it seems.it seems.All the comments are highly valuable. I overlapped the two plots and basically there is a ~ 0.1 shift in peeks and when looking all the above factors into consideration, it can be quite logical it seems.

after looking to the file it seems to due to misalignment of one in one of the diffractometers or may be due to the sample displacement error 

The shift is not not the same for all the samples. it sems to be a problem of sample displacement error and not misalignment of one of the diffractometers... You could make another analysis to verify the stability of your samples verus time because some (porous) materials are very sensitive to oxygen hydrogen or water vapor...

Thank you very much everyone for your kind suggestions and discussions.

These were sol-gel spin coated, doped ZnO samples on soda glass substrate. Both the XRD has Cu source. The Zn:O should be 1. Though there would be some possibility of having oxygen vacancy or Zn interstitial. The instruments have sample holders and we put the samples on it. Both cases were theta - 2theta scan. Technicians have taken the data and I dont have any idea about misalignment or displacement of the samples.

One thing, I am not worried about the absolute shift of the samples (black/red/blue/pink /......). I mean the difference of angles in between black data. This may happen depending on the above discussions. (considering every factors).

But the data indicates a contrast result. One result telling us about lattice expansion (the upper one) and other about lattice contractions (the lower one). The pattern of the shift should be the same (with respect to the mother sample as : ZnO-black data) and should be instrument independent.

Maybe it is the way you prepare the specimen that matters.

These are the same samples..data are taken at the same day.

I think that this is a problem of adjustment.

Check both diffractometer using standard samples of GaAs - or Si single crystals. - Which results are closer to the ICDD (JCPDS) cards that installation you have to believe.

It seems to me there are three main candidates relating to the X-ray source, the diffractometers and the sample (or a mix of all three):

1. wavelength - a little unlikely as an explanation, nevertheless the combined copper (unresolved) K-alpha-1 and K-alpha doublet has a combined wavelength of ~1.5418 Ang. whereas the resolved copper-K-alpha-1 singlet of the -1- and -2 doublet is 1.54056 Ang.  You say both diffractometers have a Cu source" but it could be that one instrument has the unresolved Copper K-alpha doublet and the other the monochromatised Cu-K-alpha1-singlet. I estimate the difference between these two for your sample d-spacing would then be about 0.015 deg. (2-theta) which is much smaller than your measured difference.  So this is an unlikely explanation, but note it is not sufficient to say "both use a copper source"; you must also specify how the doublet is treated by the instrument.

2. diffractometer: as others have pointed out, the 2 diffractometers could differ in their misalignments or sample displacements and a run with a calibration sample would asses this possibility.

3. sample: in spite of what you might think, there could be some small change in the sample (hydration, dehydration, air-sensitivity etc.) occurring over the course of "the same day".  Research often finds the unexpected.  Again a calibration sample run would have helped here. 

Are they in the same sample holder for both instruments? If it is sample displacement error this can account for the differences. It as already been mentioned to use an internal standard in order to remove this effect.

"I have got two different kind of shift of the same samples taken at the same day in two different XRD instrument. Is not it absurd?"

No not at all! In fact, the contrary would be absurd. I always keep in mind that the diffracted signal is a convolution of:

Conventional point counters average the XRD signal over the "sampled 2D area" (typically 1mm x 10mm or so) causing "spatial blindness". This is the only reason they even appear to be identical. Such conventional spatial "smearing" or "averaging" does still yield useful results. With a sensitive enough 2D real time detector, it is possible to quantify these differences that you are observing.

As mentioned earlier, the use of standards to calibrate your diffractometer is the best and unequivocal way to compare results from various diffractometers consistently, even from the same make/model but different location or different optics or different operator (sample prep/loading). The only assumption needed is that the diffraction pattern from a "standard" remains unchanged.

See the linked RG post for an example of "calibration" of a Bruker D8 using the very well known NIST 2000 SRM (standard reference material):

https://www.researchgate.net/post/What_is_the_best_way_to_interpret_REAL_TIME_3D_X_Y_Omega_2Theta_reciprocal_space_relative_intensity_data_from_HRXRD_rocking_curve_analyses

Please revise experiment. Which wave length are you using in both diffractometers. Some times the radiation is composed of many principal wave lenghts that can be or not filtered or selected, This can change the diffraction diagram. Small displacements can have difrent origins depending on the geometry used.  The angular dependende of the observed displacement is related to the possible origin.

Thank you everyone for your valuable inputs.

@Barnes: One can easily get from the diffraction pattern that the radiation consists of both Cu K alpha 1 and K alpha 2, as there is a kink at almost half intensity at the right side of the main peak (higher theta). We think the samples is not that much unstable so that in one day structure would be changed. We have checked the PL spectra, transmission and that is OK with expected result.

@Artur: This is a thin film and can not mix Si or any thing with my samples. Only thing I can do is to take a std sample data from both the instrument.

@Ian: The instruments are different so the sample holders.

By assuming that the sample is not changed between the two measures, only a possible sample displacement could explain the little differences between the patterns. The samples, due to the fact that are thin films, are measured with what kind of geometry? Have you verified if the displacement is constant in the entire 2theta range or if it has an angular dependence? In this way you can also distinguish the kind of error. You can also try to do a refinement of the patterns to check the eventual errors (zero error or displacement). 

 Arindam! Good discussion with lots of data flying around :-)

Do you expect any "preferred orientation" in your film? Have you checked for it? The method of deposition you are using would be highly prone to "preferred orientation", I'd think :-)

Please annotate the figure with multiple diffractograms (XRD.pdf) better to clarify your hypotheses.

See below examples of conventional diffractograms taken on the same instrument (Rigaku MiniFlex) with the same "fixed Aluminum sample holder" using similar optics as you. Observe the shift in the diffraction pattern from the "fixed Aluminum sample holder" which we actually used to match the various diffractograms. The shifts are in the order of magnitude as in your case. So before you start concluding these shifts are due to "crystallographic strain state", eliminate the obvious culprits. These are eloquently discussed already by many here.

As a matter of fact, if you are able to resolve the K Alpha 1 & 2 clearly, you may use the difference between them to calibrate your 2-Theta/Omega space  and observe any " lattice expansion" and "lattice contractions".

Download image and magnify with MS Paint!

https://www.researchgate.net/post/Is_this_a_reasonable_way_to_eliminate_effects_of_sample_surface_misalignment_with_the_diffractometer_axis_Theta-2Theta_Diffractograms?_tpcectx=profile_questions

"Maybe this, maybe that" can be conclusively avoided if it becomes a habit to align and calibrate the diffractometer as a matter of "standard operating procedure" (SOP) using a "known standard" before and after each sample run :-) I do so at least once during, before or after for now. This is the reason why the data acquisition rate has to jump orders of magnitude, in my humble opinion. It is also the "root cause" of so much ambivalence ("hand waving") and effort in XRD data analyses. XRD is a fairly precise and well understood in situ Nano structure evaluation tool which should be used as such.

The conventional linear diffractograms you are using will not suffice as they have several limitations:

• Lack of spatial perception of Nano structure on the sample
• Inordinate data acquisition time with 0D detectors
• Limited real time feedback control 

What are your thoughts? I mean beyond the mundane issue of "alignment" all the way to quantifying "lattice distortion" or "preferred orientation" topographically on a sample surface. Spatial homogeneity of film, I'd think, to be important in all cases. I'm learning with sputtered Pt film on monocrystalline (001) Si :-)

Bottom-Line for Arindam regarding this question: Always use a "known standard" to compare results from the same or different diffractometers to eliminate many "unknowns" and draw unequivocal conclusions regarding nanostructural strain state.

The possible reason may be due to the calibration problem. Please check whether the sample to detector distance is calibrated or not.

I think you should check two things: 2Theta zero shift (with standard sample) and the displacement of the sample. Any of them can be corrected.