[Paper Review] A Virtual Diffractometer For Creating Synthetic HEDM Images of Tessellated and Meshed Finite Element Polycrystals

Paul R. Dawson, Matthew P. Miller|arXiv (Cornell University)|Mar 30, 2023

X-ray Diffraction in CrystallographyMaterials Science3 citations

TL;DR

This paper presents a virtual diffractometer in MATLAB that simulates synthetic HEDM (High Energy Diffraction Microscopy) images for tessellated and meshed finite element polycrystals under in situ loading. By modeling diffraction conditions, detector response, and point spread functions, it generates realistic pixelated detector images of diffraction spots, enabling researchers to predict experimental outcomes and optimize HEDM setups before beamtime is used.

ABSTRACT

To assist in the planning of in situ loading, HEDM experiments by generating synthetic diffraction images of virtual samples in loaded and unloaded states. The user designates a target grain in the virtual sample and specifies the set of reflections for which images are to be generated. The code generates several intermediate images, including: (1) the points of intersection between the diffracted beam direction vector the detector plane; (2) reflection-dependent frequency distributions of the diffraction angle, $ω$; and (3) plots of the diffraction volume-weighted intensity distributions for the specified set of reflections. The final sets of plots are facsimiles of pixelated detector images which take into account characteristics of specific detectors, including its pixel size and point spread behavior.

Motivation & Objective

• To address the challenge of limited access to high-energy X-ray facilities by enabling virtual planning of HEDM experiments.
• To help researchers assess whether detector images will capture relevant microstructural behaviors before conducting real experiments.
• To simulate diffraction spot formation under varying lattice orientations, strains, and loading conditions in polycrystalline materials.
• To incorporate realistic detector characteristics such as pixel size and point spread function to improve simulation fidelity.
• To support experimental design by predicting detectability of lattice distortions and strain changes under load.

Proposed method

• The virtual diffractometer uses a meshed finite element representation of polycrystalline samples with grain-level lattice orientations and elastic strains.
• It computes Laue diffraction conditions for user-specified hkl reflections and scattering vectors, identifying which crystal planes satisfy Bragg's law.
• It calculates the intersection points of diffracted beams with the detector plane and maps the resulting intensity distributions using volume-weighted integration.
• It applies a user-defined point spread function (PSF) to simulate detector blurring, using a 5x5 kernel derived from experimental line spread data.
• It generates pixelated detector images by sampling the intensity field at detector resolution, incorporating beam divergence and attenuation.
• The code is modular and configurable, allowing users to input custom material parameters, beam geometry, and detector specifications.

Experimental results

Research questions

• RQ1 Can a virtual diffractometer accurately simulate synthetic HEDM detector images that reflect real experimental conditions?
• RQ2 To what extent do detector resolution and point spread function affect the visibility and shape of simulated diffraction spots?
• RQ3 How do changes in lattice strain and orientation under tensile loading influence the position and intensity of simulated diffraction peaks?
• RQ4 Can the simulation predict whether key reflections will be detectable and spatially resolved in real HEDM experiments?
• RQ5 How well do the simulated intensity distributions match the expected behavior of real diffraction patterns for specific crystallographic planes?

Key findings

• The virtual diffractometer successfully generates synthetic HEDM images that replicate key features of real detector data, including spot positions, intensities, and blurring effects.
• Detector resolution and point spread function significantly influence spot morphology, with broader PSFs leading to greater peak broadening and reduced spatial resolution.
• For the stainless steel tensile sample, the most axial reflections (e.g., 111, 020) showed distinct peak shifts and intensity changes under load, indicating measurable strain response.
• The 020 reflection exhibited the most pronounced shift in peak position under load, consistent with expected elastic anisotropy in the BCC structure.
• The simulated detector images with PSF applied closely resemble real HEDM data, validating the model's ability to predict experimental observability.
• The code is freely available on GitHub and supports dynamic reconfiguration of material, beam, and detector parameters for diverse experimental scenarios.