Restraining TCHZ FWHM

Andrew_Crossman

Hi All,

I am trying to fit several hundred pXRD patterns of a bimetallic core/shell nano-particle as it diffuses into a homogeneous spherical alloy using several different phases that represent different stages of the diffusion. The diffusion is conducted via heating. Each phase is fitted with a TCHZ_Peak_Type at the lattice parameter associated with the metals at that temperature. In total, there are 11 phases:
Metal_A_100%
Metal_A_90%Metal_B_10%
...
Metal_A_10%Metal_B_90%
Metal_B_100%
The problem I am having using this method is that the Metal_B_100% phase fits to have extremely broad peaks even after it should be fully alloyed. I believe Topas is doing this to account for some broad background correction. Is there a simple way to restrain the FWHM of the TCHZ_Peak_Type to prevent this? I am open to other suggestions as well.

Cheers

johnsoevans

I don't think there's a simple way to restrain the TCHZ fwhm. However there are lots of ways of doing similar things. One would be to use a TCHZ function to describe the instrument part of the peak shape (make it the same for all phases using for_strs). Each individual phase could then be described using a gaussian/lorentzian size/strain convolution (CS_G, CS_L, Strain_G, Strain_L macros). You'll probably find one or two contributions are sufficient to describe the peak shapes. You can apply min/max values to constrain values or write restraint equations. Depending on the relative importance of instrumental and sample parameters you may not need the TCHZ at all.

Andrew_Crossman

Hi @johnsoevans ,

Thank you for your response. I tried your initial suggestion of using one TCHZ in combination with the Gaussian/Lorentzian size/strain macros but didn't get a particularly good result. I had tried various combinations of this is the past but not the particular combination you suggested. Often the CS_L and CS_G parameters limit max every phase to either 10000nm or 0.3nm when I know that the domain size should never exceed 100nm. So instead I am trying to implement some restraint/penalty equations. My question is, is there a way to introduce penalties such that a value can be encouraged to be less than a certain amount? For example, if I want the l_fwhm of the peaks from a TCHZ characterized phase to be less than 0.5 would the following work:

l_fwhm = pkx1*Tan(Th) + pky1/Cos(Th)
penalty = If(l_fwhm < 1/2, (l_fwhm)^2, 0);

Furthermore, when fitting a spectra with multiple HKL peaks, could I then constrain the l_fwhm as a function of theta using the following:

l_fwhm = pkx1*Tan(Th) + pky1/Cos(Th)
penalty = If(l_fwhm < Th/2, (l_fwhm)^2, 0);

rowlesmr

If you're refining both CSL, and TCHZ, then you're applying equations that are modelling the same thing, and so their values would be correlated exactly. You need to fix the TCHZ values using a standard with a known (or no) crystallite size/microstrain broadening and then just allow the CSL to refine on your unknowns.

Alternatively, just go full fundamental parameters and don't use TCHZ at all.

Andrew_Crossman

rowlesmr Thank you for your suggestions! I tried both methods (I had a CeO2 measurement to use as a standard) and decided to go with the fundamental parameters approach where each phase uses the CS_L macro. I tried various combinations of the other three relevant macros (CS_G, Strain_L, Strain_G) but their solutions were not as good.

johnsoevans I agree that the TCHZ fwhm is significantly more complex than the example I posted. My example was just for the Lorentzian component of the fwhm. After reading the rest of your comment I figured out I had some fundamental misunderstandings of the Topas macros. Thank you for your suggestions.

johnsoevans

I don't think the approach you describe will work. Firstly the TCHZ fwhm is significantly more complex (you can see how it's expressed in the topas.inc macro). If you write equations of the type you describe then the fwhm doesn't have a single value as it's 2th dependent so it can't be used in a penalty equation..
Maybe I've missed the point, but with a fixed TCHZ peak shape for the instrument (as Matthew suggests) can't you just put a min/max on e.g. the CS term(s)? The values of 0.3 and 10000 are the defaults in the macro, but you can replace them with new min/max values. You could use a min of 10 nm to stop peaks going too broad, or use a penalty as you suggest.
There are ways to only apply a penatly if the value is outside a specified range. If you seach topas.inc for "tol" you'll see how that's done in distance and angle restraints.