An approach to the micro-strain distribution inside nanoparticle structure

Abstract

Abstract The importance of nanotechnology is increasing day by day, and to allow the nanoparticles to do what we hope, explicit modelling of nanostructures 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 nanoscale. Williamson-Hall, Stocks-Wilson, Debye-Scherrer, Halder-Wagner, and Size-Strain Plot (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 functions. In this work, when modelling a nanostructure as a liquid drop where surface tension controls the particle position and 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 a Gaussian-like (or Lorentzian-like) function that is 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 approximations for this model, and once the negative strain is explained, possible approximations can show Halder-Wagner and SSP another face of the strain distribution model equation.