Relative pair dynamics in simple supercooled liquids: longitudinal contributions.

The pair dynamics of simulated argon samples is investigated at the melting (85 K), supercooled (55 K), and quenched (20 K) liquid states, and in the crystal (20 K) state. Tagged pairs, initially lying in a given shell, were divided into incoming and outgoing groups and followed along simulated trajectories. Over them, specific correlation functions deltaB(r(0);t), involving the pair separation vector projected along its initial value r(0) (longitudinal dynamics), have been evaluated. More or less pronounced oscillations are detected according to the temperature of the thermodynamic states (and, obviously, their solid or liquid nature); for each state, they depend on the initial pair distance r(0), too. The oscillations vanish after few picoseconds (fast dynamics) in the case of crystal, whereas in the supercooled liquid they decay towards a plateau, whose height increases with the temperature. It is shown that the power spectrum of deltaB(r(0);t) practically yields the same density of states (DOS) produced by the pair velocity correlation function. The deltaB(r(0);t) functions obtained from the argon crystal at 20 K produce DOS curves dominated by two main frequency contributions, at about 40 and 60 cm(-1) (Einstein and Debye frequency, respectively). Their shape is quite well reproduced by damped harmonic oscillator-like (DHO) functions vibrating at that frequencies. In liquid states, the deltaB(r(0);t) plateau, that forms after the fast DHO dynamics, accounts for the system diffusivity. The relaxation towards the plateau is modeled by an exponential function whose decay time is comparable with the average vibration period. Evidence that the liquid states conserve a certain memory of the vibrational modes of the crystal is obtained. In these states, the DHO functions at the Einstein and Debye frequencies plus an exponential function cannot reproduce the deltaB(r(0);t) shape. A pronounced shoulder, that forms around 0.5 ps, requires the contribution of a third DHO. In the DOS, it yields a band centered below 20 cm(-1) that produces low frequency DOS excess in comparison with the DOS of the crystal. This contribution is present in liquid and supercooled high temperature states and survives near the temperature of the glass transition whereas the diffusion practically vanishes.