Debye-Scherrer diffraction patterns of powder samples with a tetragonal lattice structure

A polycrystalline powder sample of lead dioxide is irradiated with the radiation from a X-ray tube with a copper anode. A Geiger-Mueller counter tube is automatically swivelled to detect the radiation that is constructively reflected from the various lattice planes of the crystallites. The Debye-Scherrer pattern is automatically recorded. The evaluation of the pattern not only allows the Bragg reflexes to be assigned to the individual lattice planes and so also the corresponding Bravais lattice type to be obtained, but in addition results in values for their spacing as well as for the lattice constant of lead dioxide and the number of atoms in the unit cell.

Tasks

1. Record the intensity of the Cu X-rays back scattered by a lead dioxide powder sample as a function of the scattering angle.
2. Calculate the lattice constant of the substance from the angular positions of the individual Bragg lines.
3. Assign the Bragg reflexes to the respective planes of the lead dioxide lattice and determine which Bravais lattice type it has.
4. Determine the number of atoms in the unit cell.

Learning objectives

• Crystal lattices
• Crystal systems
• Bravais-lattice
• Reciprocal lattice
• Miller indices
• Structure factor
• Atomic scattering factor
• Bragg scattering
• Characteristic X-rays
• Monochromatization of X-rays