Molecular dynamic simulation of glass formation in binary liquid metal: Cu Ag using EAM

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1 Intermetallics 12 (2004) Molecular dynamic simulation of glass formation in binary liquid metal: Cu Ag using EAM L. Qi, H.F. Zhang*, Z.Q. Hu Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, No. 72 Wenhua Road, Shenyang , China Available online 28 May 2004 Abstract Based on the embedded-atom method, a constant-pressure, constant-temperature molecular dynamics technique is applied to obtain an atomic description of glass formation process in eutectic Cu 40 Ag 60 alloy. By using radial distribution function and pair analysis methods, the structure and glass forming ability of this alloy is studied by quenching from the liquid at different cooling rates ( , , , and K/s). It is observed that the retention of amorphous structure requires extremely high cooling rates. Structure analyses of the alloys in the simulations reveal the evolvement of the different clusters at various quenching rate during the quenching process. q 2004 Elsevier Ltd. All rights reserved. Keywords: B. Glasses, metallic; C. Rapid solidification processing; E. Simulations, atomistic 1. Introduction When a liquid metal is quenched through the supercooled region, a phase transition from liquid to glass takes place. Several techniques have been proposed to obtain a disordered state [1 3]. Among them the rapid solidification method is widely used for the amorphous phase. However, due to the demand of a high cooling rate this method is restricted in most experimental cases. The computer simulation of molecular dynamics (MD) is therefore applied. Recent years have witnessed considerable progress in the development of empirical or semi-empirical many-body potentials for MDs simulations. The embedded-atom method (EAM) of Daw and Baskes [4,5] (and further developed by Johnson [6 9]), N-body potentials proposed by Finnis and Sinclair (FS) [10] (and further developed by Ackland et al. [11 13]) and the tight-binding model of many-body potentials given by Rosato et al. [14] consist of three main aspects of the present empirical or semiempirical many-body potentials [15]. The EAM has been successfully applied to a wide range of aspects in the solid state, such as in point defects, dislocations and surfaces [16 18]. * Corresponding author. Tel./fax: þ address: hfzhang@imr.ac.cn (H.F. Zhang). Mei [19] applied the nearest-neighbor model of EAM proposed by Johnson [3] to the liquid state by using MDs simulations; the results for structure factors and diffusive coefficients of noble metals are in good agreement with experiments. In 1999, Qi and Çagin [20] had simulated the glass formation and crystallization of Cu Ag alloy using MDs in conjunction with the quantum Sutton Chen (Q-SC) force fields (FF), last year Sheng et al. [21] also studied Cu Ag alloy based on the same potential. In this paper, a different potential EAM developed by Mei is used to discuss the structure and glass formation ability of the eutectic Cu Ag alloy (Cu 40 Ag 60 ) with different cooling rates ( , , , and K/s). 2. Simulation methods In the EAM, the total energy of an N-atom system has the form [4] E tot ¼ X i F i ðr i Þþ X f i;j ðr i;j Þ i;j i j where F i;j ðr i;j Þ is a two-body central potential between atom i and j with the separation distance r i;j; ; F i ðr i Þ is the embedding energy of atom i with the electron density /$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi: /j.intermet

2 1192 L. Qi et al. / Intermetallics 12 (2004) Table 1 Model parameters for the Cu and Ag metals Cu Ag E C f e a b 5.85 a 5.96 a d a a g a a f e a a f e is in unit of ev. Other parameters are dimensionless. a Reference [19]. r i due to all its neighbors: r i ¼ X f j ðr ij Þ jð iþ Three formulae to establish the EAM potential of Cu 40 Ag 60 can be obtained as follows: r ¼ r e exp½2bðr 1 =r 1e 2 1ÞŠ ð1þ fðrþ ¼2f e ½1 þ dðr=r 1e 2 1ÞŠexp½2gðr=r 1e 2 1ÞŠ ð2þ FðrÞ ¼2E C 1 2 a b ln r r a=b r e re þ 1 2 f X e s m exp½2ðp m 2 1ÞgŠ m d 1 þðp m 2 1Þd 2 p m b ln r r pm ðg=bþ ð3þ r e re The parameters in these formulae are listed in Table 1. The details can be searched in Ref. [19]. The simulations were performed with the system consisting of 640 atoms in a cubic box with periodic boundary conditions along all the three directions. The simulations are based on constant-temperature, constantpressure method (NPT-MD). The typical time step is order of a few femtoseconds when the system settles down in a thermal equilibrium. Equations of motion are numerically integrated using the Verlet algorithm. For each quenching experiment, the starting liquid state is obtained by heating the solid slowly through the liquidus temperature. The system is melted and homogenized at a temperature well above the liquidus in the range of K and then rapidly cooled with the desired rate (e.g , , , and K/s) down to room temperature, noting the change of volume and structure to decreasing of temperature, using pair analysis (PA) method [22] to study the change of microstructure during the cooling process, and radial distribution function (RDF) to analyze the glass forming ability of the alloy. 3. Results and discussion Fig. 1 shows the variation of the volume as Cu 40 Ag 60 is cooled at different cooling rates. A step downward jump in Fig. 1. Average volume of Cu 40 Ag 60 during cooling at a series of cooling rates. volume for the cooling process is due to the crystallization of the Cu 40 Ag 60 alloy. Different cooling rate leads to different crystallization temperature, the larger the cooling rate the lower the crystallization temperature. At and K/s cooling rate, the crystallization temperature is about 880 and 840 K; at K/s cooling rate, the crystallization temperature becomes 540 K. However, at K/s cooling rate, the variation of the volume is continuous. This indicates the formation of a metallic glass. Fig. 2 shows the RDF of the model structure during the cooling process at different cooling rates. The RDF shows the melting structure as the sample is cooled from 1100 to 900 K. In Fig. 2(a) and (b), it proves the presence of an fcc crystal structure at 800 K. However, at 800 K, the RDF still shows the melting structure in Fig. 2(c) which is of cooling rate, the reason is that fast cooling rate leads to low crystallization temperature, at K/s the sample crystallization temperature is about 530 K (Fig. 1) so the RDF still shows the melting structure at 800 K. In Fig. 2(d), from 1100 to 700 K, the RDF exhibits the melting structure, at 600 K the RDF shows the splitting of second peak. This splitting of the second peak is a well-known characteristic feature in the RDF of the existence of a metallic glass. Thus, quenching the Cu 40 Ag 60 alloy from the liquid to 300 K at the rate of K/s forms a metallic glass. The amorphous formation temperature is decided by Wendt Abraham parameter R A ; defined by R A ¼ g min =g max : Here, g min ðg max Þ is the value of gðrþ at the first minimum (maximum) in the RDF, as the result, the amorphous formation temperature is about 620 K. One method that can be used to analyze the local environments is the pair analysis (PA) [22]. The PA is a method for analyzing structures by a decomposition of the RDF according to the local environment of the bonded pairs. The PA can be used to distinguish between various local packing orders, in particular fcc, bcc, hcp, and liquid environments. Specifically, most of bonded pairs in fcc are of type 1421, bcc are of 1442 and 1661, liquid and amorphous are of 1551, 1431 and 1541, as shown in Fig. 3.

3 L. Qi et al. / Intermetallics 12 (2004) Fig. 2. Radial distribution function (RDF) of Cu 40 Ag 60 during the cooling processes at various cooling rates. (a) , (b) (c) and (d) K/s. Using the atomic positions stored for the Ag Cu alloy during cooling, its RDF is decomposed into a set of RDF s, each for a specified PA type. The four major types of pairs (1421, 1551, 1431, 1541) for Cu 40 Ag 60 are monitored during quenching. Fig. 3 shows the relative fraction of the various PA pair types, as a function of temperature during a set of quenching rates from to K/s. Fig. 3(a) clearly indicates that there is an abrupt decrease of 1431, 1551 and 1541 pairs, at K/s cooling rate, and the population of 1421 pairs (representing fcc) shows abrupt increase at the same temperature which indicates the crystallization of the liquid alloy. In Fig. 3(b) the case is almost the same as in Fig. 3(a), the only difference is that the crystallization temperature is lower than (a), this result is in coincidence with the RDF and volume curve. In Fig. 3(c), there is no decrease of 1431, 1551, 1541 pairs, and 1421 pairs do not change abruptly also. This indicates that the liquid structure is held till room temperature, so at this cooling rate a metallic glass is formed. Fig. 4 shows the two-dimensional cross-sectional projections of the structures obtained at the different quenching rates. These projections straightly exhibit Fig. 3. The schematic diagram for some bond pairs. Fig. 4. Two-dimensional cross-sectional projections of the structures obtained at different quenching rates. (a) , (b) , and (c) K/s.

4 1194 L. Qi et al. / Intermetallics 12 (2004) the structure of the Cu 40 Ag 60 alloy. The open ball represents Ag and the close ball represents Cu. Note that a clearer visualization would require a three-dimensional view with crystal rotations. However, some differences in terms of homogeneity can already be seen in these two-dimensional cross-sectional projections [21]. For the two slower cooling rates Fig. 5(a) and (b) shows clustering. Moreover, the distribution of atoms in Fig. 5(a) is more orderly than that in Fig. 5(b), this is because lower cooling rate means more diffuse time, that is, at K/s cooling rate, the atoms have more time to move than at K/s cooling rate. In Fig. 5(c), the open ball and the close ball distribute unorderly and homogeneously. This means due to slower atomic movements the alloy remains liquid structure at the quench rate of K/s, e.g. a metallic glass is formed. 4. Summary and conclusion This MD study is aimed at studying the glass forming ability and uncovering the atomic-level structure of the Ag Cu alloy obtained through rapid quenching at different extreme cooling rates. A series of simulations has been performed and the following results are summarized. (1) The results presented here shown that the EAM function can correctly predict the glass transition and crystallization of liquid alloys during rapid solidification. (2) The retention of amorphous structures requires extremely high-cooling rate ( K/s). (3) The crystallization temperature depend on the quenching rate, the larger the quenching rate the lower the crystallization temperature. (4) Structure analyses of the alloys in the simulations revealed the evolvement of the different clusters at different quenching rates during the quenching process. Acknowledgements This work was supported by the National High Technical Research and Development Programme of China (2001AA331010) and National Key Basic Research and Development Programme of China (G ). References Fig. 5. Relative amounts of various atomic-bonded pairs in Cu 40 Ag 60 at different temperatures during different cooling rates. (a) , (b) and (c) K/s. [1] Massobric C, Pontikis V, Martin G. Phys Rev 1990;B41: [2] Cardellini F, Contini V, Mazzone G. Scripta Metall Mater 1995;4:641. [3] Jang JSC, Koch CC. J Mater Res 1990;5:498. [4] Daw MS, Baskes MI. Phys Rev Lett 1983;50:1285. [5] Daw MS, Baskes MI. Phys Rev 1984;B29:6443. [6] Johnson RA. Phys Rev 1988;B37:3924.

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