Explanation
Ideally, every possible crystalline orientation is represented very equally in a powdered sample. The resulting orientational averaging causes the three-dimensional reciprocal space that is studied in single crystal diffraction to be projected onto a single dimension. The three-dimensional space can be described with (reciprocal) axes x*, y*and z*or alternatively in spherical coordinates q, φ*, and χ*. In powder diffraction, intensity is homogeneous over φ*and χ*, and only q remains as an important measurable quantity. In practice, it is sometimes necessary to rotate the sample orientation to eliminate the effects of texturing and achieve true randomness.
When the scattered radiation is collected on a flat plate detector, the rotational averaging leads to smooth diffraction rings around the beam axis, rather than the discrete Laue spots observed in single crystal diffraction. The angle between the beam axis and the ring is called the scattering angle and in X-ray crystallography always denoted as 2θ (in scattering of visible light the convention is usually to call it θ). In accordance with Bragg's law, each ring corresponds to a particular reciprocal lattice vector G in the sample crystal. This leads to the definition of the scattering vector as:
Powder diffraction data are usually presented as a diffractogram in which the diffracted intensity I is shown as function either of the scattering angle 2θ or as a function of the scattering vector q. The latter variable has the advantage that the diffractogram no longer depends on the value of the wavelength λ. The advent of synchrotron sources has widened the choice of wavelength considerably. To facilitate comparability of data obtained with different wavelengths the use of q is therefore recommended and gaining acceptability.
An instrument dedicated to performing powder measurements is called a powder diffractometer.
Read more about this topic: Powder Diffraction
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