The asymmetry Kamachali describes is subtle but consequential. In most RIS frameworks, the governing description is closed through coupled transport equations for solutes and irradiation-generated point defects, augmented by source, recombination, and sink terms. The microstructural defects, such as grain boundaries, dislocations, and cavities, typically enter the equations through sink strength, capture efficiency, geometry, or boundary conditions. Their thermodynamic identity, however, is represented only in simplified form. Even where segregation energetics are included, they are often projected onto bulk thermodynamic factors or effective interfacial properties rather than being based on a sink-specific free-energy landscape. In other words, the equations know how fast solutes flow, but they know surprisingly little about the thermodynamic character of the destination. Kamachali argues that a more complete understanding of RIS can emerge when sink-specific thermodynamic landscapes and their interaction with non-equilibrium fluxes are taken explicitly into account.

This is not a call to discard existing models, which have grown increasingly sophisticated. Recent RIS models are already aware of the assumptions of perfect-sink behavior or homogeneous chemical potentials and aim to relax them. Thomas Schuler and colleagues, for instance, have emphasized the need to move beyond static sink idealizations and to describe the coupled interplay between segregation kinetics and sink evolution itself using atomistic simulations. Multiscale RIS frameworks such as those of Laurine Thuinet and co-workers and of Liangzhao Huang and collaborators have combined atomistic transport information with continuum-level segregation modeling, moving beyond purely phenomenological sink treatments. Phase-field investigations by Gauthier Bertrand Moladje and colleagues on RIS near dislocations and low-angle grain boundaries have shown that biased sinks require an explicit treatment of local defect character rather than a neutral-sink approximation. Experimental studies have reinforced this viewpoint, showing that grain boundary plane and character strongly influence the resulting segregation and precipitation behavior under irradiation.

Further recent developments have broadened the scope of RIS modeling and validation even more, including two- and three-dimensional treatments of sink geometry and morphology, nonlinear coupling between neighboring nanoscale sinks, machine-learning-assisted parameterization of defect-mediated diffusion kinetics, and correlative atom probe tomography and scanning transmission electron microscopy validation of RIS profiles. These advances suggest, Kamachali writes, that the important next step is not only to refine transport coefficients, but also to develop thermodynamic representations of sinks as structurally and chemically differentiated states. A grain boundary is not a neutral drain for solutes; it is a quasi-two-dimensional region with its own atomic density, its own coordination numbers, and its own mixing enthalpies and entropies, all of which can differ dramatically from the bulk crystal that surrounds it.

The systematic step forward that Kamachali proposes connects RIS frameworks with ongoing advances in the thermodynamic and kinetic theory of defects, in particular the density-based thermodynamic and phase-field framework known as DPF. The DPF theory offers a route to view defects as local thermodynamic states with their own structural, chemical, and energetic degrees of freedom, describing them through a density parameter that represents their local structural state, while restoring the thermodynamic properties of the parent bulk phase. The significance of this idea is far-reaching: defects and bulk phases are no longer treated as conceptually separate objects, but as distinguishable yet continuously connected states within a single free-energy landscape. This provides a natural thermodynamic language for describing defect stability, segregation, and defect-phase transitions in direct continuity with the surrounding bulk material.

Within the broad landscape of existing theory, DPF can be understood as a strong addition rather than a replacement. Classical rate-theory and sink-strength models remain central for describing defect production, recombination, migration, and biased fluxes under irradiation. Atomistic simulations, kinetic Monte Carlo, and cluster-dynamics approaches provide essential information on defect-solute binding, transport pathways, cascade debris, and the evolution of defect clusters. DPF offers a thermodynamically adaptable and compatible route for representing defect states and sinks, and it can be directly integrated with phase-field models, which have become increasingly important for connecting irradiation-modified thermodynamic driving forces to precipitation, phase stability, and mesoscale microstructure evolution. Crucially, DPF opens a comprehensive route for integrating defect thermodynamics with existing bulk CALPHAD databases, the vast repositories of assessed thermodynamic data that underpin computational materials design. Recent detailed investigations have shown that the density parameter can be derived from atomistic simulations, establishing a streamlined bridge between atomistic calculations and continuum thermodynamic and phase-field modeling.

Kamachali identifies two profound ways in which DPF can enrich RIS studies. The first is by remapping phase stability under irradiation through irradiation-conditioned phase diagrams. The framework begins with a density-based free-energy functional, in which the atomic density acts both as a field variable in simulations and as a mean-field descriptor in the free-energy formulation. For a grain boundary embedded in a multicomponent alloy, the functional combines a volume integral over the density-based Gibbs free energy density with a plane integral accounting for the interfacial contribution of the grain boundary, whose potential and gradient coefficients relate to the underlying grain-boundary properties such as atomic planes and misorientation and can be derived from atomistic simulations. The elastic energy density is formalized for multicomponent alloys with lattice strain coefficients due to solutes in the host lattice and elastic constants defined as a function of local atomic density. These equations are fed by CALPHAD thermodynamic data of the corresponding alloy system together with a minimum set of grain-boundary-specific quantities, including the free energy of the homogeneous bulk substance, gradient energy coefficients, and the bulk mixing enthalpy and entropy.

If a steady irradiation condition is viewed, at a coarse-grained thermodynamic level, as maintaining a supersaturated population of point defects, it can be connected to density-based phase diagrams through two intermediate links: the well-established connection between irradiation intensity and the resulting excess concentration of point defects, and the recent demonstration that point defects can be effectively described based on an atomic density field through both a reduction in coordination number and a change in excess free volume. Once these links are established, CALPHAD-integrated density-based free-energy functionals can be constructed and minimized to compute irradiation-conditioned phase diagrams. These differ fundamentally from so-called radiation-modified phase diagrams constructed essentially in terms of radiation-modified solubility, the solute concentration at which the growth rate of an irradiated precipitate vanishes. The density-based diagrams have a free-energy foundation and enable studying the conditions of phase stability, including nucleation and dissolution of various phases, directly not only in the supersaturated bulk but also at defects acting as sinks. Notably, it has been shown that the miscibility gap in Fe-Mn-X alloy systems can dramatically change for a reduced atomic density, meaning that even modest defect-induced reductions in atomic density can shift local thermodynamic driving forces and phase equilibria.

The second enrichment is defect-sensitive transport and phase evolution. In the Onsager framework, the quantities entering the RIS equations are not independent objects but descend from the underlying thermodynamic structure of the system. Once the free-energy landscape is allowed to depend explicitly on the local defect state, both the driving forces and the kinetic couplings become functions of the local defect state. The generalized diffusional potentials of the alloying species follow from the variational derivatives of the density-based defect free-energy functional, and the fluxes are expressed in Onsager form as linear responses to gradients in these generalized potentials, with the Onsager coefficients themselves depending on the local atomic density and hence on the local defect state. The vacancy and self-interstitial concentrations and fluxes can be consistently expressed in terms of the atomic density field while still being retained as distinct transport variables when required, allowing interstitial-mediated RIS mechanisms to be incorporated. Segregation, counter-segregation, and coupled solute-defect transport need not be described through fixed sink parameters alone but can be treated as consequences of a defect-dependent free-energy landscape and its associated mobilities, with parameterization obtained from atomistic simulations, kinetic Monte Carlo calculations, rate-theory estimates, or spatially resolved irradiation experiments.

Recent applications demonstrate the promise of this approach. Kadambi and colleagues explicitly coupled the atomic density field to CALPHAD-informed free-energy descriptions to capture segregation and phase stability in the vicinity of defects, with particular emphasis on maintaining thermodynamic consistency across bulk and defect regions in ternary Fe-Cr-Ni alloys. A more extensive effort by Calbert, Messina, and Thuinet embedded the DPF concept, together with a density-dependent Gibbs free-energy functional directly linked to CALPHAD-accessible quantities, into a classical phase-field framework to describe grain boundaries and radiation-induced segregation in Fe-Cr alloys, treating the grain-boundary density as a governing parameter and systematically varying it to show how the grain-boundary state directly modifies segregation profiles and sink efficiencies. A key aspect lies in making the defect-elastic interaction explicitly dependent on the local atomic density field: rather than prescribing a constant eigenstrain at the grain boundary, the eigenstrain of each defect species is derived as a continuous function of local density, leading to a density-dependent relaxation volume for solutes, vacancies, and interstitials. In terms of experimental validation, a thermodynamic defect-state framework generates measurable predictions beyond classical enrichment or depletion profiles, including possible transitions between distinct chemical or structural states of the sink, sink-specific excess compositions, and variations in segregation behavior with grain-boundary character. A particularly useful strategy would be to compare chemically resolved segregation profiles at different sinks exposed to the same irradiation condition: if two sinks experience comparable fluxes but display different segregation levels or precipitation tendencies due to their structural character, this would suggest the necessity for adopting thermodynamic-aware sink-strength parameters. The view of defects as passive sinks characterized by fixed parameters, Kamachali concludes, can and should be replaced by a dynamic framework that captures their thermodynamic identity, a necessary step toward preventative and ultimately design-driven strategies for materials under irradiation.

Subject of Research: Thermodynamics of radiation-induced segregation and phase change in nuclear materials

Article Title: Thermodynamics for radiation-induced segregation and phase change needed

Article References: Kamachali, R. D. (2026). Thermodynamics for radiation-induced segregation and phase change needed. Frontiers in Nuclear Engineering, 5, Article 1868886. https://doi.org/10.3389/fnuen.2026.1868886

Image Credits: AI Generated

DOI: 10.3389/fnuen.2026.1868886

Keywords: radiation-induced segregation, thermodynamics, nuclear materials, CALPHAD, phase diagrams, density phase-field, grain boundaries, irradiation, radiation-induced, segregation, phase, change