Ab initiotest of the Warren–Averbach analysis on model palladium nanocrystals

Abstract

Model powder diffraction patterns were calculatedviathe Debye formula from atom positions of a range of energy-relaxed closed-shell cubooctahedral clusters. The energy relaxation employed the Sutton–Chen potential scheme with parameters for palladium. The assumed cluster size distribution followed lognormal distribution of a crystallite volume centred with the diameter of 5 nm, as well as two bimodal lognormal distributions centred around 4 nm and 7 nm. These models allowed an in-depth analysis of the Warren–Averbach method of separating strain and size effects in a peak shape Fourier analysis. The atom-displacement distribution in the relaxed clusters could be directly computed, as well as the strain Fourier coefficients. The results showed that in the case of the unimodal size distribution, the method can still be successfully used for obtaining the column length distribution. However, the strain Fourier coefficients obtained from three reflections (002, 004 and 008) cannot be reliably estimated with the Warren–Averbach method. The primary cause is a non-Gaussian strain distribution and a shift of the diffraction maximum, inherent to the nanoparticles, differing for every constituent cluster in the size distribution. For the bimodal size distributions, the obtained column length distributions tend to be shifted towards the centres of the modes and are less sensitive to the larger size mode.