[Big-Daddy]

Is there a general method for calculating the edge length of a unit cell in a solid structure, where only 1 atom/ion is involved (e.g. Cu or Au), in terms of the radius of that atom/ion (assumed to be spherical), given the crystal structure (but without resorting to using formulae specific to that structure alone)?

I say "general" because I know formulae exist for separate types of structure, e.g. body-centred, but I don't know how to arrive at these formulae from the basic picture of the crystal structure. Any guides I find are relevant only for those specific structures. That's why I seek a general method instead.

[AWK]

You cannot know a precise radius without knowledge of structure and the unit cell. Radius is calculated just from these data.

[Big-Daddy]

You cannot know a precise radius without knowledge of structure and the unit cell. Radius is calculated just from these data.

Yes - all I'm looking at is the calculations that go from the structure to the radius, i.e. the inverse of what you said! Given the radius and the 4 important structural values (number of atoms in the body of the cell, N_body, number of atoms on a face of the cell, N_face, number of atoms on an edge of the cell, N_edge, and number of atoms on the corners of the cell, N_corner) how do you then work out the edge length, face diagonal length and body diagonal length?

In the real world, I presume you would use these features and then a rearrangement of the method I ask for to solve for radius instead of the other way round (i.e. to solve for the lengths in terms of the radius is what I want to learn).

[AWK]

You should know radius and type of packing: fcc or hcp, bcc, simple cubic or diamond cubic for calculations in this direction. The rest is a simple geometry.
If you want to check which type of packing is real you should know density of real crystal. Shape of crystal allows you for distingushing between fcc and hcp.

[Big-Daddy]

You should know radius and type of packing: fcc or hcp, bcc, simple cubic or diamond cubic for calculations in this direction. The rest is a simple geometry.
If you want to check which type of packing is real you should know density of real crystal. Shape of crystal allows you for distingushing between fcc and hcp.

How is it simple? Can you give me an example by linking to a web-page that shows the maths?

[UG]

Do you mean something like this page?

http://www.science.uwaterloo.ca/~cchieh/cact/c123/bcc.html

[Big-Daddy]

Do you mean something like this page?

http://www.science.uwaterloo.ca/~cchieh/cact/c123/bcc.html

Yes.

As I predicted, once you know the value of the edge length (a), you can convert this directly to the volume (a3), body diagonal length ((3a²)^1/2) or face diagonal length ((2a²)^1/2).

The trouble is in finding a in terms of r. In the case of the structure on your website, bd is easily found as 4r, but in other situations it may be less obvious. Is there a general route to take? Or will it always be possible to line up the atoms in a way that finds an expression for r in terms of either a, bd or fd?

Packing Fraction = Number of Atoms in Unit Cell (calculated) * (4/3)*pi*r³ / a³ (a is a function in r, so this may simplify)