Crystal Structures from Powder Diffraction: Principles, Difficulties and Progress

Abstract

Abstract:The structure solution from powder diffraction has undergone an intense evolution during the last 20 years, but is far from being routine. Current challenges of powder crystallography include ab initio crystal structure determination on real samples of new materials with specific microstructures, characterization of intermediate reaction products from in situ, in operando studies and novel phases from in situ studies of phase diagrams. The intense evolution of electron diffraction in recent years, providing an experimental (precession) and theoretical (still under intense development) solution to strong dynamic scattering of electrons, smears the traditional frontier between poly-and single-crystal diffraction. Novel techniques like serial snapshot X-ray crystallography point in the same direction. Finally, for the computational chemistry, theoreticians hand-in-hand with crystallographers develop tools where the theory meets experiment for crystal structure refinement, which becomes an unavoidable step in the validation of crystal structures obtained from powder diffraction.Keywords: powder diffraction; structure solution; X-ray diffraction; DFT calculations; electron diffraction The structure solution means in this article determination of the (average) 3D-periodic arrangement of the atoms in the crystal using mainly the information content of Bragg scattering in the diffraction pattern. The case of aperiodic crystals (modulated and quasicrystals), of short-range order (diffuse scattering), as well as of nano-crystals (crystals without measurable Bragg signals) will not be discussed here. The structure prediction, on the other hand, will be used in the sense of the determination of the 3D arrangement of the atoms in the crystal using mainly first-principle calculations, and any experimental observation, like the diffraction pattern, is used only for the validation of the predicted structural model. Indexing: Still a BottleneckDespite an intense development of indexing algorithms in the last 20 years, the detection of the correct lattice may still be a bottleneck of the structure solution in the case of low resolution powder patterns or in the case of monoclinic and triclinic symmetry. A review of known indexing algorithms may be found in Chapter 7 of [3], Chapter 5 of [6] and Chapter 7 of [7]. Each crystallographer and each crystal may work better with a particular algorithm, but as is said in another excellent indexing The advantage of the dichotomy algorithm is its speed (especially in Fox) and its robustness towards low data quality. Indexing is followed by space group determination, which is based on systematic extinction analysis supported by the knowledge of crystal physical properties, like piezoelectricity, the presence of which excludes centrosymmetric space groups. Fairly robust algorithms for space group determination are based on full pattern fitting (Le Bail or Pawley), available in most software packages. The indexing can be quite difficult for the crystals lying on opposite ends of the s...

Synthesis, Characterization, and Crystal Structure Determination of a New Lithium Zinc Iodate Polymorph LiZn(IO3)3

“…This refinement procedure led otherwise to nonphysical results with some I-O bond distances too short and a reduced χ 2 smaller than 1. In order to optimize the above crystal structure determination, we also performed DFT calculations [38]. By considering the above-described structural model as the starting structure (with space group P2 1 ), we calculated the unit-cell parameters and atomic positions of all atoms for LiZn(IO 3 ) 3 by minimizing the total energy.…”

Synthesis, Characterization, and Crystal Structure Determination of a New Lithium Zinc Iodate Polymorph LiZn(IO₃)₃

“…This refinement procedure led otherwise to nonphysical results with some I-O bond distances too short and a reduced  2 smaller than 1. In order to optimize the above crystal structure determination we also have performed DFT calculations [36]. By considering our structural model (with space group P21) and the crystal structure of the other double iodates, we actually found that the above described structural model is the one leading to the lowest calculated enthalpy at ambient conditions.…”

Periodic DFT Calculations—Review of Applications in the Pharmaceutical Sciences

“…PXRD is also of a great use in situations when a single crystal could never be obtained, as it happens when some polymorphs can be reached only after spray-drying or milling [66]. Crystal structure determination using powder diffraction is difficult and may be inaccurate [67]. Often, in the PXRD, experimentally obtained crystal structures of organic solids the positions of the hydrogen atoms are not included and a DFT geometry optimization before further calculations is necessary [68].…”