Single-crystal structure analysis


Single-crystal structure analysis uses – like the phase analysis and structure refinements on powders – the scattering properties of a selected kind of radiation on solid matter in order to determine crystalline structures.

Nevertheless, there are distinct differences concerning the following aspects:

Powder samples contain (ideally) all crystalline orientations randomly to the same extent. This allows the parallel collection of reflection intensities within a given 2θ (respectively Q or d) range to get a diffractogram. This can be processed by Rietveld refinement afterwards to determine the structure. Thus, this method is extremely fast and most suitable for in-situ studies (e. g. of chemical processes in batteries).
In contrast, single-crystal samples fulfill Bragg’s law usually only for one set of planes at the same time (see Ewald construction). Therefore, suitable rotations of the sample in the incoming beam are mandatory in order to collect reflection intensities of one lattice plane after another. Obviously this sequential process is usually more time consuming than a powder diffraction experiment.
In addition, studies on single crystals require sufficiently large crystals. This demands in the case of single-crystal diffraction with neutrons the growth of crystals of few cubic millimetres at least.

On the first glance powder diffraction seems to be superiour against single-crystal diffraction. Nevertheless, powder diffraction considers only the projections of Bragg intensities against diffraction angles and Q values or d values respectively. Angular ratios between different lattice planes are taken into account only to a very limited extent. This is problematic in different aspects: firstly, not only the intensities of symmetry-equivalent lattice planes but also intensities of all even non-symmetry equivalent planes with same d value superimpose. Secondly, reflections from similar d values tend to overlap due to the always limited instrumental resolution. Both aspects yield uncertainties concerning the correct relationship between intensities and corresponding lattice planes. Especially concerning the determination of mean-square displacements (atomic oscillations around their average positions) this can become an issue. Instead, for single crystals each set of lattice planes can be measured separately. This reveals hidden symmetry reductions more precisely (reflections assumed to be equivalent show in reality different intensities). Furthermore, modulations and twinning can be proved precisely as building of domains of different orientation becomes visible in single-crystal diffraction by profile splitting. Also, special effects like multiple scattering on same sets of lattice planes (extinction effect) or on different sets of lattice planes (Renninger effect) can be studied.

  Diagrams Copyright: © IfK

Reflection splitting of twinned La2CuO4 single crystal: left: (006) reflection, right: (220) reflection; each reflection profile is a superposition of 4 domain types generated by a phase transition from a tetrahedral to an orthorhombic space group (Rocking scans (= sample rotation at fixed Bragg angle) made on HEiDi@MLZ at room temperature).


In summary single-crystal diffraction is favourable in those cases that require very high accuracy or information of anisotropic effects (e. g. magnetic order) to solve a scientific topic. Beyond this, as the different natures of interaction of X-ray and neutron radiation with matter – electronic vs. nuclear and/or magnetic interaction – reveal different structural aspects, the combination of different methods is highly recommended for comprehensive structure analysis.

Further information can be found here, for instance:

Powder and single crystal diffractometry: chemical and magnetic structures; M. Meven; Lecture Notes of the 50th IFF Spring School 'Scattering! Soft, Functional and Quantum Materials' Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich, Reihe Schlüsseltechnologien / Key Technologies 190, D3 - D3.32 (2019)

Single-Crystal X-Ray Diffraction; Ulli Englert, in Handbook of Solid State Chemistry, Part 3. Characterization (eds R. Dronskowski, S. Kikkawa and A. Stein) (2017); DOI:10.1002/9783527691036.hsscvol3001

Neutron Diffraction; Meven, M. and Roth, G.; in Handbook of Solid State Chemistry, Part 3. Characterization (eds R. Dronskowski, S. Kikkawa and A. Stein) (2017); DOI:10.1002/9783527691036.hsscvol3004