An explicit model for micro-strain distribution inside nanoparticle structure

Abstract

Abstract The importance of nanotechnology is enlarged day by day and to tolerate the nanoparticles to do what we hope, the existence of explicit modeling for nanostructure is necessary. Considering the strain inside the nanoparticle is the major subject that changes the point of view to the unique properties of the material on the nano-scale. Williamson-Hall, Stocks-Wilson, Debye-Scherrer, Halder-Wagner, and SSP methods are used essentially to insure the material particle size falls at the nano-level, they treat the broadening in the XRD peak as a sum of Gauss and Lorentz diffraction probability function. In this work, modeling for nanostructure as a liquid drop where surface tension controls the particle position, the strain controls the geometry and spacing of the lattice parameters, the number of the diffraction planes is used instead of the line intensity and shows Gaussian-like (or Lorentzian-like) function which investigated with numerical analysis. The model writes an equation about the broadening, peak position, and lattice parameters to estimate the crystalline size and strain exponent. Williamson-Hall, Stocks-Wilson, and Debye-Scherrer can be explained as an approximation for this model and the negative strain is explained, possible approximations can show Halder-Wagner and SSP another face of the strain distribution model equation.