Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition

Abstract

Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid–solid coexistence using the additivity principle. The results are shown to agree well with the “exact” values obtained from their relations to excess energy and pressure. Some consequences, in particular in the context of the Lindemann’s melting rule and Stokes–Einstein relation between the self-diffusion and viscosity coefficients, are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.

Sound Velocities of Generalized Lennard-Jones (n − 6) Fluids Near Freezing

“…Calculated in this way, the sound velocities of the (12-6) LJ system at the solid coexistence boundary are numerically close to those at the fluid boundary, except for in the vicinity of the triple point (see Figure 4 from Ref. [ 9 ]).…”

“…For further details regarding the evaluation of sound velocities and their relation to the instantaneous elastic moduli, see Ref. [ 9 ].…”

“…Equations ( 5 )–( 8 ) can be considered as a generalization of the Zwanzig and Mountain result for the conventional (12-6) LJ potential. In this special case, the constants are , , , and [ 9 , 13 ].…”

“…Motivated by these observations, it was recently investigated in detail how the longitudinal and transverse sound velocities behave at the liquid–solid phase transition of 3D Lennard–Jones (LJ) systems [ 9 ]. It was observed that the sound velocities maintain quasi-universal values along the liquid–solid coexistence boundaries and that their magnitudes are comparable with those of repulsive soft-sphere and hard-sphere models.…”

Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids

“…The last step is to neglect the difference between and at melting conditions (which is particularly appropriate for soft repulsive interactions and less appropriate for HS interactions) and use the fact that for many simple melts, including Lennard–Jones, soft-spheres, hard-spheres, and liquid metals [ 31 , 32 , 33 ]. We obtain at the melting temperature.…”