Diffraction post-processing of 3D dislocation dynamics simulations for direct comparison with micro-beam Laue experiments Felix Hofmann a,n , Sine ´ ad Keegan b , Alexander M. Korsunsky c a Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA b Department of Mathematics, Northeastern University, 360 Huntington Ave., Boston, MA 02115, USA c Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK article info Article history: Received 28 June 2012 Accepted 13 August 2012 Available online 24 August 2012 Keywords: Defects Dislocation dynamics simulations Synchrotron micro-beam Laue diffraction abstract We present a method of computing lattice rotations and elastic strains due to 3D dislocation structures discretised into straight segments. Combined with ray-tracing, it enables virtual scattering experiments where X-ray diffraction patterns that would arise from such dislocation structures are simulated. We demonstrate the diffraction post-processing of a Frank–Read source simulated using the ParaDiS discrete dislocation dynamics code. This simulation is compared to experimental synchrotron X-ray micro-beam Laue diffraction measurements of a single grain within a deformed nickel polycrystal. The simulated pattern captures the experimentally observed anisotropic broadening of Laue reflections and illustrates that heterogeneous and anisotropic lattice (re)orientation effects dominate the peak shape. & 2012 Elsevier B.V. All rights reserved. 1. Introduction Self-organisation of dislocations into non-homogeneous struc- tures during deformation of structural alloys is well documented [1–3]. Visualisation of these structures is key to understanding their behaviour and their influence on material response. Trans- mission Electron Microscopy (TEM) is a powerful tool for imaging dislocation arrangements [4] but is limited to ‘‘post-mortem’’ analysis of thin sections. A non-destructive tool for in-situ studies is the diffraction of highly penetrating synchrotron X-rays. Micro- beam Laue (mLaue) diffraction uses a micro-focussed polychro- matic X-ray beam to probe small intragranular volumes [5–9,23]. The resulting single crystal diffraction patterns consist of a large number of Laue reflections. From their positions, crystal lattice orientation and deviatoric elastic strain, averaged over the scat- tering volume, can be determined. Laue spot shape captures the spread of these quantities within the scattering volume and can be interpreted in terms of geometrically necessary dislocation (GND) density, geometrically necessary boundaries (GNBs) and active slip systems [7,8]. The information provided by mLaue cannot be directly inverted to find the real-space distribution of lattice orientations within the scattering volume. One approach is to compare experimental Laue patterns to diffraction patterns simulated by physically based mechanical models [10]. To capture the effects of disloca- tion interaction and self-organisation, dislocation dynamics (DD) models must be considered. The 2D framework of [11] captures some key features of experimentally observed deformation beha- viour [12], but requires ‘‘2.5 D’’ assumptions for dislocation self- organisation [13]. The computationally more expensive 3D approach of [14–16] promises to capture dislocation self- organisation without additional assumptions. Dislocations are treated as line defects, discretised into straight segments, moving in an elastic continuum. Their motion is computed incrementally and interactions are governed by a set of constitutive rules. This model is implemented in the Parallel Dislocation Simulator (ParaDiS) code. We establish a diffraction post-processing routine to compute diffraction patterns resulting from a virtual scattering experiment on a 3D dislocation structure. It is based on Barnett and Balluffi’s [17,18] solution for the displacement field of a triangular disloca- tion loop in an isotropic elastic continuum. Using this routine we compute the mLaue patterns arising from a Frank–Read source (FRS) simulated using ParaDiS. We compare these patterns to experimental mLaue patterns from a deformed single grain in a nickel polycrystal. Results are discussed in terms of the relative contributions of orientation and strain heterogeneity to Laue peak broadening. 2. lLaue diffraction dislocation post-processing An expression for the displacement field u(P) at a point P due to a triangular dislocation loop in an isotropically elastic medium is given in [17,18]. All segments in the loop share the same Burgers vector b, and line directions are such that the loop forms a Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/matlet Materials Letters 0167-577X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2012.08.052 n Corresponding author. E-mail address: hofmann@mit.edu (F. Hofmann). Materials Letters 89 (2012) 66–69