arXiv subjects

Marco Salvalaglio

Publications and source records attributed to Marco Salvalaglio.

At least 37 records · Page 2Linked to original sources

arXiv2024

Persistent homology and topological statistics of hyperuniform point clouds

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.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium hyperuniform states in active turbulence

We demonstrate that the complex spatiotemporal structure in active fluids can feature characteristics of hyperuniformity. Using a hydrodynamic model, we show that the transition from hyperuniformity to non-hyperuniformity and anti-hyperuniformity depends on the strength of active forcing and can be related to features of active turbulence without and with scaling characteristics of inertial turbulence. Combined with identified signatures of Levy walks and non-universal diffusion in these systems, this allows for a biological interpretation and the speculation of non-equilibrium hyperuniform states in active fluids as optimal states with respect to robustness and strategies of evasion and foraging.

cond-mat.soft↗

arXiv2023

Evaluation of the elastic field in phase-field crystal simulations

The phase-field crystal model (PFC) describes crystal structures at diffusive timescales through a periodic order parameter representing the atomic density. One of its main features is that it naturally incorporates elastic and plastic deformation. To correctly interpret numerical simulation results or devise extensions related to the elasticity description, it is important to have direct access to the elastic field. In this work, we discuss its evaluation in classical PFC models based on the Swift-Hohenberg energy functional. We consider approaches where the stress field can be derived from the microscopic density field (i.e., the order parameter), and a simple novel numerical routine is proposed. By numerical simulations, we demonstrate that it overcomes some limitations of currently used methods. Moreover, we shed light on the elasticity description conveyed by classical PFC models, characterizing a residual stress effect present at equilibrium. We show explicitly and discuss the evaluation of the elastic fields in prototypical representative cases involving an elastic inclusion, a grain boundary, and dislocations.

cond-mat.mtrl-sci↗

arXiv2023

Amplitude phase-field crystal model for the hexagonal close-packed lattice

The phase field crystal model allows the study of materials on atomic length and diffusive time scales. It accounts for elastic and plastic deformation in crystal lattices, including several processes such as growth, dislocation dynamics, and microstructure evolution. The amplitude expansion of the phase field crystal model (APFC) describes the atomic density by a small set of Fourier modes with slowly-varying amplitudes characterizing lattice deformations. This approach allows for tackling large, three-dimensional systems. However, it has been used mostly for modeling basic lattice symmetries. In this work, we present a coarse-grained description of the hexagonal closed-packed (HCP) lattice that supports lattice deformation and defects. It builds on recent developments of the APFC model and introduces specific modeling aspects for this crystal structure. After illustrating the general modeling framework, we show that the proposed approach allows for simulating relatively large three-dimensional HCP systems hosting complex defect networks.

cond-mat.mtrl-sci↗

arXiv2023

A unified field theory of topological defects and non-linear local excitations

Topological defects and smooth excitations determine the properties of systems showing collective order. We introduce a generic non-singular field theory that comprehensively describes defects and excitations in systems with $O(n)$ broken rotational symmetry. Within this formalism, we explore fast events, such as defect nucleation/annihilation and dynamical phase transitions where the interplay between topological defects and non-linear excitations is particularly important. To highlight its versatility, we apply this formalism in the context of Bose-Einstein condensates, active nematics, and crystal lattices.

cond-mat.soft↗

arXiv2023

Disconnection Flow-Mediated Grain Rotation

Interface migration in microstructures is mediated by the motion of line defects with step and dislocation character, i.e., disconnections. We propose a continuum model for arbitrarily-curved grain boundaries or heterophase interfaces accounting for disconnections' role in grain rotation. Numerical simulations show that their densities evolve as grain size and shape change, generating stresses and increasing or decreasing misorientation; the predictions agree with molecular dynamics simulations for pure capillarity-driven evolution, and are interpreted through an extended Cahn-Taylor model.

cond-mat.mtrl-sci↗

arXiv2023

Amplitude expansion of the phase-field crystal model for complex crystal structures

The phase-field crystal (PFC) model describes crystal lattices at diffusive timescales. Its amplitude expansion (APFC) can be applied to the investigation of relatively large systems under some approximations. However, crystal symmetries accessible within the APFC model are limited to basic ones, namely triangular and square in two dimensions, and body-centered cubic and face-centered cubic in three dimensions. In this work, we propose a general, amplitudes-based description of virtually any lattice symmetry. To fully exploit the advantages of this model, featuring slowly varying quantities in bulk and localized significant variations at dislocations and interfaces, we consider formulations suitable for real-space numerical methods supporting adaptive spatial discretization. We explore approaches originally proposed for the PFC model which allow for symmetries beyond basic ones through extended parametrizations. Moreover, we tackle the modeling of non-Bravais lattices by introducing an amplitude expansion for lattices with a basis and further generalizations. We study and discuss the stability of selected, prototypical lattice symmetries. As pivotal examples, we show that the proposed approach allows for a coarse-grained description of the kagome lattice, exotic square arrangements, and the diamond lattice, as bulk crystals and, importantly, hosting dislocations.

cond-mat.mtrl-sci↗

arXiv2023

Germanium-based nearly hyperuniform nanoarchitectures by ion beam impact

We address the fabrication of nano-architectures by impacting thin layers of amorphous Ge deposited on SiO$_{2}$ with a Ga$^{+}$ ion beam and investigate the structural and optical properties of the resulting patterns. By adjusting beam current and scanning parameters, different classes of nano-architectures can be formed, from elongated and periodic structures to disordered ones with a footprint of a few tens of nm. The latter disordered case features a significant suppression of large length scale fluctuations that are conventionally observed in ordered systems and exhibits a nearly hyperuniform character, as shown by the analysis of the spectral density at small wave vectors. It deviates from conventional random fields as accounted for by the analysis of Minkowski functionals. A proof of concept for potential applications is given by showing peculiar reflection properties of the resulting nano-structured films that exhibit colorization and enhanced light absorption with respect to the flat Ge layer counterpart (up to one order of magnitude at some wavelength). This fabrication method for disordered hyperuniform structures does not depend on the beam size. Being ion beam technology widely adopted in semiconductor foundries over 200 mm wafers, our work provides a viable pathway for obtaining disordered, nearly-hyperuniform materials by self-assembly with a footprint of tens of nanometers for electronic and photonic devices, energy storage and sensing.

cond-mat.mtrl-sci↗

arXiv2022

Controlling magnetic anisotropy in amplitude expansion of phase field crystal model

The amplitude expansion for a magnetic phase-field-crystal (magnetic APFC) model enables a convenient coarse-grained description of crystalline structures under the influence of magnetic fields. Considering higher-order magnetic coupling terms, we demonstrate the possibility of tuning the magnetic anisotropy in these models. This allows for reproducing the easy and hard direction of magnetization. Such a result can be achieved without increasing the computational cost, enabling simulations of the manipulation of dislocation networks and microstructures in ferromagnetic materials. As a demonstration, we report on the simulation of the shrinkage of a spherical grain with the magnetic anisotropy of Fe.

cond-mat.mtrl-sci↗

arXiv2022

Improved time integration for phase-field crystal models of solidification

We optimize a numerical time-stabilization routine for the phase-field crystal (PFC) models of solidification. By numerical experiments, we showcase that our approach can improve the accuracy of underlying time integration schemes by a few orders of magnitude. We investigate different time integration schemes. Moreover, as a prototypical example for applications, we extend our numerical approach to a PFC model of solidification with an explicit temperature coupling.

cond-mat.mtrl-sci↗

arXiv2022

Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks

We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model captures better than previous formulations the dynamics of complex interfaces and dislocations in single crystals as well as grain boundary migration in poly-crystals where the long-range elastic field is properly relaxed. The proposed model features a diffusivity that depends non-linearly on the local phase. It induces more localized interfaces between a disordered phase (liquid-like) and an ordered phase, e.g., stripes or crystal lattices. For stripes, the interface dynamics are shown to be strongly anisotropic. We also show that the model is able to evolve the classical PFC at mechanical equilibrium. However, in contrast to previous approaches, it is not restricted to a single-crystal configuration or small distortions from a fixed reference lattice. To showcase the capabilities of this approach, we consider a few examples, from the annihilation of dislocation loops in a single crystal at mechanical equilibrium to the relaxation of a microstructure including crystalline domains with different orientations and grain boundaries. During the self-annihilation of a mixed type dislocation loop (i.e., not shear or prismatic), long-range elastic effects cause the loop to move out of plane before the annihilation event.

cond-mat.mtrl-sci↗

arXiv2022

Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage

We derive the amplitude expansion for a phase-field-crystal (APFC) model that captures the basic physics of magneto-structural interactions. The symmetry breaking due to magnetization is demonstrated, and the characterization of the magnetic anisotropy for a BCC crystal is provided. This model enables a convenient coarse-grained description of crystalline structures, in particular when considering the features of the APFC model combined with numerical methods featuring inhomogeneous spatial resolution. This is shown by addressing the shrinkage of a spherical grain within a matrix, chosen as a prototypical system to demonstrate the influence of different magnetizations. These simulations serve as a proof of concept for the modeling of manipulation of dislocation networks and microstructures in ferromagnetic materials within the APFC model.

cond-mat.mtrl-sci↗

arXiv2022

Explicit temperature coupling in phase-field crystal models of solidification

We present a phase-field crystal (PFC) model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the microscopic density field. We showcase the model capabilities via selected numerical investigations which focus on the prototypical growth of two-dimensional crystals from the melt, resulting in faceted shapes and dendrites. This work sets the grounds for a comprehensive mesoscale model of solidification including thermal expansion.

cond-mat.mtrl-sci↗

arXiv2022

Interface Faceting-Defaceting Mediated by Disconnections

An intrinsic feature of nearly all internal interfaces in crystalline systems (homo- and hetero-phase) is the presence of disconnections (topological line defects constrained to the interface that have both step and dislocation character). Disconnections play a major role in determining interface thermodynamics and kinetics. We demonstrate that elastic interactions between disconnections lead to a thermodynamic, first-order, finite-temperature, faceting-defaceting transition, in agreement with experiments. These elastic interactions strongly modify equilibrium interface morphologies (compared with those solely determined by anisotropic surface energy) as well as the kinetics and morphologies of migrating interfaces. We demonstrate these phenomena through numerical simulations based upon a general, continuum disconnection-based model for interface thermodynamics and kinetics applied to embedded particles/grains, steady-state interface migration geometries, and nominally flat interfaces.

cond-mat.mtrl-sci↗

arXiv2022

A phase field crystal theory of the kinematics of dislocation lines

We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach-Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane.

cond-mat.mtrl-sci↗

arXiv2022

Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview

Comprehensive investigations of crystalline systems often require methods bridging atomistic and continuum scales. In this context, coarse-grained mesoscale approaches are of particular interest as they allow the examination of large systems and time scales while retaining some microscopic details. The so-called Phase-Field Crystal (PFC) model conveniently describes crystals at diffusive time scales through a continuous periodic field which varies on atomic scales and is related to the atomic number density. To go beyond the restrictive atomic length scales of the PFC model, a complex amplitude formulation was first developed by Goldenfeld et al. [Phys. Rev. E 72, 020601 (2005)]. While focusing on length scales larger than the lattice parameter, this approach can describe crystalline defects, interfaces, and lattice deformations. It has been used to examine many phenomena including liquid/solid fronts, grain boundary energies, and strained films. This topical review focuses on this amplitude expansion of the PFC model and its developments. An overview of the derivation, connection to the continuum limit, representative applications, and extensions is presented. A few practical aspects, such as suitable numerical methods and examples, are illustrated as well. Finally, the capabilities and bounds of the model, current challenges, and future perspectives are addressed.

cond-mat.mtrl-sci↗

arXiv2022

The elastic inclusion problem in the (amplitude) phase field crystal model

In many processes for crystalline materials such as precipitation, heteroepitaxy, alloying, and phase transformation, lattice expansion or compression of embedded domains occurs. This can significantly alter the mechanical response of the material. Typically, these phenomena are studied macroscopically, thus neglecting the underlying microscopic structure. Here we present the prototypical case of an elastic inclusion described by a mesoscale model, namely a coarse-grained phase-field crystal model. A spatially-dependent parameter is introduced into the free energy functional to control the local spacing of the lattice structure, effectively prescribing an eigenstrain. The stress field obtained for an elastic inclusion in a 2D triangular lattice is shown to match well with the analytic solution of the Eshelby inclusion problem.

math-ph↗

arXiv2021

Disconnection-Mediated Migration of Interfaces in Microstructures: I. continuum model

A long-standing goal of materials science is to understand, predict and control the evolution of microstructures in crystalline materials. Most microstructure evolution is controlled by interface motion; hence, the establishment of rigorous interface equations of motion is a universal goal of materials science. We present a new model for the motion of arbitrarily curved interfaces that respects the underlying crystallography of the two phases/domains meeting at the interface and is consistent with microscopic mechanisms of interface motion; i.e., disconnection migration (line defects in the interface with step and dislocation character). We derive the equation of motion for interface migration under the influence of a wide range of driving forces. In Part II of this paper [Salvalaglio, Han and Srolovitz, 2021], we implement the interface model and the equation of motion proposed in this paper in a diffuse interface simulation approach for complex morphology and microstructure evolution.

cond-mat.mtrl-sci↗