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The effect of thermal history on structure and mechanical properties of Cu64Zr36 metallic glass
Journal of Non-Crystalline Solids 528 (2020) 119742
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
The effect of thermal history on structure and mechanical properties of Cu64Zr36 metallic glass ⁎
Jinyong Moa, Baolong Shena,b, , Wan Yixinga, Zhou Zhidana, Sun Bob, Xiubing Liangc,
T
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a Institute of Massive Amorphous Metal Science, School of Chemistry and Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, People's Republic of China b School of Materials Science and Engineering, Jiangsu Key Laboratory for Advanced Metallic Materials, Southeast University, Nanjing 211189, People's Republic of China c Academy of Military Science PLA China, National Innovation Institute of Defense Technology, Beijing 100071, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Metallic glasses Thermal history Cooling rate Liquid temperature
It is well known that the thermal history can affect the local atomic structure and thus may possibly affect the mechanical properties of metallic glasses (MGs). In spite of considerable efforts on the thermal history, its effect on the microstructure remains controversial at the present time. In this work, the combined effect of cooling rate and liquid temperature on the microstructure and mechanical properties are systematically investigated by molecular dynamics simulations. With the decrease of cooling rate, the polyhedrons with higher local five-fold symmetry is greatly enhanced, and thereby the ultimate compressive strength is increased. However, the effect of liquid temperature on the formation of MGs is negligible, mainly due to the relatively high cooling rates adopted. This work may increase our understanding in the effect of thermal formation history on the formation of MGs and provide a promising avenue for improving the mechanical properties.
1. Introduction Usually, metallic glasses (MGs) are fabricated by rapid quenching the molten liquids into amorphous state [1–4]. In this process, the thermal history such as the cooling rate and liquid temperature plays a crucial role on the formation of MGs [5–7]. On the one hand, a cooling rate higher than a critical value is required for the formation of MGs because of the strong tendency of crystallization for metallic liquids. Turnbull once prophesied that any liquid can be frozen into amorphous state supposing the cooling rate is high enough [8]. Recently, this prophecy has been verified experimentally by the vitrification of monatomic metallic liquids with an ultrahigh cooling rate of 1014 K/s [9]. The cooling rate also shows great influence on the microstructure of MGs [10]. For instance, higher cooling rate may result in looser atomic structure with more free volume [5], while lower cooling rate may lead to significant enhancement of structural short- and mediumrange order [11,12]. As a result, the changed microstructure has a pronounced influence on the crystallization behavior of MGs [6], and there is a close relationship between the onset crystallization temperature, crystallization entropy, and the cooling rate [13,14]. More impressively, enhanced hardness [15–17], strength [18], and plasticity [19–21] by adjusting the cooling rate have been reported in lots of literature, proving a promising avenue to further improve the
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mechanical properties of MGs. On the other hand, since the structure of MGs is inherited from their liquids and the atomic structure of liquids is strongly affected by temperature, the liquid temperature for quenching is also important. Liquid temperature is related to the glass transition and the structure of the formed MGs [22,23]. Meanwhile, dependence of GFA, thermal stability and crystallization behavior on the temperature-functioned different liquid state has been reported in lots of studies [7,24–28]. Similar to the cooling rate, liquid temperature can also serve as an essential parameter for changing the mechanical properties, and higher liquid temperature may induce more free volume and thus larger plasticity [29,30]. Although lots of work has been carried out to study the effect of thermal history on the formation of MGs, the underlying mechanism remains a mystery. With the in-depth research, a set of exotic phenomena has been found in this topic. For example, by changing the cooling rate, Schawe et al. have reported the formation of two types of MGs, where the first type forms quenched-in nuclei while the second type is chemically homogeneous [31]. Meanwhile, Han et al. discovered the abnormal correlation between phase transformation and cooling rate for pure metals [32]. These results reveal the complex influence of thermal history on the formation of MGs, thus further research is needed. Recently, computational simulations have been widely used to study various fundamental physical problems in materials science and
Corresponding authors. E-mail addresses: [email protected] (B. Shen), [email protected] (X. Liang).
https://doi.org/10.1016/j.jnoncrysol.2019.119742 Received 20 August 2019; Received in revised form 7 October 2019; Accepted 17 October 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
Journal of Non-Crystalline Solids 528 (2020) 119742
J. Mo, et al.
the periodic boundary conditions were applied in all directions. During the simulations, atomic positions and velocities are calculated with a time step of 1 fs, and the NPT isobaric-isothermal ensemble with constant atomic number, pressure and temperature was adopted. To study the effect of cooling rate and liquid temperature on the formation of glassy state, the initial model was first equilibrated at three temperature: 1500 K, 2000 K, and 2500 K for 5 ns, then quenched to 300 K with three cooling rate of 1011, 1012 and 1013 K/s, respectively. The quenched models were further relaxed for 2 ns to obtain their stable structure. Accordingly, the nine relaxed models are named as S1 to S9, as shown in Table 1. The amorphous nature of the models has been checked by radial distribution functions (RDFs), and detailed structural features have been discussed by coordination numbers and Voronoi polyhedron distribution. To analyze the effect of changed atomic structure on mechanical behaviors, the compression tests were performed along z-axis for the all nine relaxed samples. During the compression tests, open boundary was used in x-direction to serve as free surface, while periodic boundary was used in y- and z-directions. For reducing the fluctuation of the strain-stress curve, the stress of the free surface was released prior to deformation by energy minimization. The whole simulations were repeated for 5 times and the errors of ultimate strength is less than 0.05 GPa.
Table 1 Nine glassy models formed with different thermal history. Melts temperature (K) 1500
2000
2500
Cooling rate (K/s) 11
1 × 10 1 × 1012 1 × 1013 1 × 1011 1 × 1012 1 × 1013 1 × 1011 1 × 1012 1 × 1013
Glassy models S1 S2 S3 S4 S5 S6 S7 S8 S9
have greatly improved our understanding on the nature of MGs. In this work, we investigate the effect of cooling rate and liquid temperature on the microstructure and mechanical properties of Cu64Zr36 MGs by means of molecular dynamics simulations. By carefully controlling the thermal formation history, the structural difference between different glassy models is directly compared at the atomic scale. 2. Simulation methods The MD simulations were performed with a classical molecular dynamics code LAMMPS [33] and a widely used embedded atom method (EAM) potential developed by Mendelev et al. was employed to describe the atomic interactions [34]. The binary Cu64Zr36 Alloy was chosen as the target model because its simple composition and outstanding GFA, providing a perfect window for studying some fundamental problem in MGs [35]. The initial model was set as a 55 × 55 × 55 Å3 cubic box with 10,000 atoms randomly filled in, and
3. Results and discussion Upon the melt-quenched processes, the initial liquid structure is crucial for the formation of MGs. A homogenous liquid structure without crystalline cluster is a precondition for the formation of monolithic MGs. After equilibrated at 1500 K, 2000 K and 2500 K for 5 ns, respectively, the RDFs of melts present a typical liquid features
Fig. 1. Pair distribution functions of the (a) melts, and amorphous models cooled from melt temperature of (b) 1500 K, (c) 2000 K, and (d) 2500 K, respectively. The inset in (a) shows the disordered atomic arrangement in liquid state; The insets in (b)–(d) show the enlarged region of first peaks. 2
Journal of Non-Crystalline Solids 528 (2020) 119742
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Fig. 2. Coordination number distribution of the (a) melts, and amorphous models cooled from melt temperature of (b) 1500 K, (c) 2000 K, and (d) 2500 K, respectively.
without any crystalline sharp peaks, indicating all the models are fully melted, as shown in Fig. 1(a). The inset in Fig. 1(a) shows the structural diagram of the melted model at 1500 K, where the disordered atomic arrangement is declared. Fig. 1(b)–(d) show RDFs of the relaxed nine models. For RDFs of all quenched models, no clear crystalline peaks are found and the splitting peaks on the second peaks provide a powerful clue as the characteristics of amorphous structure [36]. Generally speaking, the RDFs of the nine glassy structure does not show any evident difference, showing similar peak positions and intensities. With the decreasing cooling rate, the intensities of the first peaks show an increasing tendency, as shown in the insets of Fig. 1(b)–(d), indicating an enhanced structural order. Although the curves in Fig. 1(b)–(d) are very similar with each other, we will discuss the detailed structural differences and mechanical behaviors in the following parts. Coordination number can serve as an important structural parameter for describing the statistical atomic banding characteristics. Although with different percentages, six main coordination numbers from 10 to 16 are common to the three melts, and 13 is the most
Fig. 3. The effect of thermal history on the density and atomic potential.
Table 2 The structural and mechanical information of the nine glassy models. Glassy models
Density (g/cm3)
Atomic Potential (eV/atom)
local fivefold symmetry
Ultimate Strength (GPa)
S1 S2 S3 S4 S5 S6 S7 S8 S9
7.540+ ± 0.002 7.527+ ± 0.002 7.511 ± 0.002 7.541 ± 0.002 7.528 ± 0.001 7.510 ± 0.002 7.538 ± 0.001 7.526 ± 0.002 7.512 ± 0.002
−4.3824 −4.3731 −4.3642 −4.3825 −4.3732 −4.3629 −4.3834 −4.3737 −4.3632
80.66 ± 0.2 79.02 ± 0.1 77.4 ± 0.1 80.51 ± 0.3 78.97 ± 0.2 77.55 ± 0.2 80.44 ± 0.2 78.99 ± 0.1 77.68 ± 0.1
3.800 3.386 2.913 3.746 3.309 2.871 3.729 3.378 2.919
± ± ± ± ± ± ± ± ±
0.0004 0.0004 0.0005 0.0005 0.0004 0.0005 0.0005 0.0004 0.0005
3
± ± ± ± ± ± ± ± ±
0.02 0.05 0.03 0.04 0.02 0.03 0.02 0.04 0.03
Journal of Non-Crystalline Solids 528 (2020) 119742
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Fig. 4. (a)–(c) The dominant polyhedrons in Cu-Zr MG; (d) The effect of cooling rate on the average five-fold symmetry.
structural information also refers to Table 2. Voronoi tessellation technique is employed to characterize the local atomic environment of the quenched models. In this method, the coordination polyhedron surrounding a center atom is designated by a Voronoi index, where ni denotes the number of i-edged faces of the polyhedron [39]. Fig. 3(a)–(c) show the top ten types of Voronoi polyhedrons (VPs) in the nine glassy samples. Among these VPs, VPs <0, 0, 12, 0>, <0, 1, 10, 2>, <0, 3, 6, 4> and <0, 2, 8, 2> are the most numerous and have much higher fractions than other VPs. Similar results have been reported in former researches. By comparing n the local five-fold symmetry of the VPs f5 = (n + n +5 n + n ) [40], these 3 4 5 6 VPs are divided into three regions, ie., region I, II, and III, respectively. In region I, the value of f5 is 0.46, 0.5, 0.53, and 0.57, respectively. In region II this value increase to 0.625, 0.67 and in region III further increase to 0.77, 0.8 and 1, respectively. In region I and II, no obvious tendency dependence on the thermal formation history is found. In region III, however, it is clear that a strong correlation exists between the fractions of VPs and the cooling rate of the melts. More specifically, with the decrease of cooling rate, the percentages of VP <0, 0, 12, 0> increase from ~10% at 1013 K/s to ~13% at 1011 K/s, from ~1.4% to ~2% for VP <0, 0, 12,3>, and from ~8% to ~9% for VP <0, 1, 10, 2>, respectively. The value of the average degree of local five-fold symmetry, where all polyhedrons are considered, of the glassy models is calculated, as shown in Fig. 4(d). It is found that the average degree of the glassy samples increasing with the decreased cooling rate, while the liquid temperature doesn't show much effect. Recently, Xie et al. investigated the deposition process of Cu-Zr alloy and found that the average degree of local fivefold symmetry is increased with lower mean kinetic energy of incoming atoms [41]. This may be due to the higher cooling rate when depositing with lower energy, which is similar to results in the present work. Generally, the change in local atomic structure can result in the different mechanical properties [42,43]. To investigate the effect of thermal history on mechanical properties, the compressive tests were
dominant among them, as shown in Fig. 2(a). With the increasing temperature, the percentages of 10-, 11- and 12-coordinated atoms increase while the 14-, 15- and 16-coordinated atomic fractions increase, indicating the structure of melts is closely dependent on the temperature [37]. Fig. 2(b)–(d) present the coordination number distribution of the nine glassy models. It is apparent that all Cu64Zr36 glassy models have a coordination number of 12~16, and 12- and 13coordinated atoms hold the maximum proportions. The reason of the higher percentages for 12- and 13-coordinated atoms may come from the fact that in Cu-Zr MGs, Cu-centered polyhedrons are mainly 12- and 13-coordinated while Zr-centered polyhedrons are coordinated with more nearest neighbor atoms than 13 [38]. In the case of Cu64Zr36, Cu atoms are dominant with percentage high up to 64%, thus the 12- and 13-coordinated atoms are dominants in the nine glassy models. With the decrease of cooling rate, the proportion of 12-coordinated atoms increased while the 14-coordinated atoms show a converse tendency, indicating the cooling rate can effectively change the local atomic structure. However, no evident difference caused by liquid temperature is observed by comparing Fig. 2(b)–(d). Fig. 3 shows the effect of thermal formation history on the density and atomic potential energy of the glassy models. Fig. 3 give the direct evidence that the cooling rate is a more effective parameter than liquid temperature for adjusting the microstructure of MGs. Under the same cooling rate, the liquid temperature has a marginal effect on the density and atomic potential. Conversely, under the same liquid temperature while decreasing the cooling rate, obvious effects are declared, with density increase from ~7.51 g/cm3 at cooling rate of 1013 K/s to ~7.54 g/cm3 and atomic potential decrease from ~4.363 eV/atom to ~4.382 eV/atom, at cooling rate of 1011 K/s, respectively. That is to say, at a lower cooling rate, the glassy samples have denser structure and are more stable in energy. Meanwhile, although the effect of liquid temperature on density is relatively weak, the tendency that higher density can be obtained by cooling from higher liquid temperature, as can be found at the cooling rate of 1011 K/s and 1013 K/s. Detailed 4
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Fig. 5. (a)–(c) Strain-stress curves of Cu-Zr MG; (d) Yield strength changes in relation to cooling rate.
the liquid temperature has much fewer effects. The increased ultimate strength mainly originates from the higher fraction of icosahedron, which has lower energy and higher strength. This icosahedron induced enhancement in ultimate strength has also been reported in previous work. The above analysis has revealed a fact that the microstructure of MGs is closely related to the cooling rate while not sensitive to the liquid temperature. This result seems to be inconsistent with the previous experimental reports, where the liquids temperature also affects the atomic structure significantly [22]. The inconformity between the simulation result and experiment is probably because the cooling rate applied in the present simulations (1011~1013 K/s) are several orders of magnitude higher than the experimental cases (~106 K/s) [32]. Fig. 6 shows the Time-temperature-Transition (T-T-T) schematic maps. Under same cooling rate, it is clear that liquid with higher temperature needs more time to solidification. During simulations, because the cooling rate is very fast, the quenching processes of both high and low temperature are far away from equilibrium and the nucleation and growth are avoided, thus the effect of liquid temperature on the formation of MGs is negligible. However, in experiments, liquid with higher temperature may pass the region of nucleation and growth. As a result, the quenched-in nuclei could result in the difference of mechanical properties, thermal stability and crystallization behavior [23,26]. While in the present simulations, the ultrahigh cooling rate avoids the formation of the quenched-in nuclei, thus the effect of liquid temperature is weak in this work.
Fig. 6. The Time-temperature-Transition schematic maps of the formation of MGs during simulations and experiments.
conducted for all modes and the strain-stress curves were compared, as shown in Fig. 5(a)–(c). It is clearly seen that all samples show similar curves, but the ultimate strength is different. For comparison, Fig. 5(d) presents the dependence of thermal history on the ultimate strength. It is found that the ultimate strengths of S3, S6, and S9 are ~2.9 GPa, and this value increase to ~3.4 GPa for S2, S5, and S8, then further increase to ~3.8 GPa for S1, S4, and S7. That is to say, pronounced enhancement in ultimate strength is observed with the decrease of cooling rate, but
4. Conclusion In summary, the effect of thermal history, i.e., cooling rate and 5
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liquid temperature, on the local atomic structure and mechanical properties has been investigated using molecular dynamics simulations. Due to relatively high cooling rates adopted in this work, the effect of liquid temperature has little influence on the formation of MGs. However, the local atomic structure as well as the mechanical properties strongly depend on the cooling rate. At a lower cooling rate, the formed MGs have higher average local five-fold symmetry, with more icosahedrons, denser atomic packing and lower energy, indicating the MGs is more stable with the decrease of cooling rate. Correspondingly, the ultimate compressive strength of MGs increases with the decreasing cooling rate. This work may provide some insight into the understanding of the formation of MGs.
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Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2018BSCXC18) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_1945). References [1] W.K. Jun, R. Willens, P. Duwez, Non-crystalline structure in solidified gold–silicon alloys, Nature 187 (4740) (1960) 869. [2] D. Turnbull, Under what conditions can a glass be formed? Contemp. Phys. 10 (5) (1969) 473–488. [3] Z.P. Lu, Y. Li, S.C. Ng, Reduced glass transition temperature and glass forming ability of bulk glass forming alloys, J. Non-Cryst. Solids 270 (1–3) (2000) 103–114. [4] Q. Qin, G.B. McKenna, Correlation between dynamic fragility and glass transition temperature for different classes of glass forming liquids, J. Non-Cryst. Solids 352 (28–29) (2006) 2977–2985. [5] X. Hu, S.C. Ng, Y.P. Feng, Y. Li, Cooling-rate dependence of the density of Pd40Ni10Cu30P20 bulk metallic glass, Phys. Rev. B 64 (17) (2001). [6] H.R. Wang, Y.L. Gao, X.D. Hui, Y. Chen, G.H. Min, Y.F. Ye, Effect of cooling rate on crystallization of metallic Zr-Cu-Ni glass, J. Alloy. Compd. 350 (1–2) (2003) 178–183. [7] J.K. Lee, D.H. Bae, W.T. Kim, D.H. Kim, Effect of liquid temperature on thermal stability and crystallization behavior of Ni-based amorphous alloys, Mater. Sci. Eng. A 375-377 (2004) 332–335. [8] W.L. Johnson, Thermodynamic and kinetic aspects of the crystal to glass transformation in metallic materials, Prog. Mater. Sci. 30 (2) (1986) 81–134. [9] L. Zhong, J. Wang, H. Sheng, Z. Zhang, S.X. Mao, Formation of monatomic metallic glasses through ultrafast liquid quenching, Nature 512 (7513) (2014) 177–180. [10] S.G. Hao, C.Z. Wang, M. Li, R.E. Napolitano, M.I. Mendelev, K.M. Ho, Prediction of cooling rate dependent ordering in metallic glass transition using a two-state model, Comput. Mater. Sci. 49 (3) (2010) 615–618. [11] Y. Sun, Y. Zhang, F. Zhang, Z. Ye, Z. Ding, C.Z. Wang, K.M. Ho, Cooling rate dependence of structural order in Al90Sm10 metallic glass, J. Appl. Phys. 120 (1) (2016). [12] T.Q. Wen, Y. Sun, B.L. Ye, L. Tang, Z.J. Yang, K.M. Ho, C.Z. Wang, N. Wang, Cooling rate dependence of structural order in Ni62Nb38 metallic glass, J. Appl. Phys. 123 (4) (2018). [13] Z.Z. Yuan, X.D. Chena, B.X. Wang, Z.J. Chen, Effect of cooling rate on crystallization and magnetic properties of metallic Co43Fe20Ta5.5B31.5 glass, J. Mater. Sci. 41 (11) (2006) 3481–3487. [14] D. Singh, R.K. Mandal, R.S. Tiwari, O.N. Srivastava, Effect of cooling rate on the crystallization and mechanical behaviour of Zr-Ga-Cu-Ni metallic glass composition, J. Alloy. Compd. 648 (2015) 456–462. [15] Z.Y. Liu, Y. Yang, S. Guo, X.J. Liu, J. Lu, Y.H. Liu, C.T. Liu, Cooling rate effect on Young's modulus and hardness of a Zr-based metallic glass, J. Alloy. Compd. 509 (7) (2011) 3269–3273. [16] S. Lesz, Effect of cooling rates on the structure, density and micro-indentation behavior of the Fe, Co-based bulk metallic glass, Mater. Charact. 124 (2017) 97–106.
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The effect of thermal history on structure and mechanical properties of Cu64Zr36 metallic glass ⁎
Jinyong Moa, Baolong Shena,b, , Wan Yixinga, Zhou Zhidana, Sun Bob, Xiubing Liangc,
T
⁎
a Institute of Massive Amorphous Metal Science, School of Chemistry and Chemical Engineering, China University of Mining and Technology, Xuzhou 221116, People's Republic of China b School of Materials Science and Engineering, Jiangsu Key Laboratory for Advanced Metallic Materials, Southeast University, Nanjing 211189, People's Republic of China c Academy of Military Science PLA China, National Innovation Institute of Defense Technology, Beijing 100071, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Metallic glasses Thermal history Cooling rate Liquid temperature
It is well known that the thermal history can affect the local atomic structure and thus may possibly affect the mechanical properties of metallic glasses (MGs). In spite of considerable efforts on the thermal history, its effect on the microstructure remains controversial at the present time. In this work, the combined effect of cooling rate and liquid temperature on the microstructure and mechanical properties are systematically investigated by molecular dynamics simulations. With the decrease of cooling rate, the polyhedrons with higher local five-fold symmetry is greatly enhanced, and thereby the ultimate compressive strength is increased. However, the effect of liquid temperature on the formation of MGs is negligible, mainly due to the relatively high cooling rates adopted. This work may increase our understanding in the effect of thermal formation history on the formation of MGs and provide a promising avenue for improving the mechanical properties.
1. Introduction Usually, metallic glasses (MGs) are fabricated by rapid quenching the molten liquids into amorphous state [1–4]. In this process, the thermal history such as the cooling rate and liquid temperature plays a crucial role on the formation of MGs [5–7]. On the one hand, a cooling rate higher than a critical value is required for the formation of MGs because of the strong tendency of crystallization for metallic liquids. Turnbull once prophesied that any liquid can be frozen into amorphous state supposing the cooling rate is high enough [8]. Recently, this prophecy has been verified experimentally by the vitrification of monatomic metallic liquids with an ultrahigh cooling rate of 1014 K/s [9]. The cooling rate also shows great influence on the microstructure of MGs [10]. For instance, higher cooling rate may result in looser atomic structure with more free volume [5], while lower cooling rate may lead to significant enhancement of structural short- and mediumrange order [11,12]. As a result, the changed microstructure has a pronounced influence on the crystallization behavior of MGs [6], and there is a close relationship between the onset crystallization temperature, crystallization entropy, and the cooling rate [13,14]. More impressively, enhanced hardness [15–17], strength [18], and plasticity [19–21] by adjusting the cooling rate have been reported in lots of literature, proving a promising avenue to further improve the
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mechanical properties of MGs. On the other hand, since the structure of MGs is inherited from their liquids and the atomic structure of liquids is strongly affected by temperature, the liquid temperature for quenching is also important. Liquid temperature is related to the glass transition and the structure of the formed MGs [22,23]. Meanwhile, dependence of GFA, thermal stability and crystallization behavior on the temperature-functioned different liquid state has been reported in lots of studies [7,24–28]. Similar to the cooling rate, liquid temperature can also serve as an essential parameter for changing the mechanical properties, and higher liquid temperature may induce more free volume and thus larger plasticity [29,30]. Although lots of work has been carried out to study the effect of thermal history on the formation of MGs, the underlying mechanism remains a mystery. With the in-depth research, a set of exotic phenomena has been found in this topic. For example, by changing the cooling rate, Schawe et al. have reported the formation of two types of MGs, where the first type forms quenched-in nuclei while the second type is chemically homogeneous [31]. Meanwhile, Han et al. discovered the abnormal correlation between phase transformation and cooling rate for pure metals [32]. These results reveal the complex influence of thermal history on the formation of MGs, thus further research is needed. Recently, computational simulations have been widely used to study various fundamental physical problems in materials science and
Corresponding authors. E-mail addresses: [email protected] (B. Shen), [email protected] (X. Liang).
https://doi.org/10.1016/j.jnoncrysol.2019.119742 Received 20 August 2019; Received in revised form 7 October 2019; Accepted 17 October 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
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the periodic boundary conditions were applied in all directions. During the simulations, atomic positions and velocities are calculated with a time step of 1 fs, and the NPT isobaric-isothermal ensemble with constant atomic number, pressure and temperature was adopted. To study the effect of cooling rate and liquid temperature on the formation of glassy state, the initial model was first equilibrated at three temperature: 1500 K, 2000 K, and 2500 K for 5 ns, then quenched to 300 K with three cooling rate of 1011, 1012 and 1013 K/s, respectively. The quenched models were further relaxed for 2 ns to obtain their stable structure. Accordingly, the nine relaxed models are named as S1 to S9, as shown in Table 1. The amorphous nature of the models has been checked by radial distribution functions (RDFs), and detailed structural features have been discussed by coordination numbers and Voronoi polyhedron distribution. To analyze the effect of changed atomic structure on mechanical behaviors, the compression tests were performed along z-axis for the all nine relaxed samples. During the compression tests, open boundary was used in x-direction to serve as free surface, while periodic boundary was used in y- and z-directions. For reducing the fluctuation of the strain-stress curve, the stress of the free surface was released prior to deformation by energy minimization. The whole simulations were repeated for 5 times and the errors of ultimate strength is less than 0.05 GPa.
Table 1 Nine glassy models formed with different thermal history. Melts temperature (K) 1500
2000
2500
Cooling rate (K/s) 11
1 × 10 1 × 1012 1 × 1013 1 × 1011 1 × 1012 1 × 1013 1 × 1011 1 × 1012 1 × 1013
Glassy models S1 S2 S3 S4 S5 S6 S7 S8 S9
have greatly improved our understanding on the nature of MGs. In this work, we investigate the effect of cooling rate and liquid temperature on the microstructure and mechanical properties of Cu64Zr36 MGs by means of molecular dynamics simulations. By carefully controlling the thermal formation history, the structural difference between different glassy models is directly compared at the atomic scale. 2. Simulation methods The MD simulations were performed with a classical molecular dynamics code LAMMPS [33] and a widely used embedded atom method (EAM) potential developed by Mendelev et al. was employed to describe the atomic interactions [34]. The binary Cu64Zr36 Alloy was chosen as the target model because its simple composition and outstanding GFA, providing a perfect window for studying some fundamental problem in MGs [35]. The initial model was set as a 55 × 55 × 55 Å3 cubic box with 10,000 atoms randomly filled in, and
3. Results and discussion Upon the melt-quenched processes, the initial liquid structure is crucial for the formation of MGs. A homogenous liquid structure without crystalline cluster is a precondition for the formation of monolithic MGs. After equilibrated at 1500 K, 2000 K and 2500 K for 5 ns, respectively, the RDFs of melts present a typical liquid features
Fig. 1. Pair distribution functions of the (a) melts, and amorphous models cooled from melt temperature of (b) 1500 K, (c) 2000 K, and (d) 2500 K, respectively. The inset in (a) shows the disordered atomic arrangement in liquid state; The insets in (b)–(d) show the enlarged region of first peaks. 2
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Fig. 2. Coordination number distribution of the (a) melts, and amorphous models cooled from melt temperature of (b) 1500 K, (c) 2000 K, and (d) 2500 K, respectively.
without any crystalline sharp peaks, indicating all the models are fully melted, as shown in Fig. 1(a). The inset in Fig. 1(a) shows the structural diagram of the melted model at 1500 K, where the disordered atomic arrangement is declared. Fig. 1(b)–(d) show RDFs of the relaxed nine models. For RDFs of all quenched models, no clear crystalline peaks are found and the splitting peaks on the second peaks provide a powerful clue as the characteristics of amorphous structure [36]. Generally speaking, the RDFs of the nine glassy structure does not show any evident difference, showing similar peak positions and intensities. With the decreasing cooling rate, the intensities of the first peaks show an increasing tendency, as shown in the insets of Fig. 1(b)–(d), indicating an enhanced structural order. Although the curves in Fig. 1(b)–(d) are very similar with each other, we will discuss the detailed structural differences and mechanical behaviors in the following parts. Coordination number can serve as an important structural parameter for describing the statistical atomic banding characteristics. Although with different percentages, six main coordination numbers from 10 to 16 are common to the three melts, and 13 is the most
Fig. 3. The effect of thermal history on the density and atomic potential.
Table 2 The structural and mechanical information of the nine glassy models. Glassy models
Density (g/cm3)
Atomic Potential (eV/atom)
local fivefold symmetry
Ultimate Strength (GPa)
S1 S2 S3 S4 S5 S6 S7 S8 S9
7.540+ ± 0.002 7.527+ ± 0.002 7.511 ± 0.002 7.541 ± 0.002 7.528 ± 0.001 7.510 ± 0.002 7.538 ± 0.001 7.526 ± 0.002 7.512 ± 0.002
−4.3824 −4.3731 −4.3642 −4.3825 −4.3732 −4.3629 −4.3834 −4.3737 −4.3632
80.66 ± 0.2 79.02 ± 0.1 77.4 ± 0.1 80.51 ± 0.3 78.97 ± 0.2 77.55 ± 0.2 80.44 ± 0.2 78.99 ± 0.1 77.68 ± 0.1
3.800 3.386 2.913 3.746 3.309 2.871 3.729 3.378 2.919
± ± ± ± ± ± ± ± ±
0.0004 0.0004 0.0005 0.0005 0.0004 0.0005 0.0005 0.0004 0.0005
3
± ± ± ± ± ± ± ± ±
0.02 0.05 0.03 0.04 0.02 0.03 0.02 0.04 0.03
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Fig. 4. (a)–(c) The dominant polyhedrons in Cu-Zr MG; (d) The effect of cooling rate on the average five-fold symmetry.
structural information also refers to Table 2. Voronoi tessellation technique is employed to characterize the local atomic environment of the quenched models. In this method, the coordination polyhedron surrounding a center atom is designated by a Voronoi index
dominant among them, as shown in Fig. 2(a). With the increasing temperature, the percentages of 10-, 11- and 12-coordinated atoms increase while the 14-, 15- and 16-coordinated atomic fractions increase, indicating the structure of melts is closely dependent on the temperature [37]. Fig. 2(b)–(d) present the coordination number distribution of the nine glassy models. It is apparent that all Cu64Zr36 glassy models have a coordination number of 12~16, and 12- and 13coordinated atoms hold the maximum proportions. The reason of the higher percentages for 12- and 13-coordinated atoms may come from the fact that in Cu-Zr MGs, Cu-centered polyhedrons are mainly 12- and 13-coordinated while Zr-centered polyhedrons are coordinated with more nearest neighbor atoms than 13 [38]. In the case of Cu64Zr36, Cu atoms are dominant with percentage high up to 64%, thus the 12- and 13-coordinated atoms are dominants in the nine glassy models. With the decrease of cooling rate, the proportion of 12-coordinated atoms increased while the 14-coordinated atoms show a converse tendency, indicating the cooling rate can effectively change the local atomic structure. However, no evident difference caused by liquid temperature is observed by comparing Fig. 2(b)–(d). Fig. 3 shows the effect of thermal formation history on the density and atomic potential energy of the glassy models. Fig. 3 give the direct evidence that the cooling rate is a more effective parameter than liquid temperature for adjusting the microstructure of MGs. Under the same cooling rate, the liquid temperature has a marginal effect on the density and atomic potential. Conversely, under the same liquid temperature while decreasing the cooling rate, obvious effects are declared, with density increase from ~7.51 g/cm3 at cooling rate of 1013 K/s to ~7.54 g/cm3 and atomic potential decrease from ~4.363 eV/atom to ~4.382 eV/atom, at cooling rate of 1011 K/s, respectively. That is to say, at a lower cooling rate, the glassy samples have denser structure and are more stable in energy. Meanwhile, although the effect of liquid temperature on density is relatively weak, the tendency that higher density can be obtained by cooling from higher liquid temperature, as can be found at the cooling rate of 1011 K/s and 1013 K/s. Detailed 4
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Fig. 5. (a)–(c) Strain-stress curves of Cu-Zr MG; (d) Yield strength changes in relation to cooling rate.
the liquid temperature has much fewer effects. The increased ultimate strength mainly originates from the higher fraction of icosahedron, which has lower energy and higher strength. This icosahedron induced enhancement in ultimate strength has also been reported in previous work. The above analysis has revealed a fact that the microstructure of MGs is closely related to the cooling rate while not sensitive to the liquid temperature. This result seems to be inconsistent with the previous experimental reports, where the liquids temperature also affects the atomic structure significantly [22]. The inconformity between the simulation result and experiment is probably because the cooling rate applied in the present simulations (1011~1013 K/s) are several orders of magnitude higher than the experimental cases (~106 K/s) [32]. Fig. 6 shows the Time-temperature-Transition (T-T-T) schematic maps. Under same cooling rate, it is clear that liquid with higher temperature needs more time to solidification. During simulations, because the cooling rate is very fast, the quenching processes of both high and low temperature are far away from equilibrium and the nucleation and growth are avoided, thus the effect of liquid temperature on the formation of MGs is negligible. However, in experiments, liquid with higher temperature may pass the region of nucleation and growth. As a result, the quenched-in nuclei could result in the difference of mechanical properties, thermal stability and crystallization behavior [23,26]. While in the present simulations, the ultrahigh cooling rate avoids the formation of the quenched-in nuclei, thus the effect of liquid temperature is weak in this work.
Fig. 6. The Time-temperature-Transition schematic maps of the formation of MGs during simulations and experiments.
conducted for all modes and the strain-stress curves were compared, as shown in Fig. 5(a)–(c). It is clearly seen that all samples show similar curves, but the ultimate strength is different. For comparison, Fig. 5(d) presents the dependence of thermal history on the ultimate strength. It is found that the ultimate strengths of S3, S6, and S9 are ~2.9 GPa, and this value increase to ~3.4 GPa for S2, S5, and S8, then further increase to ~3.8 GPa for S1, S4, and S7. That is to say, pronounced enhancement in ultimate strength is observed with the decrease of cooling rate, but
4. Conclusion In summary, the effect of thermal history, i.e., cooling rate and 5
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liquid temperature, on the local atomic structure and mechanical properties has been investigated using molecular dynamics simulations. Due to relatively high cooling rates adopted in this work, the effect of liquid temperature has little influence on the formation of MGs. However, the local atomic structure as well as the mechanical properties strongly depend on the cooling rate. At a lower cooling rate, the formed MGs have higher average local five-fold symmetry, with more icosahedrons, denser atomic packing and lower energy, indicating the MGs is more stable with the decrease of cooling rate. Correspondingly, the ultimate compressive strength of MGs increases with the decreasing cooling rate. This work may provide some insight into the understanding of the formation of MGs.
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Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2018BSCXC18) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_1945). References [1] W.K. Jun, R. Willens, P. Duwez, Non-crystalline structure in solidified gold–silicon alloys, Nature 187 (4740) (1960) 869. [2] D. Turnbull, Under what conditions can a glass be formed? Contemp. Phys. 10 (5) (1969) 473–488. [3] Z.P. Lu, Y. Li, S.C. Ng, Reduced glass transition temperature and glass forming ability of bulk glass forming alloys, J. Non-Cryst. Solids 270 (1–3) (2000) 103–114. [4] Q. Qin, G.B. McKenna, Correlation between dynamic fragility and glass transition temperature for different classes of glass forming liquids, J. Non-Cryst. Solids 352 (28–29) (2006) 2977–2985. [5] X. Hu, S.C. Ng, Y.P. Feng, Y. Li, Cooling-rate dependence of the density of Pd40Ni10Cu30P20 bulk metallic glass, Phys. Rev. B 64 (17) (2001). [6] H.R. Wang, Y.L. Gao, X.D. Hui, Y. Chen, G.H. Min, Y.F. Ye, Effect of cooling rate on crystallization of metallic Zr-Cu-Ni glass, J. Alloy. Compd. 350 (1–2) (2003) 178–183. [7] J.K. Lee, D.H. Bae, W.T. Kim, D.H. Kim, Effect of liquid temperature on thermal stability and crystallization behavior of Ni-based amorphous alloys, Mater. Sci. Eng. A 375-377 (2004) 332–335. [8] W.L. Johnson, Thermodynamic and kinetic aspects of the crystal to glass transformation in metallic materials, Prog. Mater. Sci. 30 (2) (1986) 81–134. [9] L. Zhong, J. Wang, H. Sheng, Z. Zhang, S.X. Mao, Formation of monatomic metallic glasses through ultrafast liquid quenching, Nature 512 (7513) (2014) 177–180. [10] S.G. Hao, C.Z. Wang, M. Li, R.E. Napolitano, M.I. Mendelev, K.M. Ho, Prediction of cooling rate dependent ordering in metallic glass transition using a two-state model, Comput. Mater. Sci. 49 (3) (2010) 615–618. [11] Y. Sun, Y. Zhang, F. Zhang, Z. Ye, Z. Ding, C.Z. Wang, K.M. Ho, Cooling rate dependence of structural order in Al90Sm10 metallic glass, J. Appl. Phys. 120 (1) (2016). [12] T.Q. Wen, Y. Sun, B.L. Ye, L. Tang, Z.J. Yang, K.M. Ho, C.Z. Wang, N. Wang, Cooling rate dependence of structural order in Ni62Nb38 metallic glass, J. Appl. Phys. 123 (4) (2018). [13] Z.Z. Yuan, X.D. Chena, B.X. Wang, Z.J. Chen, Effect of cooling rate on crystallization and magnetic properties of metallic Co43Fe20Ta5.5B31.5 glass, J. Mater. Sci. 41 (11) (2006) 3481–3487. [14] D. Singh, R.K. Mandal, R.S. Tiwari, O.N. Srivastava, Effect of cooling rate on the crystallization and mechanical behaviour of Zr-Ga-Cu-Ni metallic glass composition, J. Alloy. Compd. 648 (2015) 456–462. [15] Z.Y. Liu, Y. Yang, S. Guo, X.J. Liu, J. Lu, Y.H. Liu, C.T. Liu, Cooling rate effect on Young's modulus and hardness of a Zr-based metallic glass, J. Alloy. Compd. 509 (7) (2011) 3269–3273. [16] S. Lesz, Effect of cooling rates on the structure, density and micro-indentation behavior of the Fe, Co-based bulk metallic glass, Mater. Charact. 124 (2017) 97–106.
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