arXiv subjects

Marco Salvalaglio

Publications and source records attributed to Marco Salvalaglio.

At least 19 recordsLinked to original sources

arXiv2026

Surface Phase-Field-Crystal-Helfrich model for out-of-plane deformations in thin crystalline sheets with lattice mismatch

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.

cond-mat.mtrl-sci↗

arXiv2026

Intrinsic grain-size gradients upon grain growth near a free surface

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 $μ$m, and 10 $μ$m), 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.

cond-mat.mtrl-sci↗

arXiv2026

Multi-GPU fast Fourier transforms in MATLAB (for large-scale phase-field crystal simulations)

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.

cs.MS↗

arXiv2026

Shear-Coupled Grain Growth Statistics

Grain growth (GG), driven by grain boundary (GB) migration, is a fundamental mechanism of microstructural 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 the evolution of microstructure 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, 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.

cond-mat.mtrl-sci↗

arXiv2026

Solid-State Dewetting of Polycrystalline Thin Films: a Phase Field Approach

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 grandpotential 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.

cond-mat.mtrl-sci↗

arXiv2026

Dislocation dynamics on deformable surfaces

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.

cond-mat.soft↗

arXiv2026

Grain-Growth Stagnation from Vacancy-Diffusion-Limited Disconnection Climb

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.

cond-mat.mtrl-sci↗

arXiv2025

A topological approach to the Cahn-Hilliard equation and hyperuniform fields

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.

cond-mat.soft↗

arXiv2025

Why Grain Growth is Not Curvature Flow

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.

cond-mat.mtrl-sci↗

arXiv2025

Modeling dislocations in quasicrystals through amplitude equations

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.

cond-mat.mtrl-sci↗

arXiv2025

Inferring traits of hyperuniformity from local structures via persistent homology

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.

cond-mat.stat-mech↗

arXiv2025

Unidirectional motion of topological defects mediating continuous rotation processes

Topological defects play a critical role across many fields, mediating phase transitions and macroscopic behaviors as they move 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, specifically magnetic dislocations in a weak magnetic stripe pattern, induced by external magnetic field in a laterally unconfined thin film. This motion is shown to mediate the overall continuous rotation of the stripe pattern. 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.

cond-mat.mes-hall↗

arXiv2024

Phase-field Modelling of Anisotropic Solid-State Dewetting on Patterned Substrates

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 behaviors that could be leveraged to direct self-assembly of nanostructures, from ordered nanoparticles to interconnected networks with complex topology.

cond-mat.mes-hall↗

arXiv2024

Mesoscale Field Theory for Quasicrystals

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 non-conserved 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 semi-coherent interfaces and dislocation kinematics are given.

cond-mat.mes-hall↗

arXiv2024

A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks

We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The thermal compatibility condition, as well as a positive entropy-production property, 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 a positive entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.

cond-mat.mtrl-sci↗

arXiv2024

Mesoscale modeling of deformations and defects in thin crystalline sheets

We present a mesoscale description of deformations and defects in thin, flexible sheets with crystalline order, tackling the interplay between in-plane elasticity, out-of-plane deformation, as well as dislocation nucleation and motion. Our approach is based on the Phase-Field Crystal (PFC) model, which describes the microscopic atomic density in crystals at diffusive timescales, naturally encoding elasticity and plasticity effects. In its amplitude expansion (APFC), a coarse-grained description of the mechanical properties of crystals is achieved. We introduce surface PFC and surface APFC models in a convenient height-function formulation encoding deformation in the normal direction. This framework is proven consistent with classical aspects of strain-induced buckling, defect nucleation on deformed surfaces, and out-of-plane relaxation near dislocations. In particular, we benchmark and discuss the results of numerical simulations by looking at the continuum limit for buckling under uniaxial compression and at evidence from microscopic models for deformation at defects and defect arrangements, demonstrating the scale-bridging capabilities of the proposed framework. Results concerning the interplay between lattice distortion at dislocations and out-of-plane deformation are also illustrated by looking at the annihilation of dislocation dipoles and systems hosting many dislocations. With the novel formulation proposed here, and its assessment with established approaches, we envision applications to multiscale investigations of crystalline order on deformable surfaces.

cond-mat.mtrl-sci↗

arXiv2024

Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation

The phase-field crystal (PFC) model describes crystal structures at 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, a coarse-grained formulation focusing on slowly varying complex amplitudes of the microscopic density field has been devised. 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 seminal 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.

cond-mat.mtrl-sci↗

arXiv2024

Gradient elasticity in Swift-Hohenberg and phase-field crystal models

The Swift-Hohenberg (SH) and Phase-Field Crystal (PFC) models are minimal yet powerful approaches for studying phenomena such as pattern formation, collective order, and defects via smooth order parameters. They are based on a free-energy functional that inherently includes elasticity effects. This study addresses how gradient elasticity (GE), a theory that accounts for elasticity effects at microscopic scales by introducing additional characteristic lengths, is incorporated into SH and PFC models. After presenting the fundamentals of these theories and models, we first calculate the characteristic lengths for various lattice symmetries in an approximated setting. We then discuss numerical simulations of stress fields at dislocations and comparisons with analytic solutions within first and second strain-gradient elasticity. Effective GE characteristic lengths for the elastic fields induced by dislocations are found to depend on the free-energy parameters in the same manner as the phase correlation length, thus unveiling how they change with the quenching depth. The findings presented in this study enable a thorough discussion and analysis of small-scale elasticity effects in pattern formation and crystalline systems using SH and PFC models and, importantly, complete the elasticity analysis therein. Additionally, we provide a microscopic foundation for GE in the context of order-disorder phase transitions.

cond-mat.mtrl-sci↗