Melting behavior of heterogenous atomic clusters: Gapless coexisting phases in(Ar–Xe) 13Vishal Mehra, Awadhesh Prasad, and Ramakrishna Ramaswamy Citation: The Journal of Chemical Physics 110, 501 (1999); doi: 10.1063/1.478110 View online: http://dx.doi.org/10.1063/1.478110 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/110/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Structural motifs and stability of small argon–nitrogen clusters J. Chem. Phys. 119, 9021 (2003); 10.1063/1.1614751 Phase diagram of argon clusters J. Chem. Phys. 108, 5826 (1998); 10.1063/1.475993 Structural transitions in metal ion-doped noble gas clusters: Experiments and molecular dynamics simulations J. Chem. Phys. 108, 4450 (1998); 10.1063/1.475856 Melting and evaporation of argon clusters J. Chem. Phys. 106, 1888 (1997); 10.1063/1.473327 Structure, dynamics, and thermodynamics of benzene-Ar n clusters (1n8 and n=19) J. Chem. Phys. 106, 1530 (1997); 10.1063/1.473301

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Melting behavior of heterogenous atomic clusters: Gapless coexistingphases in „Ar–Xe …13

Vishal Mehra,a) Awadhesh Prasad, and Ramakrishna RamaswamySchool of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India

~Received 24 February 1997; accepted 24 September 1998!

We study the structural and dynamical aspects of 13–atom binary rare-gas clusters of Ar and Xeusing constant–energy molecular dynamics simulations. The ground state geometry for ArnXe132n ,n51212, remains near-icosahedral, with an Ar atom occupying the central position. Thethermodynamic properties of these clusters are significantly different from the pure 13-atom Ar orXe clusters and for Xe–dominated compositions, melting is preceded by a surface–melting stage.Slow oscillations of the short-time-averaged~STA! temperature are observed both for surface–melting and complete melting stage, suggesting dynamical coexistence between different phases. Atthe complete melting stage, the oscillations in the STA temperature and the species of the centralatom are correlated. ©1999 American Institute of Physics.@S0021-9606~99!01201-5#

I. INTRODUCTION

Phase–change behavior in small clusters has been exten-sively studied in the past few years as the finite system ana-logue of bulk phase transitions.1–13 Phase transitions in bulkmaterial differ from phase changes in finite systems in sev-eral important ways. In finite systems, there can be phenom-ena which do not have a parallel in the bulk. One of the mostremarkable among these is phase coexistence,2 and studieshave shown that melting and freezing in a finite cluster occurat different temperatures, between which the system can bepartially solid and partially melted.3 Phase coexistence is dy-namical as well, so that a given system can fluctuate betweenphases. Coexistence requires that the fluctuation between thephases to be much slower than the dynamics within the re-gion of the potential energy surface~PES! which corre-sponds to a given phase. Existence of such time scale sepa-ration makes it possible to define separate order parametersfor the coexisting phases.

Another main effect of finite system size is that the dis-continuities in characteristic quantities~the specific heat, forexample! which occur at bulk phase transitions get softened.Furthermore, there is a strong size and statistical ensembledependence of cluster properties.

These aspects of phase changes or phase transition–likebehavior in cluster systems have been extensively investi-gated from a variety of points of view, particularly for clustermelting both through experiments as well as throughsimulations.1,4–7 Studies of melting in finite systems haveprobed phenomena such as magic number effects,7,8 dynami-cal coexistence2 and the connections to the underlyingPES.9–11 It appears that the change from the solid phase tothe liquid in a cluster is mediated by the appearance of anumber of different stages~whether one should call thesephase or not appears to be a matter of taste! characterized byincreasing fluidity,9,11 when the number of atomic rearrange-

ments that are possible increase significantly.Transitions can be detected by examining a number of

different indices or order parameters. Several studies havefocused on the caloric curve, which is the variation of theinternal temperature with total energy, or the Lindemann pa-rameter, which is the relative rms deviation of the atoms, orthe specific heat variation with temperature. Purely dynami-cal features of such transitions are revealed by examiningindices such as the variation of the Kolmogorov entropy orthe largest Lyapunov exponent with total energy. In finitesystems, these different signatures of a change in phase donot always coincide:7 indeed, since these systems are farfrom the thermodynamic limit, it is not clear that these indi-ces should coincide, since different order parameters probedifferent aspects of the system dynamics or structure. Thereare instances when a transition is not signaled by one or theother of these indices: for example, Ar15, which has a well–defined melting transition according to the Lindemann index,does not have a peak in the specific heat.7 Phase coexistenceis most clearly revealed by a bimodal distribution of therelevant order parameter. In the microcanonical ensemble,the short-time-averaged~STA! temperature is often a goodorder parameter although other geometric order parametershave also been used.12 The existence of an energy gap be-tween a unique lowest-energy structure and high–energystructures is usually considered to be necessary for dynami-cal solid–liquid coexistence,13 although as Matsuokaet al.14

have shown, provided a gap exists in the spectrum ofquenched energies separating the band of solidlike statesfrom liquid-like states, coexistence can occur even in theabsence of a single low–lying structure.

In this paper we study the dynamics of mixed rare–gasclusters,~Ar–Xe!13. Our principal motivation is to under-stand some of the details of melting behavior that can bemade more evident by making the different atoms in a clus-ter nonequivalent. A variable that strongly influences bothstructural and dynamical properties is heterogeneity, andmixed clusters have recently begun to be studied both

a!Present address: Departamento de Fisica, Universidade Federal de SaoCarlos, Caixa Postal 676, 13565-905 Sao Carlos, SP, Brasil.

JOURNAL OF CHEMICAL PHYSICS VOLUME 110, NUMBER 1 1 JANUARY 1999

5010021-9606/99/110(1)/501/7/$15.00 © 1999 American Institute of Physics

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experimentally15,16 and theoretically.9,16–22 As may be ex-pected, these clusters exhibit phenomena which are not eas-ily identifiable in homogeneous systems, as for example,phase segregation,23 surface or core melting5 ~more generallymelting restricted to a region in the configuration space11!and secondary features in the specific heat curve6,9,24,25

which suggest other phase transitions. Systems studied in-clude two–component rare–gas systems21 and metallicclusters.9,22

The global minimum energy structures of~Ar–Xe!n

clusters have been previously obtained by Robertsonet al.18

for n57, 13 and 19. Robertson and Brown19 have comparedthe phase–transition behavior of mixed clusters to the homo-geneous case. They found that the melting temperatures ex-hibit a plateau in the near-equal mixture region of~Ar–Xe!7 .Temporal correlations in the case ofn51 and 12 inArnXe132n clusters have also been studied by Nayak andRamaswamy,26 and the signature of the melting transitionwas seen in interesting spectral effects: the spectrum of po-tential energy fluctuations for individual atoms, which in theliquid phase has a marked 1/f character,27 was seen to bevery different depending on whether the cluster was solid orliquid–like, and whether the atom was Ar or Xe.

The specific heats of the related~Ar–Kr!13 and~Ar–Ne!13 systems have been recently calculated in the ca-nonical ensemble by Frantz7,24 using the J–walking MonteCarlo method28 in order to enhance the exploration of theconfiguration space. The specific heat curves for Ar–Kr andAr–Ne mixed clusters show a variety of behaviors which canbe rationalized in terms of the energy spectra of the localminima and their distributions at different temperatures.Large difference in the size and the interaction energy of theconstituents in~Ar–Ne!13 makes for a greater diversity ofthermodynamical properties than the~Ar–Kr!13 clusterswhich also retain the magic–number characteristics of thecorresponding pure cluster.

The organization of this paper is as follows. The detailsof the molecular dynamics simulations are given in Sec. II.Our major focus is on the melting behavior and associatedgapless coexisting phases, and these results are presented inSec. III. We conclude in Sec. IV with a discussion of ourmain results and comparison with recent related works.

II. SIMULATION METHOD

The present molecular dynamics simulations employ thepairwise Lennard–Jones potential for the interatomic inter-action,

V~r i j !54e i j F S s i j

r i jD 12

2S s i j

r i jD 6G ,

wherer i j is the distance between atomsi and j and the en-ergy and length parameterse i j , s i j used are given in Table I.Energies are measured in units of the Ar–Ar interaction pa-rameter,e51.67310214 erg and distances in units of theAr–Ar length parameter,s50.34 nm. The equations of mo-tion are integrated using the velocity Verlet algorithm; thetime step of integration is 3.125 fs, which keeps the totalenergy conserved to one part in 104.

All calculations are started at the ground state configu-ration, which is determined through a simulated annealingprocedure29 and which has also been verified during exten-sive searches of local minima using the method of steepestdescent. Trajectories are typically integrated for 12.5 ns andvelocities are appropriately rescaled after each such integra-tion to attain the desired energy. The rescaling of velocitiesdoes not affect the total angular momentum of the cluster asthe initial conditions are chosen such that the total angularmomentum of the cluster is zero. The temperature is definedin terms of the averaged kinetic energy in the usual manneras30

T52^Ek& t

~3N26!kB, ~1!

whereEk is the internal kinetic energy,kB is the Boltzmannconstant and̂ & t denotes a time average over the wholetrajectory.

One standard method to describe the thermodynamics ofclusters is through the caloric curve which is the time aver-age of the kinetic energy, namely, the temperature as a func-tion of total energy. In the different phases, the slope of thecaloric curve attains different constant values, with thechange in slope corresponding to phase-transition-like be-havior. Starting from different conditions, the temperaturemay take different values implying that the system is notergodic on the time scale of the simulation.

The structural dynamics of the clusters is monitored bythe Lindemann index31 which is defined as

d52

n~n21! (i . j

~^r i j2 & t2^r i j & t

2!1/2

^r i j & t, ~2!

where r i j is the distance between atomsi and j . At lowtemperatures, when the cluster is confined to its globalminima, the Lindemann index depends linearly on tempera-ture and is small, being of the order of few percent. Theindex increases sharply at the onset of isomerizations. Vari-ous partial melting stages may show up on the Lindemanncurve as substeps,5,9,11 though these may not have a corre-sponding signature in the caloric curve or the specific heatcurve. In the liquid phased does not increase rapidly.

III. RESULTS

The ground state structures of the mixed~Ar–Xe!13 sys-tems, namely, the configurations that correspond to the glo-bal minimum in the PES are shown in Fig. 1. Note that allthese mixed rare–gas clusters retain the icosahedral~ICO!motif of the ‘‘parent’’ pure cluster. Furthermore, the groundstate is Ar–centered (CAr). The lowest Xe–centered (CXe)state is also ICO in all cases. The difference in energy be-

TABLE I. Lennard–Jones parameters for different rare–gas interactions.

Interacting atoms s(A°) e/kB(K)

Ar–Ar 3.40 120.0Ar–Xe 3.65 177.6Xe–Xe 4.10 222.3

502 J. Chem. Phys., Vol. 110, No. 1, 1 January 1999 Mehra, Prasad, and Ramaswamy

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tween the lowestCAr andCXe states increases from Ar12Xeto Ar6Xe7 then decreases, eventually nearly vanishing forArXe12 ~Table II!. The stronger Xe binding favorsCXe

ground state which is opposed by the loss in the packingefficiency which follows from having the larger atom in thecentral position. The size factor dominates energetic consid-erations in~Ar–Xe!13 but this is probably not the case inlarger clusters when atoms of the more weakly bound speciesprefer surface sites.17

The structural properties of the mixed clusters of Ar withvarious rare–gas species strongly depend on the actual na-ture of the constituents.24,25 13-atom Ar–Kr systems haveAr–centered ground states for all compositions but the en-ergy difference between the ground state and lowest Kr–centered state decreases steadily with increasing Kr concen-

tration but a near degeneracy is never obtained. In contrast,in ~Ar–Ne!13 where the discrepancy in the size and interac-tion energy between the two species is the largest, the globalminima are not always of the icosohedral type and are Ar~resp. Ne!–centered in Ar~resp. Ne! rich clusters.25 Similardistinctions have been observed in model bimetallicclusters.9

Shown in Fig. 2 are typical caloric curves and the Lin-demann parameter as a function of energy for ArnXe132n

clusters. We first discuss ArXe12 in detail. Other clusters willalso be discussed subsequently. As mentioned earlier, thiscluster has two nearly degenerate ICO ground states, with Arand Xe in center, respectively. Separate heating cycles areinitialized from these structures. Belowe;24.65e the re-spective caloric and the Lindemann curves are different andwhile above this energy certain anomalous features can beseen@see Fig. 2~a!#. The caloric curve obtained by heatingfrom CAr ICO has a suddenincrease, together with a slightdecrease in the Lindemann index. In contrast, starting fromCXe ICO, the temperaturedecreaseswhen the Lindemannindex shows an increase. These features imply that the twoICO ground states form separate basins in the PES, and thesebecome mutually accessible only ate;24.65e. The discon-tinuities in the caloric and the Lindemann index result fromthe fact that the two basins have separately undergone sig-nificant ‘‘melting’’ before merging albeit to differentextents—that in theCXe basin to a lower extent than thatwithin the CAr basin. A similar caloric curve was found byShelly et al.32 in MD simulations of (SF6) –Ar9 . At 15 K,the Ar atoms surrounding the central SF6 become fluid butare able to move into the central position only above 35 K.The Ar–centered configurations are more rigid thanSF6–centered ones and hence in isoergic MD simulations,this transition is marked by a rapid increase in temperature.

Results of our analysis of a representative high–energytrajectory ate524.45e are shown in Fig. 3. The short–

FIG. 1. Ground state structures of ArnXe132n for n5 0–13. The dark atomsrepresent Xenon.

TABLE II. Energies of the lowest lying Ar–centered and Xe–centered state@in units of (eAr–Ar)] for mixed ~Ar–Xe!13 clusters. Our results agree withthe energies obtained by Robertsonet al. ~see Ref. 18! to within 1 part in104.

Composition Energy (CAr) Energy (CXe)

Ar13 244.3268 •••Ar12Xe 247.6954 245.2654Ar11Xe2 251.1184 248.6122Ar10Xe3 254.5957 251.7268Ar9Xe4 257.8514 254.9254Ar8Xe5 260.7363 257.8762Ar7Xe6 263.7978 260.1004Ar6Xe7 266.5918 262.5108Ar5Xe8 269.0209 265.6722Ar4Xe9 271.5984 268.7156Ar3Xe10 274.0185 272.2007Ar2Xe11 276.2724 274.6360ArXe12 278.6989 278.6707Xe13 ••• 282.1127

FIG. 2. Caloric and the Lindemann curves of~Ar–Xe!13 clusters from 12.5ns integrations.~a! ArXe12 . Data from two different heating cycles areshown: filled squares are the results of a heating cycle initialized at lowenergies with slightly distortedCAr ICO, while the curve marks the datafrom a heating cycle initialized from a slightly distortedCXe ICO; ~b! samefor Ar5Xe8 from one heating cycle initialized at low energies with slightlydistortedCAr ICO; ~c! same as~b! but for Ar12Xe.

503J. Chem. Phys., Vol. 110, No. 1, 1 January 1999 Mehra, Prasad, and Ramaswamy

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time–average of the temperature, formed by averaging theinstantaneous kinetic energy~IKE! over 156 ps is shown inFig. 3~a!. The histogram of the STAs using different timeperiods for averaging is shown in Fig. 3~b!, and it can beseen that the distribution is essentially bimodal, and this bi-modality persists even after averaging over very longtimes.33 Small local peaks in the Fig. 3~b! can be expected tovanish in longer runs.

In order to further explore the nature of local tempera-ture fluctuations, we analyze the energetics of the localminima by quenching along a trajectory to the inherent struc-tures. Remarkably,all minima in the high-temperature phasehave Xe in a central position, while all the minima in the lowtemperature phase have a central Ar@see Fig. 3~d!#.

The low-temperature phase, which corresponds toCAr

states has a unimodal STA temperature distribution, whilethe high-temperature phase has bimodal STA temperaturedistribution @Fig. 3~c!#. This is consistent with the fact thatjust before theCAr basin becomes accessible for the trajec-tories starting from theCXe basin, the Lindemann index~ofthe CXe basin! has not attained the magnitude typical of theliquid phase (;0.2520.3). It is somewhat surprising thatCXe ‘‘phase’’ has a higher temperature, given thatCAr ICOis the global minimum. Note, however, that the difference inCAr andCXe ICO is very slight~Table II! and theCAr basinhas more low–lying isomers than theCXe basin; the trajec-tory in the CAr basin is appears to sample the ground staterelatively less frequently compared to when it is in theCXe

basin. So the effective configuration energy of theCXe basinis lowered belowCAr basin.

The species of the central atom is also correlated withthe frequency of rearrangements in the two phases. Typi-cally, in the CXe and CAr ‘‘phases,’’ the frequencies areabout 40 and 230 ns21, respectively, and these numbers aretypical of coexistence and liquid phase respectively in thisfamily of clusters. We therefore interpret the dynamics asthat of solid–liquid coexistence on short time scales withinthe hot phase; there is, at the same time, a slower fluctuationin which this phase coexists with apurely liquid-like phase.The two liquid-like phases inhabit entirely different regionsof the configuration space.

The dynamical coexistence is also found at lower ener-gies corresponding to the jump in theCAr Lindemann index.Trajectories, confined to theCAr basin, show first bimodaland at higher energies trimodal STA temperature distribu-tions ~Fig. 4!, but only when averaged over shorter times;10ps. Surface–core exchanges do not take place at thisenergy and if the surface rearrangements are fast enoughthen it is possible to speak of a surface melting stage.9 Herewell–developed surface–melting can be inferred from theunimodality of theCAr STA distribution at24.65e @Fig.4~c!#.

The qualitative picture that emerges is of a particularorganization of the PES: there are two basins in the PES,each with a set of low and high energy states. These low andhigh energy states dynamically coexist with each other in acertain energy range~which may be different for each basin!.When the energy is high enough to allow interbasin motions,the states in two basins coexist on a longer time scale. Typi-cally the spectrum of energies of the local minima constitut-ing theCAr and theCXe basin overlap, hence the later coex-istence occurs without a band gap. The spectra of theindividual basins may possess a gap but that is associatedwith the coexistence between the states belonging to thatbasin which is similar to the usual solid–liquid coexistence.

FIG. 3. ~a! STA temperatures along 12.5 ns trajectories: ArXe12 at e524.45e extracted by averaging IKE over 156 ps.~b! Distribution of STAtemperatures for ArXe12 at e524.45e obtained by averaging IKE over 31ps~solid line! and 6.2 ps~dashed line!. ~c! Distribution of STA temperaturesfor ArXe12 at e524.45e obtained by averaging IKE over 6.2 ps: dashedline is the distribution for STA temperatures extracted from 2 to 9.25 nsonly, solid line from the remaining data.~d! Energies of the structures ob-tained by steepest–descent quenchings done every 1.25 ps for ArXe12 at e524.45e. A total of 201 minima were located. In the middle portion of thegraph~n51600–7400! the lowest energy points refer to theCXe ICO whichhas slightly higher energy thanCAr ICO ~Table II!. Every tenth point isshown.

FIG. 4. Histograms of the STA temperatures from 12.5 ns integration ofArXe12 averaged over 6.2 ps. These trajectories are initialized from theCAr

basin and remain entirely inside it.~a! at 25.12e. ~b! at 24.75e. ~c! at24.65e. The bimodal distribution in~a! is the result of the structural fluc-tuation between theCAr ICO ground state and a defective icosahedra ofenergy276.43213e . The higher–lyingCAr states form the third componentof the trimodal distribution in~b!. At slightly higher energy, these higherenergy states dominate and a unimodal distribution is obtained~c!.

504 J. Chem. Phys., Vol. 110, No. 1, 1 January 1999 Mehra, Prasad, and Ramaswamy

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The absence of a band gap does not preclude the local tem-perature from being a good order parameter because thelower and the higher lying states may be differently occupiedin the two basins. A recent study suggests a similar structureof the PES for small~NaF!n clusters, although the distribu-tion of STA temperatures was not studied.11 Such PES gen-erally yield multistage melting dynamics.9,11

The liquid-like phases which access only a restricted re-gion of the configuration space have been called ‘‘isomeriza-tion fluids’’ by Calvo and Lebastie11 who observe that therecan be more than one such distinct phase before a fully liquidstate is reached. Krissinel and Jellinek9 investigated the de-pendence of the dynamical properties of the~Ni–Al !13 clus-ters on the initial zero–temperature structure: Al centered orNi centered. Two–step Lindemann curves when obtainedwhen the threshold energy for the surface rearrangementswas lower than for rearrangements involving the centralatom; however, only one step occurred if the surface rear-rangements gave rise to a well–developed surface–meltingstage. Precisely the same mechanism operates here to givesingle–step Lindemann curve forCAr basin; bimodal STAtemperature distribution forCXe basin at24.45e shows thatthe surface melting is incomplete forCXe states, hence giv-ing a two–stepped Lindemann index.

Such dynamics is characteristic of a number of the otherclusters in the series. There are important contrasts as well,though. In the case of Ar12Xe, the scenario is similar—a hotsolid–liquid phase coexists with a cool liquid phase, excepthere the cool phase isCXe while the hot phase isCAr . But nopeculiarity in the caloric and Lindemann curves is seen ex-cept that the Lindemann index increases in a rather narrowenergy range; correspondingly the temperature decreases@Fig. 2~c!#. TheCXe ground state is high up in the spectrumand lies within the band of theCAr liquid states with nosignificant gap separating this state from otherCXe states.The CXe states are accessed from theCAr basin at onlyslightly higher energy than theCAr liquid states, indicatingthat there are no high barriers between the two basins. Hencethe cluster melts in a single stage. The clusters withn>9share similar phenomenology, and consequently their caloricand Lindemann curves are very similar.

In the middle range of compositions,n5328, the fluc-tuation between the two phases occurs within the manifold ofliquid-like configurations. For the system Ar5Xe8 , a typicalexample, we calculate the energies of inherent structuresalong a 10.6 ns trajectory at energye523.95e. The corre-sponding timeseries of the STA temperatures obtained byaveraging the IKE is shown in Fig. 5~a!; the correlation be-tween the two figures is apparent. Further examination of thestructures reveals that all states which lie in an upper band inthe middle part of the time series are ofCXe type and theremaining areCAr @Fig. 5~c!#. The CXe phase also corre-sponds with lower temperatures but the distribution of STAtemperatures obtained by averaging IKE over 15.6 ps is notbimodal owing to the large temperature fluctuations in theindividual phases themselves compared to the difference inthe mean temperatures@Fig. 5~b!#. The caloric curve itself issmooth, but the Lindemann index marks the basin mergingby a small step@Fig. 2~b!#. As the individual basins are

melted before they are mutually accessible it is possible tospeak of a surface–melting stage here also. The two meltingstages gradually merge as the number of Ar atoms is in-creased.

In Fig. 6 we plot the temperatures which correspond tothe onset of surface isomerizations and the onset of basin–crossing isomerizations, respectively, for all the composi-tions. The former temperature is obtained as the temperatureof the first abrupt change in the Lindemann index~restrictedto theCAr basin!. Interestingly, this temperature is constantin the middle range of the compositions. The onset of barrier

FIG. 5. ~a! STA temperatures along 10.6 ns trajectory: Ar5Xe8 at e523.95e extracted by averaging IKE over 62.5 ps.~b! Distribution of STAtemperatures for Ar5Xe8 at e523.95e obtained by averaging IKE over15.6 ps.~c! Energies of the structures obtained by steepest–descent quench-ings done every 1.25 ps for Ar5Xe8 at e523.95e. Total of 741 minimawere located. Every tenth point is shown.

FIG. 6. Phase–transition temperatures for~Ar–Xe!13 as a function of thenumber of Xe atomsnXe : (h) temperature at which a trajectory initializedfrom CAr basin begins to accessCXe basin; (n) temperature of the firstabrupt change in the Lindemann index~restricted to theCAr basin!. Theestimated errors in these quantities are within the symbol size.

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crossing roughly marks the complete melting in the clusterand its temperature increases with increasing Xe atoms.

IV. DISCUSSION

In this paper we have presented results of constant en-ergy MD simulations of the structural and dynamical prop-erties of binary rare-gas clusters~Ar–Xe!13 interactingthrough the simple Lennard-Jones potential. The size of theconstituent atoms plays an important role compared to en-ergy and other factors in determining the ground state. Thegain in the packing efficiency with smaller Ar atom in thecenter overweighs weaker Ar binding due to which Ar atomalways goes in the center. Both this state and the lowestXe–centered state are icosahedral. For compositions domi-nated by a single species, the isomer energy spectra has aband structure similar to Ar13 but in nearly equal mixtures,no large gaps remain in the spectra as a consequence of alarge number of permutational isomers.

Our focus has been on nonergodic effectswithin themelting transition, which are exhibited as structural fluctua-tions. Below a threshold energy, exchanges between the cen-tral atom and a neighbor do not take place even if the surfaceis fluidlike, particularly in the Xe–dominated compositions.The cluster passes through a surface–melting stage whichhas oscillations in the STA temperature akin to the usualsolid–liquid coexistence in pure clusters. There are two dis-tinct surface–melted phases depending upon which speciesoccupies the central position—Ar or Xe; thus we speak ofmelting in Ar– or Xe–centered basin, respectively. Veryslow oscillations in the STA temperature again set in withthe onset of surface–core exchanges at higher energies.These oscillations correlate with the replacement of an Aratom with a Xe atom in the central position and vice versa. Ifthe difference in the mean configurational energies of Ar–centered and Xe–centered states is large enough then theSTA temperature has bimodal distribution even after averag-ing over rather long time scales. This slow oscillation cancoexist with a faster oscillation in one of its components: onshorter time scales the high-temperature phase can be re-solved into a low–temperature and high–temperature sub-phase. This occurs when the melting in a particular basin isincomplete.

This leads to a picture of the configuration space of thesesystems divided into two basins with all the states in a par-ticular basin having central atom of the same species. Thesestates formprimary basinsin the terminology of Berry andKunz.34 The barrier height, measured from the global mini-mum, between these basins increases with the number of Xeatoms. Consequently, the temperature at which this barrier isfirst crossed also increases. At these temperatures the dynam-ics is intermittent, and trajectories tend to stay for long timesin each basin, occasionally crossing from one side to theother.

The energy range of this phenomenon depends on thecluster composition: from Ar12Xe to Ar9Xe4 the energyrange is coincident with the energy at which the surface at-oms become mobile, so the cluster can be said to havemelted in a single stage. They also have a bend–like regionin the caloric curve, probably as a consequence of the sudden

opening of configuration space relative to the clusters whichmelt in stages. In the remaining members of the cluster se-ries, the surface atoms become mobile at lower energies thanthe threshold for core–surface exchange and the cluster has asurface–melting stage which is particularly well defined asthe number of Xe atoms increases.

At higher energies when the basins merge, the differencein temperatures in the two basins is not large enough to giverise to any particular signature in the caloric curve. Only forArXe12 and Ar2Xe11, where the Xe basin is incompletelymelted at the energy of basin merging do we find a sharp risein the temperature of the trajectories coming from the fullymelted Ar basin.

This particular basin structure does not seem to exist in~Ar–Kr!13 and ~Ar–Ne!13 clusters studied recently byFrantz.24,25 Relative similarity of size and energy parametersbetween Ar and Kr makes the properties of their mixtureslike the Ar13. However, despite the Ar–Ne parameter differ-ence being larger than the difference between Ar and Xe,only ArNe12 has coexistence between Ar–centered and Ne–centered isomers. There are some differences between thisfluctuation and the structural fluctuation in the presentAr–Xe systems. The volume of the two phases in the con-figuration space is of the same order in Ar–Xe clusters, so athigh temperatures both types of structures are seen while inArNe12 only Ar–centered states are observed. Some of the13-atom Ar–Ne clusters, in contrast with 13-atom Ar–Krand Ar–Xe clusters exhibit a type of differential melting inwhich all Ne atoms become mobile at a lower temperaturethan Ar atoms.25 This is probably a purely energetic effectsince the ratio of the binding energies of the constituent spe-cies is highest for Ar–Ne.

Similar questions have been studied by Krissinel andJellinek9 for 13-atom Ni–Al clusters. The Lindemann curveshave either a single–step or a two–step form depending onthe species of the central atom of the zero–temperature struc-ture from which the heating cycle is initialized. The stepsoccur at the onset of surface and global isomerizations, re-spectively. However, if the onset energies are not well re-solved or the surface isomerizations are frequent enough thenonly a single step is seen.

The structural fluctuation phenomena described here—which is not related to any band gap in the spectra of localminima—coexist with the more well–known solid–liquiddynamic coexistence. This phenomena is, however, quitegeneral, and is likely to play a major role in the dynamics ofheterogeneous atomic and molecular clusters9,11,25,32since itis a direct consequence of the more complex potential energylandscape of heterogenous systems.

ACKNOWLEDGMENTS

We thank Dr. C. Chakravarty for fruitful discussions andcomments, and acknowledge the support of the Departmentof Science and Technology, India. R.R. would also like tothank the Institute for Nuclear Theory at the University ofWashington for its hospitality during the completion of thismanuscript.

506 J. Chem. Phys., Vol. 110, No. 1, 1 January 1999 Mehra, Prasad, and Ramaswamy

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507J. Chem. Phys., Vol. 110, No. 1, 1 January 1999 Mehra, Prasad, and Ramaswamy

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