# X-Ray Diffraction

1. Oct 19, 2014

### Lemenks

1. The problem statement, all variables and given/known data

A crystal composed of two fractions, one having the a cell parameters of 4.123A and the other of 3.997A are subjected to X-ray diffraction using both Cu k-alpha and a Mo k-alpha radiation. Derive the angular position of (2theta) for (100) and (110) planes.
Explain the procedure you used for the calculation.

2. Relevant equations

Bragg's law: n*lambda = 2*d*sin(theta)

d = a/(h^2 + k^2 + l^2)^(1/2)

3. The attempt at a solution

I found both equations - I understand them but I don't know why a is different for both ions. I know that the ions radius will be different but when we scan the crystal, the value of a should be the same?

Anyway I will show one calculation, I know the method but I am not sure I can fully explain it.

d = a/(1+0+0) = a

n = 1

lambda = 1.542A for the Cu k-alpha radiation

1.542 = 4.123 sin(theta)

theta = 21.96

2*theta = 43.92 degrees.

I would repeat this 7 more times to find every peak for the two planes, the two forms of ka radiation and the two atomic radii. ~ I don't know why a is different for both atoms, if the lattice repeats infinitely and there are equal numbers of both atoms, then it seems like there should be equal distances between both atoms.

2. Oct 19, 2014

### Staff: Mentor

I think the different cell parameters refer to different crystals or crystal structures - your sample has both, but not at the same place.