Materials Science Forum Vols. 495-497

Abstract: Grain structures in crystalline material are commonly identied by orientation inhomogeneities in orientation maps. A statistical approach is introduced to extract quantitative information on the chord length distribution of grains from orientation data gathered by electron back-scattering diffraction.

Abstract: This paper describes progress in improving the spatial resolution of the well-established Orientation Imaging Microscopy technique, OIM, by developing an analogous procedure for the transmission electron microscope. The transmission orientation micrographs are obtained by recording a large series of dark field micrographs taken from the chosen area in the specimen. This area is selected so that it contains all of the grains of interest and is imaged at sufficiently high magnification to yield the spatial resolution required. The changing intensity of each pixel in different dark field micrographs permits the equivalent of a diffraction pattern for that pixel to be constructed. This enables determination of the lattice orientation of small volumes in the sample corresponding to that imaged in each individual pixel. Experimentation has shown that problems arise however, that decrease the fraction of correctly measured points due to ambiguities in determining the index of higher order reflections, especially when the total number of reflections observed is small. The solution has been to both modify the indexing procedure and to sum the diffraction vectors observed within a single grain. The paper concentrates on a detailed analysis of a heavily deformed aluminium sample, chosen because of the fragmentation of the structure.

Abstract: The effect of orientation noise in EBSP data on measurement of percolation threshold values has been investigated by use of computer simulated microstructures. A 2-D Monte Carlo Potts model run on a square lattice of size 200 x 200 was used to generate a microstructure containing approximately 150 grains. Orientations were then assigned to each of these grains to generate single texture component microstructures of differing texture tightness (“model” data). In order to simulate the effect of orientation noise on the experimental data, the orientation at each point in the 200 x 200 grid was adjusted in a manner consistent with experimental observations of the effect of orientation noise. The model data represent therefore an underlying real grain structure, and the noise-adjusted data represent the orientation map that would be measured using EBSP analysis at a given orientation noise level. The misorientation angle q70% at which 70% of the grains were percolatively connected was then determined for both the ideal data and for the orientation noise adjusted data. A comparison of the two allows calibration of the extent to which percolation data may be incorrectly estimated by EBSP measurements.

Abstract: Three-dimensional (3D) microscopy is a new and rapidly expanding area. A DualBeam system, with both a focused ion beam (FIB) column and an electron column, is a powerful instrument for imaging and sectioning microstructures to generate a full 3D sample reconstruction. When an electron backscatter diffraction (EBSD) system is attached to the DualBeam, it becomes a unique tool for making 3D crystallographic measurements on a wide variety of materials. Combining the successive removal by FIB, with sequential EBSD maps taken with the electron beam requires clear geometric considerations and a high level of automation to obtain a decent resolution in the third dimension, including positional sub-pixel re-alignment. Complete automation allows controlled sectioning and analysis of a significant volume of material without operator intervention: a process that may run continuously and automatically for many hours. Using a Nova600, a Channel 6 EBSD system and dedicated control software, Aluminium, Nickel and Steel specimens have been examined and volumes with up to 200 slices have been successfully analysed.

Abstract: The crystal structure of R-phase in Ti50.75.Ni47.75.Fe1.50 shape memory alloy (SMA) has been studied at a temperature of (290 ± 7) K on cooling by combined synchrotron and neutron powder diffraction using Rietveld refinement with generalized spherical harmonic (GSH) description for preferred orientation (PO). The results showed that (i) no significant improvement in the crystallographic RWP-factor was found when the inversion center was removed from the 3 P model, suggesting that the space group was indeed 3 P and not lower symmetry 3 P neither m P31 and (ii) the refined atomic parameters were converging only when the 3 P space group was used in the refinement.

Abstract: A new method of computing of normal distributions [1] on rotation groups is suggested. Monte Carlo method allows to calculate the orientation of grains function (ODF) and correspondent pole figures (PFs) using approximation by normal distributions [2]. The developed Monte Carlo method is applied for construction of PFs mathematical statistical model corresponding to experimental measurement. This model is based on statistical simulation of normal distributions on SO(3) group for discrete representation of pole figures. It is possible to calculate effective physical properties of polycrystals using the given discrete representation. The mathematical simulation for texture with two components of polycrystalline sample with hexagonal symmetry is developed. Two experimental PFs } 0 1 10 { and } 0002 { for Be measured by X-ray experiment are being used. For this case the effective property as a tensor of elastic compliance was calculated. The mathematical simulation of PFs also allows to determine the statistical errors of pole figures measurement.

Abstract: A long time has past since the introduction of the harmonic method for the reconstruction of the ODF from polefigure measurements, and it has been replaced by discrete methods of inversion, because of its incapability with respect to ghost effects. The harmonic method is still not in its best possible state: it disregards the high order harmonics; it disregards measurement errors and therefore gives suboptimal results; it does not provide standard errors, neither for the C-coefficients nor for the ODF; and there are the ghost effects. However, the harmonic method is a well established inversion method and it can improved at these points. Statistical considerations based on geostatistics and a model of the unknown ODF as a random function in a Baysian approach yields an inversion method, which can be characterized as a smoothing spline method. This new method is statistically optimal among all linear methods and resembles favorable features of the harmonic method in an improved way. It provides an optimal linear reconstruction of the even part of the ODF. It does not truncate the harmonic series expansion at a fixed level, but accounts for every even harmonic space in an optimal way with respect to its signal to noise ratio in the polefigure measurements. The method applies for irregularly sampled and incomplete pole figures. The method accomplishes standard errors for the ODF and the C-coefficients. Discrete inversion methods, explicitly or not, reconstruct the odd harmonic part of the function based on the principle of maximum entropy. Based on the theory of exponential families a continuous odd part (and the truncated even part) can be computed based on the entropy principle and the C-coefficients estimated by the spline method.

Abstract: Experimental pole figures are measured by x-ray method for materials with hexagonal symmetry (Ti and Mg alloys). The Orientation Distribution Function is calculated by approximation method with central normal distribution. Texture inhomogeneities and effects of defocusing are the main sources of pole density errors. The measurement errors depend on crystal direction {hkl} and are different for maximum and minimum regions on pole figure. The influence of texture measurement errors on accuracy of the ODF calculation is investigated.