Automated crystal orientation and phase mapping

Most functional and structural materials are polycrystalline, and their properties depend on grain size, texture, grain boundary character, and phase distribution. Automated crystal orientation mapping (ACOM) in 4D-STEM Rauch & Véron (2014) measures all of these: at every probe position, the recorded diffraction pattern is matched against a library of patterns simulated over all possible crystal orientations, and the best match assigns a local orientation, similar to electron backscatter diffraction (EBSD) in the SEM but in transmission, with nanometer resolution, and on the same datasets used for every other analysis in this course.

How it works¶

1. Reference structures. Load the candidate crystal structures (e.g., from CIF files) and compute their structure factors up to the maximum scattering vector recorded on the detector.

2. Orientation plan. Simulate diffraction patterns over a grid of orientations covering the symmetry-reduced zone axis range: a lookup table of expected Bragg peak positions and intensities. Grid spacings of a few degrees, with local refinement, balance accuracy against speed.

3. Bragg peak detection. As for strain mapping, detect the diffraction peaks at every probe position (the same calibrated Bragg vectors feed both analyses).

4. Correlation matching. For each probe position, score the measured peaks against the orientation library Ophus et al. (2022) and keep the best match(es). Returning multiple matches with a minimum angular separation handles overlapping grains along the beam direction.

5. Orientation and phase maps. The result is an orientation map (typically displayed with inverse-pole-figure coloring for in-plane and out-of-plane directions), plus per-position correlation scores. Running plans for multiple candidate phases and comparing their correlation scores produces a phase map, along with quantitative phase-fraction estimates.

Precession and pattern quality¶

Zone-axis nanobeam patterns are strongly dynamical: intensities oscillate with thickness and small mistilts, which degrades matching against kinematical templates. Precession electron diffraction (PED) Midgley & Eggeman (2015), which rocks the beam on a cone (typically ~0.3–1°) while descanning below the sample, integrates through the rocking curve and produces more kinematical-like, more complete patterns:

Precession substantially improves both orientation reliability and phase discrimination, and the tutorial dataset for this module is a precession 4D-STEM measurement of a two-phase (α + β) titanium alloy MacLaren et al. (2024), archived openly at the University of Glasgow research data repository.

Phase mapping in hard cases¶

Phase discrimination gets genuinely difficult when the candidate structures are closely related: polymorphs sharing a parent lattice, with only subtle differences in symmetry and spacing. Ferroelectric hafnium zirconium oxide (HZO) is a canonical example:

Practical notes¶

• Pattern matching is only as good as the calibration: the reciprocal pixel size can be refined by fitting the measured Bragg peak radial distribution against the structure factors of a known phase in the sample.

• Correlation score maps are worth inspecting on their own: low scores flag overlapping grains, unindexed phases, or regions where the library doesn’t contain the right structure.

• Template matching of the full patterns (as in pyxem Cautaerts et al. (2022)) and sparse peak matching (as in py4DSTEM’s ACOM) are complementary approaches; both are open source, so you can try each on your data.

• ACOM gives you strain for free: the distortion between each measured pattern and its best-matched simulation yields a per-phase strain map, with no manual choice of basis vectors.