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--- advanced:2pi_or_not [2019/02/20 18:46] – created smerkel
+++ advanced:2pi_or_not [2019/02/21 07:27] (current) – smerkel
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 ====== 2π or not? ======
-Single-crystal diffraction calculations rely on
+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 **G**<sub>hkl</sub> are defined as a perpendicular to the diffracting plane (hkl) with a norm of 2π/d<sub>hkl</sub>.
+In crystallography, authors often do not include the 2π factor in the calculation of **G**. In this case, the norm of **G**<sub>hkl</sub> is 1/d<sub>hkl</sub> or 2sin(θ)/λ.
+Among multigrain XRD software:
+  * [[software:imaged11|ImageD11]] assumes ||**G**|| = 1/d,
+  * g-vector files [[fileformat:gve|gve]] generated by [[software:imaged11|ImageD11]] also assume ||**G**|| = 1/d,
+  * [[software:polyxsim|polyxsim]], [[software:fitallb|fitallb]], or the [[software:xfab|xfab]] library use a 2π prefactor in the calculations of **G** and the **B** matrix,
+  * [[software:grainspotter|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
+  * {{ :processing:fable_geometry_version_1.0.8.pdf |}},
+  * or the 1967 Busing and Levy publication: W. R. Busing and H. A. Levy, Angle calculations for 3- and 4-circle X-ray and neutron diffractometers, //Acta Cryst.//  **22**, 457-464 (1967) [doi: [[https://doi.org/10.1107/S0365110X67000970|10.1107/S0365110X67000970]] ]
-G-vectors are the scattering vector associated with the diffraction. The are nodes of the reciprocal space or, in direct space, normal to the diffracting plane.
-For a given reflection in the crystal, **G**<sub>hkl</sub> is perpendicular to the diffracting plane (hkl) and its norm is 2π/d<sub>hkl</sub>. Pay attention, however, as some authors do not include the 2π factor in the calculation of **G**. In this case, the norm of **G**<sub>hkl</sub> is 1/d<sub>hkl</sub>. For a detailed discussion: [[advanced:2pi_or_not|2π or not?]]