Indexing Of Diffraction Patterns Research Articles

Icosahedrally related 1D quasicrystals

Taking a cut/section of a hyper lattice has proved a very elegant method of investigating the structure of incommensurate structures including the quasicrystals. We present here a method of generating a one dimensional incommensurate structure by distorting the six dimensional hypercubic lattice and the icosahedral basis vectors a long the 3 fold axis. Indexing of electron diffraction patterns of τ ∞ phase has been accomplished on this model and a structure for this phase having 3 symmetry a long the incommensurate direction and periodicity in planes normal to it has been proposed. The requirement of alternating Al and transition metal/vacancy layers in such structures can be satisfied by ordering the hyper unit cell a long three of the six directions.

Automatic indexing of rotation diffraction patterns

A method is described which assigns indices to a set of single-crystal reflections recorded by the rotation-oscillation technique using a fixed X-ray wavelength. It is assumed that the space group and approximate unit-cell parameters are known. The unknown crystal orientation is determined directly from the observed diffraction pattern of one or several oscillation data records. A local indexing procedure is described which tolerates large initial errors in the parameters controlling the diffraction pattern. These parameters are refined subsequently, thereby satisfying the constraints imposed by the space-group symmetry.

Identifying characteristics of the fibrous cesium titanate Cs 2Ti 5O 11

Electron microscopic studies of the fibrous cesium titanate Cs 2Ti 5O 11 reveal characteristic features not readily apparent using standard methods of phase analysis (optical microscopy, X-ray diffraction). Its fibrous needle-like laths give characteristic diffuse scattering, complicating the indexing of electron diffraction patterns. The hydrated form Cs 2Ti 5O 11 · (1 + x)H 2O (0.5 < x < 1) is typically grossly distorted, resembling pyrolytic graphite. Cs 2Ti 5O 11 is unstable when stored under ambient conditions at room temperature for ∼1 year when disproportionation into Cs 2Ti 4O 9 and Cs 2Ti 6O 11 · nH 2O occurs. The structure of Cs 2Ti 5O 11 and intergrowth defects in the unstable forms have been studied by high-resolution electron microscopy. It is evident that these phases would be undesirable in titanate ceramics such as SYNROC, which are designed for immobilization of radioactive 137C s.

EMS - a software package for electron diffraction analysis and HREM image simulation in materials science

EMS is a set of computer programs which has been developed not only for the simulation and analysis of High-Resolution Electron Microscopy images, but also for the analysis of diffraction patterns. It is composed of small, dedicted tasks which have a well defined function. Schematically EMS can be divided into two parts. The first part is able to handle the typical calculations of crystallography encountered in electron microscopy such as automatic indexing of diffraction and Kikuchi patterns, simulation of spot and powder patterns, drawing of stereographic projections, calculation of the Bravais lattice of an unknown structure from two diffraction patterns, etc. The second part offers the possibility of the simulation of structure images of both perfect and defect structures using either a Fast-Fourier-Transform-based multislice approach or the Bloch wave formalism. The dialogue with EMS is “menu”-driven and completely interactive. Moreover numerous “note” and “help” files are available on-line for the convenience of the user.

The direct indexing of two-beam electron diffraction patterns

A technique is described for the direct indexing of two-beam electron diffraction conditions in the electron microscope. The technique involves the calculation of angles between the g-vector to be indexed and a set of three known reference vectors. The experimentally obtained angles may be compared with calculated interplanar angles, leading to an unambiguous indexing of the two-beam situation. In-situ indexing is possible when the microscope is equipped with a device for the direct measurement of diffraction spot positions.

Indexing of electron double diffraction patterns from partially-decomposed cadmium halide crystals

Indexing of electron double diffraction patterns from partially-decomposed cadmium halide crystals

A computer program for unique indexing of electron diffraction patterns

A computer program for unambiguous and consistent indexing of a series of single-crystal diffraction patterns is discussed which allows determination of the unit triangle and therefore tilting of the specimen into any special orientation even if no Kikuchi patterns can be observed.

Indexing of electron double diffraction patterns from partially-decomposed cadmium halide crystals

Indexing of electron double diffraction patterns from partially-decomposed cadmium halide crystals

Computer-aided indexing of transmission electron diffraction patterns

This paper demonstrates that computer-aided indexing and orientation determination of transmission electron diffraction patterns is possible. For the particular examples considered in this investigation, the second-phase particle electron diffraction patterns are apparently those of the orthorhombic iron carbide, Fe 3C. The uniqueness of this approach arises primarily from the fact that the tedious task of routine, manual indexing is avoided and any degree of accuracy for position and angle error of the diffraction spots is on demand by the operator. In addition, the program considers all possible alternative diffraction pattern orientations which might be overlooked if conventional indexing methods are used.

Estimating the unit-cell volume from one line in a powder diffraction pattern: the triclinic case

In the computer indexing of powder diffraction patterns, an advance estimate of the volume of the unit cell is quite helpful. This paper describes an extremely rapid and easy to use method for estimating the cell volume directly from the powder diffraction data for the case of triclinic materials. Examination of a number of high-quality experimental patterns shows that the cell volume can often be estimated from only one line in the data. The relation is V = 13.39d320, where V is the cell volume and d320 is the d value of the 20th observed line. Other diffraction lines in the powder pattern can also be used for estimating unit-cell volumes. The analogous relations for the 25th and 30th lines are V = 17.24d325 and V = 21.32d330. This method is an outgrowth of one previously described by the author [Smith (1976), J. Appl. Cryst. 9, 424–4281 which involved the slope of a data plot. Within the set of some 40 high-quality triclinic patterns, the present one-line method predicts the unit-cell volume to an average discrepancy of 10.6%, 12.6% and 12.7% for the 20th, 25th and 30th lines respectively: the slope method, to 9.3%.

A method for the solution of electron diffraction patterns.

A simple aid to the indexing of electron diffraction patterns from multicomponent systems is described. An example of the method, which uses slide rule scales, is also given.

Computer Indexing of Electron Diffraction Patterns Including the Effects of Lattice Symmetry

In the 50 year period since the discovery of electron diffraction from crystals there has been much theoretical effort devoted to the calculation of diffracted intensities as a function of crystal thickness, orientation, and structure. However, in many applications of electron diffraction what is required is a simple identification of an unknown structure when some of the shape and orientation parameters required for intensity calculations are not known. In these circumstances an automated method is needed to solve diffraction patterns obtained near crystal zone axis directions that includes the effects of systematic absences of reflections due to lattice symmetry effects and additional reflections due to double diffraction processes.Two programs have been developed to enable relatively inexperienced microscopists to identify unknown crystals from diffraction patterns. Before indexing any given electron diffraction pattern, a set of possible crystal structures must be selected for comparison against the unknown.

Estimating unit cell volumes from powder diffraction data: the triclinic case

In the computer indexing of powder diffraction patterns, an advance estimate of the volume of the unit cell is extremely valuable. This paper describes a method for estimating it directly from powder-pattern data for the case of triclinic materials. The method involves an easily prepared graphical plot, the slope of which is proportional to the unit-cell volume. First, the diffraction lines are numbered consecutively, starting with the largest d value (N = 1). A plot is then made of 1/N versus d3. Theoretically, the resulting line has a slope of 3/(2πV) = 0.4775/V for triclinic compounds, where V is the unit-cell volume. Examination of the graphs plotted for a number of triclinic materials where the experimental data are of high quality shows that the slope consistently falls around 0.60/V. Hence, the volume of the unit cell and/or the calculated density can be estimated. In addition, this analysis gives a numerical measure of the fraction of possible diffraction lines actually observed.

An Interactive Minicomputer Program for the Indexing and Simulation of Electron Diffraction Patterns

Computer programs are now available in various laboratories for the indexing and simulation of transmission electron diffraction patterns. Although these programs address themselves to the solution of various aspects of the indexing and simulation process, the ultimate goal is to perform real time diffraction pattern analysis directly off of the imaging screen of the transmission electron microscope. The program to be described in this paper represents one step prior to real time analysis. It involves the combination of two programs, described in an earlier paper(l), into a single program for use on an interactive basis with a minicomputer. In our case, the minicomputer is an INTERDATA 70 equipped with a Tektronix 4010-1 graphical display terminal and hard copy unit.A simplified flow diagram of the combined program, written in Fortran IV, is shown in Figure 1. It consists of two programs INDEX and TEDP which index and simulate electron diffraction patterns respectively. The user has the option of choosing either the indexing or simulating aspects of the combined program.

Automated computer indexing of powder patterns: the monoclinic case

A procedure for the computer indexing of powder diffraction patterns of monoclinic crystals is described. The method is based on locating the orthogonal hk0 and 0kl zones by means of two relationships among the Q (= 1/d2) values: 2Q020 + Qh10 = Qh30 and 3Q020 + Qh20 = Qh40. The monoclinic angle is determined by trying certain low-index h0l and hkl values for the reflections not already indexed and by determining if the entire pattern can then be indexed. A computer program has been written in Fortran IV and extensively tested on a variety of known patterns of various degrees of experimental accuracy and inherent difficulty. At present, about 60% of the test patterns can be indexed in an automated fashion.

A contribution to the indexing of transmission electron diffraction patterns

AbstractA method for the indexing of TED spot patterns is presented. The reduced cell of the TED pattern defined by the two shortest vectors, which enclose an acute angle, serves as reference cell for the indexing. The d‐values of both the cell defining vectors and of their sum and difference vectors are determined being the four largest d‐values, which can be determined from the pattern. These four d‐values are compared with suitable d‐value sets of the possible crystalline phases and probable phase identifications are made. Generally, there exist several indexing variants for the individual d‐values of the separate phase identification possibilities. It is possible to find the correct indexing by the determination of the indices of the sum and difference vectors, occasionally, for one pair of the indexing variant from the vectors defining the reference cell and by comparison of these indices with the indexing variants for the d‐values of the sum and difference vectors of the corresponding phase identification variant. The measuring and calculation of the intervectorial angles formerly necessarily hasn't to be made in this method. However, the determination of the sum and difference vectors involves it. The reliability of the indexing can be increased in a strong manner if two or three different reciprocal lattice planes of the specimen under investigation are recorded in the corresponding TED patterns and if, in the following, these patterns can be indexed by the mentioned method without any doubt.

Computer-Aided Indexing and Simulation of Transmission Electron Diffraction Patterns

The process of indexing electron diffraction patterns is well established and reasonably straightforward. However, in the more complicated crystal systems (e.g. hexagonal, rhombohedral, orthorhombic and monoclinic), indexing and orientation determination is not always simple. In order to considerably ease the tedium of routinely indexing such electron diffraction patterns, automation of the procedure has been carried out in our laboratory by the use of two computer programs written in conversational Fortran.Simplified flow diagrams of the two programs are shown in Figure 1. The first program (Figure 1a) indexes diffraction spots whose x and y coordinates are obtained from an experimental pattern and supplied, along with crystal structure, lattice constants, space group restrictions, camera constant, and the position and angle errors allowable.

Indexing rhombohedral powder diffraction patterns

Based on statistical data of 21 rhombohedral structure types, a systematic procedure has been developed for the rapid unique indexing of rhombohedral powder diffraction patterns. The key to the graphical method is a novel semilogarithmic chart of log d versus 1 − tan2 (α/2) with α ranging from 2 to 118°. Convenient tables and formulas are given to expedite the evaluation of the lattice constants of an unknown phase.

A geometrical method for the determination and indexing of electron diffraction patterns

A geometrical method for the determination and indexing of electron diffraction patterns was developed by making use of descriptive geometry. This method is especially advantageous for noncubic structures. The general geometrical principles are presented, and a typical problem is solved in order to illustrate the procedures that can be followed to simplify the operations.

Complete indexing of electron diffraction patterns by computer

Complete indexing of electron diffraction patterns by computer