What exactly are crystal planes and how do they reflect x-rays?

1. What exactly are crystal planes and how do they reflect x-rays?

2. Are crystal planes real physical planes or just an abstract concept?

3. What are these planes made of?

4. If they are an abstraction, what do the x-rays hit and get reflected by? Individual atoms?

5. Then where is the concept of a plane coming in?

6. And why do different crystal structures have different 'active' reflecting planes?

7. Could someone please clear up the concept of these planes and Bragg's Law for me?

1. In the image above, you can see a series of Bragg planes drawn in the crystal. This is called one "set of planes". Another "set of planes" would be if one would just draw a series of horizontal lines through the atoms. (Of course by lines I mean planes, but they are projected here onto a 2D image).

2. The planes are those formed by the atoms, so in that sense they are real -- but they are not "mathematical" planes as those stretch to infinity.

3. These planes are made from the atoms that form the crystal. Different crystals will have different structures and therefore the planes will be different.

4. X-rays are actually reflected by electrons most strongly. Therefore, what they are actually scattering off of are the core electrons around the nuclei. What is happening is that because of the structure of the crystal, one can make each of the reflected X-rays constructively interfere by hitting the crystal just at the right angle with the right wavelength of X-ray.

5. The concept of the plane arises when one considers constructive interference as I have described in 4. The atoms effectively form an X-ray diffraction grating (in a reflective geometry as opposed to a transmissive geometry that we are used to).

6. As you can see from the picture above, there are many different "sets of planes" that one could draw. Depending on the angle of incidence and reflection with respect to the crystal, one can reflect off any of these planes in principle.

7. The Bragg Law is a constructive interference condition. The path-length difference between planes is $2d\sin\theta$ and this must be equal to an integer number of wavelengths, $n\lambda$, for the X-rays to constructively interfere with one another. Therefore $2d sin\theta = n\lambda$ is the condition to get "Bragg Scattering".

1. and 2. Crystal planes contain sets of atoms, which occupy identical positions in the primitive cell.

2. So to say, the planes are made out of atoms (and nothing in between). Or if you want a more quantum mechanical picture, you would have electron orbitals in between, which are responsible for the chemical bonding.

3. X-rays get scattered by individual atoms. If many atoms act as scattering centers (e.g. a crystal plane or a set of), the scattered spherical waves, originating from the atoms as point sources, become a planar wave again.

4. This depends on the crystal structure and symmetry.

5. Wikipedia might help with nice pictures there.