The Rietveld method is a powerful to extracting detailed crystal structural information from X-ray and neutron powder diffraction data. Since then structural details dictate much of the physical and chemical attributes of materials, knowledge of them is crucial to our understanding of those properties and our ability to manipulate them. Since most materials of technological interest are not available as single crystals but often are available only in polycrystalline or powder form, the Rietveld method has become very important and is now widely used in all branches of science that deal with materials at the atomic level. For more information please check the attached file below. By Luca Lutterotti

XRD is the experimental technique primarily used to determine the geometrical arrangement of the atoms or molecules within matter (crystal structure). When a crystal is bombarded by a beam of X-rays, X-rays are scattered by electron shells, and the angles through which the beam is diffracted reveal the shape and dimensions of the crystal’s unit cell. Diffraction experiments require the use of monochromatic Kα (or very close to monochromatic) radiation. This nearly monochromatic K α X-rays can be selected by the use of a filter or a monochromator. Since the wavelengths of Kα1 and Kα2 Xrays are so close in value, they are observed as a single Kα line when powder samples are probed. In XRD systems, single crystals are sometimes used as reference samples for calibration purposes. However, single crystals have narrow diffraction peaks that, when collected at high resolution, reveal doublets. To understand the origin of these doublets one needs to understand how X-rays are generated in a typical PXRD instrument.  diffraction experiments. These characteristic X-rays are produced when high-energy electrons knock out the inner shell electrons of the anode material. The electrons from higher shells of the target atoms then drop down and fill the created vacancies and, in this process, emit X-rays with well-defined energy. For example, if a 1s electron from the K shell of copper atom is ejected, the resulting vacancy can be filled by an electron from the L shell (2p1/2 or 2p3/2) (I ask students why not from 2s orbital), the M shell (3p1/2 or 3p3/2), or the N shell (4p1/2 or 4p3/2). Subscripts 1/2 and 3/2 are the values of j, the total angular momentum quantum number.

XRD is the experimental technique primarily used to determine the geometrical arrangement of the atoms or molecules within matter (crystal structure). When a crystal is bombarded by a beam of X-rays, X-rays are scattered by electron shells, and the angles through which the beam is diffracted reveal the shape and dimensions of the crystal’s unit cell. Diffraction experiments require the use of monochromatic Kα (or very close to monochromatic) radiation. This nearly monochromatic K α X-rays can be selected by the use of a filter or a monochromator. Since the wavelengths of Kα1 and Kα2 Xrays are so close in value, they are observed as a single Kα line when powder samples are probed. In XRD systems, single crystals are sometimes used as reference samples for calibration purposes. However, single crystals have narrow diffraction peaks that, when collected at high resolution, reveal doublets. To understand the origin of these doublets one needs to understand how X-rays are generated in a typical PXRD instrument.  diffraction experiments. These characteristic X-rays are produced when high-energy electrons knock out the inner shell electrons of the anode material. The electrons from higher shells of the target atoms then drop down and fill the created vacancies and, in this process, emit X-rays with well-defined energy. For example, if a 1s electron from the K shell of copper
atom is ejected, the resulting vacancy can be filled by an electron from the L shell (2p1/2 or 2p3/2) (I ask students why not from 2s orbital), the M shell (3p1/2 or 3p3/2), or the N shell (4p1/2 or 4p3/2). Subscripts 1/2 and 3/2 are the values of j, the total angular momentum quantum number.