Claire Maurice

Accuracy assessment of elastic strain measurement by EBSD

A detailed accuracy analysis of electron backscatter diffraction (EBSD) elastic strain measurement has been carried out using both simulated and experimental patterns. Strains are determined by measuring shifts between two EBSD patterns (one being the reference) over regions of interest (ROI) using an iterative cross‐correlation algorithm. An original minimization procedure over 20 regions of interests gives a unique solution for the eight independent components of the deviatoric displacement gradient tensor. It is shown that this method leads to strain measurements on simulated patterns with an accuracy better than 10−4. The influence of the projection parameters is also investigated. The accuracy assessment is illustrated by two worked examples: (i) four‐point bending of a silicon single crystal and (ii) Si1 –xGex layers on a Si substrate. Experimental results are compared with finite‐element simulations.

Factors affecting the accuracy of high resolution electron backscatter diffraction when using simulated patterns

High resolution EBSD directly compares electron backscattering patterns (EBSPs), generated in a scanning electron microscope, to measure relative strain and rotation to a precision of ∼ 10(-4) in strain and 10(-4)rad (0.006 °) in rotation. However the measurement of absolute strain and rotation requires reference EBSPs of known strain and orientation (or a far field region of known strain). Recent suggestions of using simulated EBSPs with known strain show much promise. However precise measurement of the experimental geometry (pattern centre) is required. Common uncertainties of 0.5% in pattern centre result in uncertainty of ∼ 10(-3) in strain state. Aberrations in the compact lenses used for EBSP capture can also result in image shifts that correspond to strains/rotations of ± 10(-3) between experimental and simulated EBSPs. Simulated EBSPs can be generated using dynamical or kinematic models (or a combination of the two). The choice in simulation model has a significant effect on the measured shifts, particularly at zone axis and high structure factor bands, due to large intensity variations, and for simple kinematic simulations can result in the measurement of rogue shifts and thus erroneous strain measurements. Calibrant samples of known strain provide a method of measuring the experimental geometry but imprecise stage movement combined with the high depth of field in the SEM could also result in uncertainties in strain of ∼ 10(-3).

A 3D Hough transform for indexing EBSD and Kossel patterns

A three‐dimensional Hough transform is designed for the detection of conic curves (hyperbolae and ellipses) formed by the gnomonic projection of diffraction Kossel cones. This new procedure is applied to a high‐angular‐accuracy analysis of electron backscatter diffraction (EBSD) patterns and to a fully automatic indexing of X‐ray Kossel patterns in the SEM. The high‐accuracy analysis of EBSD patterns allows for the determination of local elastic strains, without any reference pattern, and with a spatial resolution of a few tens of nanometres. An accuracy of 2 × 10−4 is achieved on geometrically calculated diagrams. This paper presents also the first fully automatic indexing of Kossel patterns. This automatic indexing procedure can be applied to local texture analysis, as well as to local elastic strain measurements. Although the spatial resolution of Kossel is about 1 μm, the accuracy of strain measurement is in this case much higher than that presently obtained on EBSD.

A method for accurate localisation of EBSD pattern centres

The moving screen technique for pattern centre localisation is revisited. A cross-correlation based iterative procedure is developed to find both the zoom factor and the zoom centre (which is also the pattern centre) between two EBSD diffraction patterns acquired at two camera positions. The procedure involves two steps: first, a rough estimate of the pattern centre position and zoom factor (the ratio of the two detector distances) is obtained by cross-correlating the entire images. Then, based on this first estimate, cross-correlation of smaller regions of interest (ROIs) gives the displacement field which is interpreted as a zoom factor misfit coupled with a zoom centre position misfit. These misfits are iteratively decreased until the displacement field is reduced to the noise level. The procedure is first applied to simulated patterns and it is shown that the iterative procedure converges very rapidly to the exact solution with an accuracy better than 1/100th of pixel. The potential of this technique for experimental patterns is discussed and recommendations for new EBSD detectors are proposed.

Towards high accuracy calibration of electron backscatter diffraction systems

For precise orientation and strain measurements, advanced Electron Backscatter Diffraction (EBSD) techniques require both accurate calibration and reproducible measurement of the system geometry. In many cases the pattern centre (PC) needs to be determined to sub-pixel accuracy. The mechanical insertion/retraction, through the Scanning Electron Microscope (SEM) chamber wall, of the electron sensitive part of modern EBSD detectors also causes alignment and positioning problems and requires frequent monitoring of the PC. Optical alignment and lens distortion issues within the scintillator, lens and charge-coupled device (CCD) camera combination of an EBSD detector need accurate measurement for each individual EBSD system. This paper highlights and quantifies these issues and demonstrates the determination of the pattern centre using a novel shadow-casting technique with a precision of ∼10μm or ∼1/3 CCD pixel.

Growth Twinning and Generation of High-Frequency Surface Nanostructures in Ultrafast Laser-Induced Transient Melting and Resolidification

The structural changes generated in surface regions of single crystal Ni targets by femtosecond laser irradiation are investigated experimentally and computationally for laser fluences that, in the multipulse irradiation regime, produce sub-100 nm high spatial frequency surface structures. Detailed experimental characterization of the irradiated targets combining electron back scattered diffraction analysis with high-resolution transmission electron microscopy reveals the presence of multiple nanoscale twinned domains in the irradiated surface regions of single crystal targets with (111) surface orientation. Atomistic- and continuum-level simulations performed for experimental irradiation conditions reproduce the generation of twinned domains and establish the conditions leading to the formation of growth twin boundaries in the course of the fast transient melting and epitaxial regrowth of the surface regions of the irradiated targets. The observation of growth twins in the irradiated Ni(111) targets provides strong evidence of the role of surface melting and resolidification in the formation of high spatial frequency surface structures. This also suggests that the formation of twinned domains can be used as a sensitive measure of the levels of liquid undercooling achieved in short pulse laser processing of metals.

Three-dimensional finite-element simulation of Zener pinning dynamics

The Zener pinning dynamics of a moving boundary interacting with one or more particles is described by a three-dimensional (3D) finite-element model. The model, based upon a variational formulation for boundary motion by viscous drag, is solved by a finite-element method to obtain the velocity at each node of triangular linear elements on the grain boundary. It is first applied to relatively simple and validated cases, for which analytical and numerical results are available. These cases correspond to an axisymmetrical geometry, in which the grain boundary interacts with a centred particle. A simple analytical pinning criterion is derived from these simulations. The model is then applied to general 3D cases, in which the grain boundary interacts with arbitrarily localized and sized particles. The aim of these 3D simulations is to quantify the influence of the position and the number of particles on the average grain-boundary velocity. It is shown, for example, that the drag effect is enhanced when the particle, or the cluster of particles, is off-centre and that pinning is less efficient with several particles than with a single particle producing the same Zener force.

Influence of crystal orientation on the formation of femtosecond laser-induced periodic surface structures and lattice defects accumulation

The influence of crystal orientation on the formation of femtosecond laser-induced periodic surface structures (LIPSS) has been investigated on a polycrystalline nickel sample. Electron Backscatter Diffraction characterization has been exploited to provide structural information within the laser spot on irradiated samples to determine the dependence of LIPSS formation and lattice defects (stacking faults, twins, dislocations) upon the crystal orientation. Significant differences are observed at low-to-medium number of laser pulses, outstandingly for (111)-oriented surface which favors lattice defects formation rather than LIPSS formation.

Orientation-dependent recovery in strongly deformed Al-0.1% Mn crystals

Single crystals of Al–0.1% Mn were channel-die compressed to a true strain of 2.3 and their recovery behaviour at 240–320°C investigated by microhardness measurements, electron backscatter diffraction (EBSD) microtexture mapping and X-ray line broadening analysis. The crystal orientations were the nominally stable Goss {110}⟨001⟩, brass {110}⟨112⟩ and S {123}⟨634⟩. For all three orientations the microhardness decreases with a logarithmic time dependence but the instantaneous recovery rates of the brass oriented crystals are systematically lower than those of the other two orientations by a factor of about 2. The dislocation densities decrease rapidly in the first stages of recovery (<1 min) by dislocation dipole annihilation and more slowly thereafter. In the Goss and S orientations the later stage of recovery is due to sub-grain growth. The orientation dependence is ascribed to the relatively low misorientations developed by plastic straining in the brass crystals (average about 4°) compared with the Goss and S orientations (about 7–8°).

Multiscale measurements of residual strains in a stabilized zirconia layer

Residual stresses in a polycrystalline material have been determined experimentally at different length scales using three different techniques, with the aim of obtaining quantitative values. The polycrystalline material used is the electrolyte of solid oxide fuel cells, made of yttria-stabilized zirconia and submitted to a high biaxial compression stress state. Macroscopic measurements were performed using traditional X-ray diffraction with the sin2ψ method. Residual stresses within the grains were determined by the X-ray microdiffraction technique using synchrotron radiation. The variation in the strain within each grain was analysed by high-resolution electron backscatter diffraction. The results are self-consistent and give further information on the relation between strain/stress values and grain orientation, and on intragranular strain variations. These results are very important for the validation of mechanical microscopic constitutive equations.