Computer simulations based on the Khachaturyan's Onsager diffusion equation have been performed to model microstructure evolution during the cubic-to-tetragonal transformation in Ni-based alloys. A 2D model was employed. The fcc-DO₂₂ ordering has been studied as a model case of this type of transformation. Particular emphasis is placed on the formation mechanism of DO₂₂ monovariant structures. Computer simulations demonstrate that strain-induced interactions between coherent DO₂₂ precipitates lead to the formation of intermediate two-variant chessboard-like structures, which are found to be unstable and coalesce into subsequent single-variant maze structures. It is shown that the stability of the chessboard-like structures is very sensitive to lattice misfits. These simulation results are in good agreement with TEM observations.

In the present work, atomistic modeling based on the quasiparticle approach (QA) was performed to establish general trends in the segregation of solutes with different atomic size at symmetric ⟨100⟩ tilt grain boundaries (GBs) in α-Fe. Three types of solute atoms X₁, X₂ and X₃ were considered, with atomic radii smaller (X₁), similar (X₂) and larger (X₃) than iron atoms, respectively, corresponding to phosphorus (P), antimony (Sb) and tin (Sn). With this, we were able to evidence that segregation is dominated by atomic size and local hydrostatic stress. For low angle GBs, where the elastic field is produced by dislocation walls, X₁ atoms segregate preferentially at the limit between compressed and dilated areas. Contrariwise, the positions of X₂ atoms at GBs reflect the presence of tensile and compressive areal regions, corresponding to extremum values of the σ_XX and σ_YY components of the strain tensor. Regarding high angle GBs Σ5 (310) (θ = 36.95°) and Σ29 (730), it was found that all three types of solute atoms form Fe₉X clusters within B structural units (SUs), albeit being deformed in the case of larger atoms (X₂ and X₃). In the specific case of Σ29 (730) where the GB structure can be described by a sequence of |BC.BC| SUs, it was also envisioned that the C SU can absorb up to four X₁ atoms vs. one X₂ or X₃ atom only. Moreover, a depleted zone was observed in the vicinity of high angle GBs for X₂ or X₃ atoms. The significance of this research is the development of a QA methodology capable of ascertaining the atomic position of solute atoms for a wide range of GBs, as a mean to highlight the impact of the solute atoms’ size on their locations at and near GBs.

A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology. We proposed a new theory that allowed us to model the most challenging cases of atomic self-assembling whose complexity prevented their modeling before. For example, the most challenging and biologically relevant case of formation of double-stranded helix polymers from a solution of monomers is successfully simulated. The self-organization is in the atomic scale resolution while a time resolution is commensurate with the typical diffusion time. These advancements are achieved due to introduction of two novel concepts, atomic fragments (fraton) regarded as interacting pseudo-particles and structural clusters that are central for the proposed construction of the model Hamiltonian as a bilinear expansion in structural clusters. Both novelties provide a self-organization of even disordered atomic distribution to a desired atomic structure of practically any complexity. Several other examples including a crystallization of the diamond and zinc-blende structures are presented.