Evaluating Dislocation Densities and Slip Systems in deformed Titanium using EBSD

Introduction

In order to predict the performance of materials in extreme environments, it is necessary to have a full understanding of their response to stress and strain. The analysis of experimentally deformed samples using electron backscatter diffraction (EBSD) is an ideal approach: the measurement of phases, grain size, texture and boundary properties are all important for building up a picture of the deformation processes that control the material's physical properties. However, the deformation is often controlled by the nature of dislocations within the crystal lattice of individual grains: by analysing these dislocations, it is possible to identify the operation of specific slip systems which in turn can determine the strength of the material.

Dislocations are usually studied via labour-intensive techniques such as transmission electron microscopy (TEM), electron channelling contrast imaging (ECCI) or via pattern correlation approaches such as High Resolution (HR) EBSD. However, it is possible to extract reliable estimates of the geometrically necessary dislocation (GND) densities from 2D EBSD datasets, using the concepts proposed by Nye [1]. In this application note, we compare 2 heavily deformed Titanium alloys and use an advanced dislocation analysis tool in AZtecCrystal to not only compare the GND densities but also to examine the dominant Burgers vector orientations, providing key insights into the activation of different slip systems in both samples.

Methodology

Two Ti-alloy samples were experimentally deformed under different conditions (temperature, strain and strain rate); both were then prepared for EBSD analysis using conventional mechanical polishing with a final stage of vibratory polishing with colloidal silica.

Focused EBSD orientation maps were collected using the Oxford Instruments AZtec software with the Symmetry S2 EBSD detector, installed on a field emission gun scanning electron microscope (SEM). The beam energy was set to 15 keV, and the measurement step size was in the range of 40–50 nm.

Following minor cleaning and the calculation of routine parameters such as grain size, texture and boundary disorientation distributions, the datasets were processed using an advanced dislocation analysis tool within AZtecCrystal. This is based on the weighted Burgers vector (WBV) approach [2], in which both the magnitude of the weighted Burgers vector and its direction are calculated using closed loops around each measurement in the dataset. The "weighted" term is in recognition of the fact that the contribution to the measurements of dislocation lines that intersect the plane of the map at a high angle will be greater than those that intersect at a shallow angle. For this reason, any GND density value, as for all 2D EBSD measurements, will be an indication of the minimum density.

The advantage of the WBV approach over conventional GND measurements using EBSD is twofold: firstly, the integration around the perimeter of loops minimises the effect of the orientation errors in the dataset providing more accurate results, and secondly the output includes the orientation of the WBV at each point which instantly provides insights into the dominant slip systems.

Results

The orientation maps show contrasting microstructures, with a more uniform elongation of the grains parallel to the load direction visible in sample 2 (Figure 1). The grains within both samples show evidence for significant plastic strain, including large intragranular disorientations and the formation of multiple low angle boundaries.

Figure 1. IPF-Z direction orientation maps of the 2 Ti samples. Top – sample 1, with the load direction parallel to X (scale bar 10 µm). Bottom – sample 2, with the load direction parallel to Y (scale bar 5 µm).

The GND density estimates are plotted in Figure 2. Although the maximum GND density recorded for sample 2 is about 30% higher than in sample 1 (1.0 × 10¹⁶ m⁻² compared to 7.6 × 10¹⁵ m⁻²), the localisation of regions with high GND densities appears broadly similar for the 2 datasets. When the GND densities are plotted in a histogram (Figure 3), the slight differences between the densities for the 2 samples are a little clearer, with once again ~30% difference between the mean values (1.62 × 10¹⁵ m⁻² for sample 2 compared to 1.25 × 10¹⁵ m⁻² for sample 1).

Figure 2. Maps showing the geometrically necessary dislocation (GND) densities for sample 1 (top) and sample 2 (bottom). Note that the 2 maps are plotted using the same scale (maximum 1.0 × 10¹⁶ m⁻²).

Figure 3. Histogram showing the full GND density distributions for the 2 samples, as calculated from the EBSD datasets.

The most striking differences between the 2 datasets are apparent when the directions of the Burgers vectors are plotted. In sample 1, the WBV orientations for the whole dataset show a very strong clustering about the <a> axis, whereas for sample 2 there is a weaker preference for the WBV to be aligned with the <c> axis (Figure 4). By itself, the Burgers vector orientations are not enough to determine the dominant active slip systems, but when combined with details on the rotation axes about low angle boundaries then it is possible to identify the slip system. In sample 1, the rotation axes for boundaries with 2–5° disorientations are very strongly clustered about the <c> axis; when coupled with the <a> Burgers vectors, this is suggestive of dominant screw dislocations in the <11-20>(0001) slip system. For sample 2, the rotation axes are predominantly lying close to the basal plane, indicative of edge dislocations in the pyramidal slip system, <1-213>(10-11).

Sample 1

Sample 2 Figure 4. Comparison of the Burgers vector orientations and low angle boundary rotation axes between the 2 samples. Top row: weighted Burgers vector orientations plotted in the crystallographic reference frame. Bottom row: rotation axes for 2–5° boundaries plotted in the crystallographic reference frame.

Summary

In-depth analysis of slip systems, Burgers vectors and geometrically necessary dislocation densities has usually required either in-depth work with a TEM, ECCI or HR-EBSD analyses, all of which are laborious methods and are ill suited to larger scale characterisation. Here we show how routine EBSD, coupled with a new advanced approach to dislocation analysis in AZtecCrystal, can provide a rapid assessment of the GND density and the Burgers vectors, permitting in-depth interpretations of slip system activity.

This approach has been demonstrated using 2 deformed Ti alloy samples. Although the microstructures and GND densities are broadly similar, the samples have very different Burgers vector orientations which, coupled with an analysis of boundary rotation axes, suggests the operation of the <11-20>(0001) slip system in the first sample and the <1-213>(10-11) slip system in sample 2.

References

1. J.F. Nye, Some geometrical relations in dislocated crystals, Acta Mater. 1 (1953) 153–162.
2. J. Wheeler, E. Mariani, S. Piazolo, D.J. Prior, P. Trimby, M.R. Drury, The weighted Burgers vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials, J. Microscopy 233 (2009) 482–494.