Structure and Dynamics of Argon

Summary

In this the structural and dynamical properties of liquid argon are studied. The radial distribution function (RDF) and structure factor, \(S(k)\), are used to extract the mean or static structure, and the mean squared displacement (MSD), van Hove self correlation function, \(G_s(r,t)\), see ref [Hove1954], and dynamic structure factor, \(S(k,ω)\) are used to examine dynamical properties.

Background

Liquid argon was one of the first liquids to be studied by molecular dynamics, ref [Rahman1964], on account of its alleged simplicity. As this exercise will show however, even simple liquids have complex properties. In this exercise we shall use some fairly typical ways of investigating the properties of liquids, beginning with probably the simplest: the radial distribution function. Next we shall look at diffusion by computing the mean squared displacement and seek to explain the mechanism of this using the van Hove self correlation function. Finally we shall calculate the dynamic structure factor and determine the velocity of sound in the liquid and from that estimate the elastic modulus.

Task

Copy or download the following files: CONFIG FIELD CONTROL The CONFIG file contains a typical argon liquid configuration simulated at 85 K. Proceed as follows:

  1. Take a look at the DL_POLY input data files CONTROL, FIELD and CONFIG. Make sure you understand what these files do. Run the simulation, when complete DL_POLY will have generated a large HISTORY.

  2. Use the generated RDFDAT file to plot the RDF for the system. Study the RDF and try to relate it to the force field specification in the FIELD file. You should understand the meaning of the features of the RDF, for instance: is the RDF liquid-like? The structure factor is obtained in a similar way using the \(S(k)\) option and works by calculating a Fourier transform of the RDF data. This function is of course related to the experimental determination of the RDF by x-ray or neutron scattering. An interesting question is how much can you believe the results at low k vector. Can you think of a way to investigate this?

  3. Write a script to calculate and plot the MSD directly from the HISTORY file (set it to run over 2800 configurations). From this estimate the diffusion constant. Note the MSD at short time is not linear, why is this?

  4. The next issue is the nature of the diffusion. Two mechanisms suggest themselves: are the atoms are hopping from place to place or they are following a continuous random walk without ‘resting’ in any particular place. We all know it is the latter, but how? Use the Van Hove self correlation function to see how the self correlation varies with time. How does this show that the diffusion is a continuous random walk?

  5. Finally calculate the dynamic structure factor \(S(k,ω)\) with \(kmax=2\). Plot the various functions \(S(k,ω)\) in which \(k\) is fixed and \(ω\) is the ordinate. Locate the Brillouin peak (if any) appearing in some of these functions. From the (approximate) position of this peak determine the velocity of sound in the liquid. Next attempt to determine the elastic modulus associated with this using the Newtonian rule that the velocity of sound (c) is equal to the square root of the ratio of the elastic modulus (\(γ\)) to the density (\(ρ\)) i.e.

    \[c=\sqrt{\frac{γ}{ρ}}\]

Check the result for more than one \(k\) vector. Do the results agree? What does the result mean in terms of the bulk properties of the liquid?

Hove1954

  1. Van Hove, Correlations in space and time and born approximation scattering in systems of interacting particles, Phys. Rev., 95, p. 249, Jul 1954, doi: 10.1103/PhysRev.95.249