Ultramicroscopy 107 (2007) 483–494 Structure solution with three-dimensional sets of precessed electron diffraction intensities Mauro Gemmi a,Ã , Stavros Nicolopoulos b,c a Dipartimento di Scienze della Terra ‘‘A. Desio’’, Universita` degli Studi di Milano, Via Botticelli, 23, 20133 Milano, Italy b Universidad Politecnica de Valencia, Anenida de los Naranjos s/n 46022 Valencia, Spain c Nanomegas sprl, Blvd Edmond Machtens 79, B-1080 Brussels, Belgium Received 25 January 2006; accepted 9 March 2006 Abstract The use of the precession technique for obtaining three-dimensional (3D) sets of electron diffraction intensities suitable for structure solution is discussed. The minerals uvarovite and a˚kermanite have been used as testing structures. The electron diffraction data sets obtained on these samples retain an acceptable linear relation with calculated structure factor amplitudes. The quality of these data is suitable to solve both structures using direct methods opening the possibility to use 3D precession ED data for solving unknown mineral structures. r 2006 Elsevier B.V. All rights reserved. Keywords: Electron diffraction; Precession technique; Electron crystallography; Mineralogy 1. Introduction The strong dynamical character of the electron interac- tion with matter is the main obstacle for electron diffraction to become a usual technique for structure solution. A lot of efforts have been carried out for solving structures with electron diffraction data in the last decades ([1–6] are just few examples) but up to now electron crystallography is still far from single crystal X-ray crystallography in developing a method that can work routinely. There are several fields that call for stronger electron crystallography methods: inorganic chemistry, material science, structural biology and mineralogy are just some examples. With an electron microscope it is possible to perform a single crystal diffraction experiment on a crystal grain having size much smaller than 1 mm. The same experiment is impossible with X-ray even if we have a synchrotron at our disposal. The crystal grain can be chosen among a multitude of different phases present in the sample if a single-phase sample is not available. This situation is quite common when we deal with synthetic samples or if we are studying rocks. In this case with the usual diffraction techniques we can obtain just a powder pattern with obvious problems for structure solution caused by peak overlapping. Therefore, if a structure solution method that can work with electron data was available, it would be the leading technique for structure investigation of powder microcrystalline or multiphase samples. It appears clear now after years of attempts that such a method must treat in some way the dynamical effects. A pure kinematical approach has a chance to retrieve the structure in projection [7], since the probabil- istic relations between the phases, exploited by direct methods, are ‘‘statistically’’ correct [8,9]. However this approach very rarely is able to furnish a reliable three- dimensional (3D) set of reflections [10] due to wrong rescaling between the plates [11]. The precession technique, proposed for the first time by Vincent and Midgley in 1994 [12] partially solves these problems by increasing the kinematical character of the diffraction pattern. In this diffraction geometry few reflections are simultaneously excited, therefore, in principle, the scattering can be well described with a few beams approximation if simple geometrical correction are applied [13]. Gjønnes et al. [14] ARTICLE IN PRESS www.elsevier.com/locate/ultramic 0304-3991/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2006.03.010 Ã Corresponding author. Tel.: +39 02 50315604; fax: +39 02 50315597. E-mail addresses: mauro.gemmi@unimi.it (M. Gemmi), info@nanomegas.com (S. Nicolopoulos).