Analysis of multiple solutions in powder pattern indexing: the common reciprocal metric tensor approach

Powder pattern indexing routines frequently yield multiple solutions,i.e.different reciprocal lattices and unit cells. Here, a method is suggested that reveals whether or not there are numerical and geometric relationships between the solutions. It is based on the detection of a reciprocal vector triplet that is common to two or more proposed reciprocal lattices. Hence, the method can be termed a common reciprocal metric tensor approach. If no such common tensor exists, the different reciprocal lattices are unrelated, but if one exists the lattices are either in a sublattice/superlattice or in a coincidence-site lattice relationship, depending on the character of the respective orientation matrix. Furthermore, the approach can also be used to generate, from a given indexing solution, further valid indexing solutions that could also be produced by indexing routines.

Fast calibration of CBED patterns for quantitative analysis

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.

E(K) OF Ni ABOVE THE VACUUM LEVEL AS MEASURED BY VLEED ON RELAXED (110) SURFACE

Varying incidence angle, VLEED spectra R(E) and dR/dE were measured on Ni(110) using target current technique. The results were interpreted with the reference spectra calculated on the basis of ground-state band structure. Some critical points (CPs) of E( k ) displayed themselves as dR/dE extremums while others remained invisible. Changing of incidence K || by a surface reciprocal vector switched manifesting CPs. Experimental CPs were determined by comparing energies of experimental dR/dE extremums with. their reference counterparts. Having mapped CPs along a variety of non-symmetry directions, bands along ΓX were constructed. Experimental E( k ) is consistent with other experimental data and APW calculations. Some peculiarities are attributed to the influence of surface relaxation. Capabilities of VLEED to provide PES with upper bands are discussed.

A novel approach to the identification of microcrystals with electrons

Measurement of conventional-cell data requires observations along several specific zone axes in most cases. On the contrary, as shown in and outlined below, primitive-cell data can be extracted ab-initio, without trial-and-error, from single CBED patterns exposed along any zone axis, and displaying at least ZOLZ and first-order Laue-zone (FOLZ) spots.The CRYSTDAT database, which is up-to-date and accessible on-line, contains over 180,000 entries, each with cell data, chemistry and reference to published work for a compound. It can be searched for primitive cell data and partial chemistry. In combination with the previous remark, this shows that crystallites can be identified from single CBED patterns, and from partial chemical information obtained on them by Energy-Dispersive X-ray spectroscopy.CBED patterns are analyzed as follows. Two-dimensional (xP.vP) cartesian coordinates are measured for centers of all diffraction spots on the CBED film from an arbitrary origin. To each Bragg spot P on the film corresponds a scaied reciprocal vector FS with projections on the three axes:

A least-squares method for the determination of the orientation matrix in single-crystal diffractometry

An appropriate choice of the function minimized permits linearization of the least-squares determination of the matrix which transforms the diffraction indices into the components of the reciprocal vector in the diffractometer φ-axis system of coordinates. The coefficients of the least-squares equations are based on diffraction indices and measured diffractometer angles of three or more non-coplanar setting reflexions.