# Homework Help: Poissons ratio close-packed spheres

1. Oct 7, 2013

Hello,

See question 7.4 from the link.

"Assuming that atoms are hard elastic spheres, show that Poisson's ratio for a close-packed array of spheres is 1/3"

I am having trouble explaining the proof for this.

I know the that the volume modulus, K, = E(elastic modulus) / ((3(1-2υ)) where υ is Poisson's ratio

K = E / (3(1-2υ))

When υ = 1/3, K=E.

I'm thinking that since for a hexagonal close packed structure, HCP, the angles between lattice sites is 120°, or 1/3 of the plane of a full crystal structure.

Refer to:
http://www.science.uwaterloo.ca/~cch...ct/fig/hcp.gif [Broken]
http://www.chem.ufl.edu/~itl/2045/lectures/h1.GIF

Therefore the elastic properties for a given volume is split in thirds? It seems like a misleading argument, but I can't find a way to explain it with math!
1. The problem statement, all variables and given/known data

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Last edited by a moderator: May 6, 2017