Monatomic model of icosahedrally ordered metallic glass formers

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Journal of Non-Crystalhne Sohds 156-158 (1993) 173-176 North-Holland

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Monatomic model of icosahedrally ordered metallic glass formers Mikhail Dzugutov Department of Neutron and Reactor Phystcs, lnstttute of Physws, Royal Instttute of Technology, S-IO0 44 Stockholm, Sweden

Many recent results indicate that the stabdlty of metalhc glass-formmg systems with respect to crystalhne nucleanon depends cruoally on a distractive lcosahedral local order Real systems are either strongly bonded or composed of more than one sort of atom The molecular dynamics s~mulanon presented in this report demonstrates that a properly tailored pair potential can reduce an lcosahedral inherent local order m a simple hquld composed of identical particles. The remarkable structural stabihty of th~s model was tested in a long slmulanon run carried out m the temperature domain where the hqmd shows clear signatures of supercooled dynamics

I. Introduction

The ability of the glass-forming liquids to freeze into a solid glassy phase when being supercooled at a finite cooling rate implies pronounced stability with respect to crystalline nucleation. In polymer and strongly bonded inorganic glass-forming systems, this phenomenon can be accounted for by the complexity of their configurational space which delays the relaxation processes leading to the structural transition well beyond the experimentally accessible timescale. This argument is apparently inapplicable to the simple atomic glass-formers; among these, metallic alloys are of special interest because of the potential technological applications. A large volume of recent results indicates that their stability depends crucially on a distinctive icosahedral local order, which is a generic characteristic of these systems in both the liquid and the glassy states [1,2]. This point has been supported by the remarkable discovery by Shechtman et al. [3] of icosahedral diffraction pattern in some alloys.

Correspondence to" Dr M. Dzugutov, Department of Neutron and Reactor Physics, Insntute of Physics, Royal Institute of Technology, S-100 44 Stockholm, Sweden. Tel +46-8 790 6395 Telefax +46-8 106 948. E-mad [email protected] se

It is convenient to discuss the stability In a supercooled liquid of simple constitution in terms of the topology of its inherent structure [4]. The latter is defined by the mechanically stable configurations which correspond to the minima of the potential energy hypersurface [5]. It was found [6-8] that the inherent structures of simple liquids closely resemble the patterns into which the liquids freeze, which explains why the liquids with the lattice-related inherent structures are unstable under supercooling. This observation accounts for the singular glass-forming ability of icosahedrally ordered liquids where the inherent structure is topologically different from the lattice-type configurations. The understanding of the microscopic mechanisms leading to the formation of the icosahedral phase is still a formidable challenge. In multicomponent glass-forming alloys, these involve both topological ordering and chemical short-range ordering (CSRO). A question of fundamental interest is whether a stable phase with an icosahedral local order can be formed by a simple system composed of identical particles. The molecular dynamics (MD) simulation results presented here show that the structure in question can be induced in a simple monatomic liquid by a properly constructed pair potential. The liquid remains stable in the supercooled domain where its icosahedral inherent structure becomes more pronounced.

0022-3093/93/$06 00 © 1993 - Elsevmr Science Publishers B V All rights reserved

M Dzugutov / Icosahedrally ordered metalhc glassformers

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Fig. 1. Pair potential given by eq. (1) ( ), the LennardJones potential, added with a constant ( . . . . . . ).

2. Pair potential The pair potential (fig. 1) has been constructed using the following form:

V( r) = Vl -{- V2( r), Vt(r ) = A ( r - ' - B ) e x p ( c / ( r - a ) ) , Vl(r) = 0, r>a, V2(r) =B e x p ( d / ( r - b ) ) , V2(r) = 0, r>b.

particles. In a simulation of a supercooled liquid, the highly collective structural relaxation processes, including those leading to the formation of a critical size crystalline nucleus, might interfere with the boundary conditions imposed. This makes the large size of the system a prerequisite for adequate simulation. It also enables the exploration of the long-wavelength domain where the structural evolution under supercooling is of particular interest. The system was cooled at constant density p = 0.88 in an equilibrium stepwise way, in the interval of reduced temperatures between 1.6 and 0.5. At every step, an equilibration run was carried out after reducing the temperature. At the last stage of cooling, the run took over a million timesteps. In order to monitor the structural evolution, the inherent structure was calculated at every step of cooling, using the steepest descent minimization [5-8].

4. Results

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The short-range repulsive part approximates to that of the Lennard-Jones (LJ) potential; therefore LJ reduced units are used in this simulation. A crucial detail of this potential is the maximum at distances between the first and second shells of neighbours in the icosahedral polytope [9]. A wide gap between the first and the second shells of neighbours is a distinctive feature of icosahedral order when compared with the alternative crystallographic configurations. Thus, the pair potential described here is expected to stabilize icosahedral order over crystallographic order.

According to mode-coupling theory [10], a liquid subject to equilibrium supercooling experiences a transition from normal liquid behaviour to the supercooled dynamics regime, where the density correlation function acquires a non-ex-

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In order to investigate the influence of the form of the pair potential on the liquid structure and its stability in the supercooled domain, a MD simulation was carried out for a model with 16 384

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M Dzugutov/ lcosahedrallyorderedmetalhcglassformers ponential component with diverging relaxation time. Figure 2 demonstrates that at T = 0.5 the dynamics of the simulated system show pronounced signatures of the supercooled regime. The fact that the system remained thermodynamically stable at that state indicates that it can be regarded as a generic simple monatomic glassformer (detailed analysis of the dynamical properties was reported elsewhere [11]). We now look at the inherent local order and the way it evolves with supercooling. The pair correlation functions and the corresponding structure factors describing the inherent structures at two temperatures, T = 1.6 and T = 0.5, are presented in figs. 3 and 4. The first observation is that the t e m p e r a t u r e variation of the inherent structure is very small, except for the long-wavelength region. Apparently, the transition to the supercooled regime is a purely dynamical p h e n o m e n o n which is not accompanied by a transformation of the local order.

5.

Discussion

Both of the inherent structures presented show clear signatures of the icosahedral ordering characteristic of metallic glasses. The most significant one is the deep split in the second peak of S(Q) which becomes more pronounced with supercool-

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Fig. 4. Inherent structure factors. - . . . . . , T = 1.6, - T = 0.5. The small-Q area Is presented m the mset ing. The two structure factors are remarkably similar to that calculated within the framework of the statistical mechanical theory of icosahedral short-range order in a simple liquid [12,13]. A particular result of that study was that if the positions of the first three peaks of S(Q) are denoted by Q1, Q2 and Q3, then Q2/QI = 1.71 and Q3/QI = 2.04. H e r e the corresponding ratios are Q2/Q1 = 1.69 and Q3/Ql = 2.01, for T = 1.6, and Qz/Q1 = 1.69 and Q3/Q1 = 2, for T = 0.5. A novel structural feature displayed by the simulated liquid is an anomalous long-wavelength maximum of S(Q). This detail, which is enhanced by cooling, may be interpreted as an indication of the tendency for icosahedral clustering. In order to see in more detail the spatial arrangement of the local neighbours the first peak of g(r), which is well defined here, was decomposed according to the routine introduced by Swope and Andersen [14] and Honeycutt and Andersen [15]. A pair of bonded neighbours (the bond length was chosen to be 1.5) were classified according to the pattern formed by their common neighbours. If the latter could be connected by bonds in a closed ring, the bond was characterized by the number of atoms in the ring; otherwise, it was regarded as open. The fivefold bonds are of most interest since their statistics is a measure of icosahedral order. In fig. 5, a distribution of the bondlengths for four relevant types of bond for both the temperatures discussed is pre-

M Dzugutov / Icosahedrally ordered metalhc glass formers

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sented. It is obvious that the closed bonds are predominantly fivefold ones. The latter are strongly localized at short distances; this explains the anomalously small value of the first minimum of g(r) in fig. 3 which is mostly composed by the open and fourfold bonds. The number of fivefold bonds increases under supercooling at the expense of other types, which results in more pronounced icosahedral order. This leads to a less compressible structure, which is indicated by a sizable reduction of S(Q) in the small Q region.

6. Conclusion

The results demonstrate that the simulated liquid is a pronounced glass-former possessing icosahedral inherent local order. It can be regarded as a monatomic prototype of multicomponent metallic glass-forming alloys. The relevance becomes apparent if one compares this simulation with that for the Mgv0Zn30 [16], a simple glass-former composed of atoms of very similar size. Both its inherent structure and the interionic potentials are very similar to those presented here. This suggests that the icosahedral order and the glass-forming ability of that alloy result from the topological ordering induced by the general form of interionic interaction. The model presented here provides an opportunity for analyzing

the role of CSRO effects in the formation of metallic glasses. This study was supported by the Swedish Natural Science Research Council.

References [1] J. Hafner, From Hamlltonlans to Phase Diagrams (Springer, Berlin, 1987) [2] M Widom, in. Introduction to Quaslcrystals, ed. M Jarlc (Academic Press, New York, 1988) p 32. [3] D. Schechtman, I. Blech, D Gratias and J W Cahn, Phys. Rev Lett 53 (1984) 1951 [4] C A Angell, J. Phys. Chem. Solids 49 (1988) 863. [5] F. Stllhnger and T. Weber, Science 225 (1984) 983. [6] F Stllhnger and T Weber, Phys Rev. A25 (1982) 978. [7] F. Stllhnger and R. LaViolette, J. Chem. Phys 83 (1985) 6413 [8] T Weber and F Stllhnger, J. Chem Phys. 81 (1984) 5089 [9] J.F Sadoc and R. Moserl, in. Extended Icosahedral Structures, ed M. Jarlc and D Gratias (Academic Press, New York, 1987) p. 163. [10] U Bengtzelius, W. Gotze and A Sjolander, J Plays C17 (1984) 5915. [11] M. Dzugutov and U Dahlborg, J Non-Cryst Solids 131-133 (1991) 62. [12] D Nelson, Phys Rev B28 (1983) 5515 [13] S Sachdev and D. Nelson, Phys. Rev. B32 (1985) 1480 [14] W Swope and H. Andersen, Phys Rev. B41 (1990) 7042. [15] J.D Honeycutt and H Andersen, J Plays Chem 91 (1987) 4950. [16] J Hafner and S.S Jaswal, Phllos Mag. 58 (1988) 61