Question

Atomic interactions can be modeled using a variety of potential energy approximations. One very common potential...

  1. Atomic interactions can be modeled using a variety of potential energy approximations. One very common potential form is the Lennard-Jones 6:12 potential: U(r)=4ε[(σ/r)12 − (σ/r)6]. Where ε and σ are constants specific to a given material (note: these terms are NOT equivalent to stress and strain, but this is the standard notation for the L-J parameters). Here, r is the interatomic spacing given in units of Angstroms, and U(r) is given in units of eV/atom. A molecular dynamics simulation was performed by Zhang and coworkers [1] to study the properties of Al thin films in which the authors proposed a Lennard-Jones potential of the form above to model Al-Al interactions. The values used for the material parameters were: ε=0.368 and σ =2.548.

Ref [1] H. Zhang and Z. N. Xia, Nuclear Instruments & Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 160 (2000) 372-376.

  1. (a) Using the given material parameters and the form of the interatomic potential energy curve, plot U(r) for aluminum from r =2 to 4 Angstroms in increments of 0.25 Angstroms.

  2. (b) Determine the equation for and graph the interatomic forces F as a function of interatomic separation r for Al over the same range of r used in part (a), indicating units of F(r). Also, analytically and graphically determine the equilibrium interatomic spacing, ro. Mark this point on the graph produced in (a) as well.

Homework Answers

Answer #1

If you have any doubts, feel free to ask.

above fig is plot of U vs r

fig(2) plot of F vs r

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