Suggested Experiments

Liquid to solid transition

First, start the simulation with the velocity scaling on, the applied temperature set at 150, and the density set to 0.069. Allow the simulation to run for about 500 timesteps (the amount of time taken to fill an entire energy plot before it clears and resets). Switch to the RDF screen. Wait for it to produce a new RDF. Note, the shape of the RDF. It should have one large peak and a second smaller peak shortly after. Note also that the function does not go to zero between the two peaks. This indicates that the atoms are moving around enough that they are moving into and out of their preferred positions. Also, note in the atomic display how the atoms are moving around in a fairly disordered manner. They seem to have no overall structure. These are both indications of a system in the liquid state.

Now, while still looking at the RDF screen, change the density from 0.069 to 0.099. Make sure that the velocity scaling is still on, and the applied temperature is still at 150 or thereabouts.

You should see the atoms in the display moving toward a very ordered, regular lattice! Once they have organized themselves into this lattice you should notice that they vibrate around their positions, but do not move from one lattice position to another. This is indicitive of the solid state.

Also, notice the radial distribution function. After enough time has passed, you should see that the peaks have become very narrow and well defined. The area in between the first and second peak now goes all the way to zero. Also, note that the second peak has now split into two peaks. Think about the new structure and try to determine why this has happened. The atoms are now stuck into their preferred positions and we have the solid state.

Fluctuations in Energy

Remember that the timestep for this simulation is 0.01 pico-seconds. This has a direct relationship to fluctuations in energy due to the way that newtons equations are integrated. This is because we are doing discrete integrations in time, and Newton's equations are of course continuous. Hence, we are introducing some error into the computation of the velocities and positions each timestep. As a general rule, energy fluctuations should be on the same order as the timestep.

Since this simulation uses a timestep of 0.01 pico-seconds, we should see fluctuations only in one part in one hundred, or in the third digit of the total energy.

Start the simulation at any reasonable density and turn velocity scaling off. Now look at the total energy graph. If necessary, wait until it clears the screen and the graph rescales itself so you can see the fluctuations. Note on the y-axis the values that the energy is fluctuating between. They should differ in no more than the third digit.

Fluctuations in Temperature

The same procedure should be followed as in the fluctuations in energy experiment. This time, look at the temperature graph. The fluctuations should be much larger. The fluctuations in temperature depend on several factors which an interested student should investigate. However, the purpose of this experiment is to show that while the fluctuations in temperature are quite large, the average value remains relatively constant, and when taking measurements of a molecular dynamics simulation one should be sure to sample over several periods of these oscillations.

The Cutoff Length

Energy conservation also depends on the choice of the cutoff length. Go to the potential screen. The default value for the cutoff is 8.5, if this is not the case, type 8.5 for the cutoff length. Now hit the graph button. The graph now shows the potential being used for the simulation. Note that the potential is very near the zero line at 8.5. Now, type in 5.5 for the cutoff and click on the graph button. The potential is now quite far from zero at the cutoff length. Clearly this imposes quite a bit of innacuracy in the potential calculation. Hit the apply button to make the changes apply to the simulation, and click over to the energy display.

Note the size of the fluctuations in energy. They are much larger than with the cutoff at 8.5.

The First Peak of the RDF

The minimum of the potential function should correspond to the first peak in the radial distribution function. Verify this by graphing the potential in the potential screen, and looking at the RDF screen while a simulation is running.
David Wolff
Last modified: Wed Sep 2 16:48:33 PDT 1998