Compositional patterning in irradiated alloys: Effective potentials and effective interfacial energy

Compositional patterning (CP) in binary alloys during energetic particle irradiation is studied using a kinetic model that considers two competing kinetic processes, a thermally activated one promoting macroscopic phase separation (MPS) of the concentration field $c(\mathbf{r},t),$ and a forced one resulting in finite-range random atomic mixing. The forced mixing is modeled by a Gaussian relocation distribution with a characteristic distance $R$. A series of approximate kinetic models are introduced by expanding the mixing function into a series of $n$ terms, thus replacing the nonlocal evaluations of the concentration field $c({\mathbf{r}}^{\ensuremath{'}}\ensuremath{-}\mathbf{r},t)$ by local derivatives of $c(\mathbf{r},t)$. This approach makes it possible to obtain exact effective potentials and build steady-state diagrams for each order-n model. Phase-field (PF) simulations using these order-n models reveal that near the onset of patterning, phase evolution is accurately described using an order-3 model, which changes smoothly from an extended Cahn-Hilliard free energy in the MPS regime to a one-mode Swift-Hohenberg functional in the CP regime. Deeper into the patterning regime, higher-order models are required to achieve convergence, yielding squarelike concentration profiles characteristic of a strong segregation regime. These higher-order effective free energies are analogous to multimodal Swift-Hohenberg functionals. An alternative definition for the effective interfacial energy is proposed in the CP regime, since the interfacial area is no longer an excess quantity in that regime, precluding the use of the standard thermodynamic definition of interfacial energy.