# Homework Help: Young's modulus for cubic Van der Waals crystal

1. Sep 22, 2014

### ZetaOfThree

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?