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Young's modulus for cubic Van der Waals crystal

  1. Sep 22, 2014 #1

    ZetaOfThree

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    Gold Member

    1. The problem statement, all variables and given/known data
    Calculate the Young’s moduli for Van der Waals solids with sc, bcc, and fcc structures.


    2. Relevant equations
    Definition of Young's Modulus
    $$Y=\frac{stress}{strain}$$
    Total energy due to Van der Waals interaction:
    $$U_{tot}=\frac{1}{2}N(4 \epsilon) \left( \sum_j{ \left( \frac{ \sigma}{p_{j}R}\right)}^{12} - \sum_j{ \left( \frac{ \sigma}{p_{j}R}\right)}^{6} \right)$$
    Where ##p_{j}R## is the distance between the atom at the origin and the ##j^{th}## atom, expressed in terms of the nearest neighbor distance ##R##.


    3. The attempt at a solution

    I am considering using the fact that ##X_x=\frac{\partial U}{\partial e_{xx}}## (where ##X_x## is stress) and dividing by ##e_{xx}##, but I'm not sure how to do that with the expression for ##U## given above. Perhaps I can get ##R## in terms of the strain and then take the derivative? Are there any tips or hints you can give me so I can start this problem?

    Thanks in advanced.
     
    Last edited: Sep 22, 2014
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