that the mobility of atoms strongly depends on the temperature and composition of the system. The diffusivities of all the three types of atoms decrease as the temperature drops. It is shown that the displacements of atoms do not change obviously at temperatures <500 K for Mg and <700 K for the other three alloys. And each system shows its specific feature. For pure Mg, the mobility smoothly decreases with the decrease in temperature. Even at 700 K, which is below the melting point of Mg, the atoms also show certain mobility. However, the atomic mobility in liquid for certain elements is highly
Fig. 1. Temperature dependence of viscosity for MZC7 alloy obtained by rotary vibration-type liquid viscometer and AIMD calculations.
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Fig. 2. MSD of Mg atoms in (a) Mg, (b) MZ, (c) MZC5 and (d) MZCC alloys, Zn atoms in (e) MZ, (f) MZC5 and (g) MZCC alloys and Ca atoms in (h) MZC5 and (i) MZCC alloys.
reduced as the second or third type of atoms is added to the system. As shown in Fig. 1b–i, the MSD of all the Mg, Zn and Ca atoms are reduced dramatically from 1500 K to 1100 K, and the atoms are difficult to move a distance of atomic radius <700 K. Fig. 3 shows the effect of the alloying element on the mobility of MZ, MZC5, MZC7 and MZCC at 1100 K. It is seen that, with the addition of Zn in pure Mg, the
˚ 2 in liquid Mg to MSD of Mg is decreased from 9.8 A 2 ˚ in MZ for the duration of 2.5 ps. The mobility of 1.8 A Mg is further decreased by the addition of 5 at.% Ca. It ˚ 2 for a duration is seen that the MSD of MZC5 is only 1 A 2.5 ps. However, as the addition of Ca is increased to 7.5 at.% and with the addition of Cu atoms, the mobility of Mg increases rather than decreases. As for Zn, it is shown that the mobility of Zn in the ternary liquid alloys
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Fig. 3. MSD of (a) Mg atoms, (b) Zn atoms and (c) Ca atoms in Mg, MZ, MZC5, MZC7 and MZCC alloys at 1100 K. The inset in (a) is the magnification of the MSD of Mg in MZ, MZC7 and MZCC alloys in the time from 1.8 ps to 2.1 ps.
is lower than that in binary MZ alloy. And the mobility of Zn in MZC5 alloy is the lowest. The mobility of Ca in the three liquid alloys is different. The MSD of Ca in liquid MZC5 is less than that in liquid MZC7 and MZCC alloys. For Mg–Zn–Ca–Cu alloy, it is seen that, under the same calculation parameters, the mobility of atoms strongly depends on the temperature of the system. The diffusion ability of Mg, Zn and Ca atoms decreases as the temperature drops. Anomalism in the diffusion ability of Mg, Zn and Ca atoms arises as Cu atoms are added to the ternary Mg–Zn–Ca systems. Compared with MZC5 alloy, the mobilities of atoms are increased with the addition of Cu resulting in the ternary system. As shown in Supplementary Fig. 1, the GFA of MZCC is obviously lower than those of MZC7 and MZC5, indicating that the dynamic slowing down of atoms indeed reflects the GFA of the Mg–Zn– Ca alloy system. It is seen that of the five systems of interest, all the values of the MSD of Mg, Zn and Ca atoms in MZC5 are lowest, i.e. the liquid MZC5 alloy has sluggish mobility. It has been proved that the dynamic properties of liquid have heredity to the solidified microstructure. And the glass transition is strongly affected by dynamic properties such as the viscosity of the liquid. Generally, as the viscosity of a metallic melt reaches 1013 Poise and no crystallization emerges, a glass structure can be formed. Therefore, from the point of view of the dynamic theory, the effect of the element on the mobility in a system is critical to the GFA, since the decrease in mobility means an increase in the viscosity of the liquid and suppression of crystallization.
3.2. Structural characteristics 3.2.1. Pair correlation functions The PCF and SF are the main parameters to reveal the feature of local structures in the liquid and glassy states. To correctly characterize the structure of these MG, the most important thing is to validate the reliability of the simulation results. Fig. 4 shows a comparison of the AIMD calculated PCF of Mg at 900 K with that at 943 K obtained by Waseda [37], and the calculated generalized SF for MZ metallic glass at 300 K with that at 293 K obtained by Rudin [38]. It is seen that both the AIMD calculated PCF and SF can reproduce the experimental curves. For Mg, not only the position, but also the height, of the peaks is in good agreement with the experimental data. In particular, a tiny shoulder commences on the right side of the second peak of the calculated generalized SF of MZ MG. The shape and position of this shoulder are in keeping with those measured by experiment. These results provide strong support for analyzing the atomic packing of the Mg–Zn–Ca BMG alloys by the AIMD simulation results. Fig. 5 shows the AIMD calculated evaluation of generalized pair correlation functions (GPCF) of Mg, MZ, MZC5 and MZCC during the quenching process. It is seen that, at temperatures >900 K, all the GPCF exhibit typical characterization of liquid structure, with the diffuse and smooth first and second peaks. The height of the first peaks of GPCF increases, and the width decreases as the temperature drops. The second and third peaks also become more and more pronounced. As the temperature is <900 K, which is close to the melting point of magnesium, the
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Fig. 4. Comparison of the calculated (a) PCF, g(r) of Mg and (b) SF, S(Q) of MZ alloy with the experimental data [37,38].
fourth and fifth peaks in the PCF become obvious. Moreover, splitting on the second peaks occurs, which indicates that the atomic arrangement tends to be in SRO during the quenching process. The differences among the four groups of GPCF are as follows. (1) The positions of the first peak r1, which represents the nearest neighbor, are different. The r1 of the PCF of Mg is largest. (2) The splitting on the second peak of the GPCF, which is a signal of the occurrence of SRO, is observed at different temperatures for Mg, MZ, MZC5 and MZCC. Of the four groups of GPCF, the formation temperature of SRO in undercooled Mg liquid seems to be the highest, and the GPCF in MZC5 shows most obvious splitting on the second peak. (3) A tiny peak is formed in the valley between the first and second peak of the PCF of Mg, indicating that partial crystallization takes place. All these three features support the point of view that the ordering in the structure of Mg is the most. The structures of MZ, MZC5 and MZCC are glassy. The structural characterization of the three systems can also be indicated visually from the snapshots of the three-dimensional atomic configurations, as shown in Fig. 5e–h. It is seen that the partial crystallization takes place in undercooled liquid Mg, and part of the structure has been transformed into an imperfect hexagonal close packed (hcp) type of structure at 300 K. The remaining liquid becomes the glass state at the glass transition temperature. For the MZ, MZC5 and
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MZCC MG, the atoms were arranged randomly in general. No long-range ordering occurs. The splitting on the second peak indicates that there are short-range orders under the glassy state condition. There are six groups of partial pair correlation functions (PPCF) in these ternary alloys. Since Mg and Zn are the major elements in this type of alloy, the focus is on Mg and Zn related PPCF at 300 K. Fig. 6 shows the PPCF of Mg–Mg, Mg–Zn, Mg–Ca, Zn–Zn and Zn–Ca pairs for Mg, MZ, MZC5, MZC7 and MZCC at 300 K. It is seen that in all the second peaks splitting occurs, indicating that there is indeed SRO in this type of metallic glasses. The interaction between the Mg–Mg pair seems to be least affected by the composition, as shown in Fig. 6a. Of the four PPCF of the Mg–Zn pair in the four alloys, the PPCF in MZC5 shows most obvious splitting on the second peak. For the PPCF of the Zn–Zn pair, both the first and second peaks are affected by the composition. The heights of both the first and second peaks of the Zn–Zn pair in MZC5 are anomalously larger than that in MZ alloy, although the content of Zn in MZC5 is lower than that in MZ. There are some differences between the PPCF of Mg–Ca and Zn–Ca pairs, which reflect the ordering tendency of the three BMG. It is shown that the splitting of the second peak of the Mg–Ca pair in MZC5 is lower than that in MZC7 and MZCC alloys. The first peak of the Zn–Ca pair in MZCC is higher than that in MZC5 and MZC7 alloys. A tiny shoulder is also found on the right side of the first peak of the PPCF of Zn–Ca in MZC7 alloy, indicating that strong ordering in this type of pair has been formed. In particular, the first peak of the Ca–Ca pair in MZCC is diminished because of the addition of Cu atoms, meaning that there is no Ca atom in the first neighbor. These results illustrate that all the partial pairs formed some extent of ordering, which may affect the GFA of the system, depending on the types of SRO and MRO. The next sections discuss the substantial types of SRO and MRO by BP and VP analysis. 3.2.2. Bond pair analysis The BP analysis method employed to describe the characteristics of the structural transition from liquid to solid for interested system in this work is based on Honeycutt and Andersen’s formula [39]. Indexes i, j, k and l are used to represent the atomic local circumstance. The typical BP are usually as follows: 1551, 1541 and 1431 representing icosahedral type of ordering; 1441 and 1661 body centered cubic (bcc) type of BP; 1421 and 1422 face centered cubic (fcc) and hcp type of BP; and 1311 and 1321 disordered atomic arrangements. The variations in the amount of BP with temperature in Mg, MZ, MZC5, MZC7 and MZCC are shown in Fig. 7. It is shown that <700 K, the hcp type of BP (1421 and 1422) in Mg increases as the temperature drops. The summation of 1421 and 1422 BP reaches 50% at 300 K, indicating that part of the liquid Mg has been transformed into hcp structure at this temperature. The icosahedral BP (1551, 1541 and 1431) reach 40% at 300 K, indicating that some
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Fig. 5. Evolution of the GPCF of (a) Mg, (b) MZ, (c) MZC5 and (d) MZCC from 1500 K/1300 K to 300 K. A view of the configurations of Mg, MZ, MZC5 and MZCC at 300 K obtained by AIMD calculation is shown in (e)–(h), respectively. The blue, green, dark green and yellow circles represent Mg, Zn, Ca and Cu atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
liquid structure has been retained, and the structure is composed of imperfect crystallized and amorphous structure. This result is consistent with the aforementioned analysis of the PCF. The total percentage of bcc and disordering type of BP (1441, 1661, 1311 and 1321) descends to zero as the temperature drops to 300 K.
It has been proved by experiments and computer simulations that icosahedral polyhedra account for a considerable portion of the structure of metallic glasses [24,28,29]. And the perfect icosahedron consists entirely of twelve 1551 BP. Even for the distorted icosahedron, the configuration is also made up of a large proportion of 1551 BP
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Although the BP results in MZCC glassy structure, indicating that the icosahedral BP are predominant, the relative content of 1551 type of BP in MZCC glassy is lower than that in MZC5, MZC7, as shown in Fig. 7f. It is also seen that the number of icosahedral BP in the glass structure of MZC5 alloy is largest among the five systems of interest in this work. Considering that the GFA of MZC5 is highest in Mg–Zn–Ca system found so far, the strong formation of icosahedral BP may be related to the high GFA for this type of MG.
Fig. 6. PPCF in Mg, MZ, MZC5, MZC7 and MZCC alloys at 300 K.
together with some 1541 or 1431 BP. From Fig. 7b, it is noted that the 1551 type of BP is significantly more than all other types of BP in the glass state of MZ alloy. Both the 1541 and 1431 BP also have high proportions in the liquid and glass state. The summation of 1551, 1541 and 1431 BP is increased from 58.1% to 74.1% with a decrease in temperature from 1500 to 300 K. The percentage of 1441 and 1661 BP is 6.5% and 10.8%, respectively, at 300 K. The 1422 and 1421 BP are only 5.0%, and hardly change during the cooling process. These results indicate that, in the glass structure of MZ alloy, icosahedral BP is predominant, the bcc type of BP the next, and the fcc and hcp types of BP in third place. The changes in BP in MZC5 and MZC7 BMG alloys with temperature are different from those in Mg and MZ alloys. As shown in Fig. 7c and d, the percentage of 1551, 1541 and 1431 type of BP is remarkably more than those of all other BP in both the alloys. For MZC5 alloy, the summation of these three types of BP increases from 56.8% to 75.7% when the temperature decreases from 1500 to 300 K. From Fig. 7e, it is noted that 1551 type of BP is more than all other types of BP in the glass state of MZCC alloy. Both the 1541 and 1431 BP account for a high percentage in the liquid and glass state. The summation of 1551, 1541 and 1431 BP is increased from 48.9% to 74.6% with the decrease in temperature from 1500 to 300 K.
3.2.3. Structural analysis by Voronoi tessellation To gain further insight into the structural features of the liquid and glass states, the atomic clusters were analyzed using the Voronoi tessellation method [40]. The VP is defined as the perpendicular bisector surfaces of the lines connecting a central atom to all of its neighboring atoms, symbolized by indices hn3, n4, n5, n6, . . .i, where ni represents P the number of i-edged faces of the polyhedron, and ni gives the total CN. The type of coordinate polyhedron referenced to a certain central atom can be identified through the Voronoi index. By the Voronoi tessellation method, it is shown that there are actually more than 10 types of polyhedral in the glass structure. To focus on the predominant local clusters, the polyhedra with amounts >1% in the glass structure were inspected. The distribution of VP in the systems of interest at 1100 K and 300 K is shown in Fig. 8. For Mg, the amount of the polyhedra with h0, 0, 12, 0i, h0, 1, 10, 2i, h0, 2, 8, 1i and h0, 2, 8, 2i is dramatically decreased with the drop in temperature, e.g. the percentage of h0, 2, 8, 1i is reduced from 4% to near zero at 300 K. It is also found that the h0, 3, 6, 4i type of polyhedra increases with the decrease in temperature from 1100 K to 300 K. In contrast to Mg, the MZ, MZC5, MZC7 and MZCC alloys exhibit a remarkable increase in the VP with h0, 0, 12, 0i with a decrease in temperature from 1100 K to 300 K. The local clusters are also affected by the composition of the systems. It is seen that the addition of element Zn results in an increase in icosahedra with h0, 0, 12, 0i in MZ alloy from 3.7% at 1100 K to 7.3% at 300 K. The addition of the third element, Ca, further promotes the formation of icosahedra in MZC5 alloy from 3.6% at 1100 K to 9.97% at 300 K, which is the most among all the clusters in the glass state of the five systems of interest. However, it is seen that the addition of 3% Cu in MZC5 alloy results in an obvious decrease in icosahedra. The icosahedra with h0, 0, 12, 0i is reduced from 9.97% in MZC5 alloy to 6.3% in MZCC at 300 K. However, the VP with h0, 2, 8, 2i, h0, 2, 8, 1i and h0, 3, 6, 4i decrease with decreasing temperature. These results mean that icosahedral clusters increase, but bcc and fcc types of clusters decrease with the decrease in temperature in Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu alloys. Fig. 9 shows the distribution of the CN of VP in the systems of interest at 1100 K and 300 K, respectively, from AIMD calculations. At 300 K, it is seen that the CN of
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Fig. 7. Variation in various types of BP in (a) Mg, (b) MZ, (c) MZC5, (d) MZC7 and (e) MZCC as a function of temperature. (f) Variation in 1551 BP in five systems as a function of temperature.
most of the VP are in the range from 12 to 14, with CN = 13 being most common. For MZ, MZC5, MZC7 and MZCC alloys, the CN demonstrate a broad scope extended from CN = 10 to CN = 16. The VP with CN = 12 and 13 in Mg–Zn–Ca are more than those in MZ alloy, indicating that the probability of forming icosahedral cluster increases. Furthermore, it is also seen that the VP with CN = 12 and 13 in MZCC alloys are lower than those in MZC5 and MZC7 alloys. The homogeneous distribution of CN in Mg–Zn–Ca alloys are controlled by the effective atomic size ratio R*, between solute and solvent. With decreasing R*, the VP changes from the Frank–Kasper type (R* > 1.2) to the icosahedral type (R* < 0.902), and then to the bi-capped square Archimedean antiprism and tri-capped trigonal prism packing type (R* < 0.835 and 0.732), respectively [41]. In Mg–Zn–Ca alloy, it is seen that, the solutes are actually Zn atoms, and its R* to Mg and Ca are equal to 0.831 and 0.675, respectively. It is noted that, since the
present authors counted the clusters referenced to every atom in the system, it is not difficult to understand that there are many more clusters with R* = 1. From the above analysis, it is seen that the broad distribution of CN in Mg– Zn–Ca alloys should be attributed to the ratio of atomic radii among the three elements. The medium-range ordering in metallic glass has been found in recent studies on BMG alloys [15,16,24,42]. From the VP information, the geometric/topological packing beyond the nearest coordinate shell can be now described, and realistic atomic packing can be constructed. Fig. 10a–d shows four types of extended clusters formed by two VP with CN = 12, in which BP are of 1551 type. These two types of VP are linked via vertex-, edge-, face- and intercross-shared (VS, ES, FS, and IS) atoms. Mg and Zn atoms are at the central position of these icosahedra, i.e. to be the solute atoms. It is seen that all the three types of component elements can serve as solvent atoms, owing to the need for efficient packing. The IS clusters, which contain 19
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Fig. 8. Distribution of the VP in Mg, MZ, MZC5, MZC7 and MZCC at (a) 1100 K and (b) 300 K.
atoms (as shown in Fig. 9d), are highly densely packed. In this work, icosahedral medium-range order (IMRO) can be formed with different types of linkage between the icosahedra. As an example, Fig. 10e shows an IMRO that is composed of seven icosahedra and reaches nanometer scale in size. Among these icosahedra, five icosahedra are accumulated in the form of IS connection, in which central atoms of Zn or Mg form a “lone string”, and Ca atoms act as connecting or glue atoms between two coordinate polyhedra. In addition to these five icosahedra, other icosahedra are connected to the intercrossed icosahedra by ES or FS atoms. 3.2.4. Correlation of GFA to dynamic properties and structural ordering In this section, the correlation of the GFA of Mg–Zn–Ca BMG with their kinetic properties and the structural feature based on the above results are discussed. The AIMD calculations in this work suggest that the large GFA of Mg–Zn– Ca BMG alloy is essentially attributed to the following characteristics: (1) the sluggish mobility of atoms induced by the confusion of the composition; and (2) the formation of a large amount of ISRO and corresponding IMRO. These two features are beneficial to the formation of the glass structure. It is known that the glass state is formed, given that the crystallization process is suppressed in the
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Fig. 9. Distribution of the CN of Mg, MZ, MZC5, MZC7 and MZCC at (a) 1100 K and (b) 300 K.
undercooled liquid. For the nucleation and growth of crystalline phases in undercooled liquid, a long duration will be required for substantial atomic diffusion and composition redistribution. Therefore, it is beneficial for the formation of the glassy structure to decrease the mobility of atoms in the undercooled liquid. Figs. 2 and 3 show that the diffusivity of atoms of Mg–Zn–Ca ternary system is generally lower than that of pure Mg and Mg–Zn alloy. This decrease in the mobility of the atoms in the ternary system is due to the interaction among the three types of atoms. According to Ref. [43], the heat of mixings of Mg–Zn, Mg–Ca and Zn–Ca pair are 6 kJ mol1, 4 kJ mol1 and 22 kJ mol1, respectively. This means that there is mutual affinity among the heterogeneous atoms. It is also known that the value of heat of mixing between Zn and Ca is largest among the three types of atom pairs, indicating that there is more strong chemical interaction in ternary Mg–Zn–Ca alloys than that in binary Mg–Zn alloys. The MSD curves as shown in Fig. 2 indicate that the atomic mobility in liquid for certain elements is highly reduced as the second or third type of atom is added to the system. The changes in atomic mobility in the five systems of interest agree very well with GFA, which deteriorates along the sequence of Mg66.25Zn28.75Ca5, Mg65Zn27.5Ca7.5 and (Mg66.25Zn28.75Ca5)97Cu3, Mg70Zn30 and Mg. Both the simulation and the experimental results (as shown in Supplementary Fig. 1) show that the
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Fig. 10. Extended icosahedral clusters in MZC5 alloy linked by (a) vertex-, (b) edge-, (c) face- and (d) intercross-shared atoms, respectively; (e) an IMRO composed of seven perfect icosahedra.
Mg65Zn27.5Ca7.5 alloy has the highest glass formation ability. The dynamic slowing down of atoms reveals the relation between atomic mobility and glass-forming ability. The influences of the addition of Cu element on the MSD, BP, CN and VP indicate that Cu is indeed not beneficial to the GFA of Mg–Zn–Ca BMG alloys. According to Ref. [43], the heats of mixing of Mg–Cu, Zn–Cu and Ca–Cu pairs are 3 kJ mol1, 1 kJ mol1 and 13 kJ mol1, respectively. For Mg–Zn–Ca–Cu alloy, under the same calculated conditions, the diffusivities of Mg, Zn and Ca atoms increases with alloying with Cu atoms compared with those MZC5 alloys (as shown in Fig. 3). Therefore, the sluggish mobility in Mg–Zn–Ca alloys cannot be explained merely by the mixing heats among the elements. The geometrical effect and entropy increase should also be considered. From the point of view of the structural characterization, the complexity in composition and atomic size will favor the formation of glass structure. The composition redistribution for the nucleation and growth of the crystal-
line phase will involve more atoms. As shown in Fig. 7b–d, with the icosahedral BP in the supercooled liquid state increasing sharply near the glass transition temperature, much more densely packed local orders are formed. And the icosahedral BP are predominant among all types of BP in liquid state owing to the relative high bonding energy of icosahedral BP. Correspondingly, some IMRO in nanometer scale develops. In this process, small atoms (Zn or Mg) located at the coordinate shell in a single icosahedron may turn out to be the central atoms when two icosahedra are connected. This means that the formation of IMRO can stabilize the undercooled liquid or restrict nucleation of crystals, i.e. increase the GFA of Mg–Zn–Ca alloys. 4. Conclusions
(1) The dynamic properties of the systems of interest were calculated by AIMD modeling. The AIMD calculated diffusivity of Mg and the viscosity of MZC7
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(2)
(3)
(4)
(5)
alloy agree well with the experimental data. It was found that Zn and Ca in Mg liquid induce remarkably sluggish mobility of atoms. However, anomalism in the diffusivity of Mg, Zn and Ca atoms was caused as Cu atoms were added to the ternary Mg– Zn–Ca systems. In this work, there is a good corresponding relation between the mobility of atoms and GFA for the systems of interest. Both the AIMD calculated PCF and SF for Mg and Mg–Zn alloys can reproduce the experimental curves, which provided strong support for analyzing the atomic packing of the Mg–Zn–Ca BMG alloys by the AIMD simulation results obtained in this work. Splitting was observed on the second peak of the PPCF of the four systems of interest, indicating that strong local ordering was formed. In the glassy structure of Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu alloys, icosahedral BP with h1551i is predominant, the bcc type of BP is next, and the fcc and hcp types of BP are third. The amount of icosahedral BP in the glassy structure of MZC5 is most among the five systems of interest in this work. The VP with h0, 0, 12, 0i in Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu alloys exhibit remarkable increase with a decrease in temperature from 1500 K to 300 K. The addition of Zn and Ca into Mg and Mg–Zn alloy results in an increase in h0, 0, 12, 0i type of icosahedra, and a decrease in bcc and fcc type of clusters. It is noticeable that further addition of Cu to MZC5 alloy results in a decrease in h0, 0, 12, 0i type of icosahedra. The CN of the VP are in the range 12– 14, with CN = 13 being most. IMRO can be formed by the linkage of VS, ES, FS and IS types of shared atoms between the icosahedra. The correlations of the GFA of Mg–Zn–Ca BMG with their dynamic properties and the structural feature were discussed. It is considered that the large GFA of Mg–Zn–Ca BMG alloy is essentially attributed to the sluggish mobility of atoms induced by the compositional confusion, and the formation of a large amount of ISRO and corresponding IMRO.
Acknowledgment The authors are grateful for the financial support of National Natural Science Foundation of China (No. 51071018, 51271018). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.actamat.2013.12.037.
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ScienceDirect Acta Materialia 67 (2014) 266–277 www.elsevier.com/locate/actamat
Sluggish mobility and strong icosahedral ordering in Mg–Zn–Ca liquid and glassy alloys Y.F. Zhao a, D.Y. Lin a, X.H. Chen a, Z.K. Liu b, X.D. Hui a,⇑ a
State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China b Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA Received 24 June 2013; received in revised form 22 December 2013; accepted 26 December 2013 Available online 1 February 2014
Abstract The dynamic properties and atomic configuration of Mg, Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu liquid and solid systems were comprehensively studied using ab initio molecular dynamics calculation. The viscosities of an Mg–Zn–Ca alloy were measured from 700 K to 960 K. It was found that Zn and Ca in Mg liquid induce remarkable slowing down of atoms, but Cu acted as a stimulus to the diffusion. Icosahedral short-range orders are most dominant in Mg–Zn–Ca alloys in view of the existence of a majority of 1551 type of bond pairs, h0, 0, 12, 0i type of Voronoi polyhedra. Icosahedral medium-range orders can be formed in Mg–Zn–Ca alloys by the perfect icosahedra via the linkage of vertex-, edge-, face- and intercross-shared atoms. It is suggested that the high glass forming ability of Mg–Zn–Ca alloys is essentially related to the sluggish mobility and strong icosahedral short- and medium-range ordering in the undercooled liquid. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Mg–Zn–Ca; Dynamic properties; Atomic structure; Ab initio molecular dynamics; Icosahedral medium-range orders
1. Introduction Bio-absorbable implants have been widely employed in orthopedic surgery and have become an important materials field today. Of the miscellaneous metallic implants developed, Mg-enriched crystalline material showed a Young’s modulus similar to that of bone (E = 3–20 GPa), favorable compatibility with bone cell and tissue growth, and antibacterial properties [1–3]. However, their wide application has been limited by their rapid corrosion rate accompanied by hydrogen evolution in vivo [2]. In recent years, Mg-based bulk metallic glasses (BMG) have attracted significant attention as potential bio-absorbable implant materials, owing to their higher strength and better corrosion resistance than traditional magnesium crystalline materials. The earliest BMG were developed in 1988 in the Mg– TM–RE (TM, transition metal; RE, rare-earth element) ⇑ Corresponding author. Tel.: +86 10 62333066; fax: +86 10 62333447.
E-mail address: [email protected] (X.D. Hui).
system [4]. This type of BMG exhibits a wide supercooled liquid region, high glass-forming ability (GFA) and high tensile strength. Based on this ternary system, many multicomponent Mg-based BMG have been prepared [5–9]. Unfortunately, RE-containing Mg-based BMG exhibit bad biocompatibility for biomedical materials. Recently, great progress has been achieved in the synthesis and properties of RE-free Mg-based BMG by adding a few per cent of Ca element to the Mg–Zn binary system. New Mg–Zn– Ca BMG with a critical diameter of 4 mm were prepared using conventional casting techniques [10–14]. Their feasibility as biodegradable metallic materials was evaluated by investigating their mechanical, corrosion and cytotoxicity properties. The experimental results show that these BMG are of higher cell viability than that of as-rolled pure Mg. Through animal experiments, Zberg et al. [10] revealed that the Mg–Zn–Ca BMG exhibit a great reduction in hydrogen evolution, as the content of Zn is below a threshold value of 28 at.%, and the same good tissue compatibility as observed in crystalline Mg implants. Wang et al. [11] synthesized Fe particle reinforced Mg69Zn27Ca4 BMG
1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.12.037
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composites by copper mold injection casting with industrial raw materials. It was shown that the corrosion resistance of this type of BMG-based composite has been remarkably improved in 3.5 wt.% NaCl solution compared with that of AZ31 and pure Mg. The reliability of the compressive fracture strength of Mg96xZnxCa4 (x = 30, 25) BMG has also been investigated [12]. It was found that the compressive fracture strength of Mg–Zn–Ca BMG exhibit surprisingly high uniformity. In the present work, as shown in Supplementary Fig. 1, it was found that the addition of Cu increases the corrosion potential and decreases the corrosion current density of Mg–Zn–Ca metallic glasses in PBS solution, thus delaying the biodegradability of this type of metallic glass alloy. The compressive fracture strength of Mg–Zn–Ca BMG is enhanced by addition of Cu. However, it was also found that the glass-forming ability of Mg–Zn–Ca BMG is reduced by the appropriate addition of Cu. Crystalline phases are precipitated, as the content of Cu is >3 at.%. The large GFA, good biocompatibility, low cost and easy recycling ability of Mg–Zn–Ca BMG make them promising for structural engineering or biomedical application. To make the most of the advantage of BMG, it is essential to thoroughly understand their dynamics properties and structural mechanism. In recent years, experimental investigations and theoretical modeling have been performed on Zr-, Pd-, Mg- and La-based BMG alloys using X-ray diffraction (XRD), extended X-ray absorption fine structure (EXAFS), anomalous X-ray scattering and neutron diffraction, molecular dynamics (MD) and ab initio molecular dynamics (AIMD). Theoretically, cluster dense packing [15] and quasi-equivalent cluster models [16] have been developed besides the structural theories, such as dense random packing of the hard sphere [17], the trigonal prism model [18] and the chemical twinning model [19]. To understand the ultrahigh strength of Co–Fe–Ta–B BMG, Inoue et al. [20] investigated the precipitates from the BMG and deduced that the ultrahigh strength of Co-based BMG results from the formation of local atomic ordering. Hui et al. [21] proved that the short-range order in Co–Fe–Ta– B BMG is of a (Co, Fe)2B-like but not (Co, Fe)23B6-like crystallographic structure. Yao et al. [22] found that the high strength in Fe–Nb–B BMG is associated with the formation of a network-like structure. Gerold et al. [23] conducted EXAFS studies on the nature of atomic correlations of Zr41.2Ti13.8Cu12.5Ni10Be22.5 (vit1) BMG alloy in the as-quenched state, and found that the atoms tend to form a dense packing. Using the AIMD calculation, Hui et al. [24] revealed that the icosahedral short- and medium-range orders (ISRO and IMRO) are most dominant in vit1 BMG in view of the presence of a majority of bond pairs (BP) and Voronoi polyhedral (VP). Short-range ordering (SRO) was found by Mattern et al. [25] in Zr–Ti–Al–Cu– Ni BMG in terms of the pair correlation function (PCF). A high degree of dense random packed structures has also been confirmed from the XRD profiles in ternary La–Al– Ni [16,26] and Mg–Cu–La [17,27] BMG alloys. Cheng
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et al. [28,29] investigated the influence of local structure on the dynamics in the Cu–Zr and Cu46Zr47Al7 systems by MD simulation using EAM potentials, and found that the local icosahedral clusters are responsible for the viscosity of the supercooled liquid. Jiang et al. [30] measured the general PCF and structure factor (SF) of the Cu46Zr46Al8 glass alloy using synchrotron radiation XRD. ISRO, of which Al atoms are caged in the center of icosahedra with Cu and Zr atoms are the vertices, have been evidenced in the Cu46Zr46Al8 BMG by AIMD simulation [31]. In spite of such great progress in the structural characterization of BMG, the dynamic properties and structural characterization of Mg–Zn–Ca glassy alloys during the glass formation process are still less understood. In particular, the mobility and short-to-medium-range order in the atomic packing of this type of BMG have not been reported. In the present work, a comprehensive study of the evolution of the dynamic properties and atomic configuration of Mg, Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu alloys from liquid to solid state was performed using AIMD calculation. The mean square displacement (MSD), PCF, SF, BP, coordination numbers (CN) and VP were analyzed for these metals and alloys with different components. The short-to-medium-range ordering was investigated in these metallic glasses. Based on these results, the nature of glass transition and the relation of GFA to the atomic structure for this type of MG are discussed. This work has implication for providing guideline for the optimization of the composition and properties of BMG alloys, especially for the alkaline–earth metal base BMG. 2. Methodology and experiments 2.1. Methodology Mg, Mg70Zn30, Mg66.25Zn28.75Ca5, Mg65Zn27.5Ca7.5 and (Mg66.25Zn28.75Ca5)97Cu3 were chosen for this work (for convenience, these four subjects are named Mg, MZ, MZC5, MZC7 and MZCC in the following context). The reason for investigating MZC5 and MZC7 is that these two BMG exhibit relatively large GFA, with critical diameters of 5 and 2 mm, respectively. And with the addition of Cu atoms, the GFA of the alloy is decreased compared with those of MZC5 and MZC7, as shown in Supplementary Fig. 1. The AIMD calculation was implemented by employing the Vienna ab initio simulation package. The electron– ion interactions and the exchange and correlation function of electrons are described by the ultra-soft pseudopotential and the generalized gradient approximation, respectively [32,33]. A canonical NVT (constant number, volume and temperature) ensemble was used. The sampling of k-mesh is on C point only. The time step used in the AIMD simulation is equal to 5 fs. The AIMD calculations were performed with a cubic supercell containing 240 atoms. These four types of atoms were distributed randomly in the supercell with the initial density obtained by the average atomic volume.
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The quenching schemes for Mg and the alloys of interest in the simulation were designed as follows. For Mg, the system was first equilibrated for 3000 steps at 1300 K to obtain a dynamic equilibrating configuration to avoid the impact of initial configuration. For the other four MG alloys, the start temperature for simulation was 1500 K. Then the system was quenched to 1100 K within 2000 time steps, and then kept at this temperature for 1000 time steps. At this temperature, the supercell volume was adjusted corresponding to zero external pressure, which is also named the “zero external pressure” method. In this process, the relative position of atoms was fixed. After that, the liquid was sequentially quenched to 900 K, 700 K, 500 K and 300 K with same cooling rate. Finally, the system was held at 300 K for 3000 time steps. The whole simulation process was run for 100 ps. The average cooling rate of Mg and the Mg-based MG alloys was 2 1013 K s1 and 2.4 1013 K s1, respectively. 2.2. Experiments To verify the calculated dynamic properties, the viscosities of MZC7 melt in the temperature range from 700 K to 960 K were measured in this work using Japanese production of a rotary vibration-type liquid viscometer in a graphite crucible. The sample of MZC7 alloys sealed in a vacuum of 103 torr was first overheated to 960 K and held at this temperature for 1 h. Then the sample was cooled to the predetermined temperature before the viscosity measurement was performed using a torsional oscillation viscometer for high temperature melts. Next, the crucible was placed in a vessel hung by a torsional suspension, and the vessel was set in oscillation about a vertical axis. The resulting motion was gradually damped on account of frictional energy absorption and dissipation within the melt. 3. Results and discussion 3.1. Dynamic properties For a time shorter than 0.1 ps, the MSD is proportional to the square of time and independent of temperature, as expected for ballistic motion and vibration [34]. For a longer time, the MSD increases with temperature, which is characteristic of a thermally activated process such as long-range diffusion. From the Einstein correlation, the diffusivity Di can be calculated via [35] PN i 2 h j¼1 jRj ðt þ t0 Þ Rj ðt0 Þj i hR2i ðtÞi Di ¼ lim ¼ lim ð1Þ t!1 t!1 6t 6N i t where hR2i ðtÞi is the mean-square displacement of atom i, Ni is the number of atom i, Rj is theP coordinates of the jth atom i i, t0 is the origin of time, and h Nj¼1 jRj ðt þ t0 Þ Rj ðt0 Þj2 i is the ensemble average of the square displacement of atom i. In this work, the self-diffusion coefficient for the liquid Mg at 1300 K was calculated as D = 5.78 108 m2 s1,
which is of the same order of magnitude as the previously reported value of D = 1.22 108 m2 s1 at 1223 K [36]. This result illustrates that the present AIMD calculation method for dynamic properties is valid. To further verify the calculated mobility of the elements, the calculated viscosities were compared with the measured data for MZC7 alloy. For a simple liquid system, the dynamic relax time of a simple particle is comparable with that of the whole group. In this case, the viscosity of the liquid can be related to the diffusivity using the Stokes–Einstein relation gSE ¼
kBT npRD
ð2Þ
where kB is the Boltzmann constant, R is the effective diameter of diffusive particles, D is the self-diffusion coefficient, n is a constant related to the ratio of diffusion particles to the medium particles, in this work n = 3. According to this scheme, the calculated viscosities for MZC7 alloy are shown in Fig. 1. It is seen that the calculated the values of viscosities for the liquid MZC7 alloy vary from g = 1.57 103 Pa s to 3.23 103 Pa s as the temperature is decreased from 1000 K to 700 K. The tested viscosities are in the range from g = 2.30 103 Pa s at 960 K to g = 3.24 103 Pa s at 700 K. Therefore, one can employ these calculated dynamics parameters for the analysis of glass transition and GFA of the Mg-based BMG. The MSD of Mg, Zn and Ca atoms in Mg, MZ, MZC5 and MZCC alloys are shown in Fig. 2. The slope of MSD curves as a function of time reflects the diffusion ability of atoms. Fig. 2 shows that the mobility of atoms strongly depends on the temperature and composition of the system. The diffusivities of all the three types of atoms decrease as the temperature drops. It is shown that the displacements of atoms do not change obviously at temperatures <500 K for Mg and <700 K for the other three alloys. And each system shows its specific feature. For pure Mg, the mobility smoothly decreases with the decrease in temperature. Even at 700 K, which is below the melting point of Mg, the atoms also show certain mobility. However, the atomic mobility in liquid for certain elements is highly
Fig. 1. Temperature dependence of viscosity for MZC7 alloy obtained by rotary vibration-type liquid viscometer and AIMD calculations.
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Fig. 2. MSD of Mg atoms in (a) Mg, (b) MZ, (c) MZC5 and (d) MZCC alloys, Zn atoms in (e) MZ, (f) MZC5 and (g) MZCC alloys and Ca atoms in (h) MZC5 and (i) MZCC alloys.
reduced as the second or third type of atoms is added to the system. As shown in Fig. 1b–i, the MSD of all the Mg, Zn and Ca atoms are reduced dramatically from 1500 K to 1100 K, and the atoms are difficult to move a distance of atomic radius <700 K. Fig. 3 shows the effect of the alloying element on the mobility of MZ, MZC5, MZC7 and MZCC at 1100 K. It is seen that, with the addition of Zn in pure Mg, the
˚ 2 in liquid Mg to MSD of Mg is decreased from 9.8 A 2 ˚ in MZ for the duration of 2.5 ps. The mobility of 1.8 A Mg is further decreased by the addition of 5 at.% Ca. It ˚ 2 for a duration is seen that the MSD of MZC5 is only 1 A 2.5 ps. However, as the addition of Ca is increased to 7.5 at.% and with the addition of Cu atoms, the mobility of Mg increases rather than decreases. As for Zn, it is shown that the mobility of Zn in the ternary liquid alloys
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Fig. 3. MSD of (a) Mg atoms, (b) Zn atoms and (c) Ca atoms in Mg, MZ, MZC5, MZC7 and MZCC alloys at 1100 K. The inset in (a) is the magnification of the MSD of Mg in MZ, MZC7 and MZCC alloys in the time from 1.8 ps to 2.1 ps.
is lower than that in binary MZ alloy. And the mobility of Zn in MZC5 alloy is the lowest. The mobility of Ca in the three liquid alloys is different. The MSD of Ca in liquid MZC5 is less than that in liquid MZC7 and MZCC alloys. For Mg–Zn–Ca–Cu alloy, it is seen that, under the same calculation parameters, the mobility of atoms strongly depends on the temperature of the system. The diffusion ability of Mg, Zn and Ca atoms decreases as the temperature drops. Anomalism in the diffusion ability of Mg, Zn and Ca atoms arises as Cu atoms are added to the ternary Mg–Zn–Ca systems. Compared with MZC5 alloy, the mobilities of atoms are increased with the addition of Cu resulting in the ternary system. As shown in Supplementary Fig. 1, the GFA of MZCC is obviously lower than those of MZC7 and MZC5, indicating that the dynamic slowing down of atoms indeed reflects the GFA of the Mg–Zn– Ca alloy system. It is seen that of the five systems of interest, all the values of the MSD of Mg, Zn and Ca atoms in MZC5 are lowest, i.e. the liquid MZC5 alloy has sluggish mobility. It has been proved that the dynamic properties of liquid have heredity to the solidified microstructure. And the glass transition is strongly affected by dynamic properties such as the viscosity of the liquid. Generally, as the viscosity of a metallic melt reaches 1013 Poise and no crystallization emerges, a glass structure can be formed. Therefore, from the point of view of the dynamic theory, the effect of the element on the mobility in a system is critical to the GFA, since the decrease in mobility means an increase in the viscosity of the liquid and suppression of crystallization.
3.2. Structural characteristics 3.2.1. Pair correlation functions The PCF and SF are the main parameters to reveal the feature of local structures in the liquid and glassy states. To correctly characterize the structure of these MG, the most important thing is to validate the reliability of the simulation results. Fig. 4 shows a comparison of the AIMD calculated PCF of Mg at 900 K with that at 943 K obtained by Waseda [37], and the calculated generalized SF for MZ metallic glass at 300 K with that at 293 K obtained by Rudin [38]. It is seen that both the AIMD calculated PCF and SF can reproduce the experimental curves. For Mg, not only the position, but also the height, of the peaks is in good agreement with the experimental data. In particular, a tiny shoulder commences on the right side of the second peak of the calculated generalized SF of MZ MG. The shape and position of this shoulder are in keeping with those measured by experiment. These results provide strong support for analyzing the atomic packing of the Mg–Zn–Ca BMG alloys by the AIMD simulation results. Fig. 5 shows the AIMD calculated evaluation of generalized pair correlation functions (GPCF) of Mg, MZ, MZC5 and MZCC during the quenching process. It is seen that, at temperatures >900 K, all the GPCF exhibit typical characterization of liquid structure, with the diffuse and smooth first and second peaks. The height of the first peaks of GPCF increases, and the width decreases as the temperature drops. The second and third peaks also become more and more pronounced. As the temperature is <900 K, which is close to the melting point of magnesium, the
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Fig. 4. Comparison of the calculated (a) PCF, g(r) of Mg and (b) SF, S(Q) of MZ alloy with the experimental data [37,38].
fourth and fifth peaks in the PCF become obvious. Moreover, splitting on the second peaks occurs, which indicates that the atomic arrangement tends to be in SRO during the quenching process. The differences among the four groups of GPCF are as follows. (1) The positions of the first peak r1, which represents the nearest neighbor, are different. The r1 of the PCF of Mg is largest. (2) The splitting on the second peak of the GPCF, which is a signal of the occurrence of SRO, is observed at different temperatures for Mg, MZ, MZC5 and MZCC. Of the four groups of GPCF, the formation temperature of SRO in undercooled Mg liquid seems to be the highest, and the GPCF in MZC5 shows most obvious splitting on the second peak. (3) A tiny peak is formed in the valley between the first and second peak of the PCF of Mg, indicating that partial crystallization takes place. All these three features support the point of view that the ordering in the structure of Mg is the most. The structures of MZ, MZC5 and MZCC are glassy. The structural characterization of the three systems can also be indicated visually from the snapshots of the three-dimensional atomic configurations, as shown in Fig. 5e–h. It is seen that the partial crystallization takes place in undercooled liquid Mg, and part of the structure has been transformed into an imperfect hexagonal close packed (hcp) type of structure at 300 K. The remaining liquid becomes the glass state at the glass transition temperature. For the MZ, MZC5 and
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MZCC MG, the atoms were arranged randomly in general. No long-range ordering occurs. The splitting on the second peak indicates that there are short-range orders under the glassy state condition. There are six groups of partial pair correlation functions (PPCF) in these ternary alloys. Since Mg and Zn are the major elements in this type of alloy, the focus is on Mg and Zn related PPCF at 300 K. Fig. 6 shows the PPCF of Mg–Mg, Mg–Zn, Mg–Ca, Zn–Zn and Zn–Ca pairs for Mg, MZ, MZC5, MZC7 and MZCC at 300 K. It is seen that in all the second peaks splitting occurs, indicating that there is indeed SRO in this type of metallic glasses. The interaction between the Mg–Mg pair seems to be least affected by the composition, as shown in Fig. 6a. Of the four PPCF of the Mg–Zn pair in the four alloys, the PPCF in MZC5 shows most obvious splitting on the second peak. For the PPCF of the Zn–Zn pair, both the first and second peaks are affected by the composition. The heights of both the first and second peaks of the Zn–Zn pair in MZC5 are anomalously larger than that in MZ alloy, although the content of Zn in MZC5 is lower than that in MZ. There are some differences between the PPCF of Mg–Ca and Zn–Ca pairs, which reflect the ordering tendency of the three BMG. It is shown that the splitting of the second peak of the Mg–Ca pair in MZC5 is lower than that in MZC7 and MZCC alloys. The first peak of the Zn–Ca pair in MZCC is higher than that in MZC5 and MZC7 alloys. A tiny shoulder is also found on the right side of the first peak of the PPCF of Zn–Ca in MZC7 alloy, indicating that strong ordering in this type of pair has been formed. In particular, the first peak of the Ca–Ca pair in MZCC is diminished because of the addition of Cu atoms, meaning that there is no Ca atom in the first neighbor. These results illustrate that all the partial pairs formed some extent of ordering, which may affect the GFA of the system, depending on the types of SRO and MRO. The next sections discuss the substantial types of SRO and MRO by BP and VP analysis. 3.2.2. Bond pair analysis The BP analysis method employed to describe the characteristics of the structural transition from liquid to solid for interested system in this work is based on Honeycutt and Andersen’s formula [39]. Indexes i, j, k and l are used to represent the atomic local circumstance. The typical BP are usually as follows: 1551, 1541 and 1431 representing icosahedral type of ordering; 1441 and 1661 body centered cubic (bcc) type of BP; 1421 and 1422 face centered cubic (fcc) and hcp type of BP; and 1311 and 1321 disordered atomic arrangements. The variations in the amount of BP with temperature in Mg, MZ, MZC5, MZC7 and MZCC are shown in Fig. 7. It is shown that <700 K, the hcp type of BP (1421 and 1422) in Mg increases as the temperature drops. The summation of 1421 and 1422 BP reaches 50% at 300 K, indicating that part of the liquid Mg has been transformed into hcp structure at this temperature. The icosahedral BP (1551, 1541 and 1431) reach 40% at 300 K, indicating that some
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Fig. 5. Evolution of the GPCF of (a) Mg, (b) MZ, (c) MZC5 and (d) MZCC from 1500 K/1300 K to 300 K. A view of the configurations of Mg, MZ, MZC5 and MZCC at 300 K obtained by AIMD calculation is shown in (e)–(h), respectively. The blue, green, dark green and yellow circles represent Mg, Zn, Ca and Cu atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
liquid structure has been retained, and the structure is composed of imperfect crystallized and amorphous structure. This result is consistent with the aforementioned analysis of the PCF. The total percentage of bcc and disordering type of BP (1441, 1661, 1311 and 1321) descends to zero as the temperature drops to 300 K.
It has been proved by experiments and computer simulations that icosahedral polyhedra account for a considerable portion of the structure of metallic glasses [24,28,29]. And the perfect icosahedron consists entirely of twelve 1551 BP. Even for the distorted icosahedron, the configuration is also made up of a large proportion of 1551 BP
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Although the BP results in MZCC glassy structure, indicating that the icosahedral BP are predominant, the relative content of 1551 type of BP in MZCC glassy is lower than that in MZC5, MZC7, as shown in Fig. 7f. It is also seen that the number of icosahedral BP in the glass structure of MZC5 alloy is largest among the five systems of interest in this work. Considering that the GFA of MZC5 is highest in Mg–Zn–Ca system found so far, the strong formation of icosahedral BP may be related to the high GFA for this type of MG.
Fig. 6. PPCF in Mg, MZ, MZC5, MZC7 and MZCC alloys at 300 K.
together with some 1541 or 1431 BP. From Fig. 7b, it is noted that the 1551 type of BP is significantly more than all other types of BP in the glass state of MZ alloy. Both the 1541 and 1431 BP also have high proportions in the liquid and glass state. The summation of 1551, 1541 and 1431 BP is increased from 58.1% to 74.1% with a decrease in temperature from 1500 to 300 K. The percentage of 1441 and 1661 BP is 6.5% and 10.8%, respectively, at 300 K. The 1422 and 1421 BP are only 5.0%, and hardly change during the cooling process. These results indicate that, in the glass structure of MZ alloy, icosahedral BP is predominant, the bcc type of BP the next, and the fcc and hcp types of BP in third place. The changes in BP in MZC5 and MZC7 BMG alloys with temperature are different from those in Mg and MZ alloys. As shown in Fig. 7c and d, the percentage of 1551, 1541 and 1431 type of BP is remarkably more than those of all other BP in both the alloys. For MZC5 alloy, the summation of these three types of BP increases from 56.8% to 75.7% when the temperature decreases from 1500 to 300 K. From Fig. 7e, it is noted that 1551 type of BP is more than all other types of BP in the glass state of MZCC alloy. Both the 1541 and 1431 BP account for a high percentage in the liquid and glass state. The summation of 1551, 1541 and 1431 BP is increased from 48.9% to 74.6% with the decrease in temperature from 1500 to 300 K.
3.2.3. Structural analysis by Voronoi tessellation To gain further insight into the structural features of the liquid and glass states, the atomic clusters were analyzed using the Voronoi tessellation method [40]. The VP is defined as the perpendicular bisector surfaces of the lines connecting a central atom to all of its neighboring atoms, symbolized by indices hn3, n4, n5, n6, . . .i, where ni represents P the number of i-edged faces of the polyhedron, and ni gives the total CN. The type of coordinate polyhedron referenced to a certain central atom can be identified through the Voronoi index. By the Voronoi tessellation method, it is shown that there are actually more than 10 types of polyhedral in the glass structure. To focus on the predominant local clusters, the polyhedra with amounts >1% in the glass structure were inspected. The distribution of VP in the systems of interest at 1100 K and 300 K is shown in Fig. 8. For Mg, the amount of the polyhedra with h0, 0, 12, 0i, h0, 1, 10, 2i, h0, 2, 8, 1i and h0, 2, 8, 2i is dramatically decreased with the drop in temperature, e.g. the percentage of h0, 2, 8, 1i is reduced from 4% to near zero at 300 K. It is also found that the h0, 3, 6, 4i type of polyhedra increases with the decrease in temperature from 1100 K to 300 K. In contrast to Mg, the MZ, MZC5, MZC7 and MZCC alloys exhibit a remarkable increase in the VP with h0, 0, 12, 0i with a decrease in temperature from 1100 K to 300 K. The local clusters are also affected by the composition of the systems. It is seen that the addition of element Zn results in an increase in icosahedra with h0, 0, 12, 0i in MZ alloy from 3.7% at 1100 K to 7.3% at 300 K. The addition of the third element, Ca, further promotes the formation of icosahedra in MZC5 alloy from 3.6% at 1100 K to 9.97% at 300 K, which is the most among all the clusters in the glass state of the five systems of interest. However, it is seen that the addition of 3% Cu in MZC5 alloy results in an obvious decrease in icosahedra. The icosahedra with h0, 0, 12, 0i is reduced from 9.97% in MZC5 alloy to 6.3% in MZCC at 300 K. However, the VP with h0, 2, 8, 2i, h0, 2, 8, 1i and h0, 3, 6, 4i decrease with decreasing temperature. These results mean that icosahedral clusters increase, but bcc and fcc types of clusters decrease with the decrease in temperature in Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu alloys. Fig. 9 shows the distribution of the CN of VP in the systems of interest at 1100 K and 300 K, respectively, from AIMD calculations. At 300 K, it is seen that the CN of
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Fig. 7. Variation in various types of BP in (a) Mg, (b) MZ, (c) MZC5, (d) MZC7 and (e) MZCC as a function of temperature. (f) Variation in 1551 BP in five systems as a function of temperature.
most of the VP are in the range from 12 to 14, with CN = 13 being most common. For MZ, MZC5, MZC7 and MZCC alloys, the CN demonstrate a broad scope extended from CN = 10 to CN = 16. The VP with CN = 12 and 13 in Mg–Zn–Ca are more than those in MZ alloy, indicating that the probability of forming icosahedral cluster increases. Furthermore, it is also seen that the VP with CN = 12 and 13 in MZCC alloys are lower than those in MZC5 and MZC7 alloys. The homogeneous distribution of CN in Mg–Zn–Ca alloys are controlled by the effective atomic size ratio R*, between solute and solvent. With decreasing R*, the VP changes from the Frank–Kasper type (R* > 1.2) to the icosahedral type (R* < 0.902), and then to the bi-capped square Archimedean antiprism and tri-capped trigonal prism packing type (R* < 0.835 and 0.732), respectively [41]. In Mg–Zn–Ca alloy, it is seen that, the solutes are actually Zn atoms, and its R* to Mg and Ca are equal to 0.831 and 0.675, respectively. It is noted that, since the
present authors counted the clusters referenced to every atom in the system, it is not difficult to understand that there are many more clusters with R* = 1. From the above analysis, it is seen that the broad distribution of CN in Mg– Zn–Ca alloys should be attributed to the ratio of atomic radii among the three elements. The medium-range ordering in metallic glass has been found in recent studies on BMG alloys [15,16,24,42]. From the VP information, the geometric/topological packing beyond the nearest coordinate shell can be now described, and realistic atomic packing can be constructed. Fig. 10a–d shows four types of extended clusters formed by two VP with CN = 12, in which BP are of 1551 type. These two types of VP are linked via vertex-, edge-, face- and intercross-shared (VS, ES, FS, and IS) atoms. Mg and Zn atoms are at the central position of these icosahedra, i.e. to be the solute atoms. It is seen that all the three types of component elements can serve as solvent atoms, owing to the need for efficient packing. The IS clusters, which contain 19
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Fig. 8. Distribution of the VP in Mg, MZ, MZC5, MZC7 and MZCC at (a) 1100 K and (b) 300 K.
atoms (as shown in Fig. 9d), are highly densely packed. In this work, icosahedral medium-range order (IMRO) can be formed with different types of linkage between the icosahedra. As an example, Fig. 10e shows an IMRO that is composed of seven icosahedra and reaches nanometer scale in size. Among these icosahedra, five icosahedra are accumulated in the form of IS connection, in which central atoms of Zn or Mg form a “lone string”, and Ca atoms act as connecting or glue atoms between two coordinate polyhedra. In addition to these five icosahedra, other icosahedra are connected to the intercrossed icosahedra by ES or FS atoms. 3.2.4. Correlation of GFA to dynamic properties and structural ordering In this section, the correlation of the GFA of Mg–Zn–Ca BMG with their kinetic properties and the structural feature based on the above results are discussed. The AIMD calculations in this work suggest that the large GFA of Mg–Zn– Ca BMG alloy is essentially attributed to the following characteristics: (1) the sluggish mobility of atoms induced by the confusion of the composition; and (2) the formation of a large amount of ISRO and corresponding IMRO. These two features are beneficial to the formation of the glass structure. It is known that the glass state is formed, given that the crystallization process is suppressed in the
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Fig. 9. Distribution of the CN of Mg, MZ, MZC5, MZC7 and MZCC at (a) 1100 K and (b) 300 K.
undercooled liquid. For the nucleation and growth of crystalline phases in undercooled liquid, a long duration will be required for substantial atomic diffusion and composition redistribution. Therefore, it is beneficial for the formation of the glassy structure to decrease the mobility of atoms in the undercooled liquid. Figs. 2 and 3 show that the diffusivity of atoms of Mg–Zn–Ca ternary system is generally lower than that of pure Mg and Mg–Zn alloy. This decrease in the mobility of the atoms in the ternary system is due to the interaction among the three types of atoms. According to Ref. [43], the heat of mixings of Mg–Zn, Mg–Ca and Zn–Ca pair are 6 kJ mol1, 4 kJ mol1 and 22 kJ mol1, respectively. This means that there is mutual affinity among the heterogeneous atoms. It is also known that the value of heat of mixing between Zn and Ca is largest among the three types of atom pairs, indicating that there is more strong chemical interaction in ternary Mg–Zn–Ca alloys than that in binary Mg–Zn alloys. The MSD curves as shown in Fig. 2 indicate that the atomic mobility in liquid for certain elements is highly reduced as the second or third type of atom is added to the system. The changes in atomic mobility in the five systems of interest agree very well with GFA, which deteriorates along the sequence of Mg66.25Zn28.75Ca5, Mg65Zn27.5Ca7.5 and (Mg66.25Zn28.75Ca5)97Cu3, Mg70Zn30 and Mg. Both the simulation and the experimental results (as shown in Supplementary Fig. 1) show that the
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Fig. 10. Extended icosahedral clusters in MZC5 alloy linked by (a) vertex-, (b) edge-, (c) face- and (d) intercross-shared atoms, respectively; (e) an IMRO composed of seven perfect icosahedra.
Mg65Zn27.5Ca7.5 alloy has the highest glass formation ability. The dynamic slowing down of atoms reveals the relation between atomic mobility and glass-forming ability. The influences of the addition of Cu element on the MSD, BP, CN and VP indicate that Cu is indeed not beneficial to the GFA of Mg–Zn–Ca BMG alloys. According to Ref. [43], the heats of mixing of Mg–Cu, Zn–Cu and Ca–Cu pairs are 3 kJ mol1, 1 kJ mol1 and 13 kJ mol1, respectively. For Mg–Zn–Ca–Cu alloy, under the same calculated conditions, the diffusivities of Mg, Zn and Ca atoms increases with alloying with Cu atoms compared with those MZC5 alloys (as shown in Fig. 3). Therefore, the sluggish mobility in Mg–Zn–Ca alloys cannot be explained merely by the mixing heats among the elements. The geometrical effect and entropy increase should also be considered. From the point of view of the structural characterization, the complexity in composition and atomic size will favor the formation of glass structure. The composition redistribution for the nucleation and growth of the crystal-
line phase will involve more atoms. As shown in Fig. 7b–d, with the icosahedral BP in the supercooled liquid state increasing sharply near the glass transition temperature, much more densely packed local orders are formed. And the icosahedral BP are predominant among all types of BP in liquid state owing to the relative high bonding energy of icosahedral BP. Correspondingly, some IMRO in nanometer scale develops. In this process, small atoms (Zn or Mg) located at the coordinate shell in a single icosahedron may turn out to be the central atoms when two icosahedra are connected. This means that the formation of IMRO can stabilize the undercooled liquid or restrict nucleation of crystals, i.e. increase the GFA of Mg–Zn–Ca alloys. 4. Conclusions
(1) The dynamic properties of the systems of interest were calculated by AIMD modeling. The AIMD calculated diffusivity of Mg and the viscosity of MZC7
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(2)
(3)
(4)
(5)
alloy agree well with the experimental data. It was found that Zn and Ca in Mg liquid induce remarkably sluggish mobility of atoms. However, anomalism in the diffusivity of Mg, Zn and Ca atoms was caused as Cu atoms were added to the ternary Mg– Zn–Ca systems. In this work, there is a good corresponding relation between the mobility of atoms and GFA for the systems of interest. Both the AIMD calculated PCF and SF for Mg and Mg–Zn alloys can reproduce the experimental curves, which provided strong support for analyzing the atomic packing of the Mg–Zn–Ca BMG alloys by the AIMD simulation results obtained in this work. Splitting was observed on the second peak of the PPCF of the four systems of interest, indicating that strong local ordering was formed. In the glassy structure of Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu alloys, icosahedral BP with h1551i is predominant, the bcc type of BP is next, and the fcc and hcp types of BP are third. The amount of icosahedral BP in the glassy structure of MZC5 is most among the five systems of interest in this work. The VP with h0, 0, 12, 0i in Mg–Zn, Mg–Zn–Ca and Mg–Zn–Ca–Cu alloys exhibit remarkable increase with a decrease in temperature from 1500 K to 300 K. The addition of Zn and Ca into Mg and Mg–Zn alloy results in an increase in h0, 0, 12, 0i type of icosahedra, and a decrease in bcc and fcc type of clusters. It is noticeable that further addition of Cu to MZC5 alloy results in a decrease in h0, 0, 12, 0i type of icosahedra. The CN of the VP are in the range 12– 14, with CN = 13 being most. IMRO can be formed by the linkage of VS, ES, FS and IS types of shared atoms between the icosahedra. The correlations of the GFA of Mg–Zn–Ca BMG with their dynamic properties and the structural feature were discussed. It is considered that the large GFA of Mg–Zn–Ca BMG alloy is essentially attributed to the sluggish mobility of atoms induced by the compositional confusion, and the formation of a large amount of ISRO and corresponding IMRO.
Acknowledgment The authors are grateful for the financial support of National Natural Science Foundation of China (No. 51071018, 51271018). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.actamat.2013.12.037.
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