All this does not sound as problematic as it seems. First I assume that you correctly take into account instrumental resolution as a fixed contribution to the line profile. Otherwise your results are largely meaningless.

A large "Gaussian size" value simply means that your size broadening (within your model assumptions) is simply of Lorentzian shape. In such I case I would exclude refinement of the Gaussian contribution. Then the conclusions are to be drawn simply from the Lorentzian contribution. The same is valid, if the microstrain contributions are at the lower limit. Also switch these off in the course of the "definite" refinement. The overall strategy of refinement or non-refinement of parameters depends on the overall context. Note that there is no single model valid for all situations of "size-strain analysis". Moreover, note that refined Lorentzian and Gaussian size values (the same holds for microstrain) are not independent microstructure effects, but the consequence of the overall size effects dependening on the "crystallite shape" (a long topic by itself) and the distribution of sizes (and shapes).

Last note: I do not know what "disordered" alumina refers to precisely. Specific types of faulting (e.g. planar faulting) can give rise to size-like line broadening where, however, much more specific line broadening can be used.

Andreas Leineweber,

Thank you for your answer. Yes, the instrumental parameters are fixed and the materials I'm working on are gamma- and delta-alumina phases. (Just in case you're not into this topic, gamma is most widely accepted as defective spinel with non-spinel contributions and that is the model (well one of them) I'm using. Planar defects is one type of disorder in gamma discussed in the literature.)

I unfortunately don't have TEM data, and am hence not able to keep the two (CS and strain) at some reasonable ratio.

Should I let the Gaussian size approach the max (which is 1000) and then use only the Lorentzian size, or should I eliminate the G size completely?

How can I get closer to a physically more meaningful balance between the Lorentzian CS and strain?

Thank you.

-I would remove the Gaussian size command/macro entirely in such a case. -In case of "How can I get closer to a physically more meaningful balance between the Lorentzian CS and strain?" I do not understand the point. Apparently microstrain contribution refine to values implying absent microstrain. I mainly referred to faulting as separate phenomenon which may the actual reason for the size broadening. Indications for this may be special hkl-dependences of the reflection widths which you currently attribute to some isotropic size broadening. This you will see, of course, on the agreement of the calculated and observed profile for the individual reflections.

Andreas Leineweber, the CS and strain are dependent but not completely equivalent to each other, are they? Strain and thus line braodening can also be due to point defects in addition to domain size. If Topas gives me only CS and no strain, I'm not sure if I can be confident about the refinement.

I know this is not easy but as a not-very-experienced Topas user I wanted to seek others' advise.

Any more input would of course be appreciated.

Thank you and best regards.

Not exactly true:

-Upon evaluating data the refined extent of microstrain broadening and size broadening will be strongly correlated, e.g. if you simultaneously refine Strain_L and CS_L.

-homogeneously distributed point defects DO NOT cause (e.g. microstrain) broadening (check the classics like Guinier or Krivoglaz)

Train yourself by checking out different models against each other. I have to stress that the very user-friedly, correlation tolerant refinement algorhithms used e.g. by TOPAS do not help young users to realize that their model might be nonsense.

Andreas Leineweber

Thank you for your answer again!

Unless I'm missing something, thinking in terms of two extremes - homogenous and non-homogenous distribution of point defects - we expect "peak shift" and "broadening," respectively. But when go down to nanocrystalline scale, we cannot have the same situation; there should be contribution from both sources as homogeneity of impurity reaches some limit.

My materials are high BET alumina nanomaterials and I'm expecting some Cl impurity.

I'll have to agree with you on your last comment though. The literature, at least for the case of transition alumina, is full of nonsense published even by experienced experts.

Thank you for sharing the references, I'll go through them.

Best regards,

Jamal

Hi Jamal,

From your volume-weighted crystallite size (referring to it here as such even if we don't yet trust the value), I assume you have relatively broad peaks and the broadening contribution from strain is likely not obvious when comparing fits with / without strain terms refined. Since you don't have complementary characterization of your samples, separating size and strain contributions is critical. As Andreas said, the LVol and e0 macros in TOPAS assume isotropic size and strain broadening (e.g., angle-dependent rather than hkl-dependent) and these assumptions do not have to be correct, especially for small (< 10 nm) nanoparticles.

Are your samples single phase? If so, an approach worth trying is using single-peak fitting to extract the peak breadths directly to make a Williamson-Hall plot. While this is a qualitative approach, here it will give you a sense for 1) if your sample has strain (proportional to slope of WH fit line) and 2) if there is some hkl-dependence indicating anisotropic size and / or strain broadening. You can also test the Stephens model for anisotropic strain broadening (Stephens 1999) and Ectors model for anisotropic size broadening (Ectors 2015, Ectors 2017) to see if these better describe your peak broadening. The anisotropic size macros are not in the TOPAS GUI and have to be implemented in launch mode - details are on the TOPAS wiki.

Single-peak fitting comes with some large warnings:

Correlation between your background and peak tails will be much higher when using single-peaks and it would be worthwhile to constrain the peak intensities (integrated area) to scale as they would when using a structural model. Likewise, the peak positions should be constrained or refined with some scale so that they are related as they would be in a Rietveld refinement. Without these constraints, your fit will necessarily improve but it won't be clear if you have resolved an issue with the peak shape, intensity, or position.

I would also suggest comparing your Rietveld refinement to a Pawley / Le Bail fit where intensity is freely refined for each peak while their shape and position is still constrained to the isotropic size-strain models and a unit cell, respectively. If you don't see an improvement, this points to a peak shape model issue over an issue with the structural model.

Best,

Adam