Reciprocal lattice points and diffraction peaks

Question

I am having a issue with the concept of what this question is asking.

Question

For a FCC crystal describe all the reciprocal lattice points corresponding to the two diffraction peaks.

Here is my issue, it how I relate the lattice points to the diffraction peaks, as I am unaware of any method to do this.

My method thus far in solving is as follows.

1. The reciprocal lattice of a FCC is a BCC so from this I can find the geometrical structure factor.

2.From geometrical structure it is seen that allowed reflections that would correspond to the first two diffraction peaks are {110} and {200}, for which are a family of planes.

3. Planes that would allow for the peak are: (110) (101) (011) and (200) (020) (002).

And this is where my issue lies, is that these are planes represented by miller indices which are not lattice points. Have I missed something vital here or are my calculations completely wrong? I just cant understand how you related the points to the diffraction peaks.

I know the planes are represented by miller indices which a inverse of x y and z coordinates but they don't necessarily have to relate to lattice points

Answer 1

The reciprocal lattice is essentially the fourier transform of the real space lattice. Each lattice point in the reciprocal lattice is such that the direction of a vector from one point to another coincides with the direction of the normal to a (set of) real space plane(s), and the distance between these reciprocal lattice points is equal to the reciprocal of the interplanar distance.

Knowing this, you should able to calculate the position of the reciprocal lattice points with respect to the origin of the reciprocal lattice space.