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advanced:2pi_or_not
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advanced:2pi_or_not [2019/02/20 17:46] smerkel created |
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| ====== 2π or not? ====== | ====== 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. |
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| + | 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>. | ||
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| + | 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. | ||
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| + | 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. | ||
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| + | 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?]] | ||
advanced/2pi_or_not.1550684797.txt.gz · Last modified: 2019/02/20 17:46 by smerkel
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