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Thermodynamic and atomistic modeling of irradiation-induced amorphization in nanosized metal–metal multilayers
Surface & Coatings Technology 196 (2005) 2 – 9 www.elsevier.com/locate/surfcoat
Thermodynamic and atomistic modeling of irradiation-induced amorphization in nanosized metal–metal multilayers B.X. Liu*, Z.C. Li, H.R. Gong Laboratory of Advanced Materials, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China Available online 28 September 2004
Abstract A brief summary is firstly presented concerning up-to-date experimental studies of the formation of amorphous alloys (metallic glasses) in binary metal systems by ion beam mixing of nanosized metal–metal multilayers. Secondly, under the framework of Miedema’s theory, thermodynamic modeling of crystal-to-amorphous transition is described with special consideration of the effect of the excess interfacial free energy on the alloy phase formation. Thirdly, in some representative systems, glass-forming ranges are calculated directly from their realistic interatomic potentials by determining the critical solid solubilities of the systems by molecular dynamics simulations. Finally, a comparison between irradiation and thermally induced amorphization in the metal–metal multilayers is also discussed. D 2004 Elsevier B.V. All rights reserved. Keywords: Amorphous; Multilayer; Atomistic modeling
1. Introduction Duwez (1960) obtained the first amorphous alloy (or metallic glass) in the Au–Si system by liquid melt quenching (LMQ) [1]. In the early 1980s, a powerful scheme [i.e., ion beam mixing (IBM)] was introduced to produce amorphous alloys as well as to study fundamental issues in the field of metallic glasses [2]. Because of its powerful capability, IBM has so far produced a great number of nonequilibrium alloys with either an amorphous or crystalline structure, not only in those glass-forming systems but also in some nonglass-forming systems, which were defined previously based on experimental results from LMQ. For example, IBM has produced a number of amorphous alloys in some equilibrium immiscible systems, in which LMQ is even unable to comelt the constituent metals [3]. It follows that some basic concepts and understanding concerning the metallic glasses should be further developed, e.g., the previously defined glassforming and nonglass-forming systems, glass-forming
* Corresponding author. Tel.: +86 10 6277 2557; fax: +86 10 6277 1160. E-mail address: [email protected] (B.X. Liu). 0257-8972/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2004.08.074
ability (GFA), or glass-forming range (GFR) of the binary metal systems, etc. In the mid 1970s, Miedema developed a semiquantitative theory, based on which one is able to calculate the thermodynamic properties of metals and alloys based on some intrinsic properties of the elements. Employing the theory, the Gibbs free energy diagram of a system can be constructed, and it includes the calculated free energy curves of all the involved alloy phases as a function of alloy composition. It turned out that the constructed free energy diagram could give relevant thermodynamic insights of alloy phase formation and transformation [4]. Since the late 1980s, Miedema’s theory has also been employed to develop a thermodynamic model for the metastable alloy phase formation [5]. In the past decades, significant progress has been achieved in computational materials science [6]. Computation and/or simulation makes it possible to approach a quantitative understanding of the alloy phase formation and transformation at an atomic scale or even into a depth of the electronic structures of the solids. Very recently, it has been initiated to study the possibility of determining the GFA of a binary metal system directly from a realistic n-body potential of the system through molecular dynamics (MD) simulation [7].
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This article attempts to present a brief summary of the recent progress concerning the understanding of irradiationinduced amorphization and calculation of GFA directly from interatomic potential. The discussion in this article will be concentrating on binary metal systems, of which fruitful experimental and thermodynamic data have so far been accumulated.
2. Metastable alloy phase formation by IBM In IBM, the multilayers consist of alternately deposited metals A and B on an inert supporting substrate. By adjusting the relative thicknesses of the two metals, an A–B alloy can be obtained with any desired composition. An energetic ion beam is used to trigger atomic collisions for inducing intermixing between the metal layers of A and B. After irradiation to an adequate dose, a uniform mixture of metals A and B can be achieved and an A–B alloy is thus obtained. At the beginning, IBM was employed mainly to study the possibility of synthesizing various metal silicides, which are known as candidate materials, to be applied in electronic devices [8]. A little later, IBM was also employed to study metastable alloy phase formation and transformation in binary metal systems [2]. Up to now, a great number of amorphous and metastable crystalline (MX) alloys have been obtained in some 100 systems [9]. Among the obtained metastable alloys, many have not been formed or are even not obtainable by other nonequilibrium techniques like LMQ, etc. Moreover, the progress in IBM experimental studies has also stimulated theoretical works to approach a better understanding of GFA/GFR of the binary metal systems.
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terminal solid solutions, but not in the central portion of the equilibrium phase diagram [12]. Such compositional dependence is sharply different from that observed in the systems with negative DH f, in which the alloy composition near the equiatomic stoichiometry is usually the most favored for amorphization because the free energy of the amorphous phase reaches its minimum [13]. Concerning the GFR of a system, the present author has proposed to define a parameter, namely MPAR, which is an abbreviation of maximum possible amorphization range, for predicting the GFR or GFA of the system. The MPAR is defined to be 100%, the total composition range minus the two maximum solid solubilities observed from the corresponding equilibrium phase diagram. Combining the effect of DH f on amorphization, Fig. 1 is a proposed map using MPAR and DH f to classify the systems into possibly, readily, and hardly glass-forming ones in terms of their GFR and GFA upon IBM. It will be shown later that the prediction of GFR or GFA based on the MPAR DH f model agrees well with the experimental results and that, by considering the excess interfacial free energy stored in the metal–metal multilayers, a unified thermodynamic model is developed for metallic glass formation by IBM in the systems with either negative or positive DH f.. 3.1. GFA of the negative heat of formation systems
3. Thermodynamic modeling of metallic glass formation
According to the MPAR DH f model, one is able to predict approximately the GFR of a system by inspecting its equilibrium phase diagram. Take the Ni–Nb system as an example; its DH f = 45 kJ/mol [4] and Fig. 2a exhibits its equilibrium phase diagram. In the diagram, the whole alloy composition can be divided into three types (i.e., terminal solid solution, intermetallic compound, and two-phase region). An amorphous alloy is readily formed by IBM in the two-phase regions and its formation can be attributed to
If a system is of negative DH f, which causes the amorphous state to have a lower free energy than that of the initial energetic state of the multilayers, the negative DH f itself serves as a driving force for amorphization. On the contrary, if a system has a large positive DH f, the two constituent metals cannot even mix together to form an alloy in melt. The system is therefore essentially equilibriumimmiscible and has been considered to be difficult to use to obtain metallic glasses by IBM [8]. Since the late 1980s, however, there have been experimental studies showing the possibility of forming metallic glasses in systems featuring large positive DH f [10]. In fact, in the mid-1990s, IBM produced a number of amorphous as well as MX alloys in many systems with positive DH f ranging from nearly 0 to +56 kJ/mol [11,12]. These results suggest that the DH f of a system is not a decisive parameter in determining whether the metallic glass can be formed or not. Interestingly, in systems with positive DH f, metallic glasses were frequently formed in the restricted composition regions close to the
Fig. 1. According to the two defined parameters, MPAR and heat of formation, the binary metal systems are classified into three categories: readily, possibly, and hardly glass-forming systems (RGF, PGF, and HGF, respectively).
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energy curve reaches the nadir and is lower than those of two terminal solid solutions. The GFR was commonly regarded as the composition range in which the free energy of the amorphous phase is lower than that of the solid solution. Consequently, the GFR of the Ni–Nb system is from 15 to 80 at.% of Nb, which is a little narrower than the MPAR. Incidentally, Zhang et al. [13] have determined by IBM experiments that the GFR was very close to 15–80 at.% of Nb, which is in excellent agreement with that deduced from the above thermodynamic calculation. It is worth mentioning that there have been many IBM results showing the readiness of metallic glass formation in such systems featuring a negative DH f (e.g., in the Ni–Zr system, the GFR is 10–90 at.% of Zr, which matches well the experimentally determined GFR around 10–80 at.% of Zr by IBM) [14]. 3.2. GFA of the positive heat of formation systems
Fig. 2. (a) The equilibrium phase diagram of the Ni–Nb system and (b) calculated Gibbs free energy diagram of the Ni–Nb system.
the competition of the crystallization between the two metals, resulting in the frustration of nucleation and growth of either crystalline metal during the extremely short relaxation period in IBM. Moreover, it has also been demonstrated that IBM could produce metallic glasses with alloy compositions located at the intermetallic compounds frequently with complicated structures, which are not allowed to grow during relaxation period in IBM. Consequently, the two-phase regions are connected to each other and are united to be a continuous composition range favoring amorphization, which is actually the total width of the two-phase regions. One sees from Fig. 2a that the MPAR of the Ni–Nb system is from 5 to 95 at.% of Nb [4]. A free energy diagram of the Ni–Nb system is accordingly calculated and shown in Fig. 2b. One sees that the free energy curves of the amorphous phase, the two terminal solid solutions and the intermetallic compounds, are all concave. As the formation of intermetallic compounds is usually hindered kinetically, they need not be considered while discussing the GFR, although they have even lower free energy than all the metastable alloy phases. By comparing the free energy of the amorphous phase with those of the crystalline phases, it is possible to predict GFR. Obviously, the formation of the amorphous phase is most favored near the equiatomic stoichiometry, where its free
For a system with a positive DH f, the free energy curve of the amorphous phase is usually higher than that of a mechanical mixture of crystalline metals A and B in the alternatively deposited multilayers, suggesting a situation not favored for metallic glass formation. However, as the interfaces in the multilayers are generally regarded as transient layers of mixed A and B atoms in a highly disordered configuration, the extra interfacial free energy plays an important role in enhancing the alloying ability of the multilayered films. If an adequate fraction of interfacial atoms is included in the multilayers, the free energy curve of the films can be elevated to intersect with that of the amorphous phase, leading to a situation favoring the formation of metallic glasses in the specific composition regions. 3.2.1. Metallic glasses formed within restricted composition ranges Take the Ag–Mo system (DH f =+56 kJ/mol) as an example; the free energy curves of the amorphous phase and multilayered films designed to contain 12 layers are calculated. Fig. 3 shows the constructed Gibbs free energy diagram of the Ag–Mo system. One sees that the free energy curve of the multilayered films intersects with that of the amorphous phase and the whole composition range is thus divided into three different regions. Obviously, in the I and III regions, amorphous phase is possible to form, as its free energy is lower than that of the initial state of the films. While in the II region, formation of metallic glass is hard to achieve because the amorphous phase still has a higher free energy than the films. IBM experiments were accordingly conducted and an amorphous alloy was indeed formed with alloy composition near 80 at.% of Mo. Moreover, another amorphous phase was also formed together with an Mobased MX phase in the Ag–Mo multilayered films with an alloy composition of around 40 at.% of Mo [12]. Such compositional discontinuity in metallic glass formation is
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closely related to the positive DH f of the system and has also be observed in the Nb–Zr [11] and Y–Ta [15] systems, which feature positive DH f of +6 and +40 kJ/mol, respectively. 3.2.2. Metallic glasses formed in broad composition range As shown above, the width and exact location of the alloy composition regions favoring amorphization depend on the designed fraction of interfacial atoms in the multilayered films. One may then ask if further increasing the fraction of interfacial atoms can broaden the two separated composition regions favoring amorphization and have them meet each other to unite into a continuous range. Take the Y–Mo system with a DH f =+35 kJ/mol as an example; Fig. 4 shows its calculated free energy diagram, which includes the free energy curves of the amorphous phase and three Y–Mo multilayered films consisting of 9, 11, and 19 layers, respectively, with a fixed total thickness of 45 nm, corresponding to the fractions of interfacial atoms of 8.1, 10.0, and 18.1 at.%, respectively [5]. Apparently, through properly designing the multilayered films, it is possible to form metallic glasses in the Y–Mo system even with an alloy composition near the equiatomic stoichiometry. In other words, for the positive DH f systems, the GFR could also be extended to a broad composition range close to the defined MPAR, provided the multilayered films were properly designed to possess sufficient interfacial free energy. 3.3. Nominal and intrinsic GFA From both practical and theoretical points of view, prediction of GFA/GFR of a binary metal system is of vital importance. First, the GFA of a system should reflect qualitatively whether or not the metallic glass can be formed. From a physical point of view, there should exist an intrinsic GFA reflecting the capability of the system itself. Second, it is also of necessity to have a quantitative measure for GFA that is able to compare the capabilities
Fig. 4. Calculated Gibbs free energy diagram of the Y–Mo system. N stands for the number of layers in the Y–Mo multilayered films.
among the systems. An experimentally determined GFR can be taken as a quantitative measure for GFA, and, naturally, the larger the GFR, the greater the GFA. If one employs LMQ technique with a greater cooling speed, one may obtain glasses in a broader composition range than that observed by a technique with a slower cooling speed. In this sense, an experimentally determined GFR can only be considered as a nominal GFA [16]. Obviously, the greater the GFR observed by a specific technique, the closer the GFR to the intrinsic GFA. In other words, to approach an intrinsic GFA of a system, one should look for a powerful glass-producing technique and, at present, IBM may be the very technique capable of revealing the maximum GFA among the currently available glass-producing techniques. Based on IBM studies for the systems with either a negative or positive DH f, the defined MPAR is a good approximation for predicting the composition range for metallic glass formation since IBM can frequently form some supersaturated solid solutions, which would actually reduce the total width of the two-phase regions, namely to reduce the width of the defined MPAR. Consequently, if one is able to determine the supersaturated solid solubilities of a specific system, the intrinsic GFA or GFR of the system can then be predicted to be 100% as the whole composition range minus the two supersaturated solid solubilities, which could be considered as a modified MPAR.
4. Calculation of GFA from interatomic potential
Fig. 3. Calculated Gibbs free energy diagram of the Ag–Mo system.
An important and fundamental issue in the field of metallic glasses is to develop a theoretical model, which is able to predict the GFA of a binary metal system [17,18]. As described above, according to IBM exper-
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solid solubilities is therefore the GFR of the system, in which the amorphous state was energetically more stable than solid solution. Such a GFR is a property intrinsic to the system itself and not connected with any specific glass-producing technique. 4.1. Calculation of GFA for some miscible Ni-based systems
Fig. 5. Total and partial pair correlation functions for the fcc Ni-rich solid solution after running MD simulation at 300 K for 10,000 MD time steps. The compositions are at (a) 10 at.%, (b) 17 at.%, (c) 21 at.%, and (d) 25 at.% of Mo, respectively. The solid line is for total g(r), the short dashed line is for Mo–Ni g(r), the dotted line is for Ni–Ni g(r), and the dot-dashed line is for Mo–Mo g(r), respectively.
imental results, the issue becomes an objective of calculating the supersaturated solid solubilities of a binary metal system. From an energetic point of view, for a specific system, the GFA is determined by the relative stability of the solid solutions compared with their amorphous counterparts. Moreover, the relative stability of the solid solution versus the amorphous phase is intrinsically determined by their corresponding atomic configurations, which are directly governed by the interatomic potential of the system. We will show in the following paragraph that MD simulation with a realistic interatomic potential of a system is capable of determining the supersaturated solid solubilities. Consequently, the central region bounded by the two determined critical
We now present the calculation results for the miscible Ni–Mo, Ni–Ti, Ni–Zr, and Ni–Ta systems with negative heats of formation. In MD simulations, the solid solution models were used. For the Ni–Mo system, the compositions of the fcc Ni-rich (bcc Mo-rich) solid solutions were selected to be in the range of 0–50 at.% of Mo (0–50 at.% of Ni). Each solid solution with a designed solute concentration was obtained by randomly substituting a corresponding amount of Ni (Mo) by Mo (Ni) in the Ni fcc (Mo bcc) lattice. The models were then simulated at 300 K for adequate time steps to reach a relatively equilibrium state. Fig. 5 displays the calculated total and partial pair correlation function g(r) for the Ni-rich fcc solid solutions with the solute concentrations of 10, 17, 21, and 25 at.% of Mo, respectively. One sees that the solid solutions with 10 and 17 at.% of Mo remain crystalline structures and that, with increasing solute concentration, the peaks of g(r) became broadened, implying that the crystals become progressively disordered. Obviously, a crystal-to-amorphous (C–A) transition took place in the solid solution with 25 at.% Mo, while for the solid solution with 21 at.% of Mo, the shape of the calculated g(r) was ambiguous, implying that the C–A transition has taken place but not yet completed. Similarly, on the Mo end, x Ni=25 at.% was determined to be the critical value for C–A transition. Consequently, the GFR of the Ni–Mo system is deduced to be within 21–75 at.% of Mo. Meanwhile, for the Ni–Ti system, the GFR was determined to be within 38–85 at.% of Ti. For the Ni–Zr and Ni–Ta systems, their critical compositions for C–A transitions were also determined based on a tight-binding Ni–Zr potential derived by Massobrio et al. [19] and a Ni–Ta potential developed by the authors, respectively. For the above four systems, the critical solid solubilities determined directly from their respective potentials through MD simulations are summarized in Table 1. It is of interest to note that the GFRs of the systems determined by MD simulations are supported by experimental observations. For the Ni–Mo system, amorphization in the Ni–Mo multilayers has been observed upon
Table 1 Calculated critical compositions of the solid solutions, beyond which solidstate amorphization can take place, in some Ni-based systems Ni as solvent matrix Ni as alloying solute
Ti (at.%)
Zr (at.%)
Mo (at.%)
Ta (at.%)
38 15
14 25
21 25
21 43
B.X. Liu et al. / Surface & Coatings Technology 196 (2005) 2–9
Fig. 6. Partial and total pair correlation functions of the Cu-based solid solution after annealing at 300 K. The Ta solute concentrations are at (a) 5 at.%, (b) 15 at.%, (c) 25 at.%, and (d) 30 at.% in Cu. The solid line is for total g(r), the dashed line is for Cu–Cu partial g(r), the dotted line is for Ta–Ta partial g(r), and the dash-dotted line is for Cu–Ta partial g(r).
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principles calculation was employed to acquire some physical properties of the possible nonequilibrium alloy phases of the systems, based on the well-established Vienna ab initio simulation package (VASP) [23]. We have successfully derived the embedded atom (EAM) potentials for the Cu–Ta and Cu–W systems. Applying the constructed Cu–Ta potential, MD simulations were conducted using Cu-based fcc solid solution models. It was found that 30 at.% of Ta in Cu solid solution was a critical concentration for C–A transition to take place. The total and partial pair correlation functions g(r) of the Cu–Ta solid solution after annealing at 300 K for 0.75 ns at various Ta solute concentrations of 5, 15, 25, and 30 at.%, respectively, are shown in Fig. 6. It can be seen that the solid solution with 30 at.% of Ta has become amorphous, while the solid solutions with 5, 10, and 25 at.% of Ta all retain crystalline structures. It is of interest to compare the simulation results with some experimental observations in the Cu–Ta system. For instance, Lee et al. [24] observed the formation of an amorphous layer 2 nm thick in the Cu61Ta39 multilayered films upon annealing at 500 8C. Nastasi et al. [25] obtained the Cu55Ta45 and Cu50Ta50 amorphous alloys by ion irradiation. These amorphous alloys were all formed in the composition range exceeding the critical value of 30 at.% of Ta determined by MD simulation. Besides, Kim et al. [26] found that the sputter-deposited Cu–Ta
solid-state reaction and the favored composition range was found to be 25–75 at.% Mo [20], which is very close to the intrinsic GFR determined by MD simulation. For the Ni–Ti system, the GFR of the system determined by LMQ data was in a composition range of 30–40 at.% of Ni [21], which is apparently within the intrinsic one revealed by MD simulation. IBM experiments were performed for the Ni–Ti multilayered samples. It was found that the Ni-based solid solutions were obtained up to a composition of 37 at.% of Ti, beyond which a unique amorphous phase was formed. Apparently, the IBM experimental results are in good agreement with those revealed by MD simulation. For the Ni–Zr system, the calculated GFR is 14–75 at.% of Zr, which is compatible with 45–70 at.% of Zr determined by solidstate reaction experiments [22]. 4.2. Calculation of GFA for some immiscible Cu-based systems We now present the calculation results for some immiscible Cu-based systems with positive heats of formation. To perform MD simulation, it is necessary to derive n-body potentials for the systems and, for the immiscible systems, it is a challenging task to derive the cross potentials as there is no any equilibrium alloy phase that could provide the necessary data required for deriving the potentials. To overcome such a difficulty, the first
Fig. 7. Partial and total pair correlation functions of (a) Cu85W15, (b) Cu80W20, (c) Cu50W50, (d) Cu35W65, and (e) Cu30W70 solid solutions after annealing at 300 K for 0.5 ns, respectively. The solid line is for the total g(r), the dashed line is for Cu–Cu partial g(r), the dotted line is for W–W partial g(r), and the dash-dotted line is for Cu–W partial g(r).
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alloys containing 44–91 at.% of Ta became completely amorphous and that when the alloy concentration was 21 at.% of Ta, with the Cu–Ta alloy consisting of an fcc solid solution and some remaining crystalline Ta. These observations are also in agreement with the present simulation results. Similarly, for the Cu–W system, the intrinsic GFA/GFR was determined to be within 20–65 at.% of W. Fig. 7 shows the calculated pair correlation functions for the Cu–W solid solutions with various compositions. One sees from Fig. 7 that after annealing at 300 K for 0.5 ns, the Cu85W15 and Cu30W70 solid solutions still remain in crystalline structures, while the Cu80W20, Cu50W50, and Cu35W65 solid solutions all become amorphous, indicating that 20 at.% of W and 65 at.% W are two critical compositions for C–A transitions in the Cu–W system. Interestingly, Rizzo et al. [27] have observed that the vapor-deposited Cu–W alloys containing 25–55 at.% of W became completely amorphous, which is very close to, and reasonably a little smaller than, the intrinsic GFR of 20–65 at.% W determined by the present MD simulations. Gaffet et al. [28] have found that using ball-milling technique, the Cu70W30, Cu60W40, Cu50W50, Cu 45W 55, and Cu 40W 60 alloys became amorphous, whereas the Cu95W5, Cu90W10, and Cu85W15 alloys retained ordered structures. Greta et al. [29] have reported that the magnetron-sputtered Cu50W50 and Cu66W34 were in the amorphous states. Obviously, these experimental observations are in good agreement with the present MD simulation results. In addition, Chen and Liu [30] have reported that the Cu84W16 multilayers upon annealing at around 350 8C for about 0.5 h kept in a fcc structure, which is also consistent with the present simulation results.
5. Concluding remarks (1) In IBM, intermixing and alloying between different metal layers are mainly induced by dynamic atomic collision, which is a process far from equilibrium. It has been shown that IBM is capable of producing metallic glasses in various binary metal systems, including those featuring positive heats of formation or even essentially immiscible in equilibrium. The GFR of a binary metal system determined by IBM can extend from the central portion almost to the edges of the two terminal solid solutions. (2) Predicting the GFA/range of a binary metal system is actually a scientific issue of determining its critical solid solubilities, which can be calculated directly from its interatomic potential through MD simulation. The GFR of the system is deduced to be within the composition range bounded by the two critical solid solubilities. It turns out that the calculated GFRs of some representative miscible
and immiscible systems are in good agreement with the experimental observations. (3) We have also shown that by combining the IBM and solid-state reaction experiments, thermodynamic calculation, MD simulation based on realistic n-body potentials, and, in some cases, first principles calculations, significant progress has been achieved to approach a better understanding of metastable phase formation and transformation in various binary metal systems. Acknowledgements The authors are grateful to many of B.X. Liu’s previous students for their valuable contributions while studying in Liu’s research group. Continuous financial support from the National Natural Science Foundation of China, the Ministry of Science and Technology of China (grant no. 20000672-07), and the Administration of Tsinghua University is also gratefully acknowledged. References [1] W.J. Klements, R.H. Willens, P. Duwez, Nature 187 (1960) 869. [2] B.X. Liu, W.L. Johnson, M.-A. Nicolet, et al., Appl. Phys. Lett. 42 (1983) 45. [3] Y.G. Chen, B.X. Liu, Appl. Phys. Lett. 68 (1996) 3096. [4] F.R. deBoer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesion in Metals: Transition Metal Alloys, North-Holland Physics Publishing, Amsterdam, The Netherlands, 1989. [5] Z.J. Zhang, O. Jin, B.X. Liu, Phys. Rev., B 51 (1995) 8076. [6] M. Meyer, V. Pontikis, Computer Simulation in Materials Science, Kluwer Academic Publishing, 1991. [7] Q. Zhang, W.S. Lai, B.X. Liu, Phys. Rev., B 59 (1999) 13521. [8] B.Y. Tsaur, S.S. Lau, J.W. Mayer, Appl. Phys. Lett. 36 (1980) 823. [9] B.X. Liu, W.S. Lai, Q. Zhang, Mater. Sci. Eng. R29 (2000) 1. [10] B.X. Liu, L.J. Huang, K. Tao, et al., Phys. Rev. Lett. 59 (1987) 745. [11] O. Jin, Z.J. Zhang, B.X. Liu, J. Appl. Phys. 78 (1995) 49. [12] O. Jin, Z.J. Zhang, B.X. Liu, Appl. Phys. Lett. 67 (1995) 1524. [13] Z.J. Zhang, H.Y. Bai, Q.L. Qiu, et al., J. Appl. Phys. 73 (1993) 1702. [14] J. Bbttiger, K. Dyrbye, K. Pampus, et al., Philos. Mag., A. 59 (1989) 569. [15] Z.J. Zhang, B.X. Liu, Phys. Rev., B 51 (1995) 16475. [16] B.X. Liu, in: Non-Equilibrium Processing of Materials Pergamon Materials Series, vol. 2, Elsevier, Amsterdam, 1999, p. 197. [17] S.J. Poon, W.L. Carter, Solid State Commun. 35 (1980) 249. [18] B.X. Liu, D.Z. Che, Z.J. Zhang, S.L. Lai, J.R. Ding, Phys. Stat. Solidi, A 128 (1991) 345. [19] C. Massobrio, V. Pontikis, G. Martin, Phys. Rev., B 41 (1990) 10486. [20] Z.J. Zhang, B.X. Liu, J. Appl. Phys. 76 (1994) 3351. [21] T. Fukunaga, W. Watanabe, K. Suzuki, J. Non-Cryst. Solids 61–62 (1984) 343. [22] B.M. Clemens, Phys. Rev., B 33 (1986) 7615. [23] J.B. Liu, Z.C. Li, B.X. Liu, Phys. Rev., B 63 (2001) 2204. [24] H.J. Lee, K.W. Kwon, C. Ryu, R. Sinclair, Acta Mater. 47 (1999) 3965.
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[28] E. Gaffet, C. Louison, M. Harmelin, et al., Mater. Sci. Eng. A134 (1991) 1380. [29] B. Grzˇeta, N. Radic´, D. Gracin, et al., J. Non-Cryst. Solids 170 (1994) 101. [30] Y.G. Chen, B.X. Liu, J. Phys., D, Appl. Phys. 30 (1997) 1729.
Thermodynamic and atomistic modeling of irradiation-induced amorphization in nanosized metal–metal multilayers B.X. Liu*, Z.C. Li, H.R. Gong Laboratory of Advanced Materials, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China Available online 28 September 2004
Abstract A brief summary is firstly presented concerning up-to-date experimental studies of the formation of amorphous alloys (metallic glasses) in binary metal systems by ion beam mixing of nanosized metal–metal multilayers. Secondly, under the framework of Miedema’s theory, thermodynamic modeling of crystal-to-amorphous transition is described with special consideration of the effect of the excess interfacial free energy on the alloy phase formation. Thirdly, in some representative systems, glass-forming ranges are calculated directly from their realistic interatomic potentials by determining the critical solid solubilities of the systems by molecular dynamics simulations. Finally, a comparison between irradiation and thermally induced amorphization in the metal–metal multilayers is also discussed. D 2004 Elsevier B.V. All rights reserved. Keywords: Amorphous; Multilayer; Atomistic modeling
1. Introduction Duwez (1960) obtained the first amorphous alloy (or metallic glass) in the Au–Si system by liquid melt quenching (LMQ) [1]. In the early 1980s, a powerful scheme [i.e., ion beam mixing (IBM)] was introduced to produce amorphous alloys as well as to study fundamental issues in the field of metallic glasses [2]. Because of its powerful capability, IBM has so far produced a great number of nonequilibrium alloys with either an amorphous or crystalline structure, not only in those glass-forming systems but also in some nonglass-forming systems, which were defined previously based on experimental results from LMQ. For example, IBM has produced a number of amorphous alloys in some equilibrium immiscible systems, in which LMQ is even unable to comelt the constituent metals [3]. It follows that some basic concepts and understanding concerning the metallic glasses should be further developed, e.g., the previously defined glassforming and nonglass-forming systems, glass-forming
* Corresponding author. Tel.: +86 10 6277 2557; fax: +86 10 6277 1160. E-mail address: [email protected] (B.X. Liu). 0257-8972/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2004.08.074
ability (GFA), or glass-forming range (GFR) of the binary metal systems, etc. In the mid 1970s, Miedema developed a semiquantitative theory, based on which one is able to calculate the thermodynamic properties of metals and alloys based on some intrinsic properties of the elements. Employing the theory, the Gibbs free energy diagram of a system can be constructed, and it includes the calculated free energy curves of all the involved alloy phases as a function of alloy composition. It turned out that the constructed free energy diagram could give relevant thermodynamic insights of alloy phase formation and transformation [4]. Since the late 1980s, Miedema’s theory has also been employed to develop a thermodynamic model for the metastable alloy phase formation [5]. In the past decades, significant progress has been achieved in computational materials science [6]. Computation and/or simulation makes it possible to approach a quantitative understanding of the alloy phase formation and transformation at an atomic scale or even into a depth of the electronic structures of the solids. Very recently, it has been initiated to study the possibility of determining the GFA of a binary metal system directly from a realistic n-body potential of the system through molecular dynamics (MD) simulation [7].
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This article attempts to present a brief summary of the recent progress concerning the understanding of irradiationinduced amorphization and calculation of GFA directly from interatomic potential. The discussion in this article will be concentrating on binary metal systems, of which fruitful experimental and thermodynamic data have so far been accumulated.
2. Metastable alloy phase formation by IBM In IBM, the multilayers consist of alternately deposited metals A and B on an inert supporting substrate. By adjusting the relative thicknesses of the two metals, an A–B alloy can be obtained with any desired composition. An energetic ion beam is used to trigger atomic collisions for inducing intermixing between the metal layers of A and B. After irradiation to an adequate dose, a uniform mixture of metals A and B can be achieved and an A–B alloy is thus obtained. At the beginning, IBM was employed mainly to study the possibility of synthesizing various metal silicides, which are known as candidate materials, to be applied in electronic devices [8]. A little later, IBM was also employed to study metastable alloy phase formation and transformation in binary metal systems [2]. Up to now, a great number of amorphous and metastable crystalline (MX) alloys have been obtained in some 100 systems [9]. Among the obtained metastable alloys, many have not been formed or are even not obtainable by other nonequilibrium techniques like LMQ, etc. Moreover, the progress in IBM experimental studies has also stimulated theoretical works to approach a better understanding of GFA/GFR of the binary metal systems.
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terminal solid solutions, but not in the central portion of the equilibrium phase diagram [12]. Such compositional dependence is sharply different from that observed in the systems with negative DH f, in which the alloy composition near the equiatomic stoichiometry is usually the most favored for amorphization because the free energy of the amorphous phase reaches its minimum [13]. Concerning the GFR of a system, the present author has proposed to define a parameter, namely MPAR, which is an abbreviation of maximum possible amorphization range, for predicting the GFR or GFA of the system. The MPAR is defined to be 100%, the total composition range minus the two maximum solid solubilities observed from the corresponding equilibrium phase diagram. Combining the effect of DH f on amorphization, Fig. 1 is a proposed map using MPAR and DH f to classify the systems into possibly, readily, and hardly glass-forming ones in terms of their GFR and GFA upon IBM. It will be shown later that the prediction of GFR or GFA based on the MPAR DH f model agrees well with the experimental results and that, by considering the excess interfacial free energy stored in the metal–metal multilayers, a unified thermodynamic model is developed for metallic glass formation by IBM in the systems with either negative or positive DH f.. 3.1. GFA of the negative heat of formation systems
3. Thermodynamic modeling of metallic glass formation
According to the MPAR DH f model, one is able to predict approximately the GFR of a system by inspecting its equilibrium phase diagram. Take the Ni–Nb system as an example; its DH f = 45 kJ/mol [4] and Fig. 2a exhibits its equilibrium phase diagram. In the diagram, the whole alloy composition can be divided into three types (i.e., terminal solid solution, intermetallic compound, and two-phase region). An amorphous alloy is readily formed by IBM in the two-phase regions and its formation can be attributed to
If a system is of negative DH f, which causes the amorphous state to have a lower free energy than that of the initial energetic state of the multilayers, the negative DH f itself serves as a driving force for amorphization. On the contrary, if a system has a large positive DH f, the two constituent metals cannot even mix together to form an alloy in melt. The system is therefore essentially equilibriumimmiscible and has been considered to be difficult to use to obtain metallic glasses by IBM [8]. Since the late 1980s, however, there have been experimental studies showing the possibility of forming metallic glasses in systems featuring large positive DH f [10]. In fact, in the mid-1990s, IBM produced a number of amorphous as well as MX alloys in many systems with positive DH f ranging from nearly 0 to +56 kJ/mol [11,12]. These results suggest that the DH f of a system is not a decisive parameter in determining whether the metallic glass can be formed or not. Interestingly, in systems with positive DH f, metallic glasses were frequently formed in the restricted composition regions close to the
Fig. 1. According to the two defined parameters, MPAR and heat of formation, the binary metal systems are classified into three categories: readily, possibly, and hardly glass-forming systems (RGF, PGF, and HGF, respectively).
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energy curve reaches the nadir and is lower than those of two terminal solid solutions. The GFR was commonly regarded as the composition range in which the free energy of the amorphous phase is lower than that of the solid solution. Consequently, the GFR of the Ni–Nb system is from 15 to 80 at.% of Nb, which is a little narrower than the MPAR. Incidentally, Zhang et al. [13] have determined by IBM experiments that the GFR was very close to 15–80 at.% of Nb, which is in excellent agreement with that deduced from the above thermodynamic calculation. It is worth mentioning that there have been many IBM results showing the readiness of metallic glass formation in such systems featuring a negative DH f (e.g., in the Ni–Zr system, the GFR is 10–90 at.% of Zr, which matches well the experimentally determined GFR around 10–80 at.% of Zr by IBM) [14]. 3.2. GFA of the positive heat of formation systems
Fig. 2. (a) The equilibrium phase diagram of the Ni–Nb system and (b) calculated Gibbs free energy diagram of the Ni–Nb system.
the competition of the crystallization between the two metals, resulting in the frustration of nucleation and growth of either crystalline metal during the extremely short relaxation period in IBM. Moreover, it has also been demonstrated that IBM could produce metallic glasses with alloy compositions located at the intermetallic compounds frequently with complicated structures, which are not allowed to grow during relaxation period in IBM. Consequently, the two-phase regions are connected to each other and are united to be a continuous composition range favoring amorphization, which is actually the total width of the two-phase regions. One sees from Fig. 2a that the MPAR of the Ni–Nb system is from 5 to 95 at.% of Nb [4]. A free energy diagram of the Ni–Nb system is accordingly calculated and shown in Fig. 2b. One sees that the free energy curves of the amorphous phase, the two terminal solid solutions and the intermetallic compounds, are all concave. As the formation of intermetallic compounds is usually hindered kinetically, they need not be considered while discussing the GFR, although they have even lower free energy than all the metastable alloy phases. By comparing the free energy of the amorphous phase with those of the crystalline phases, it is possible to predict GFR. Obviously, the formation of the amorphous phase is most favored near the equiatomic stoichiometry, where its free
For a system with a positive DH f, the free energy curve of the amorphous phase is usually higher than that of a mechanical mixture of crystalline metals A and B in the alternatively deposited multilayers, suggesting a situation not favored for metallic glass formation. However, as the interfaces in the multilayers are generally regarded as transient layers of mixed A and B atoms in a highly disordered configuration, the extra interfacial free energy plays an important role in enhancing the alloying ability of the multilayered films. If an adequate fraction of interfacial atoms is included in the multilayers, the free energy curve of the films can be elevated to intersect with that of the amorphous phase, leading to a situation favoring the formation of metallic glasses in the specific composition regions. 3.2.1. Metallic glasses formed within restricted composition ranges Take the Ag–Mo system (DH f =+56 kJ/mol) as an example; the free energy curves of the amorphous phase and multilayered films designed to contain 12 layers are calculated. Fig. 3 shows the constructed Gibbs free energy diagram of the Ag–Mo system. One sees that the free energy curve of the multilayered films intersects with that of the amorphous phase and the whole composition range is thus divided into three different regions. Obviously, in the I and III regions, amorphous phase is possible to form, as its free energy is lower than that of the initial state of the films. While in the II region, formation of metallic glass is hard to achieve because the amorphous phase still has a higher free energy than the films. IBM experiments were accordingly conducted and an amorphous alloy was indeed formed with alloy composition near 80 at.% of Mo. Moreover, another amorphous phase was also formed together with an Mobased MX phase in the Ag–Mo multilayered films with an alloy composition of around 40 at.% of Mo [12]. Such compositional discontinuity in metallic glass formation is
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closely related to the positive DH f of the system and has also be observed in the Nb–Zr [11] and Y–Ta [15] systems, which feature positive DH f of +6 and +40 kJ/mol, respectively. 3.2.2. Metallic glasses formed in broad composition range As shown above, the width and exact location of the alloy composition regions favoring amorphization depend on the designed fraction of interfacial atoms in the multilayered films. One may then ask if further increasing the fraction of interfacial atoms can broaden the two separated composition regions favoring amorphization and have them meet each other to unite into a continuous range. Take the Y–Mo system with a DH f =+35 kJ/mol as an example; Fig. 4 shows its calculated free energy diagram, which includes the free energy curves of the amorphous phase and three Y–Mo multilayered films consisting of 9, 11, and 19 layers, respectively, with a fixed total thickness of 45 nm, corresponding to the fractions of interfacial atoms of 8.1, 10.0, and 18.1 at.%, respectively [5]. Apparently, through properly designing the multilayered films, it is possible to form metallic glasses in the Y–Mo system even with an alloy composition near the equiatomic stoichiometry. In other words, for the positive DH f systems, the GFR could also be extended to a broad composition range close to the defined MPAR, provided the multilayered films were properly designed to possess sufficient interfacial free energy. 3.3. Nominal and intrinsic GFA From both practical and theoretical points of view, prediction of GFA/GFR of a binary metal system is of vital importance. First, the GFA of a system should reflect qualitatively whether or not the metallic glass can be formed. From a physical point of view, there should exist an intrinsic GFA reflecting the capability of the system itself. Second, it is also of necessity to have a quantitative measure for GFA that is able to compare the capabilities
Fig. 4. Calculated Gibbs free energy diagram of the Y–Mo system. N stands for the number of layers in the Y–Mo multilayered films.
among the systems. An experimentally determined GFR can be taken as a quantitative measure for GFA, and, naturally, the larger the GFR, the greater the GFA. If one employs LMQ technique with a greater cooling speed, one may obtain glasses in a broader composition range than that observed by a technique with a slower cooling speed. In this sense, an experimentally determined GFR can only be considered as a nominal GFA [16]. Obviously, the greater the GFR observed by a specific technique, the closer the GFR to the intrinsic GFA. In other words, to approach an intrinsic GFA of a system, one should look for a powerful glass-producing technique and, at present, IBM may be the very technique capable of revealing the maximum GFA among the currently available glass-producing techniques. Based on IBM studies for the systems with either a negative or positive DH f, the defined MPAR is a good approximation for predicting the composition range for metallic glass formation since IBM can frequently form some supersaturated solid solutions, which would actually reduce the total width of the two-phase regions, namely to reduce the width of the defined MPAR. Consequently, if one is able to determine the supersaturated solid solubilities of a specific system, the intrinsic GFA or GFR of the system can then be predicted to be 100% as the whole composition range minus the two supersaturated solid solubilities, which could be considered as a modified MPAR.
4. Calculation of GFA from interatomic potential
Fig. 3. Calculated Gibbs free energy diagram of the Ag–Mo system.
An important and fundamental issue in the field of metallic glasses is to develop a theoretical model, which is able to predict the GFA of a binary metal system [17,18]. As described above, according to IBM exper-
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solid solubilities is therefore the GFR of the system, in which the amorphous state was energetically more stable than solid solution. Such a GFR is a property intrinsic to the system itself and not connected with any specific glass-producing technique. 4.1. Calculation of GFA for some miscible Ni-based systems
Fig. 5. Total and partial pair correlation functions for the fcc Ni-rich solid solution after running MD simulation at 300 K for 10,000 MD time steps. The compositions are at (a) 10 at.%, (b) 17 at.%, (c) 21 at.%, and (d) 25 at.% of Mo, respectively. The solid line is for total g(r), the short dashed line is for Mo–Ni g(r), the dotted line is for Ni–Ni g(r), and the dot-dashed line is for Mo–Mo g(r), respectively.
imental results, the issue becomes an objective of calculating the supersaturated solid solubilities of a binary metal system. From an energetic point of view, for a specific system, the GFA is determined by the relative stability of the solid solutions compared with their amorphous counterparts. Moreover, the relative stability of the solid solution versus the amorphous phase is intrinsically determined by their corresponding atomic configurations, which are directly governed by the interatomic potential of the system. We will show in the following paragraph that MD simulation with a realistic interatomic potential of a system is capable of determining the supersaturated solid solubilities. Consequently, the central region bounded by the two determined critical
We now present the calculation results for the miscible Ni–Mo, Ni–Ti, Ni–Zr, and Ni–Ta systems with negative heats of formation. In MD simulations, the solid solution models were used. For the Ni–Mo system, the compositions of the fcc Ni-rich (bcc Mo-rich) solid solutions were selected to be in the range of 0–50 at.% of Mo (0–50 at.% of Ni). Each solid solution with a designed solute concentration was obtained by randomly substituting a corresponding amount of Ni (Mo) by Mo (Ni) in the Ni fcc (Mo bcc) lattice. The models were then simulated at 300 K for adequate time steps to reach a relatively equilibrium state. Fig. 5 displays the calculated total and partial pair correlation function g(r) for the Ni-rich fcc solid solutions with the solute concentrations of 10, 17, 21, and 25 at.% of Mo, respectively. One sees that the solid solutions with 10 and 17 at.% of Mo remain crystalline structures and that, with increasing solute concentration, the peaks of g(r) became broadened, implying that the crystals become progressively disordered. Obviously, a crystal-to-amorphous (C–A) transition took place in the solid solution with 25 at.% Mo, while for the solid solution with 21 at.% of Mo, the shape of the calculated g(r) was ambiguous, implying that the C–A transition has taken place but not yet completed. Similarly, on the Mo end, x Ni=25 at.% was determined to be the critical value for C–A transition. Consequently, the GFR of the Ni–Mo system is deduced to be within 21–75 at.% of Mo. Meanwhile, for the Ni–Ti system, the GFR was determined to be within 38–85 at.% of Ti. For the Ni–Zr and Ni–Ta systems, their critical compositions for C–A transitions were also determined based on a tight-binding Ni–Zr potential derived by Massobrio et al. [19] and a Ni–Ta potential developed by the authors, respectively. For the above four systems, the critical solid solubilities determined directly from their respective potentials through MD simulations are summarized in Table 1. It is of interest to note that the GFRs of the systems determined by MD simulations are supported by experimental observations. For the Ni–Mo system, amorphization in the Ni–Mo multilayers has been observed upon
Table 1 Calculated critical compositions of the solid solutions, beyond which solidstate amorphization can take place, in some Ni-based systems Ni as solvent matrix Ni as alloying solute
Ti (at.%)
Zr (at.%)
Mo (at.%)
Ta (at.%)
38 15
14 25
21 25
21 43
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Fig. 6. Partial and total pair correlation functions of the Cu-based solid solution after annealing at 300 K. The Ta solute concentrations are at (a) 5 at.%, (b) 15 at.%, (c) 25 at.%, and (d) 30 at.% in Cu. The solid line is for total g(r), the dashed line is for Cu–Cu partial g(r), the dotted line is for Ta–Ta partial g(r), and the dash-dotted line is for Cu–Ta partial g(r).
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principles calculation was employed to acquire some physical properties of the possible nonequilibrium alloy phases of the systems, based on the well-established Vienna ab initio simulation package (VASP) [23]. We have successfully derived the embedded atom (EAM) potentials for the Cu–Ta and Cu–W systems. Applying the constructed Cu–Ta potential, MD simulations were conducted using Cu-based fcc solid solution models. It was found that 30 at.% of Ta in Cu solid solution was a critical concentration for C–A transition to take place. The total and partial pair correlation functions g(r) of the Cu–Ta solid solution after annealing at 300 K for 0.75 ns at various Ta solute concentrations of 5, 15, 25, and 30 at.%, respectively, are shown in Fig. 6. It can be seen that the solid solution with 30 at.% of Ta has become amorphous, while the solid solutions with 5, 10, and 25 at.% of Ta all retain crystalline structures. It is of interest to compare the simulation results with some experimental observations in the Cu–Ta system. For instance, Lee et al. [24] observed the formation of an amorphous layer 2 nm thick in the Cu61Ta39 multilayered films upon annealing at 500 8C. Nastasi et al. [25] obtained the Cu55Ta45 and Cu50Ta50 amorphous alloys by ion irradiation. These amorphous alloys were all formed in the composition range exceeding the critical value of 30 at.% of Ta determined by MD simulation. Besides, Kim et al. [26] found that the sputter-deposited Cu–Ta
solid-state reaction and the favored composition range was found to be 25–75 at.% Mo [20], which is very close to the intrinsic GFR determined by MD simulation. For the Ni–Ti system, the GFR of the system determined by LMQ data was in a composition range of 30–40 at.% of Ni [21], which is apparently within the intrinsic one revealed by MD simulation. IBM experiments were performed for the Ni–Ti multilayered samples. It was found that the Ni-based solid solutions were obtained up to a composition of 37 at.% of Ti, beyond which a unique amorphous phase was formed. Apparently, the IBM experimental results are in good agreement with those revealed by MD simulation. For the Ni–Zr system, the calculated GFR is 14–75 at.% of Zr, which is compatible with 45–70 at.% of Zr determined by solidstate reaction experiments [22]. 4.2. Calculation of GFA for some immiscible Cu-based systems We now present the calculation results for some immiscible Cu-based systems with positive heats of formation. To perform MD simulation, it is necessary to derive n-body potentials for the systems and, for the immiscible systems, it is a challenging task to derive the cross potentials as there is no any equilibrium alloy phase that could provide the necessary data required for deriving the potentials. To overcome such a difficulty, the first
Fig. 7. Partial and total pair correlation functions of (a) Cu85W15, (b) Cu80W20, (c) Cu50W50, (d) Cu35W65, and (e) Cu30W70 solid solutions after annealing at 300 K for 0.5 ns, respectively. The solid line is for the total g(r), the dashed line is for Cu–Cu partial g(r), the dotted line is for W–W partial g(r), and the dash-dotted line is for Cu–W partial g(r).
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alloys containing 44–91 at.% of Ta became completely amorphous and that when the alloy concentration was 21 at.% of Ta, with the Cu–Ta alloy consisting of an fcc solid solution and some remaining crystalline Ta. These observations are also in agreement with the present simulation results. Similarly, for the Cu–W system, the intrinsic GFA/GFR was determined to be within 20–65 at.% of W. Fig. 7 shows the calculated pair correlation functions for the Cu–W solid solutions with various compositions. One sees from Fig. 7 that after annealing at 300 K for 0.5 ns, the Cu85W15 and Cu30W70 solid solutions still remain in crystalline structures, while the Cu80W20, Cu50W50, and Cu35W65 solid solutions all become amorphous, indicating that 20 at.% of W and 65 at.% W are two critical compositions for C–A transitions in the Cu–W system. Interestingly, Rizzo et al. [27] have observed that the vapor-deposited Cu–W alloys containing 25–55 at.% of W became completely amorphous, which is very close to, and reasonably a little smaller than, the intrinsic GFR of 20–65 at.% W determined by the present MD simulations. Gaffet et al. [28] have found that using ball-milling technique, the Cu70W30, Cu60W40, Cu50W50, Cu 45W 55, and Cu 40W 60 alloys became amorphous, whereas the Cu95W5, Cu90W10, and Cu85W15 alloys retained ordered structures. Greta et al. [29] have reported that the magnetron-sputtered Cu50W50 and Cu66W34 were in the amorphous states. Obviously, these experimental observations are in good agreement with the present MD simulation results. In addition, Chen and Liu [30] have reported that the Cu84W16 multilayers upon annealing at around 350 8C for about 0.5 h kept in a fcc structure, which is also consistent with the present simulation results.
5. Concluding remarks (1) In IBM, intermixing and alloying between different metal layers are mainly induced by dynamic atomic collision, which is a process far from equilibrium. It has been shown that IBM is capable of producing metallic glasses in various binary metal systems, including those featuring positive heats of formation or even essentially immiscible in equilibrium. The GFR of a binary metal system determined by IBM can extend from the central portion almost to the edges of the two terminal solid solutions. (2) Predicting the GFA/range of a binary metal system is actually a scientific issue of determining its critical solid solubilities, which can be calculated directly from its interatomic potential through MD simulation. The GFR of the system is deduced to be within the composition range bounded by the two critical solid solubilities. It turns out that the calculated GFRs of some representative miscible
and immiscible systems are in good agreement with the experimental observations. (3) We have also shown that by combining the IBM and solid-state reaction experiments, thermodynamic calculation, MD simulation based on realistic n-body potentials, and, in some cases, first principles calculations, significant progress has been achieved to approach a better understanding of metastable phase formation and transformation in various binary metal systems. Acknowledgements The authors are grateful to many of B.X. Liu’s previous students for their valuable contributions while studying in Liu’s research group. Continuous financial support from the National Natural Science Foundation of China, the Ministry of Science and Technology of China (grant no. 20000672-07), and the Administration of Tsinghua University is also gratefully acknowledged. References [1] W.J. Klements, R.H. Willens, P. Duwez, Nature 187 (1960) 869. [2] B.X. Liu, W.L. Johnson, M.-A. Nicolet, et al., Appl. Phys. Lett. 42 (1983) 45. [3] Y.G. Chen, B.X. Liu, Appl. Phys. Lett. 68 (1996) 3096. [4] F.R. deBoer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesion in Metals: Transition Metal Alloys, North-Holland Physics Publishing, Amsterdam, The Netherlands, 1989. [5] Z.J. Zhang, O. Jin, B.X. Liu, Phys. Rev., B 51 (1995) 8076. [6] M. Meyer, V. Pontikis, Computer Simulation in Materials Science, Kluwer Academic Publishing, 1991. [7] Q. Zhang, W.S. Lai, B.X. Liu, Phys. Rev., B 59 (1999) 13521. [8] B.Y. Tsaur, S.S. Lau, J.W. Mayer, Appl. Phys. Lett. 36 (1980) 823. [9] B.X. Liu, W.S. Lai, Q. Zhang, Mater. Sci. Eng. R29 (2000) 1. [10] B.X. Liu, L.J. Huang, K. Tao, et al., Phys. Rev. Lett. 59 (1987) 745. [11] O. Jin, Z.J. Zhang, B.X. Liu, J. Appl. Phys. 78 (1995) 49. [12] O. Jin, Z.J. Zhang, B.X. Liu, Appl. Phys. Lett. 67 (1995) 1524. [13] Z.J. Zhang, H.Y. Bai, Q.L. Qiu, et al., J. Appl. Phys. 73 (1993) 1702. [14] J. Bbttiger, K. Dyrbye, K. Pampus, et al., Philos. Mag., A. 59 (1989) 569. [15] Z.J. Zhang, B.X. Liu, Phys. Rev., B 51 (1995) 16475. [16] B.X. Liu, in: Non-Equilibrium Processing of Materials Pergamon Materials Series, vol. 2, Elsevier, Amsterdam, 1999, p. 197. [17] S.J. Poon, W.L. Carter, Solid State Commun. 35 (1980) 249. [18] B.X. Liu, D.Z. Che, Z.J. Zhang, S.L. Lai, J.R. Ding, Phys. Stat. Solidi, A 128 (1991) 345. [19] C. Massobrio, V. Pontikis, G. Martin, Phys. Rev., B 41 (1990) 10486. [20] Z.J. Zhang, B.X. Liu, J. Appl. Phys. 76 (1994) 3351. [21] T. Fukunaga, W. Watanabe, K. Suzuki, J. Non-Cryst. Solids 61–62 (1984) 343. [22] B.M. Clemens, Phys. Rev., B 33 (1986) 7615. [23] J.B. Liu, Z.C. Li, B.X. Liu, Phys. Rev., B 63 (2001) 2204. [24] H.J. Lee, K.W. Kwon, C. Ryu, R. Sinclair, Acta Mater. 47 (1999) 3965.
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[28] E. Gaffet, C. Louison, M. Harmelin, et al., Mater. Sci. Eng. A134 (1991) 1380. [29] B. Grzˇeta, N. Radic´, D. Gracin, et al., J. Non-Cryst. Solids 170 (1994) 101. [30] Y.G. Chen, B.X. Liu, J. Phys., D, Appl. Phys. 30 (1997) 1729.