Partial structure factors derived from coarse-grained phase-separation dynamics on a disordered lattice with density fluctuations

The simplest and most time-efficient phase-separation dynamics simulations are carried out on a disordered lattice to calculate the partial structure factors of coarse-grained A-B binary mixtures. The typical coarse-grained phase-separation models use regular lattices and can describe the local concentrations but cannot describe both local density and concentration fluctuations. To introduce fluctuation for local density in the model, the particle positions from a hard sphere fluid model are determined as disordered lattice points for the model. Then we place the local order parameter as the difference of the concentrations of A and B components on each lattice point. The concentration at each lattice point is time-evolved by discrete equations derived from the Cahn-Hilliard equation. From both fluctuations, Bhatia and Thornton’s structure factor can be accurately calculated. The structure factor for concentration fluctuations at the large wavenumber region gives us the correct mean concentrations of the components. Using the mean concentrations, partial structure factors can be converted from three of Bhatia and Thornton’s structure factors. The present model and procedures can provide a means of analysing the structural properties of many materials that exhibit complex morphological changes.

Bounds on the Lattice Point Enumerator via Slices and Projections

Gardner et al. posed the problem to find a discrete analogue of Meyer’s inequality bounding from below the volume of a convex body by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated by this problem, for which we provide a first general bound, we study in a more general context the question of bounding the number of lattice points of a convex body in terms of slices, as well as projections.

Thermodynamic model for lattice point defect-mediated semi-coherent precipitation in alloys

The formation of precipitates with an atomic volume different from their parent phase eventually leads to a loss of the lattice continuity at the matrix–precipitate interface. Here, we show the creation or removal of lattice sites mediated by lattice point defects is an accommodation mechanism of the coherency loss and even a precipitation driving force. We introduce a thermodynamic approach that rationalizes the selection of phases resulting from chemical and crystallographic constraints in relation to point defect properties. The resulting semi-coherent phase diagram and the precipitation kinetic model depend on the equilibrium phase diagram, the eigenstrain of the precipitating phase, and the chemical potential of point defects. From a joint experimental and modeling study, we uncover the prominent role of excess point defects in unforeseen phase transformations of the Fe–Ni metallic system under irradiation. By addressing the fundamental role of lattice point defects in the accommodation mechanisms of precipitation, we provide a step torwards the understanding of semi-coherent phase transformations occurring in solid materials upon synthesis and in use.