An approach to the micro-strain distribution inside nanoparticle structure

Williamson-Hall, Stocks-Wilson, Scherrer, Halder-Wagner, and Size-Strain Plot (SSP) methods are used essentially to ensure 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, an approach to the microstrain distribution is presented as a strain distribution (SD) model, assuming a nanostructure as a liquid drop where surface tension controls the particle positions while strain controls the geometry and spacing of the lattice parameters. The number of diffraction planes is considered in the model, treated as a Gaussian-like (or Lorentzianlike) function, and estimated with numerical analysis. The SD 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 Scherrer can be explained as approximations for this model, and the presence of negative strain is explained. Possible approximations can show Halder-Wagner and SSP as another face of the SD model equation. The strain exponent, which is estimated here, is more useful than the average micro-strain, which is obtained from previous models. The strain exponent role in the nanoparticle reactions with materials can be discussed and explained. The change in crystal system as bulk material is reduced to nanostructure can be negated according to the SD model.