again, check the meaning of the L and G. There is little physical quantitative information you get out of those. What is sure, on a first order approximation, is that you can use Vegard's law with the cation sizes to get an information on the lattice parameter expansion or contraction. This is where the number of electrons you talk about come into play (roughly, the larger the number of electrons, the larger the ionic size, thus the larger the effects). Just notice that point defects give some diffuse scattering contribution that is hard to be seen then in the broadening. So do not expect to see huge differences in peak profiles if you have substitutionals (at low level)

perhaps you should do a little step back and open a good book on X-ray diffraction!

TOPAS is just a mathematical tool and it gives you numbers.

A distribution of local lattice strain inside the domains of your material results in line profile  broadening. IF the average of this microstrain is nonzero, then the whole lattice is on average expanded or compressed and this results in a shift of the peak positions. The two information (peak broadening and peak position) give therefore two different types of information.

Just beware as "line profile boadening" involves a change in the shape of the WHOLE peaks (not just in the breadth..) and each profile is broadened by several effects.. TOPAS gives you just an effective idea but does not tell you the physical source of this broadening. The macroscopic stress results in an anisotropic change of the peak positions relate to the macroscopic residual stress tensor and grain-grain coupling so again a model considering the actual microstrucuture of your system (powder vs film for instance) should be employed!

PS even if my answer to your question seem a bit harsh, the same initial suggestion is directed ESPECIALLY to most of the editors and reviewers of papers containing diffraction data that keep accepting manuscripts containing this sort of mistakes....

There are two different types of strains.

One is macrostrain, when the lattice parameters change uniformly in the whole sample. In this case XRD peaks shift correspondingly, but their shape remains unchanged.

Another is microstrain, when lattice parameters appear to be different in different parts of sample, while average value remains the same. In this case positions of the peaks will be unchanged, but their width will increase (you can imagine that your sample is a mixture of many phases with slightly different lattice parameters). 'Strain' parameters in the refinement programs describe this broadening, so they refer only to microstrain.

Of course, both effects can be observed in the same material.

As far as I understood from your description, you have only macrostrain, but not microstrain. Substitution defects are more likely in this case, but this conclusion requires additional confirmation.

Dear all,

Thank you so much for your profound answer.  Let me be clear, we can observe the macrostrain by using peak shifting, FWHM by JADE while microstrain can be evaluated by Strain L or Strain G in TOPAZ package. Is there any misunderstanding, please acknowledge me.    

However, I have read the paper. They suggested that the interstitial defect of small atomic number will carry out smaller strain because of less number of electron. Is it sound or not?

again, check the meaning of the L and G. There is little physical quantitative information you get out of those. What is sure, on a first order approximation, is that you can use Vegard's law with the cation sizes to get an information on the lattice parameter expansion or contraction. This is where the number of electrons you talk about come into play (roughly, the larger the number of electrons, the larger the ionic size, thus the larger the effects). Just notice that point defects give some diffuse scattering contribution that is hard to be seen then in the broadening. So do not expect to see huge differences in peak profiles if you have substitutionals (at low level)

I have to agree to Matteo. The peak shift you are observing has nothing to do with strain. You simply change your composition what only very rarely won't have any influence on the lattice parameters and therefore on the peak positions. Strain caused by interstitials or replacements etc affect the lattice perfection and will influence the peak width. Only this is considered in the mathematical models used in programs like TOPAZ,  but these are only least square fits so that you need to decide what do they mean. 

The strain mentioned by Alexander you cannot measure by only a single scan. There the formation of a gradient is required which changes in fact by tilting the diffraction vector (psi or omega scan).

Dear all, 

Thank you so much for you suggestion. I will acquire for more explanation in term of definition and related stuff.If all you have suggestion, please acknowledge me. I would love to hear form expert.