Separation of Diffusive Jump Motion and Trapped Motion of Atoms in a Glass Forming Process Via Molecular Dynamics Simula
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J. MATSUI, M. FUJISAKI AND T. ODAGAKI Department of Physics, Kyushu University, Fukuoka 812-81, Japan
ABSTRACT We have carried out the molecular dynamics (MD) simulation for a binary soft-sphere system and calculated the self part of the generalized susceptibility x,(q, w) at various temperatures. At higher temperatures in liquid state, only one peak appears in the imaginary part of Xs, which tends to split into two peaks, the so-called a- and 3- peaks, as the temperature is reduced. The temperature dependence of the peak frequency is well described by the Vogel-Fulcher law for the a- peak, and the peak frequency does not change much for the 0- peak. We have also measured the trajectory volume of a tagged atom V(t), which is related to the dynamical order parameter, the "generalized capacity", in structural glass transitions recently proposed by J. F. Douglas. These results show the transition temperature which is in good agreement with that determined by the trapping diffusion model. INTRODUCTION The viscosity of supercooled fluids increases gradually as the temperature decreases, which can be well fitted by the empirical law, so-called Vogel-Fulcher law, known in glass blowers. In a microscopic point of view, solidification is thought to be a transformation of the diffusive random motions of atoms in the liquid state into the localized oscillatory motions in the solid state. Such a transformation of atomic motion occurs gradually in glass forming processes, while it occurs drastically at the melting point in crystallization. Furthermore, the structure is disordered in supercooled liquids and glasses, while periodic in crystals. Therefore, the localization of atomic motion seems to be a good criterion for defining such transition. The aim of the present paper is to investigate how the dynamics transforms in vitrification process and to quantify the 'localization of atomic motion which indicates the order of transition. First, we calculate the self part of the generalized susceptibility xs(q, w) via the molecular dynamics (MD) simulation, and to see how the characteristic time scale of the dynamics changes in the vicinity of the transition point. Next we try to measure the trajectory volume V(t), namely the first visit volume where the tagged atom has passed during the time t, here the re-visited volume where the tagged particle had visited already between the time t = 0 and t is not counted more than once. In liquid state, the trajectory volume V(t) in the long time t increases in proportion to t, where atoms move randomly without localization. On the other hand, V(t) in solid state, both crystals and glasses, takes a constant value at large t, where the atomic motion is completely localized in a certain area. According to J. F. Douglas' proposal in Ref. 1, the long time limit of V(t)/t, which 285 Mat. Res. Soc. Symp. Proc. Vol. 455 ©1997 Materials Research Society
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Figure 1: The frequency dependence of x"(q, w) at different temperature in liquid states, supercooled states and
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