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2π or not?

Single-crystal diffraction calculations rely on g-vectors, U-matrices for defining grain orientation, and B-matrices for conversion between the Cartesian grain system and reciprocal space.

In physics in particular, g-vectors Ghkl are defined as a perpendicular to the diffracting plane (hkl) with a norm of 2π/dhkl.

In crystallography, authors often do not include the 2π factor in the calculation of G. In this case, the norm of Ghkl is 1/dhkl or 2sin(θ)/λ.

Among multigrain XRD software:

  • ImageD11 assumes ||G|| = 1/d,
  • g-vector files gve generated by ImageD11 also assume ||G|| = 1/d,
  • polyxsim, fitallb, or the xfab library use a 2π prefactor in the calculations of G and the B matrix,
  • GrainSpotter multiplies g-vectors by 2π when reading in and uses a B matrix that includes the 2π internally.

For details on U and B matrices calculations, refer to

advanced/2pi_or_not.txt · Last modified: 2019/02/21 06:27 by smerkel