https://en.wikipedia.org/wiki/Vapor–liquid–solid_method

You can read following paper and thesis :

Saunders, Ruth B., Enda McGlynn, and Martin O. Henry. "Theoretical analysis of nucleation and growth of ZnO nanostructures in vapor phase transport growth." Crystal Growth & Design 11.10 (2011): 4581-4587.

http://doras.dcu.ie/17138/

Hello Binaya Kumar Sahu!

The theory of the Gibbs mechanism acting in the nucleation process during the formation of the solid nanostructure, from the precursor vapor and the liquid catalyst, could certainly help you ;D

Greetings from Brazil!

Hello Fernando Maia de Oliveira ,

Thanks for your answer. Ya, by considering the Gibbs free energy we can predict the growth of nano-syrusture. We have written a paper regarding this.

Sub-wavelength waveguide properties of 1D and surfacefunctionalized SnO2 nanostructures of various morphologies

Thanks