X-ray diffraction

Key points: The scattering of radiation with wavelengths of about 100 pm from crystals gives rise to diffraction; the interpretation of the diffraction patterns gives quantitative structural information and, in many cases, the complete molecular or ionic structure. Diffraction is the interference between waves that occurs as a result of an object in their path. X-rays are scattered elastically (with no change in energy) by the electrons in atoms, and diffraction can occur for a periodic array of scattering centres separated by distances similar to the wavelength of the radiation (about 100 pm), such as exist in a crystal. If we think of scattering as equivalent to reflection from two adjacent parallel planes of atoms separated by a distance d (Fig. 8.1), then the angle at which constructive interference occurs (to produce a diffraction intensity maximum) between waves of wavelength is given by Bragg’s equation:

where n is an integer. Thus an X-ray beam impinging on a crystalline compound with an ordered array of atoms will produce a set of diffraction maxima, termed a diffraction pat tern, with each maximum, or reflection, occurring at an angle Ɵ corresponding to a different separation of planes of atoms, d, in the crystal.

Figure 8.1 Bragg’s equation is derived by treating layers of atoms as reflecting planes. X-rays interfere constructively when the additional path length 2d sin is equal to an integral multiple of the wavelength λ.

An atom or ion scatters X-rays in proportion to the number of electrons it possesses and the intensities of the measured diffraction maxima are proportional to the square of that number. Thus, the diffraction pattern produced is characteristic of the positions and types (in terms of their number of electrons) of atom present in the crystalline compound and the measurement of X-ray diffraction angles and intensities provides structural information. Because of its dependence on the number of electrons, X-ray diffraction is particularly sensitive to any electron-rich atoms in a compound. Thus, X-ray diffraction by NaNO₃ displays all three nearly isoelectronic atoms similarly, but for Pb(OH)₂ the scattering and structural information is dominated by the Pb atom. There are two principal X-ray techniques: the powder method, in which the materi als being studied are in polycrystalline form, and single-crystal diffraction, in which the sample is a single crystal of dimensions of several tens of micrometres or larger.

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مواضيع ذات صلة

Thermal analysis

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CHN analysis

Atomic absorption spectroscopy

Ionization and detection methods

X-ray absorption spectroscopy

Photoelectron spectroscopy

Spectroscopic monitoring of titrations and kinetics

Absorption spectroscopy

Neutron diffractionNeutron diffraction

Single-crystal X-ray diffraction

Powder X-ray diffraction