Units and conventions

These are load-bearing. A master pattern is only comparable to EMsoft’s or kikuchipy’s because every one of them matches, so read this page before interpreting a number or feeding a de-ebsd array to another library. The design notes under Contributing explain the reasoning behind them.

Units

Lengths are in nanometres and reciprocal lengths in nm^-1. Energies are in eV at the API surface (Microscope(energy=20e3)) but keV internally and in the transport API, which is why Microscope exposes energy_kev. Fourier coefficients U_g are in nm^-2 and V_g in volts.

Cartesian crystal frame

EMsoft’s mod_crystallography.f90 convention: x parallel to a, z parallel to c*. The direct structure matrix dsm and the reciprocal rsm = inv(dsm)^T are element-for-element EMsoft’s, verified against the source. Every beam direction and g-vector in the dynamical computation lives in this frame.

Square-Lambert storage

The master pattern is stored as [row, col] with row = Lambert Y and col = Lambert X, both spanning [-sqrt(pi/2), +sqrt(pi/2)]. The hemisphere index is 0 = north (z >= 0) and 1 = south. Interpolation is bilinear torch.nn.functional.grid_sample() with align_corners=True.

These are exactly kikuchipy’s conventions, so a de-ebsd master pattern feeds an external projector unchanged – and vice versa, which is what makes examples/simulation/compare_emsoft.py a meaningful comparison rather than a re-derivation.

Orientations and detector geometry

Quaternions are in orix order (a, b, c, d), scalar first. Projection centers use the Bruker convention, and detector geometry follows kikuchipy (tilt, azimuthal, twist, gnomonic bounds per Britton et al. 2016); direction_cosines() is tested equal to kikuchipy’s to 1e-10.

The orientation returned by an indexer is the sample orientation passed to project() – no inverse, no transpose. A convention error here does not degrade gracefully; it puts the answer 90 to 180 degrees away, which is exactly what the round-trip tests are built to catch.

Space groups and origin choice

Space-group operators come from the diffpy tables, which use origin choice 1. For the 24 two-origin groups, Crystal defaults to origin choice 2 by conjugating the operators onto the nearest inversion center.

Warning

This is verified for the cubic groups. Other two-origin groups should be checked against the International Tables before use – pinning the full ITA shift table is roadmap item M3. Getting this wrong moves atoms, so it changes structure factors and therefore band intensities.