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Solid State Physics | ionic crystal bonding | Born & Meyer equation

  1. Jan 28, 2013 #1
    1. The problem statement, all variables and given/known data
    1) Find the expression for the equilibrium interatomic distance as a function of A, n, and α
    2) Determine the expression for the binding energy at equilibrium.
    3) Calculate the constant n for NaCl, using the data from the Table 1.2 of Omar book and the fact that the measured binding energy is 7.95 3V per molecule (pair of ions). The Madelung constant for NaCl is 1.75.
    4)What does the Madelung constant depend on?

    2. Relevant equations
    The only equation given to us, the energy: U(R)=-N(m*e2)/(4∏ε0*R)+N(A/Rn)


    3. The attempt at a solution
    for 1) I took the derivative of the equation and set that to zero which seems like it would give me the expression at equilibrium however, I do not know where I am supposed to get α. Assuming I did it correctly,
    I got: dU/(dR)=A*R-n-(0.588002*m)/(ε0[/SUB*R2)=0.
    I am not sure if this even answers the question in all honesty.

    for 2) Not sure how to go about this one, I think it is just the above (derived) equation equal to some U(R)equilibrium. But am not too sure.

    for 3) If I have my numbers correct,
    N=6.022*10^23 (Avogadro constant)
    ε0=8.854*10^-12
    e=1.602*10^-19 (elementary charge)
    R=5.63 angstroms (the value in book)
    U(R)=7.95
    m=1.75 (given Madelung constant)

    So I need to solve for n, however I do not know what A is! I think that A is the Born constant but I have no idea how to get that. All I need is to figure out the Born constant then I can solve for n.

    for 4) I said that the madelung constant depends on the shape (Dimension) and the geometry of the crystal.

    Please help me I am lost!!!
     
  2. jcsd
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