View source for Third year simulation experiment/Structural properties and the radial distribution function

'''<big><span style="color:blue; ">This is the fifth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Running_simulations_under_specific_conditions|Running simulations under specific conditions]], or jump ahead to the next section, [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]].</span></big>'''

We can characterise the structure of systems that we simulate using [http://en.wikipedia.org/wiki/Radial_distribution_function radial distribution functions], which we denote <math>g(r)</math>. Calculating the RDF for a simulation is very useful &mdash; it can tell us the distances from an atom at which it is more likely to find its nearest neighbour, second nearest neighbour, and so on; it is also a quantity that can be accessed [[experimentally]], and so provides a good check that the forcefield in our simulation is correctly reproducing the structural features.

In this section, you are going to use VMD to calculate the radial distribution function for the solid, liquid, and vapour phases of the Lennard-Jones fluid.

===Simulations in this section===

The '''RDF''' subfolder contains an example input script that you can use to record an atomic trajectory to generate RDFs for the solid, liquid, and vapour phase Lennard Jones systems. Make three copies of that script (one for each phase), and modify the density and temperature parameters to give the phase that you want (a phase diagram for the Lennard-Jones system can be found [http://journals.aps.org/pr/abstract/10.1103/PhysRev.184.151 here]). <big>'''Note: when simulating the solid, you will need to change the lattice type in the lattice command to fcc, rather than sc. '''</big>

'''<big>TASK 9: perform simulations of the Lennard-Jones system in the three phases (solid, liquid and vapour). When each is complete, open the trajectories (.dump files) and calculate <math>g(r)</math> and <math>4\pi \int g(r) r^{2}\mathrm{d}r</math>.  See instructions at the end of this page.</big>'''

=== Briefly explain what a Radial Distribution Function is. What is the relationship between the coordination number and RDF? [2] ===

=== Plot the RDFs for the three systems. [2] ===

=== Discuss qualitatively the differences between the three RDFs, and what this tells you about the structure of the system in each phase. [5] ===

=== In the solid case, illustrate which lattice sites the first three peaks correspond to [2]. What is the lattice spacing [1]? What are the coordination number for each of the first three peaks [1]? ===
'''<big><span style="color:blue; ">This is the sixth section of the third year simulation experiment. You can return to the previous page, [[Third_year_simulation_experiment/Running simulations under specific conditions|Running simulations under specific conditions]], or jump ahead to the next section, [[Third year simulation experiment/Dynamical properties and the diffusion coefficient|Dynamical properties and the diffusion coefficient]].</span></big>'''

===Calculating <math>g(r)</math> in VMD===

# Start VMD as before and load the trajectory that you want to analyse.
# Select '''Extensions''' -> '''Analysis''' -> '''Radial Pair Distribution Function g(r)'''
# Set '''Selection 1''' to '''all''' and '''Selection 2''' to '''all'''
# Change '''delta r''' to '''0.05''' &mdash; this is the distance between points in the generated RDF.
# Ensure that '''Use PBC''', '''Display g(r)''', '''Display Int(g(r))''', and '''Save to File''' are checked
# Click '''Compute g(r)'''

After a short pause while it performs the calculation, VMD will display both the RDF, and its running integral. You will then be prompted to save this data &mdash; choose a location for the file that you will be able to find easily later.