Solid State | Lattice constant | BCC -> HCP

[heycoa]

Homework Statement

Sodium transforms from bcc to hcp at about T=23K. Assuming that the density remains fixed and the c/a ratio is ideal (1.633), calculate the hcp lattice constant a, given that the lattice constant a'=4.23 Angstrom in the cubic phase

Homework Equations

I can't find any equations regarding this

The Attempt at a Solution

We haven't gone over this in class so I don't even know where to begin.

 

[TSny]

Using your text or the internet, you should be able to find the following information for bcc and hcp:

1. Shape of a unit cell.

2. Number of atoms per unit cell.

3. Volume of a unit cell in terms of the lattice constant(s). (If you can't find formulas for this, see if you can derive the volumes using geometry and the known shape of the unit cell.)

Think about the condition required for the density not to change in going from bcc to hcp.