asymmetric strain

celinem

Hi !

I have a powder sample with asymmetric broadening evolving under particular external constrain. There is clear physical reasons to believe that it is related to sample strain.

I can describe properly the pattern by using an exponential convolution (2Th dependant exp_conv_cst).

Here is my problem: the evolution of the unit cell parameters I obtain do not really make sense to me. What I would be interested in is the "center of mass" of the parameters distribution. This does not correspond to the extracted parameters values in this case of an asymmetric broadening.

Is there a more appropriate way to do the convolution in this case? (Or a way to extract the "mean/median parameters values" afterward?)

Céline

johnsoevans

Dear Celine,

I don't know if it's applicable to your experiments, but one relatively straightforward approach is to use a set of strs to fit the data. You could use the same structural coordinates for each, but with slightly different cell parameters. The cell parameters could be controlled with equations to keep them sensible. From the scale factors of each phase you get an indication of the distribution in your sample. It's relatively easy to fit 10s or 100s of phases. This type of approach might make sense if you think you have a range of compositions in the sample.

John

rowlesmr

I've done that before too.

You need to make sure that the microstructural prms for each of the phases is the same.

You would fix the cell prms and let the scale factors refine, either freely, or linked to some sort of distribution.

Matthew

olofgustafsson

Hi,

I am trying out something similar as Celine where I have asymmetric strain with a physical origin in compositional variation. I have a time series of data which I would like to fit sequentially and thus adressing the asymmetry with a function would be of interest. I have found a similar case in the literature where an exponential function for the profile is convoluted with the symmetrical strain profile. The exponential function looks like this:

f(θ) = exp(- (2θ-2θ_hkl)/ε)

Where ε is the refined parameter and 2θ_hkl is the peak position. My question is how one would write this function in Topas? I have tried the following, receiving the error "Parameter exp_prm21407040_ of type exp_prm cannot be a function of xdd_x"

prm e_hkl 0.001 min = 0.001;
exp_conv_const = If(X > Xo,(-((2 X) - (2 Xo))/e_hkl),0);

Olof

rowlesmr

Hi Olof

I learnt how to implement convolutions by reading [1], and then looking at topas.inc to see how the equivalent equations were implemented.

I sent really add much more as I'm on mobile and about to do a small child thing...

Matthew

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4849620/

olofgustafsson

Hi Matthew,

Thank you for your reply and the nice resource. The issue for me is what parameter I should use for 2θ in this case in my convolution. Since the exponential function should vary from the position of the Bragg peak (2θ_hkl) as a function of 2θ. I guess that either of the keywords Xo or Th should work in this case as "2θ_hkl", but I am struggling to find what I should use for "2θ".

Olof

rowlesmr

Hi Olof

The TechRef says that exp_conv_const can be a function of "H, K, L M, Xo, Th and D_spacing". AFAIK, convolutions are always centred on the peak to which they belong, so I think the 2θ-2θ_hkl may be redundant.

By looking at eqn 12 in the reference and comparing to the same equation in topas.inc, I think it may be as simple as

prm e_hkl  0.001 min = 0.001;
exp_conv_const = Ln(0.001) e_hkl;

You might want to stick a negative sign in there. Maybe.

See how that goes.

Matthew

olofgustafsson

Hi Matthew,

This works well, thank you so much for the help!

Olof