Notes: Refer to the Lennard-Jones (L-J) pair potential for solid Argon. You need to know the form of this potential along with the smooth cut-off to zero that is needed for modeling studies.
Both the potential and the cut-off are described in Prof. Vitek’s notes in a separate file titled the L-J potential. Please read this before attempting the homework or wait until Sep 12 class lecture to know more. In the meantime, you may look up or convince yourself what close-packed crystal structures are in one, two and three dimensional space. You may search the web if you are not familiar with this concept. Once you know how a close-packed structure is defined, you should be able to figure out the close-packed lattice in two dimensions. Draw a rough sketch by hand or make a plot using a code and identify how many neighbors an atom has in this lattice. Make a table of the nearest neighbors, next-nearest neighbors, etc., at least up to the fourth neighbor shell along with their distances in terms of a lattice parameter ‘a’ for the lattice. The pair potential only depends on the distance between the atoms and not their orientation. Such potentials are called “central” potentials in physics. With this background, you may proceed to do the homework. Please prepare your answers in the form of a report (in pdf format) where you explain your thinking and procedure in words briefly before solving the problem.