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Homework Help: Schottky's defect

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data
    A ‘lattice gas’ consists of a lattice of N sites. Each of these sites can be empty, in which
    case its energy is zero, or occupied by one particle, in which case its energy is e. Each particle
    has a magnetic moment of magnitude μ which in the presence of an applied magnetic field
    B, can adopt two orientations (parallel or anti-parallel to the field). Evaluate the mean energy
    and mean magnetic moment of the system assuming that the particles are not interacting with
    each other.


    2. Relevant equations
    [tex]Z=\sum_r e^{-\beta E_r}[/tex]
    [tex]p_r=\frac{1}{Z}e^{-\beta E_r}[/tex]

    For a system of n defects in a system of N sites,
    [tex]\frac{n}{N}=\frac{1}{e^{\beta \epsilon}+1}[/tex]
    where ε is the energy associated with the defect

    Mean energy,
    [tex]\bar{E}=\frac{\partial \ln{Z}}{\partial\beta}[/tex]


    3. The attempt at a solution
    My problem is that I'm not sure whether there are three separate states for each site, or are there only 2 energy states and the schottky's defect must be considered separately.

    If I consider that there are 3 possible states, then the possible energies are
    [tex]\epsilon+\mu\beta,0\ \textrm{and}\ \epsilon-\mu\beta[/tex]

    But if this is not right, then I'm not sure how to go about on this question.
     
  2. jcsd
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