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The elements of crystallography have been introduced many years ago, perhaps already by the work of Kepler (1611) followed by e.g. Miller (indices of crystal planes), Hessel (32 point groups), Bravais (translation types), Fjodorov, Schoenflies (230 space group types) etc. Symmetry was always the crucial in the description.
Powder diffraction (PD) is used for structural and microstructural characterization of materials. It includes not only the analysis of powder samples but also all kinds of polycrystalline materials. There are several monographies available devoted to this technique. Much has already been described for example in [1] and more recently in [2]. In addition to original Debye-Scherrer method, nowadays mainly the so-called Bragg-Brentano parafocusing geometry is used with symmetrical 2θ − θ or θ − θ scan when the information contained in each diffraction peak hkl is related only to the corresponding (hkl) planes parallel to the surface, so that different peaks are related to different crystallite families. Each crystalline phase has its typical PD pattern as a fingerprint. Therefore, by using databases like PDF-5+ we can perform qualitative and quantitative phase analysis (e.g. [1-2]). PD peak positions are also related to the unit cell size, i.e. lattice parameters connected also to possible non-stoichiometry,lattice defects and residual stresses. Integrated intensities are given mainly by the structure factor – i.e. the crystal structure that can be refined or even sometimes solved from the PDXRD pattern (e.g. [3, 4]). They are also determined by the irradiated volume of suitably oriented crystallites, so that possible preferred orientation - texture can be estimated. Broadening of diffraction peaks can be influenced by small crystallite sizes and/or microstrains (e.g. due to dislocations) that can also be determined for each phase [e.g. 5, 6]. For detailed analysis of thin films, textures and stresses also asymmetric geometries and often parallel beam techniques are used.
References
[1] H.P. Klug, L.E. Alexander, X-ray Diffraction Procedures. John Wiley and Sons. 1974. https://doi.org/10.1107/S0021889875011399.
[2] Powder Diffraction: Theory and Practice, R. Dinnebier, S.J.L. Billinge. RCS Publ, 2008. https://doi.org/10.1039/9781847558237
[3] V.K. Pecharsky and P. Zavalij, Fundamentals of Powder Diffraction and Structural Characterization of Materials, Springer, 2025 https://doi.org/10.1007/978-3-031-91504-8
[4] Structure Determination from Powder Diffraction Data. Edited by W.I.F. David, K. Shankland, L.B. McCusker, Ch. Baerlocher. IUCr. Oxford Publ., 2002.https://doi.org/10.1093/acprof:oso/9780199205530.001.0001
[5] Modern Diffraction Methods, Edited by E.J. Mittemeijer and U. Welzel, Wiley, 2013. https://DOI:10.1002/9783527649884
[6] M.A. Krivoglaz: Theory of X-Ray and Thermal Neutron Scattering by Real Crystals. Springer. 1995. DOI: https://doi.org/10.33542/SRU-0350-0
