Multi-scale phase analyses of strain-induced martensite in austempered ductile iron (ADI) using neutron diffraction and transmission techniques

The content of strain-induced martensite in austempered ductile iron has been quantitatively determined using three different kinds of neutron methods: (1) high-resolution powder diffraction with subsequent standard Rietveld refinement, (2) phase quantification using pole figure measurements and (3) Bragg edge neutron transmission. The accuracy and scope of applications of these neutron diffraction and imaging techniques for phase quantification have been compared and discussed in detail. Combination of these methods has been confirmed as effective for dealing with problems like peak overlap in multi-phase materials and texture formation after plastic deformation. Further, the results highlight the potential of using single peak pole figure data for quantitative phase analysis with high accuracy.

Texture Analysis with MTEX – Free and Open Source Software Toolbox

The MATLAB™ toolbox MTEX provides a unique way to represent, analyse and interpret crystallographic preferred orientation, i.e. texture, based on integral (“pole figure”) or individual orientation (“EBSD”) measurements. In particular, MTEX comprises functions to import, analyse and visualize diffraction pole figure data as well as EBSD data, to estimate an orientation density function from either kind of data, to compute texture characteristics, to model orientation density functions in terms of model functions or Fourier coefficients, to simulate pole figure or EBSD data, to create publication ready plots, to write scripts for multiple use, and others. Thus MTEX is a versatile free and open-source software toolbox for texture analysis and modeling.

Elaboration on the hexagonal grid and spiral trace schemes for pole figure data collection

A practical description of the mathematics required to implement the hexagonal grid and spiral trace pole figure data collection schemes is presented. Applying the concepts of stereographic and equal area projections with geometry, spreadsheets were created to calculate the angular settings of the goniometer. Using the generated settings, the hexagonal grid and spiral trace schemes were programmed into the existing X-ray software and employed to collect data for a sample of aluminum foil. The resulting (111) pole figures were similar to those collected with the conventional 5°χ×5°ϕ grid. The hexagonal grid has been shown by others to reduce the number of data points and time needed to complete a pole figure, while providing equal area sampling. Although not optimized, the spiral method was also investigated as another alternative to the 5°χ×5°ϕ grid.

A new method for texture measurements using a general area detector diffraction system

Advances in X-ray texture solutions require new methods and descriptions for the texture analysis process, e.g., when using general area detector diffraction systems. A new method is presented that defines a general pole figure resolution and provides the possibility to optimize strategies for efficient pole figure data collection. Application of the new method improves resolution and (!) speed. New software enables simultaneous monitoring of pole and detector space. This allows a fundamentally better understanding of the collected information, e.g., in situations where peaks overlap or high backgrounds compromise data quality.

Pole Figure Inversion Using Finite Elements Over Rodrigues Space

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.

Defocusing Correction of X-Ray Pole Figures by Means of Neutron Pole Figure Measurement

A rather simple empirical defocusing correction method is described which makes use of X-ray and neutron measurement of pole figure data from a sample with a weak preferred orientation.

Use of a Two-Dimensional, Position Sensitive Detector for Collecting Pole Figures

Conventional pole figure instruments consist of a scintillation detector mounted on a 4-circle goniometer operating under computer control. A few instruments make use of a linear PSD detector, which allows collecting data for multiple pole figures sinmltaneously. A PSD does not reduce the required data collection time for the primary pole figure; however, it does save time by eliminating the need to recollect multiple pole figure data. By using a 2D “area” detector, one can simultaneously collect multiple pole figures and reduce the data collection time for the primary pole figure, such an area detector pole figure processing package, GADDS v2, was developed at Siemens and will be discussed.

A Method for the Generation of Various Ghost Correction Algorithms—the Example of the Positivity Method and the Exponential Method

A theoretical strategy is presented that can derive the algorithms of several existing ghost correction methods. The examples of the positivity method and the “GHOST” method are elaborated. A new method is derived as well: the “exponential” method. It can successfully replace the quadratic method as a method that yields an exactly non-negative complete C.O.D.F. from pole figure data. The theoretical scheme that can generate all these algorithms makes use of the fact, that several parameter sets can be defined in order to describe a C.O.D.F. The parameters of one set are then functions of those of the other. The algorithms are derived from Taylor series expansions of these functions.

An Evaluation of the Single Orientation Method for Texture Determination in Materials of Moderate Texture Strength

New microscopy technology has made it feasible to consider using single orientation measurements to obtain Orientation Distribution Functions (ODF). Single orientations are preferred over pole figure data in ODF calculations because the odd terms of the series expansion are not directly accessible when pole figures are used. However, the number of single orientation measurements required to calculate a statistically reliable ODF has generally been considered too large to practically obtain. This study found that the location of the major features of the ODF in rolled aluminum sheet were identifiable after only 100 measurements. However, the heights of the peaks and the secondary features required many more measurements to stabilize. Unless the orientation measurements can be automated or orientation correlation data is needed the pole figure method remains a more efficient means of obtaining the data necessary to measure texture.

An X-ray Diffraction Procedure for Measuring Retained Austenite in High Chromium White Cast Iron

High chromium white cast irons are used in the mineral processing industry as grinding balls and grinding mill liner plates. The effect of retained austenite on the field performance of these irons is not clearly understood, but it is believed that control of the retained austenite level is essential in optimizing field behavior. Improved analysis techniques are required to provide this control.This paper presents an equal area pole figure data collection procedure for determining retained austenite in textured material in which few diffracted peaks are available for analysis. As analysis techniques improve, the significance of retained austenite in high chromium white cast irons can be better evaluated.