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Ab initio test of the Warren–Averbach analysis on model palladium nanocrystals
Author(s) -
Kaszkur Zbigniew,
Mierzwa Bogusław,
Pielaszek Jerzy
Publication year - 2005
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889804033291
Subject(s) - log normal distribution , molecular physics , fourier transform , materials science , diffraction , gaussian , cluster (spacecraft) , atom (system on chip) , range (aeronautics) , debye–waller factor , crystallography , analytical chemistry (journal) , chemistry , physics , computational chemistry , optics , mathematics , statistics , chromatography , quantum mechanics , computer science , embedded system , programming language , composite material
Model powder diffraction patterns were calculated via the 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.