Use the Elastic Sphere Model (ESM) (for grain size: ~ 5nm to ~ 15 nm) and the Phonon Confinement Model (PCM) (for grain size: ~ 10nm to ~ 50 nm). In first approximation, the peak shift and half-width at half-height are both proportional to the inverse of the grain size with PCM. However, with use of both models for grain size determination comes with certain

approximations.

Nandha, are you using nanoparticles? Back when I was at Tufts U. we were doing research with TiO2 nanoparticles about 3 - 5 nm in diameter in an aqueous media. At that size, they're really too small for HR-TEM, AFM, dynamic light scattering, etc. There are ways to get down that small using STM, etc. But not IN WATER. This problem sounds similar to your question.

We discovered that at this nano-scale, we could take advantage of the Wulff shape of the nanoparticle and the fact that each face produces a unique vibrational mode that is observable via Raman spectroscopy. It turns out that each phase has a unique Wulff shape too and therefore a unique Raman spectrum.

In particular, each FACE (i.e.: crystallographic plane) produces a characteristic mode in the spectrum because of it's unique structure. (This is not unlike single crystal ice, which I have a lot more experience with.). By looking for the characteristic peak for say, the 001 face (about 190 cm-1 for anatase as I recall, but you can find this in the literature) we could tell if our synthesis was producing anatase or rutile phase. Rutile also has characteristic spectral fingerprints but it doesn't have a significant peak at 190cm-1  due to it's different Wulff shape. Thus, our ability to determine phase.

By looking at relative amplitudes of key peaks, we thought we could calculate relative concentrations between the phases. Though, we never went that far. We just wanted to see how much 001 face was being exposed (Wulff shape is somewhat sensitive to synthesis).

Nandha, I hope this helps!

You can not select nano size for Raman spectroscopy but for grain size you can use Raman microscopy techniques.

  HAW used Elastic Sphere Model (ESM) and Phonon Confinement Model (PCM) to calculate grain size in have an oxide layer TiO2 PREPARED BY ANODIC OXIDATION

You can easily calculator here,

https://instanano.com/characterization/theoretical/raman-spectroscopy-crystallite-size-calculator-tuinstra-koenig-relation/