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Homework Help: What other configuration could the molecule adopt that would lower its LJ energy

  1. Feb 2, 2012 #1
    1. The problem statement, all variables and given/known data

    i) Write down an expression for the LJ cohesive energy of a molecule consisting of four atoms lying on the corners of a square of side a.
    ii) Deduce the equilibrium value of the nearest-neighbour separation, a, assuming the molecule retains its square shape
    iii) What other configuration could the molecule adopt that would lower its LJ energy further?

    Relevant equation:

    U[itex]_{tot}[/itex]=2N[itex]\epsilon[/itex][A[itex]_{12}[/itex]([itex]\frac{σ}{a}[/itex])[itex]^{12}[/itex]-A[itex]_{6}[/itex]([itex]\frac{σ}{a}[/itex][itex])^{6}[/itex]]

    3. The attempt at a solution

    I have done parts i) and ii). It is part iii) that I am stuck on. Because bcc, hcp and fcc all have higher N, number of atoms per unit cell, and higher values of A[itex]_{12}[/itex], making the cohesive energy higher - this is the case, isn't it? So what other configuration could the molecule adopt?
     
  2. jcsd
  3. Feb 3, 2012 #2
    Re: What other configuration could the molecule adopt that would lower its LJ energy.

    yes and no. you have to realise that U is a potential energy and therefore negative in nature. you have to do work to remove these molecules from their square setup into something else. in a simple cubic structure ( 2 sets of these squares make a simple cubic of 8 atoms), the cohesive energy between the molecules is stronger, and so the the potential U is more negative at the equilibrium position, making these bonds more stable.so yes N increases, and maybe even A12, A6 increase, but U is inherently negative making the cohesive energies stronger.
     
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