Abstract
The velocity distribution functions of particles in one- and three-dimensional harmonic solids are investigated through molecular dynamics simulations. It is shown that, as in the case of dense fluids, these distribution functions still obey the Maxwell-Boltzmann law and the assumption of molecular chaos remains valid even at low temperatures.
Highlights
In the classical theory of ideal gases, the velocity distribution function is derived from the Boltzmann transport equation based on the assumption of molecular chaos and a dilute enough gas so that ternary and higher collisions can be ignored [1]
The velocity distribution of the particles is described by the Maxwell-Boltzmann distribution function
Extremely dense fluid systems with strong interactions between its particles were investigated through molecular dynamics simulations
Summary
In the classical theory of ideal gases, the velocity distribution function is derived from the Boltzmann transport equation based on the assumption of molecular chaos and a dilute enough gas so that ternary and higher collisions can be ignored [1]. In an ideal gas trajectories of the particles are straight lines, meaning that the particles interact through short range potentials, such as hard-sphere or Lennard-Jones potentials. Under these conditions, the velocity distribution of the particles is described by the Maxwell-Boltzmann distribution function. It can be shown that the Maxwell-Boltzmann distribution function describes molecular velocities even in non-ideal gases [2] [3], even in the presence of long-range interactions between the particles of the system such as Coulomb potential, as long as the assumption of molecular chaos remains valid [4]. To the best of the author’s knowledge, velocity distribution of atoms in these solids, which is the subject of this investigation, has not been discussed or reported in the literature
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