- Consider a two-dimensional crystal of close-packed
pennies.
- What is the coordination number?
- How many nearest neighbors does a given penny have?
- Call the nearest neighbor distance d, one penny diameter between the centers.
- How many next-to-nearest neighbors does a given penny have?
- What is their distance in terms of d?
- How many next-to-next-to-nearest neighbors does a given penny have?
- What is their distance in terms of d?
- Compute the Lennard-Jones sums Σ p
_{ij}^{-6}and Σ p_{ij}^{-12}

- The Madelung constant for the infinite line of ions of
alternating sign (page 64) is a conditionally (not absolutely) convergent
series. Show by explicit calculation (a computer program would be handy
since you need a lot of terms) that
- (1 - 1/2) + (1/3 - 1/4) + (1/5 - 1/6) + ... converges to ln(2)
- but (1 - 1/2 -1/4) + (1/3 - 1/6 - 1/8) + (1/5 - 1/10 - 1/12) + ... converges to ln(2)/2

- Consider a bcc lattice in which the cubic (non-primitive) cell dimension is "a". What is the volume of the truncated octahedron Wigner-Seitz primitive cell?