Grain boundary (GB) migration has traditionally been described as capillarity-driven, with GBs moving toward their centre of curvature to reduce total interfacial area and energy. However, recent observations have shown that GB migration is largely mediated by disconnections that couple with internal and external stress, thereby inducing additional phenomenology and grain growth even under ambient conditions. These observations are often influenced by multiple, simultaneously active factors, including elevated temperatures, complex nanocrystalline microstructures, and heterogeneity of stress or strain states. In addition, surface or beam effects during in-situ transmission electron microscopy make it difficult to directly link GB crystallography to migration propensity under applied stress or strain. Using a controlled multiscale bicrystal experimental framework combined with multiscale simulations, we demonstrate that GB migration under ambient conditions occurs in a copper bicrystal above a certain threshold strain. The strain dependence and selective migration of an asymmetric Σ5 GB, as opposed to its symmetric counterpart, are explored synergistically through micropillar compression experiments, crystal plasticity simulations, phase-field crystal plasticity modelling, and molecular statics simulations. Interestingly, the material’s strain-hardening response is altered when GB migration sets in, and, contrary to classical expectations, the total GB area increases. Together, these results provide clear evidence and a detailed understanding of GB migration driven by plastic deformation, accounting not only for crystallography but also for its interplay with strain rate and dislocation–GB interactions. The implications of this study are critical for understanding and controlling microstructural evolution during thermomechanical processing.

We present a MATLAB-based framework for two- and three-dimensional fast Fourier transforms on multiple GPUs for large-scale numerical simulations using the pseudo-spectral Fourier method. The software implements two complementary multi-GPU strategies that overcome single-GPU memory limitations and accelerate spectral solvers. This approach is motivated by and applied to phase-field crystal (PFC) models, which are governed by tenth-order partial differential equations, require fine spatial resolution, and are typically formulated in periodic domains. Our resulting numerical framework achieves significant speedups, approximately sixfold for standard PFC simulations and up to sixtyfold for multiphysics extensions, compared to a purely CPU-based implementation running on hundreds of cores.

Thin, flexible crystalline sheets exhibit unique elastic properties due to their ability to undergo out-of-plane deformations. Understanding this behavior requires a description that couples in-plane elasticity, out-of-plane deformation, and their coupling, taking the crystalline structure and its defects into account. We develop a multiscale description for these systems by extending the surface Phase-Field-Crystal-Helfrich model. The extension permits a spatially varying equilibrium lattice spacing, enabling the representation of localized lattice eigenstrain to mimic lattice mismatch in heterostructures. We validate the extended model against analytical predictions from classical Föppl-von Kármán equations for uniaxial compression and from Eshelby's inclusion problem. Using this validated framework, we then show how locally induced compressive stresses drive out-of-plane deformation in the sheets.

Grain growth in polycrystals typically stagnates at long times. We identify disconnection climb, limited by vacancy diffusion, as a fundamental microscopic mechanism underlying this behavior. Using a phase-field crystal framework extended to model vacancy diffusion, we resolve grain-boundary migration on diffusive time scales and show that disconnection climb rates correlate with the characteristic grain size at which growth arrests. These results link vacancy transport, disconnection dynamics, and microstructural evolution, establishing vacancy diffusion as a key governing factor.

We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a general kinematic expression for dislocation velocity directly from the complex-amplitude evolution equations, which is also applicable to deformed surfaces through curvature-modified differential operators. From numerical simulations, we show that even small out-of-plane deformations reshape the phenomenology of defect motion through curvature-induced self-propulsion, modified glide directions, and non-classical defect-defect interactions. Our results show how surface geometry profoundly influences defect dynamics and establish the surface-APFC model as a powerful framework for predicting and interpreting curvature-defect coupling across a wide range of systems, from stiff but deformable layers to soft matter surfaces and membranes that retain crystalline order.

Grain growth fundamentally shapes the microstructure of crystalline materials upon annealing, affecting their overall mechanical and functional properties. Recently, it has been rationalized that grain growth in polycrystals does not result solely from weighted curvature flow, but elastic effects (intrinsic stress) arised from shear coupling also need to be taken into account. We characterize and examine the effect of free surfaces on grain growth kinetics of high-purity, bulk polycrystalline nickel. By analyzing the microstructural evolution on cross sections of 1 mm thick specimens from the surface to the interior, as well as through in-plane investigations on specimens with varying thickness (1 mm, 40 μm, and 10 μm), an intrinsic grain-size gradient was identified, characterized by a gradual increase in grain size towards the interior. Interestingly, this grading was not restricted to the very surface but continued to depths of five to ten layers of grains, where effects from thermal grooves are considered negligible. We demonstrate that this behavior is significantly affected by elastic relaxation at the free surface, which alters the internal stress fields generated by shear-coupled grain boundary migration. These findings emphasize the relevance of free surfaces to the microstructural evolution of polycrystal.

Solid-state dewetting is the process by which thin solid films break up and retract on a substrate, forming nanostructures. While dewetting of single-crystalline films is understood as a surface-energy-driven process mediated by surface diffusion, polycrystalline films exhibit additional complexity due to the presence of grain boundaries. Most theoretical and computational studies have focused on single-crystalline dewetting. Here, we present the application of the grand-potential multi-phase-field model to the dewetting of thin polycrystalline films in three dimensions, reproducing the key phenomenology of this process. By considering isotropic interface/surface energy, we illustrate its consistency with predictions based on energetic arguments and the morphological evolution towards equilibrium. We also provide novel analytical criteria for the onset of three-dimensional dewetting, serving as fundamental theoretical benchmarks, and highlight the critical role of triple junctions. Moreover, we unveil the dewetting behavior of polycrystalline patches, extending the scenarios of their single-crystalline counterparts.

Grain growth (GG), mediated by grain boundary (GB) migration, is a fundamental mechanism of microstructure evolution in polycrystalline materials. GB migration is frequently accompanied by a relative shear displacement of grains meeting at GBs, a phenomenon known as shear-coupling. This coupling induces internal stresses within the microstructure, which recent studies have shown to play a decisive role in dictating microstructure evolution and GG pathways. This work provides a detailed characterization of the statistical features of two-dimensional GG in the presence of GB shear-coupling through continuum modeling of GB migration that incorporates fundamental microscopic mechanisms and diffuse-interface simulations. We demonstrate that incorporating shear-coupling produces a more heterogeneous, less equiaxed microstructure than conventional curvature-driven GG, while yielding topological and geometric properties consistent with experimental and atomistic observations. We further demonstrate that as grain grows in this regime, internal stress relaxes. Highly stressed grains shrink faster, and lightly stressed grains grow faster than other grains. These findings demonstrate that internal stress, an intrinsic feature of GG, profoundly changes essential features of GG microstructure and kinetics, consistent with experiments and atomic-scale simulations. Moreover, we discuss their implications for GG regimes and scaling behavior.

Hyperuniform structures are disordered, correlated systems in which density fluctuations are suppressed at large scales. Such a property generalizes the concept of order in patterns and is relevant across diverse physical systems. We present a numerical characterization of hyperuniform scalar fields that leverages persistent homology. Topological features across different lengths are represented in persistence diagrams, while similarities or differences between patterns are quantified through Wasserstein distances between these diagrams. We apply this framework to numerical solutions of the Cahn-Hilliard equation, a canonical model for generating hyperuniform scalar fields. We validate the approach against known features of the Cahn-Hilliard equation, including its scaling properties, convergence to the sharp interface limit, and self-similarity of the solutions. We then generalize the approach by studying Gaussian random fields exhibiting different degrees and classes of hyperuniformity, showing how the proposed approach can be exploited to reconstruct global properties from local topological information. Overall, we show how hyperuniform characteristics systematically correlate with distributions of topological features in disordered correlated fields. We expect this analysis to be applicable to a wide range of scalar fields, particularly those involving interfaces and free boundaries.

Topological defects play a crucial role across various fields, mediating phase transitions and macroscopic behaviors as they propagate through space. Their role as robust information carriers has also generated much attention. However, controlling their motion remains challenging, especially towards achieving motion along well-defined paths, which typically require predefined structural patterning. Here, we demonstrate the tunable, unidirectional motion of topological defects in a laterally unconfined thin film. The motion of these defects-specifically magnetic dislocations-is shown to mediate the overall continuous rotation of the stripe pattern in which they are embedded. We determine the connection between the unidirectional motion of dislocations and the underlying three-dimensional (3D) magnetic structure by performing 3D magnetic vectorial imaging with in situ magnetic fields. A minimal model for dislocations in stripe patterns that encodes the symmetry breaking induced by the external magnetic field reproduces the motion of dislocations that facilitate the 2D rotation of the stripes, highlighting the universality of the phenomenon. This work establishes a framework for studying the field-driven behavior of topological textures and designing materials that enable well-defined, controlled motion of defects in unconfined systems, paving the way to manipulate information carriers in higher-dimensional systems.

We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The fundamental thermodynamic relation between internal energy and entropy, as well as entropy production, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within an entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.

Grain growth in polycrystals is traditionally considered a capillarity-driven process, where grain boundaries (GBs) migrate toward their centers of curvature (i.e., mean curvature flow) with a velocity proportional to the local curvature (including extensions to account for anisotropic GB energy and mobility). Experimental and simulation evidence shows that this simplistic view is untrue. We demonstrate that the failure of the classical mean curvature flow description of grain growth mainly originates from the shear deformation naturally coupled with GB motion (i.e., shear coupling). Our findings are built on large-scale microstructure evolution simulations incorporating the fundamental (crystallography-respecting) microscopic mechanism of GB migration. The nature of the deviations from curvature flow revealed in our simulations is consistent with observations in recent experimental studies on different materials. This work also demonstrates how to incorporate the mechanical effects that are essential to the accurate prediction of microstructure evolution.

Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to understand mechanisms of pattern formation and to exploit peculiar attributes, e.g., interaction with light and transport phenomena. While hyperuniformity is a global property, ideally defined for infinitely extended systems, several disordered correlated systems have finite size. It has been shown in [Phys. Rev. Research 6, 023107 (2024)] that global hyperuniform characteristics systematically correlate with distributions of topological properties representative of local arrangements. In this work, building on this information, we explore and assess the inverse relationship between hyperuniformity and local structures in point patterns as described by persistent homology. Standard machine learning algorithms trained on persistence diagrams are shown to detect hyperuniformity of periodic point patterns with high accuracy. Therefore, we demonstrate that the information on patterns' local structures allows for characterizing whether finite size arrangements are analogous to those realized in hyperuniform patterns. Then, addressing more quantitative aspects, we show that parameters defining hyperuniformity globally can be reconstructed by comparing persistence diagrams of targeted patterns with reference ones. We also explore the generation of patterns entailing given topological properties. The results of this study pave the way for advanced analysis of hyperuniform patterns including local information, and introduce basic concepts for their inverse design.

The phase-field crystal (PFC) model describes crystal structures on diffusive timescales through a periodic, microscopic density field. It has been proposed to model elasticity in crystal growth and encodes most of the phenomenology related to the mechanical properties of crystals like dislocation nucleation and motion, grain boundaries, and elastic or interface-energy anisotropies. To overcome limitations to small systems, previous studies introduced a coarse-grained formulation focusing on slowly varying complex amplitudes of the microscopic density field. This amplitude-PFC (APFC) model describes well elasticity and dislocations while approximating microscopic features and being limited in describing large-angle grain boundaries. We present here the foundational concepts for a hybrid multiscale PFC-APFC framework that combines the coarse-grained description of the APFC model in bulk-like crystallites while exploiting PFC resolution at dislocations, grain boundaries, and interfaces or surfaces. This is achieved by coupling the two models via an advanced discretization based on the Fourier spectral method and allowing for local solution updates. This discretization also generalizes the description of boundary conditions for PFC models. We showcase the framework capabilities through two-dimensional benchmark simulations. We also show that the proposed formulation allows for overcoming the limitations of the APFC model in describing large-angle grain boundaries.

Quasicrystals (QCs) are a class of aperiodic ordered structures that emerge in various systems, from metallic alloys to soft matter and driven non-equilibrium systems. Within a mesoscale theory based on slowly-varying complex amplitudes for QCs, we track dislocations as topological defects harbored by the amplitudes and characterize their Burgers vectors and induced deformations. We study the formation of dislocations at semicoherent interfaces, particularly those emerging from rotated inclusions, and find a hierarchy of dislocations forming at such interfaces. We further analyze interfaces in strained systems, revealing conditions for the emergence of periodic dislocation arrays and discussing the energetics of dislocations associated with different phonon and phason deformations. The stability, interaction, and motion of dislocation dipoles and quadrupoles are also discussed. These findings provide new insights into the mesoscale modeling of dislocations in QCs and their distinct behavior compared to conventional crystals, while demonstrating a versatile framework for studying dislocations in systems exhibiting quasicrystalline order.

We present a phase-field model for simulating the solid-state dewetting of anisotropic crystalline films on non-planar substrates. This model exploits two order parameters to trace implicitly the crystal free surface and the substrate profile in both two and three dimensions. First, we validate the model by comparing numerical simulation results for planar substrates with those obtained by a conventional phase-field approach and by assessing the convergence toward the equilibrium shape predicted by the Winterbottom construction. We then explore non-planar geometries, examining the combined effects of surface-energy anisotropies and parameters controlling the contact angle. Our findings reveal that crystalline particles on curved supports lose self-similarity and exhibit a volume-dependent apparent contact angle, with opposite trends for convex versus concave profiles. Additionally, we investigate the migration of faceted particles on substrates with variable curvature. Applying this model to experimentally relevant cases like spheroidal and pit-patterned substrates demonstrates various behaviours that could be leveraged to direct self-assembly of nanostructures, from ordered nanoparticles to interconnected networks with complex topology.

We present a mesoscale field theory unifying the modeling of growth, elasticity, and dislocations in quasicrystals. The theory is based on the amplitudes entering their density-wave representation. We introduce a free energy functional for complex amplitudes and assume nonconserved dissipative dynamics to describe their evolution. Elasticity, including phononic and phasonic deformations, along with defect nucleation and motion, emerges self-consistently by prescribing only the symmetry of quasicrystals. Predictions on the formation of semicoherent interfaces and dislocation kinematics are given.

Light-emitting complex defects in silicon have been considered a potential platform for quantum technologies based on spin and photon degrees of freedom working at telecom wavelengths. Their integration in complex devices is still in its infancy, and it was mostly focused on light extraction and guiding. Here we address the control of the electronic states of carbon-related impurities (G-centers) via strain engineering. By embedding them in patches of silicon on insulator and topping them with SiN, symmetry breaking along [001] and [110] directions is demonstrated, resulting in a controlled splitting of the zero phonon line (ZPL), as accounted for by the piezospectroscopic theoretical framework. The splitting can be as large as 18 meV and it is finely tuned by selecting patch size or by moving in different positions on the patch. Some of the split, strained ZPLs are almost fully polarized and their overall intensity is enhanced up to 7 times with respect to the flat areas, whereas their recombination dynamics is slightly affected. Our technique can be extended to other impurities and Si-based devices such as suspended bridges, photonic crystal microcavities, Mie resonators, and integrated photonic circuits.

We demonstrate that grain boundaries (GBs) behave as Brownian ratchets, exhibiting direction-dependent mobilities and unidirectional motion under oscillatory driving forces or cyclic thermal annealing. We observed these phenomena for nearly all nonsymmetric GBs but not for symmetric ones. Our observations build on molecular dynamics and phase-field crystal simulations for a wide range of GB types and driving forces in both bicrystal and polycrystalline microstructures. We corroborate these simulation results through in situ experimental observations. We analyze these results with a Markov chain model and explore the implications of GB ratchet behavior for materials processing and microstructure tailoring.

Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity only utilizes information at the largest scales, hyperuniform configurations have distinctive local characteristics. However, the influence of global hyperuniformity on local structure has remained largely unexplored; establishing this connection can help uncover long-range interaction mechanisms and detect hyperuniform traits in finite-size systems. Here, we study the topological properties of hyperuniform point clouds by characterizing their persistent homology and the statistics of local graph neighborhoods. We find that varying the structure factor results in configurations with systematically different topological properties. Moreover, these topological properties are conserved for subsets of hyperuniform point clouds, establishing a connection between finite-sized systems and idealized reference arrangements. Comparing distributions of local topological neighborhoods reveals that the hyperuniform arrangements lie along a primarily one-dimensional manifold reflecting an order-to-disorder transition via hyperuniform configurations. The results presented here complement existing characterizations of hyperuniform phases of matter, and they show how local topological features can be used to detect hyperuniformity in size-limited simulations and experiments.