Soft Report - Dipartimento di Fisica - Sapienza

Scientific Report – Non Equilibrium Dynamics and ComplexityTemperature-dependent vibrational heterogeneitiesin harmonic glassesThe question as to whether the structure of glassesat the scale of tens to hundreds of interatomicdistances is homogeneous or inhomogeneous, hasattracted recently much interest. Traditionally,following the continuous random network modelsuggested by Zachariasen, the homogeneoushypothesis has prevailed, also because noheterogeneity was clearly observed by small-angleneutron or X-ray scattering and electron microscopy.However, these techniques show only that there isno density heterogeneity, but tell nothing about thecohesion at the nano-metric scale, and cannot ruleout vibrational dynamical heterogeneities.Actually, recent molecular dynamics simulations onbinary Lennard-Jones (LJ) mixtures showed that inthe supercooled state highly mobile and immobileparticles exist, which are spatially correlated over arange that grows with temperature as the glasstransition is approached.the local force constants, motion in a given directionwill only occur if allowed by the excitable modes. Astemperature is increased and higher-energy modesbecome appreciably excited, the displacementpatterns will be changed, and the same is expectedto happen to the characteristics of theheterogeneities.Our mono-atomic samples consisted of N 0 = 6980,2048, 1500, 1000, and 500 atoms, interactingthrough the LJ pair potential with parameters, massand density suitable for Argon. The soft (hard) atomshave been identified as those with small (large)variation of potential energy under the displacementpattern produced by all (temperature-weighed)normal modes.The presence of vibrational heterogeneities isdetected by comparing the pair correlation functionof the whole system, g W(R), to that of the Nsoftest/hardest atoms, g N(R). An excess ofcorrelation in the peaks corresponding to nearestneighbours(nn) and next-nearest neighbours, i.e. g N> g W, indicates the existence of heterogeneity. InFig. 1 we report the pair correlation functions of the2048-atom LJ system for various numbers of soft (a)and hard (b) atoms, at T = 03 in units of themaximum frequency. Clear differences appear in thefirst peak for both classes.One important question is whether with the presentsystem size it is possible to estimate the dimensionthat the dynamical heterogeneities would have in an"infinite" sample. To evaluate the size of theheterogeneities, we evaluated the ratio g N/g W; thedistance R 0 at which it stabilizes around 1, can beconsidered as an indication of the "radius" of theheterogeneity. The estimated size of heterogeneitiesdoes not depend very much on the sample size, andresults to be of the order of 7.5 ºA.Fig. 1 Pair correlation functions for N 0 = 2048(averaged over 3 samples). Top panels: differentnumber of soft (a) and hard (b) atoms, at ¯fixed T =0.3. Bottom panels: different temperatures for the200 softest (c) and hardest (d) atoms.One important issue is whether or not suchheterogeneities are, in some sense, "frozen down"through the glass transition, so that even in the cold,harmonic glass, they leave a memory and, as aconsequence, softer and harder zones exist. In thepresent paper [1] we are concerned with two mainaspects of this problem: on the one hand we look forthe existence of dynamical heterogeneities in 3-dimensional harmonic LJ glasses, and investigatetheir size; on the other hand, we study the effect oftemperature. The latter is expected on the basis ofthe following argument. Consider a harmonic glass atlow temperature; in this case only the modes of lowfrequency will be excited and the atoms will onlyperform the cooperative motions corresponding tothese ; therefore, irrespective of the magnitude ofReferences[1] B. Rossi, G. Viliani, E. Duval, W. Garber,Europhysics Letters 71 256 (2005).Authors:B. Rossi (a,b), G. Viliani (a,b), E. Duval (c), W.Garber (d) - (a) Dipartimento di Fisica Università diTrento, Italy; (b) INFM CRS-SOFT, c/o Università diRoma "La Sapienza", Roma, Italy ; (c) LPCML, UMR-CNRS 5620, Université Lyon I, 69622 VilleurbanneCedex, France; (d) Department of AppliedMathematics and Statistics, Stony Brook University,Stony Brook, New York 11794-3600, USASOFT Scientific Report 2004-0678