Diffraction Principles

a reflection

Each individual bright beam that a crystal sends out is called a reflection, and it is labelled by three integers (hkl). The word is a leftover from Bragg's mirror picture, where the beam looked as if it had reflected off a plane of atoms; the name stuck even though, strictly, nothing reflects. So when a crystallographer says the (111) reflection is strong, they mean the diffracted beam indexed 111 is intense.

A reflection ties together three descriptions you have already met. It is one family of parallel (hkl) planes in the real crystal; it is one point of the reciprocal lattice; and it is one diffracted beam on the detector. Each reflection carries three things: a position (the angle it comes out at, fixed by the plane spacing through Bragg's law), an amplitude (how strong, set by the structure factor F_hkl), and a phase (which the experiment does not directly measure). Collect thousands of reflections and you have sampled the crystal's reciprocal lattice, spot by spot.

A small but important convention: the label (hkl) already absorbs the order of reflection, so the second-order (100) beam is simply the (200) reflection, with its own spacing d_200 = d_100 / 2. That is why an indexed pattern runs (100), (110), (111), (200), (210), ... — each is one reflection, one reciprocal lattice point, one number to measure. The full list of reflections and their intensities is the raw data from which a structure is solved.

A silicon powder pattern is a list of reflections: (111) at 2 theta = 28.4 degrees, (220) at 47.3 degrees, (311) at 56.1 degrees, and so on. Each is one reciprocal lattice point sampled; its angle gives d and its height gives |F|^2.

Every peak is a single reflection (hkl): a position (from d) and a height (from |F|^2), one reciprocal lattice point at a time.

The word 'reflection' is historical, not literal — a crystal diffracts, it does not truly reflect. And (hkl) already includes the order, so (200) is a reflection in its own right, not merely the second order of (100).

Also called
Bragg reflection(hkl) reflection繞射斑點反射點