Dear Dr. Rajesh:

It is non trivial to find structural parameters from mid infrared, seems that Fe----O stretching is more adequated. It  is necessary justify the non dependence of this vibration with anothers. This aproximation allow to consider the vibration similar to one developed by a harmonic -oscillator. Please, consider to read the paper copy in attached. I think that some insigth can be emerge. Also, it is necessary the refinement of structure that allow to derive bond length, in an alternative way.

Kind regards.

Marcos Nobre (M. A. L. Nobre)

Dear Rajesh

From the FTIR you can calculate the bond length and force constants provided you may know that the octahedral or tetrahedral sites for this complex oxides.  Moreover the bending vibrations of O-Fe-O may be the octahedral complexes.  Fe-O stretching vibrations may be tetrahedral complexes.  Pl. refer the following references you may more about the relationship between bond length and force constants.

1.Synthesis and Reactivity in organic, metal organic and nano metal chemistry, 42, 2012, 121

2. Indian Pure J. Applied Physics,  32, 1994, 193.

3. Materials letters, 60, 2006, 371

4. Applied Journal of Physics, 53, 1982, 8184

kind regards

S.Angappan

Best forces/lengths by IR are in the gas phase. In the solid state, the underlying assumption of harmonic oscillator (or even an anharmonic oscillator) is not strictly true. Still, good correlations between the trends in IR stretching and the structural parameters still hold.

Two ways to go - a look up table/graph - e.g. Fe2O3 bond length vs IR stretch, FeO bond length vs IR stretch etc.

OR/ Hookes law calculation from the actual stretch frequency - then some interpretation of the force constant obtained by calculation.

When I want to find out something about IR of transition metals - Nakamoto is the place to start - it always yields the right approach to doing it RIGHT.

As an aside - Raman is also useful for studying oxides.

I'm sure the answers seem fuzzy - but that's because the question is trying to take an approach for studying isolated diatomics or low MW clusters, and apply it to a bulk oxide. It's an apples and oranges kind of thing at that point.

I would imagine the look up table will give the most insight, then Nakamoto, then Hookes law in that order.

Dear Rajesh

1. you have to calculate the effective mass

2. using effective mass, and vibrational freq, you can calculate force constant k

3. then you can calculate Fe-O bond length using force constant data.

Please go through the attached article to have an overlook on the equations used.

still you find difficult, contact me

Dear Mr Sheik Mohammed Abdul kader , I have read the paper you suggested.

I am wondering where does the 17 in the equation of k=17/r^3 come from?

What is the physical meaning?

Dear Ms Efi Dwi Indari, please refer to the basic paper where the result is extracted. I hope it may help..

Article Theoretical and Experimental IR Spectra of Binary Rare-Earth...

R. Rajesh

Dear Mr. R. Rajesh , thank you very much for your answer.

By the way, it is reported on the paper you suggested that the formula is determined by using the bond length of cation-anion in the crystalline state. If my sample is amorphous, then the formula would not describe the characterized materials then. Do you have any suggestions?

Dear Ms Efi Dwi Indari, I am attaching herewith an article explaining the Far-infrared study of amorphous Ge0.17Se0.83−xSbx chalcogenide glasses. Here the bond order, reduced mass and force constant are calculated and compared with theoretical results.

Hope it may help...

Thanks and regards

R. Rajesh

You may follow the attached paper. The ans. is given in detail here. The sample is BiFeO3 too in this paper.

https://doi.org/10.1016/j.matchemphys.2020.123362

Dear Mr R. Rajesh ,

Thank you very much for the article. Really appreciate it.

Best regards,

Efi