Molecular Dynamics Simulations of Glass Formation and Crystallization in Binary Liquid Metals

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1 Citation & Copyright (to be inserted by the publisher ) Molecular Dynamics Simulations of Glass Formation and Crystallization in Binary Liquid Metals Hyon-Jee Lee 1,2, Tahir Cagin 2, William A. Goddard III 2, and William L. Johnson 1 2 Materials Science Department, California Institute of Technology, Pasadena, CA 91125, U.S.A. 1 Materials and Process Simulation Center (MSC), , California Institute of Technology, Pasadena, CA 91125, U.S.A. Keywords: metallic glass, molecular dynamics, glass transition, atomic size ratio mismatch, cohesive energy ratio mismatch, phase separation, Honeycutt-Andersen. Abstract. The glass formation of binary liquid metals are studied using molecular dynamics simulations, where the atomic interactions are modeled with a Sutton-Chen many-body potential. We use a model binary alloy system (Cu * 50 Cu** 50 ) which differ in their atomic radii and/or cohesive energies between Cu* and Cu **. First, when we change the atomic size ratio ( 1.0) only, we find that there are three regimes defined by the magnitude of upon cooling. When is close to 1.0, crystallization occurs. Glass formation occurs at moderate values. When the is small, the alloy phase separates into pure phases. Second, when we vary and the cohesive energy ratio ε (ε 1.0) along the line in constant energy density space (ε/ 3 =constant), glass formation occurs at moderate values but no phase separation is observed at any. Therefore, we find that the energy density is the dominant parameter in controlling the phase separation behavior of metallic alloys. From the studies of structural properties, we find that the fivefold symmetry becomes prominent in glasses and shows a maximum at =0.85 in both cases. Finally, when we vary ε only while keeping constant, the system shows a very limited glass forming regime (ε<0.3), indicating that the atomic size ratio is more crucial to frustrate the crystallization. Introduction The development of new generations of bulk metallic glass (BMG) has utilized qualitative reasoning about the role of atomic size ratio (topological disorder) and valence electron configuration (chemical disorder) in promoting glass formation [1]. In order to provide more quantitative understanding of topological/chemical disorder on glass formation, we report here systematic studies of the glass forming properties for a series of binary metallic alloy (Cu * 50 Cu** 50 ) as a function of the atomic size ratio () and/or the cohesive energy ratio (ε). Here, Cu * and Cu ** have the same properties as Cu except atomic radii [2,3] and/or cohesive energy. We define the atomic size ratio of Cu * to Cu ** as ( 1.0) and the cohesive energy ratio of Cu * to Cu ** as ε (ε 1.0). These studies use Molecular Dynamics (MD) with the Sutton-Chen (SC) many-body force field developed to described metallic systems [4-6]. The simulation was performed at constant temperature, constant thermodynamic tension (TtN) MD conditions [7-9]. The TtN MD was started from a Cu * 50Cu ** 50 random FCC solid solutions with 500 atoms in a simulation unit cell subject to periodic boundary conditions. The heating experiment was carried out by increasing the temperature from 300K to 1600K using a K/s heating rate. After the system reaches 1600K, we cooled down the system to 300K using a K/s cooling rate and obtained a glass or crystal. The structural properties were calculated on the quenched sample at T=300K. Results and Discussion

2 2 Title of Publication (to be inserted by the publisher) To put the topological disorder and the chemical disorder in perspective, let us refer to Figure 1. The figure shows a schematic diagram of size ratio (topological disorder) and cohesive energy ratio (chemical disorder) of constituting elements. First, to determine the effect of atomic size ratio () on the glass transition and crystallization, we change only the lattice parameter of Cu * and Cu ** (scheme (a) in Fig. 1). From this set of simulations, we find glass transition occurs in the alloy with 0.95 while the crystallization occurs at >0.95. To further investigate how the size ratios affect the properties of glasses, we analyze the structure of glasses as a function of. For glasses, we find that a very useful assessment of local structure is provided by Honeycutt and Andersen (HA) analysis [10]. In HA analysis, each type of bonding is classified by a sequence of four integers. The first integer is 1 if the atoms in the root pair are bonded, otherwise it is 2. The second integer is the number of near-neighbor atoms commonly shared by the root pair. The third integer is the number of nearest-neighbor bonds among the shared neighbors. The forth integer provides the information about nearest bond geometry. For example, the analysis of various structures in terms of HA pairs is given in Table I. The HA analysis results of the quenched binary Cu * 50 Cu** 50 system is shown in Figure 2. At =1.0, the system becomes an FCC/HCP crystal, therefore it shows almost no 1551 pair character. As decreases, the system becomes a glass, and the 1551 and 2331 pairs dominate. The 1551 and 2331 pairs show a maximum at =0.85. The 1551 and 2331 pairs decrease abruptly while the 1421 and 1422 pairs start to increase at <0, implying the growth of crystallization tendency at small. Cohesive energy ratio ε Atomic size ratio (a) Size effect only (b) Constant energy density line: ε()= 3 (c) Bond character effect only HA pair fraction Figure 1. Schematic diagram comparing the size ratio effect (topological disorder, scheme (a)), constant energy density effect (topological and chemical disorder, scheme (b)), and cohesive energy ratio ε effect (chemical disorder, scheme (c)) of constituting elements (Cu * and Cu ** ). Figure 2. Honeycutt-Andersen pair fraction as a function of atomic size ratio () at T=300K of cooling run. At =1.0, the system has many 1421 and 1422 pairs and almost no 1551 pairs indicating that it is composed of FCC and HCP phases. As decreases, the 1551 and 2331 pairs increase dramatically, showing a maximum at =0.85.

3 Journal Title and Volume Number (to be inserted by the publisher) 3 Table I. Honeycutt-Andersen (HA) pair fractions for several reference structures. Here FCC and HCP denotes bulk systems while ICO-N denotes an icosahedral clusters with N atoms. These pairs are normalized to make the total number of nearest neighbor pairs unity. In general, the 1421 and 1422 pairs are characteristic of a closed packed crystalline structures (FCC or HCP). The 1551 and 2331 pairs are characteristics of icosahedral ordering, being found in the icosahedral clusters FCC HCP ICO_ ICO_ ICO_ ICO_ To understand the crystallization at small, the binary Cu * 50Cu ** 50 system with =0.50 is visualized (Figure 3). In this system, two separate phases (Cu * phase and Cu ** phase) with a well-defined phase boundary are observed. The detailed structural analysis of each phase by partial radial distribution functions (PRDF) and HA analysis shows that Cu ** phase is crystallized [3]. Therefore, we attribute the crystallization at small to the phase separation. To further quantify the phase separation behavior as a function of, we calculate the pair fraction, defined as the number of a specific pair type present in the sample normalized by the total number of pairs in the system. For a completely mixed system (e.g. =1.0), a pair fraction should be 5 for like pairs (Cu * -Cu * and Cu ** -Cu ** ) and 0.50 for unlike pairs (Cu * -Cu ** ). As decreases, the fraction of unlike pairs decreases while the total fraction of like pairs increases (Figure 4). This is due to the phase separation between different atomic species. The decrease of unlike pair fraction becomes abrupt at 0.75, indicating the existence of a threshold for phase separation. Pair fraction Cu ** Cu ** Cu * Cu * Cu * Cu ** Figure 3. A snapshot of the binary alloy with = 0.50 at 300K after cooling from the liquid state (T=1600K). Dark colored small balls are Cu * and light colored big balls are Cu **. Cu * and Cu ** are phase separated with Cu ** showing crystalline order. Figure 4. The pair fraction in the binary Cu * 50 Cu** 50 system as a function of. The fraction of unlike pairs (Cu * -Cu ** ) is nearly constant above 0.75, but decreases rapidly below 0.75, indicating the onset of a phase separation

4 4 Title of Publication (to be inserted by the publisher) To avoid the phase separation, the free energy of mixed/separate phases should be considered. More specifically, the heat of mixing should be minimized. To the end, we manipulate the cohesive energy of Cu * and Cu ** along with the atomic size to minimize the heat of mixing (scheme (b)). In this set of simulation, all samples remain as well-mixed states upon cooling from the liquid state. One extreme case (Cu * 50 Cu** 50 alloy at =0.5,ε=0.125) is shown in Figure 5. In comparison with the Figure 3 (Cu * 50 Cu** 50 alloy at =0.5), this sample shows no phase separation but crystallizes upon cooling to NaCl structure. This agrees well with the simple crystallographic prediction that the NaCl structure is favored in [11]. To ensure no phase separation in the glass regime ( 0.95), the pair fraction quantity is shown as a function of in Figure 6. The pair fraction of unlike pairs (Cu * -Cu ** ) remain2 almost constant as changes, implying no phase separation with respect to. In addition to that, we analyze the structural properties as a function of. Crystallization occurs at 0.95, showing large fraction of 1421 and 1422 pairs. The glass transition occurred at 0 <0.95 and the 1551 pair shows a maximum at =0.85 Figure 5. A snapshot of the binary alloy with = 0.50 and ε=0.125 at 300K after cooling from the liquid state. Dark colored balls are Cu * and light colored balls are Cu **. Cu * and Cu ** are completely mixed and the sample shows the NaCl crystalline order Pair fraction 0.3 HA pair fraction Figure 6. The pair fraction in the binary Cu * 50 Cu** 50 system as a function of (scheme (b)). The fraction of unlike pairs (Cu * -Cu ** ) is nearly constant as 0.5, indicating no phase separation between unlike species (Cu * and Cu ** ).

5 Journal Title and Volume Number (to be inserted by the publisher) 5 Figure 7. Honeycutt-Andersen pair fraction as a function of atomic size ratio () at T=300K of cooling run (scheme (b)). In the glass forming regime (0 <0.95), the system has many 1551 and 2331 pairs and shows a maximum at =0.85.

6 6 Title of Publication (to be inserted by the publisher) Finally, the cohesive energy ratio ε effect on the glass formation is examined (scheme (c)). This set of simulation corresponds to a binary system that has similar atomic size but different bond character between constituting elements (e.g., AgAl or AuAl). Upon cooling the system crystallize at ε 0.30, showing a relatively small glass forming regime compared scheme (a) and (b). This indicates that the size ratio (topologic al disorder) is the dominant factor to control the glass forming ability over the chemical disorder. Summary We have investigated the phase transition, local ordering and phase separation in the binary glass forming liquids in terms of size ratio and/or cohesive energy ratio ε. When only the size ratio is introduced, the system shows crystallization (>0.95), glass transition (0 0.95) and phase separation (<0.75) as decreases upon cooling. When we consider the system with a constant energy density, the system shows no phase separation. However, both cases (scheme (a) and scheme (b)) have a very similar glass forming regimes (0 0.95) and show a maximum in the five fold symmetry at =0.85 regardless of ε. When we change ε only, the system shows a very limited glass forming regime (ε 0.30), confirming the importance of size ratio in the glass formation. Acknowledgments This work was supported in part by the MRSEC Program of the National Science Foundation under Award Number DMR and ARO-DARPA-SAM project. The facilities of the MSC used for these studies were funded partly by NSF MRI, ARO/DURIP, and IBM-SUR. In addition support for the MSC is also provided by grants from DOE-ASCI, ARO/MURI, ChevronTexaco, NIH, ONR, Seiko- Epson, Avery-Dennison, Kellogg s, General Motors, Beckman Institute, Asahi Kasei, Toray, and Nippon Steel. References [1] W. L. Johnson, MRS Bull. 24, 42 (1999) [2] H. J. Lee, Mat. Res. Soc. Symp. Proc. 644, L (2001) [3] H. J. Lee, J. Chem. Phys. Submitted [4] A. P. Sutton and J. Chen, Philos. Mag. Lett. 61, 139 (1990) [5] H. Rafii-Tabar and A. P. Sutton, Philos. Mag. Lett. 63, 217 (1991) [6] Y. Kimura, T. Cagin, Y. Qi, and W. A. Goddard III (unpublished) [7] M. Parrinello and A. Rahman, Phys. Rev. Lett. 45, 1196 (1980) [8] W. G. Hoover, Phys. Rev. A, 31, 1695, (1985) [9] J. R. Ray and A. Rahman, J. Chem. Phys. 82, 4243 (1985) [10] J. D. Honeycutt and H. C. Anderson, J. Phys. Chem. 91, 4950 (1987) [11] W. A. Goddard III: Nature of the Chemical Bond (California Institute of Technology, 1986)