Diffraction: directions of diffraction

For a set of plane (hkl), an incident x-ray

beam with wavelength will be diffracted when

(1) incident, diffracted and plane normal are coplanar

(2) incident and diffracted beams both make a Bragg angle B with the (hkl) plane, where =2d sin B

Provided the structure factor for (hkl) plane F(hkl) is not zero

∑ )(π2

n

lzkyhxinhkl

nnnefF ++=

Summation over all atoms in a unit cell with positions [xn, yn, zn] and atomic scattering factor fn (to be defined later).

Difference between powder and single crystal diffraction

• For a single crystal sample, the whole sample is a large, continuous crystal

• A powder sample is an assembly of randomly or partial randomly oriented tiny crystals called grains, it may be in a form of true powder or a piece of solid bulk.

• For single crystal diffraction, both background and characteristic radiations from an x-ray tube are diffracted.

• In powder diffraction, only characteristic radiations are considered because diffraction of weak background radiations by small grains is usually negligibly weak.

Single crystal diffraction-Laue method

Laue camera

(a) Transmission (b) back-reflection Laue

W radiation, 30kV, 19mA

Powder diffraction

Powder diffraction: poles of plane normals for (hkl) planes of all grains distribute uniformly on the surface of the reference sphere

Powder diffraction-Pinhole camera

Powder diffraction-Hull/Debye-Scherrer camera

Powder diffraction-Hull/Debye-Scherrer camera

Homework assignment

•Cullity 3-1•Cullity 3-3