I'm trying to understand how theoretical powder XRD patterns are calculated in VESTA. I figured one way to learn that without the computer programming based nuances is to just do it in Excel.
If anyone knows of any links to where this has been done before or links to material for it, please answer.
Dear friend Akash Menon
Generating theoretical XRD patterns from crystal structure data in Excel can be a bit challenging but is definitely possible. Here are some general steps you can follow:
Alternatively, if you don't want to use external software, you can manually calculate the XRD pattern using the Bragg equation:
nλ = 2d sinθ
where n is the order of the reflection, λ is the wavelength of the X-rays, d is the interplanar spacing of the crystal lattice, and θ is the angle of incidence of the X-rays.
You can calculate the interplanar spacing using the unit cell parameters and the Miller indices of the planes you are interested in. Then you can calculate the angles of incidence for each reflection and plot the XRD pattern using Excel or any other plotting software.
Keep in mind that calculating the XRD pattern manually can be time-consuming and prone to errors, especially for complex crystal structures with many atoms and planes.
First you need unti cell parameters and atomic positions
Then you need planar spacing formula. For asymmetric crystals like triclinic, the formula can be a bit messy, but Metric Tensor approach in any advanced XRD Books (e.g. Graef and McHenry) can help
Then you need to generate structure factor for the planes. The formula is straightforward, but finding atomic scattering factor as a function of angle is difficult. Most often that not the data is provided in tabulated form in books. Nevertheless, you can do some decent peak-fitting
For multiplicity Factor of planes calculation, you need to look at both crystals structure and permulation-combination. So if you are using excel, VB programming might come in handy.
And as for Powder XRD data, Lorentz-polarization Factor is easily calculable on excel (of course, you know the X-ray wavelength you are diffracting with, right?)
The formula for X-ray absorption factor is almost tabular, and Temperature factor might be fitted into gaussian form quite easily, These two factors are ignored except for most tedious of calculations since their product is almost 1
And then you arrive at your results. New XRD books like Graef & McHenry and old ones like Culity both shows this approach, older ones perhaps more since computers were not strong back then!
My favourite is ELEMENTS OF X-RAY DIFFRACTION by B.D. Cullity; ADDISON-WESLEY, 1st edition (1956); pg. 133 (couldn't upload for copyright reasons!)
Dear Colleagues,
The full text of this paper (ELEMENTS OF X-RAY DIFFRACTION by B.D. Cullity) is available at ResearchGate: https://www.researchgate.net/profile/Ahmed-Saeed-Hassanien-2/post/What-is-X-ray-Powder -Diffraction-XRD/attachment/59d64e6a79197b80779a7c1f/AS%3A492613493313536%401494459617709/download/B.+D.+CULLITY-Elements+of+X-RAY+DIFFRACTION-SECOND+EDITION.pdf
more precisely here: https://www.researchgate.net/profile/Ahmed-Saeed-Hassanien-2/post/What-is-X-ray-Powder-Diffraction-XRD/attachment/59d64e6a79197b80779a7c1f/AS%3A492613493313536%401494459617709/download /B.+D.+CULLITY-Elements+of+X-RAY+DIFFRACTION-SECOND+EDITION.pdf
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