How to Find the Volume of a Cubic FCC Unit Cell Using X-Ray Diffraction Data

[Dampi]

The question I'm confused about it below:-

A unit cell of copper is cubic FCC. X ray data was measured at Lambda= 1.5406 angstroms. What is the volume?

I think to find volume, I need to find lattice constant which is the length of the unit cell.

The peaks were given and they are at 43, 50.5, 74, 90 and 95 degrees. These are angles of 2Theta.

Do I need to find the crystallographic planes which the angles are reflected from? If so how?

I know how to use Bragg's Law and find d spacing. 2dsin(theta)= n(Lambda). Also d= a/SQRT(l^2 + k^2 + h^2) where a is the lattice constant. and l, h and k are Miller indices of the plane.

 

[Rajini]

I think as you mentioned, first you need to index the peaks then find 'a' from each peak and take a average of all 'a's. Then a³ will be the volume.
You can index easily.
please see this paper..
you will know how to index peaks:
http://arxiv.org/a/thirugnanasambandan_t_1

see 'X-Ray Diffraction Studies of Copper Nanopowder'

I hope your problem will be solved.

 

[Dampi]

Thanx for the reply.

How do you find that constant (on the paper) to divide by so that 3rd column becomes an integer? (eg. 46=184-138) ??

 

[Dampi]

i don't have all of the data from x ray diffraction. how do u assign the peaks to the specific planes? so confused :(

 

[Rajini]

Oh it is clearly mentioned in that paper..
you need to find a constant (any constant) such that 3rd col. will becomes an integer..you have to try..1st take the 1st value (138), then 2nd (184), then 3rd (366),then the difference between 1st and 2nd..
Homework problem: Just play with it...you will get a const.
and now you know whether FCC or BCC and therefore you know which is allowed and forbidden reflections.
Now you can tell the reflection...for eg., 3 has 1 1 1, 4 has 2 0 0, etc (see remarks in that paper)