X-Ray Diffraction Homework: Deriving (2theta) Values

[Lemenks]

Homework Statement

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.

Homework Equations

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

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

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.

 

[mfb]

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