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Gathering 3D material microstructural information is time-consuming,expensive, and energy-intensive. Acquisition of 3D data has been accelerated bydevelopments in serial sectioning instrument capabilities; however, forcrystallographic information, the electron backscatter diffraction (EBSD)imaging modality remains rate limiting. We propose a physics-based efficientdeep learning framework to reduce the time and cost of collecting 3D EBSD maps.Our framework uses a quaternion residual block self-attention network (QRBSA)to generate high-resolution 3D EBSD maps from sparsely sectioned EBSD maps. InQRBSA, quaternion-valued convolution effectively learns local relations inorientation space, while self-attention in the quaternion domain captureslong-range correlations. We apply our framework to 3D data collected fromcommercially relevant titanium alloys, showing both qualitatively andquantitatively that our method can predict missing samples (EBSD informationbetween sparsely sectioned mapping points) as compared to high-resolutionground truth 3D EBSD maps.

Q-RBSA: High-Resolution 3D EBSD Map Generation Using An Efficient Quaternion Transformer Network