skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Elasticity versus phase field driven motion in the phase field crystal model
Abstract The inherent inconsistency in identifying the phase field in the phase field crystal theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase field crystal occurs on a diffusive time scale through a dissipative permeation mode. The very same phase field distortion that is included in solid elasticity drives diffusive motion, resulting in a non physical relaxation of the phase field crystal. We present two alternative theories to remedy this shortcoming. In the first case, it is assumed that the phase field only determines the incompatible part of the elastic distortion, and therefore one is free to specify an additional compatible distortion so as to satisfy mechanical equilibrium at all times (in the quasi static limit). A numerical solution of the new model for the case of a dislocation dipole shows that, unlike the classical phase field crystal model, it can account for the known law of relative motion of the two dislocations in the dipole. The physical origin of the compatible strain in this new theory remains to be specified. Therefore, a second theory is presented in which an explicit coupling between independent distortion and phase field accounts for the time dependence of the relaxation of fluctuations in both. Preliminary details of its implementation are also given.  more » « less
Award ID(s):
1838977
PAR ID:
10380833
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Modelling and Simulation in Materials Science and Engineering
Volume:
30
Issue:
6
ISSN:
0965-0393
Page Range / eLocation ID:
064005
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, Mathematical Models and Methods in Applied Sciences)
    A nonlocal phase-field crystal (NPFC) model is presented as a nonlocal counterpart of the local phase-field crystal (LPFC) model and a special case of the structural PFC (XPFC) derived from classical field theory for crystal growth and phase transition. The NPFC incorporates a finite range of spatial nonlocal interactions that can account for both repulsive and attractive effects. The specific form is data-driven and determined by a fitting to the materials structure factor, which can be much more accurate than the LPFC and previously proposed fractional variant. In particular, it is able to match the experimental data of the structure factor up to the second peak, an achievement not possible with other PFC variants studied in the literature. Both LPFC and fractional PFC (FPFC) are also shown to be distinct scaling limits of the NPFC, which reflects the generality. The advantage of NPFC in retaining material properties suggests that it may be more suitable for characterizing liquid–solid transition systems. Moreover, we study numerical discretizations using Fourier spectral methods, which are shown to be convergent and asymptotically compatible, making them robust numerical discretizations across different parameter ranges. Numerical experiments are given in the two-dimensional case to demonstrate the effectiveness of the NPFC in simulating crystal structures and grain boundaries. 
    more » « less
  2. ; ; ; ; ; (, Physical Review E)
    Platinum-coated Janus colloids exhibit self-propelled motion in aqueous solution via the catalytic decomposition of hydrogen peroxide. Here, we report their motion in a uniformly aligned nematic phase of lyotropic chromonic liquid crystal, disodium cromoglycate (DSCG). When active Janus colloids are placed in DSCG, we find that the anisotropy of the liquid crystal imposes a strong sense of direction to their motion; the Janus colloids tend to move parallel to the nematic director. Motion analysis over a range of timescales reveals a crossover from ballistic to anomalous diffusive behavior on timescales below the relaxation time for liquid crystal elastic distortions. Surprisingly we observe that smaller particles roll during ballistic motion, whereas larger particles do not. This result highlights the complexity of phoretically-driven particle motion, especially in an anisotropic fluid environment. 
    more » « less
  3. ; (, International Journal for Multiscale Computational Engineering)
    A micropolar phase field fracture model is implemented in an open source library FEniCS. This implementation is based on the theoretical study in Suh et al. (2020) in which the resultant phase field model exhibits the consistent micropolar size effect in both elastic and damage regions identifiable via inverse problems for micropolar continua. By leveraging the automatic code generation technique in FEniCS, we provide a documentation of the source code expressed in a language very close to the mathematical expressions without comprising significant efficiency. This combination of generality and interpretability therefore enables us to provide a detailed walk-through that connects the implementation with the regularized damage theory for micropolar materials. By making the source code open source, the paper will provide an efficient development and educational tool for third-party verification and validation, as well as for future development of other higher-order continuum damage models. 
    more » « less
  4. (, Journal of Fluid Mechanics)
    In the phase-field description of moving contact line problems, the two-phase system can be described by free energies, and the constitutive relations can be derived based on the assumption of energy dissipation. In this work we propose a novel boundary condition for contact angle hysteresis by exploring wall energy relaxation, which allows the system to be in non-equilibrium at the contact line. Our method captures pinning, advancing and receding automatically without the explicit knowledge of contact line velocity and contact angle. The microscopic dynamic contact angle is computed as part of the solution instead of being imposed. Furthermore, the formulation satisfies a dissipative energy law, where the dissipation terms all have their physical origin. Based on the energy law, we develop an implicit finite element method that is second order in time. The numerical scheme is proven to be unconditionally energy stable for matched density and zero contact angle hysteresis, and is numerically verified to be energy dissipative for a broader range of parameters. We benchmark our method by computing pinned drops and moving interfaces in the plane Poiseuille flow. When the contact line moves, its dynamics agrees with the Cox theory. In the test case of oscillating drops, the contact line transitions smoothly between pinning, advancing and receding. Our method can be directly applied to three-dimensional problems as demonstrated by the test case of sliding drops on an inclined wall. 
    more » « less
  5. ; ; (, Journal of Applied Physics)
    Entropy stabilized oxide of MgNiCoCuZnO5, also known as J14, is a material of active research interest due to a high degree of lattice distortion and tunability. Lattice distortion in J14 plays a crucial role in understanding the elastic constants and lattice thermal conductivity within the single-phase crystal. In this work, a neuroevolution machine learning potential (NEP) is developed for J14, and its accuracy has been compared to density functional theory calculations. The training errors for energy, force, and virial are 5.60 meV/atom, 97.90 meV/Å, and 45.67 meV/atom, respectively. Employing NEP potential, lattice distortion, and elastic constants is studied up to 900 K. In agreement with experimental findings, this study shows that the average lattice distortion of oxygen atoms is relatively higher than that of all transition metals in entropy-stabilized oxide. The observed distortion saturation in the J14 arises from the competing effects of minimum site distortion, which increases with increasing temperature due to enhanced thermal vibrations, and maximum site distortion, which decreases with increasing temperature. Furthermore, a series of molecular dynamics simulations up to 900 K are performed to study the stress–strain behavior. The elastic constants, bulk modulus, and ultimate tensile strength obtained from these simulations indicate a linear decrease in these properties with temperature, as J14 becomes softer owing to thermal effects. Finally, to gain some insight into thermal transport in these materials, with the so-developed NEP potential, and using non-equilibrium molecular dynamics simulations, we study the lattice thermal conductivity (κ) of the ternary compound MgNiO2 as a function of temperature. It is found that κ decreases from 4.25 W m−1 K−1 at room temperature to 3.5 W m−1 K−1 at 900 K. This suppression is attributed to the stronger scattering of low-frequency modes at higher temperatures. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email