The Ewald Construction

A most useful means to understand the occurrence of diffraction spots is the Ewald construction. Let's begin slowly: We draw a sphere of radius 1/lambda, in the center of which we imagine the real crystal. The origin of the reciprocal lattice lies in the transmitted beam, at the edge of the Ewald sphere.

We know already that diffraction maxima (reflections, diffraction spots) occur only when the Bragg equation is satisfied. This condition occurs whenever a reciprocal lattice point lies exactly on the Ewald sphere.

As you may have assumed already, the chance for this to occur is modest, and we need to rotate the crystal in order to move more reciprocal lattice points through the Ewald sphere. In the following, I have drawn a reciprocal lattice in the origin, and we rotate it along the vertical axis of the drawing. We actually accomplish this by rotating the crystal along the same axis.

Just imagine turning the RL through the Ewald sphere : in the beginning, only (101) and (10-1) give rise to a reflection. After you turned the RL a bit (which actually means turning the crystal around the same axis), the reciprocal lattice point 201 will enter the sphere and create a diffraction spot.

For a Reciprocal Lattice Point (RLP) to be recorded as a reflection or diffraction spot, a number of non-trivial conditions need
to be fulfilled :
  1. The RLP needs to move through the Ewald sphere (ES) at least once, which is usually accomplished by turning the crystal around the vertical goniostat axis (omega), referred to as omega-scan.
  2. The RLP must lie within the resolution sphere (RS) of the crystal.
  3. The diffracted x-ray beam must hit the detector.