This is may be due to the need to balance stress at grain boundaries, and satisfy constraints on the strain tensor (for example a tensile stress along one direction must be balanced by a compressive stress in the normal direction, so the direction of peak shift is often hkl dependent. Is there any reference related to this issue?
Dr. Bakr,
In my point of view, your sample will have so many inter-phases/inter-faces. From W-H plot (From XRD) you can differentiate the tensile stress or compressive stress in your sample. The negative plot gives you compressive strain and positive plot gives you tensile strain.
Dr. Bhatt,
Thank you very much for your answer ... I know the details of W-H plot ... W-H plot for this sample has negative slope.... but my question was that in the same sample some xrd peaks shift in one direction, and other peaks in the opposite direction ....
The peak positions are related to the lattice. If they are changing something with the lattice happens. There are two options: a) a "scaling of the lattice which does shift all peaks into the same direction, or b) a change of the lattice parameter ratio, i.e. one lattice parameter becomes shorter, the other longer. A typical example is stress-related symmetry-reduction of a cubic into a tetragonal phase. Not that not all anisotropic changes cause this effect since when both moving into the same direction but in different strength again all reflections are shifting to higher or smaller angles, however differently strong.
Dr. Gert Nolze,
Can you give a reference about this argument ... "change of the lattice parameter ratio, i.e. one lattice parameter becomes shorter, the other longer" ... ?
This is fundamental mathematics :-). You can check this by investigating the d-spacings using
d=a/sqrt(h*h+k*k+l*l) (cubic)
and
d=a/sqrt(h*h+k*k+l*l*a*a/c/c)
The easier way is to look, what happens in a simulated pattern when I am using e.g. ZrO2 with a cubic lattice parameter: 5.129A, and compare this with a theoretical ZrO2 using a=5.156 and c=5.075A.
The result you can see in the attached diffractogram using PowderCell. You have obviously unshifted peaks (here 111 and of course 222 as well), but commonly peaks are splittet because of the lower symmetry and shifted, one to lower angles and one to higher angles.
This you can also do with an original tetragonal phase which already shows splitted peaks. Increase one lattice parameter and decrease the other one. I don't think that this is specifically explained somewhere since it is ...fundamental. Don't you think so?
Dr. Gert Nolze,
Thank you very much for your answer and nice explanation. I need a reference just to compare my results. My samples are CZTS thin films which have tetragonal structure. For the same sample, some of the xrd peaks shift to lower angles and the others shift to higher angles (With respect to the standard 2Theta positions). I need a reference to compare my results and support the explanation you gave .. Mathematically, it seems obvious and fundamental as you said... but reference is needed for publishing this work and convince the reviewers !! ... Thanks again Dr. Gert ...
Then you simply need to refine the diffractogram. Simple examples I am doing with PowderCell, since I am one of the authors and therefore know it very well. But you can use also more advanced software like Fullprof, MAUD etc. All of them are free. Do you have the Angle/ Intensity data? I could have a look...
Dear Dr Bakr,
Stress induced morphological changes are well known. Please look at the findings from this angle.
Regards,
Bedii Erdemir
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