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Pressure And Unit Cell Optimizations

Unit cell optimizations

From the fit of the lattice strain equations, we obtain d-spacings under hydrostatic pressure d_p for each of the measured diffraction line. Those can be used to adjust unit cell parameters using well known relations.

The Stress and strain -> Unit cell menu item well let you plot, list, and export, various things such as

• the d-spacings under hydrostatic pressure d_p fitted to the experimental data for each measured diffraction line
• the unit cell parameters a, c, c/a...

Plots can be saved as images for further use.

Plot of unit cell parameter vs. image number in polydefix

Data can also be exported as ascii files for further processing. Those ascii files are very simple text files. If you give them a csv extension, they can be read by spreadsheets and plenty of scientific softwares.

You can also ask for details of the unit cell refinements. For each diffraction image, Polydefix will show you

• the d-spacings under hydrostatic pressure d_p(hkl) fitted to the experimental data,
• the unit cell parameters adjusted to the measured d_p(hkl),
• the d-spacings under hydrostatic pressure d_p(hkl) recalculated from the adjusted unit cell parameters.

In theory, agreement between the d_p(hkl) fitted to the experimental data and those recalculated from the adjusted unit cell parameters should be good.

If they are not, something is wrong. Could be indexing, could be something else.

Pressure optimizations

Once the unit cell is known, one can use the 3rd order Birch-Murnaghan equation of state to calculate the pressure in the sample.

where

• V is the unit cell volume,
• V₀ is the unit cell volume under ambient pressure,
• K₀ is the bulk modulus under ambient pressure,
• K'₀ is the first pressure derivative of the bulk modulus with pressure under ambient pressure.

Those parameters should have been entered while starting up Polydefix.

Results of the pressure analysis in Polydefix can be seen in the Stress and strain -> Pressure menu item.