Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Applying crystal data
Another tutorial covers the import of crystal data to the format used in this package. In this tutorial we will see a few examples on how to make use of that information.
The package must be loaded:
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Needs["StianRamsnes`MaXrd`"]
This package comes with many convenient functions that utilises the stored crystal data. They can mainly be divided into two categories: those used to extract data and those used for calculations.
returns f+ ′ f ″ f | |
return the metric G | |
return the lattice parameters associated with the crystal | |
returns the corresponding Laue class of the group/crystal | |
GetScatteringCrossSection | returns σ for given elements and wavelength |
extract space group information easily | |
returns alle the symmetry operations for a point- or space group | |
import crystallographic information from cif files |
Functions that are mainly used for easy extraction of data.
† denotes functions that use data files located $MaXrdPath ▶ Core ▶ Data.
† denotes functions that use data files located $MaXrdPath ▶ Core ▶ Data.
calulate the μ abosrption factor | |
calculate the Bragg angle, given λ hkl | |
calculate theoretical value for the density | |
calculate the Darwin width of a given hkl | |
calculate the extinction (Pendellösung) distance of a given hkl | |
simulate the reflections (nodes) of a plane in reciprocal space | |
calculate the structure factor F(hkl) | |
transform among alternative unit cell representations |
Functions in the package which can operate on data in , or directly to perform calculations.
‡ denotes functions related to dynamical diffraction theory.
‡ denotes functions related to dynamical diffraction theory.
2D simulation of reciprocal space
With the metric information of a crystal contained in and the function for generating appropriate reflections, , one can relatively easily create a function that simulates a section of reciprocal space. is a simple function that does this. We can use to check which other package components it is made of:
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 | RelatedFunctionsGraph |
| ReciprocalSpaceSimulation |
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The essential inputs are the crystal label – which contains the lattice specification – and the orientation details of the plane in reciprocal space. Information on the function syntax:
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?
| ReciprocalSpaceSimulation |
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Symbol | |
ReciprocalSpaceSimulation[crystal,{ L 1 L 2 d min crystal L 1 L 2 origin d min L 1 L 2 d min crystal λ L 1 L 2 origin d min | |
From this we see that the function also requires an origin for the plane, a resolution and wavelength (if not contained along with crystal data). Let us look at some examples:
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| ReciprocalSpaceSimulation |
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The image above shows the plane of an orthorhombic structure.
Below is an example of a hexagonal structure:
(h2l)
Below is an example of a hexagonal structure:
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| ReciprocalSpaceSimulation |
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Adjusting the resolution will have the effect of “zooming” in and out. The resolution governs which reflections we are able to see. Note that the indices of the reflections can be read from the tooltips (hover the mouse over any node).
Please see the documentation page for more example of usage.
Atomic scattering factors
The data is stored in two different ways: either as coefficients (so-called Cromer–Mann coefficients) to approximate the scattering factor with the function
For completeness, the f1f2 files are:
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f1f2_asf_Kissel.dat
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f1f2_BrennanCowan.dat
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f1f2_Chantler.dat
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f1f2_CromerLiberman.dat
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f1f2_EPDL97.dat
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f1f2_Henke.dat
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f1f2_Sasaki.dat
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f1f2_Windt.dat
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Organisation scheme for f0 functions (those with data point format):
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Organisation scheme for f1f2 functions:
where the f* functions are the corresponding interpolation functions generated, which require a wavelength input and return the value of f0, f1 or f2.
The f0 interpolation functions use interpolation order 3, while the f1f2 functions use order 1 (linear). All use the Hermite interpolation method.
Note that for all f0, f1 and f2 interpolation functions the desired scattering factor is obtained with:
After running the code above, the symbols are created. Let us check this:
Structure factors
There are also some options available:
MaXrd ▶ Kernel ▶ Data ▶ AtomicScatteringFactor
Which in the current version include:
The sources for the anomalous corrections are contained in a subfolder:
MaXrd ▶ Kernel ▶ Data ▶ AtomicScatteringFactor ▶ AnomalousCorrections
Please see the documentation page for more example of usage and elaboration on the options.
Unit cell transformation
First import the crystal data from a .cif file (in the package)
Notice how the lattice parameters have been permuted: