If I know the refined cell parameters of XRD pattern with significant digit like
a= 3.789456(12) and 9.3345(5) how do I multiply them to get correct value of
Volume= a2 c (angstrom) with significant digits
Volume = ......... (..)
Please tell me
The volume would be v = 134.0430(72) or 134.043 +- 0.0072. We can get that from the differential expression for error propagation (https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Simplification). There is an online calculator for error propagation (https://web.mst.edu/~gbert/JAVA/uncertainty.HTML).
Still, these significant digits come from the computational method for data refining. They do not reflect your actual experimental uncertainty. For example, your uncertainty for a is the order of femtometers, i.e., the "diameter" of a proton. You should be very critical of these numbers and always refer back to accuracy and limits of your experimental setup. Take a look at your diffractograms and ask yourself if you'd be able to resolve two peaks from two different atomic planes distances that differ by 1fm.
The volume would be v = 134.0430(72) or 134.043 +- 0.0072. We can get that from the differential expression for error propagation (https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Simplification). There is an online calculator for error propagation (https://web.mst.edu/~gbert/JAVA/uncertainty.HTML).
Still, these significant digits come from the computational method for data refining. They do not reflect your actual experimental uncertainty. For example, your uncertainty for a is the order of femtometers, i.e., the "diameter" of a proton. You should be very critical of these numbers and always refer back to accuracy and limits of your experimental setup. Take a look at your diffractograms and ask yourself if you'd be able to resolve two peaks from two different atomic planes distances that differ by 1fm.
Be careful about the 12 digits. What is the resolution in your XRD experiments?
Dear all,
please have a look at a nice discussion of the 'precision topic' of XRD some years ago here on RG.
https://www.researchgate.net/post/How_precise_can_one_really_determine_crystal_lattice_constants_with_X-ray_diffraction
You have to give more information. Nature of your sample, sample preparation, temperature, instrument configuration and refinement strategy will give a significant impact on those values.
I attached example from ICSD card.
When you say "If I know..." you should already stop since the more correct sentence would be "If I would know....". What do you really know about these data? Do you know the temperature, air pressure, humidity....of the experiment? The number you refer to are in the order that you need to add these values since otherwise they are useless. If you don't know them you should estimate how much experimental errors could affect your brilliant result and then you should reduce them to a realistic error. In other words, an error does not describes the uncertainty of the mathematical procedure applied but also needs to consider all other experimental uncertainty...like an incorrect radiation (only an example...Did you use Cu? Some other radiations are much worse described so that also the lattice parameters inherit this uncertainty already). In so far, I agree with all former comments!
How you got these parameters? If you got it from rietveld refinement then volume with standard deviation should be in your output file.
The number of significant digits (or the error) of the Volume must be the minimum of the unit cell parameter ones (=5 in c= 9.3345). For example the volume should be 134.04 instead of 134.0432 A3 .
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