The necessary parameters (rotation axis, incident electron beam direction and beam tilt path) in order to describe the diffraction geometry in the Rotation Electron Diffraction (RED) method during data collection are determined and refined. These parameters are prerequisites for the subsequent calculations of excitation errors, sg, for zero (ZOLZ) or higher order Laue zones (HOLZ) reflections. Comparison with simulated results, for a CoP3 thermoelectric crystal, shows excellent agreement between the two approaches -calculated and simulated. In addition to their determination, a thorough refinement methodology for the incident electron beam direction and beam tilt path has been applied, too, based on Kikuchi lines of HOLZ reflections. Incorporation of the refined excitation error values can be considered both in theoretical calculations for diffracted beam intensities, based on the Bloch wave method, as well as in deducing integrated intensities from experimental rocking curves. The methodology described in this study is quite indispensable, as it forms an essential step for performing dynamical calculations in RED, enabling thus enhanced accuracy in structural parameter clarification. The latter is especially important in the case of thermal factors refinement for e.g. thermoelectrics, which are imperative for material properties’ evaluation.

Methods to determine the rotation axis using the rotation electron diffraction technique are described. A combination of rotation axis tilt, beam tilt, and simulated experimental diffraction patterns with nonintegers zone axis has been used. Accurate knowledge of the crystallographic direction of the incident beam for deducing the excitation error of reflections simultaneously near Bragg positions is essential in quantitative electron diffraction. Experimental patterns from CoP₃ are used as examples.

A diverse array of complex materials and structures are driving the nanotechnology and molecular biology revolutions.To understand and design these materials, it is essential to perform high precision structural characterization at the nanoscale.Often,even sub-Angstrom changes in inter-atomic bond lengths have profound consequences for the chemistry and functionality of these structuresensitive materials.Crystallographic methods are the gold standard for atomic structure determination, however a broad and growing class of materials and/or nanophase morphologies do not yield to a crystallographic analysis.The scattering is diffuse and Braggpeaks become broad and overlapped.This is "the nanostructure problem" which currently has no robust solution.I will discuss recent developments using the atomic pair distribution function (PDF) analysis of x-ray and neutron diffraction data that results in quantitative structural information on the nanoscale.I will describe the data collection and modelling methods that allow this, using a number of examples from materials science, physics and chemistry.

The η’-precipitate is the main strengthening agent in age-hardening Al-Mg-Zn alloys. A new structure model of the phase has been derived by a combination of electron microscopy techniques and synchrotron X-ray diffraction. Samples for intensity measurements were prepared from an alloy casting with large matrix grains alloyed with 88.1 Al, 10.2 Zn, and 1.68 Mg. wt per cent, after aging by a standard procedure. Electron microscope images reveal a distribution of precipitates 3-10 nm wide, with varying degree of stacking disorder, in four different lattice orientations, embedded in the aluminiummatrix. Electron diffraction patterns confirmed the hexagonal lattice, a = 0.496 nm, c = 1.405 nm reported earlier. Intensities were measured by the precession technique [1], which suppressed multiple scattering viamatrix reflections, but incurred a high background of diffuse scattering. Systematic absences are consistent with three hexagonal, P63mc (186), P62c (190) and P63/mmc (194) or two trigonal space groups, P31c (159) and P31c (163). Due to the extensive overlap and high background level, we could not distinguish between amodified version in (190) of the earlier model [2] or a trigonal structure in (163) from electron diffraction data. Three-dimensional synchrotron data were collected at the Swiss Norwegian Beamlines at ESRF from two single aluminium grains. More than 2000 intensities were extracted from each of the four orientations of these precipitate. The preliminary analysis points towards an average structure best described in the centrosymmetric space group P31c. A trigonal model adopted for an average η’-structure can be described as a faulted stacking of units of the Laves phase stable MgZn2, in a way that retains the trigonal stacking as in the parent FCC aluminium lattice.

OTED patterns arise from samples with preferred orientation of crystals.Reflections on OTED patterns from plate-like crystals appear as arcs.Structure amplitude could be determined either from integral intensity of reflection (integration of intensity of hole arc) or from local intensity of reflection (integration of intensity along radial profile of arc).Equations of intensity of reflections on OTED patterns were derived by Vainstein [1].Local intensity is given in [1] as:(1), where I hkl 'and I hkl -local and integral intensity of reflection, respectively, razimuthal length of reflection, -width of profile.New registration systems (Imaging Plate, CCD), suitable for electron diffraction, allow investigation of shape of reflections on OTED patterns in much more detailed way than ever.As can be seeing directly, distribution of intensity in azimuthal direction of arc is not uniform and thus, equation ( 1) is not correct.Precise determination of structure amplitude could be done with the respect to the shape of arc in azimuthal direction.The last depends on deviation of sample from ideal "texture" and could not be predicted in advance.The only way is to describe shape of reflections with analytical functions for each particular sample, assuming that shape of reflection is one and the same for all reflections on OTED pattern.

Two spinel dunite xenoliths (Fo(89.8-91.2) in olivine) from La Palma contain minor amounts (<1%) of a pale-blue sodalite-group mineral with hauyne/lazurite chemistry. Selected-area electron diffraction (SAED) patterns of this phase indicate a cubic unit cell with dimensions 9.12 +/- 0.02 Angstrom, and space group P (4) over bar 3n. Superstructure spots along three <110> directions are common, implying commensurate or incommensurate modulations along <110> directions. Raman spectra show peaks typical of both lazurite and hauyne. It is concluded that the mineral has a structure intermediate between those of pure lazurite and pure hauyne, and it is here referred to as hauyne(ss). The hauyne(ss) occurs together with strongly nepheline-normative glass in thin veinlets (<0.1 mm), in interstitial glass pockets, and as inclusions in olivine porphyroclasts. To our knowledge lazurite or hauyne has not previously been described in mantle rocks. The hauyne(ss) is strongly depleted in REE and most other highly lithophile elements relative to the coexisting glass, whereas D-mineral/glass for Sr is approximate to 1.0, and D-Eu higher than the other REE. The hauyne(ss) crystallized from a melt now present as phonolitic glass, probably in response to rapidly decreasing pressure during transport of the xenoliths to the surface. The coexistence of hauyne(ss) and FeS-rich sulfide globules in some samples suggests slightly more oxidizing conditions than for samples in which the glass contains sulfide globules alone.

Electron diffraction intensities can be obtained at large scattering angles (sinθ/λ ≥ 2.0), and thus structure information can be collected in regions of reciprocal space that are not accessable with other diffraction methods. LACBED intensities in this range can be utilized for determination of accurate temperature factors or for refinement of coordinates. Such high index reflections can usually be treated kinematically or as a pertubed two-beam case. Application to Y Ba2Cu3O7 shows that a least square refinememt based on integrated intensities can determine temperature factors or coordinates.LACBED patterns taken in the (00l) systematic row show an easily recognisable pattern of narrow bands from reflections in the range 15 < l < 40 (figure 1). Integrated intensities obtained from measured intensity profiles after subtraction of inelastic background (figure 2) were used in the least square fit for determination of temperature factors and refinement of z-coordinates for the Ba- and Cu-atoms.