Complex modeling for the quantification of nanoscale disorder using genetic algorithms, density functional theory and line-profile analysis

A new, computationally efficient, complex modeling approach is presented for the quantification of the local and average atomic structure, nanostructure and microstructure of an Au_0.25Cu_0.75 alloy. High-resolution X-ray powder diffraction and whole pattern fitting show that the sample is phase pure, with isotropic lattice strain and a distribution of equiaxed crystallites of mean size 144 (11) nm, where each crystallite has on average four twin boundaries and an average of three deformation faults per four crystallites. Both small- and large-box model optimizations were used to extract local and long-range information from the pair distribution function. The large-box, 640 000-atom-ensemble optimization approach applied herein relies on differential evolution optimization and shows that the alloy has chemical short-range ordering, with correlation parameters of −0.26 (2) and 0.36 (8) in the first and second correlation shells, respectively. Locally, there is a 1.45 (8)% tetragonal distortion which on average results in a cubic atomic structure. The isotropic lattice strain is a result of atom-pair-dependent bond lengths, following the trend d_Au—Au > d_Au—Cu > d_Cu—Cu, highlighted by density functional theory calculations. This approach is generalizable and should be extensible to other disordered systems, allowing for quantification of localized structure deviations.