Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model

Phase field crystal models with applications to laser deposition: A review

In this article, we address the application of phase field crystal (PFC) theory, a hybrid atomistic-continuum approach, for modeling nanostructure kinetics encountered in laser deposition. We first provide an overview of the PFC methodology, highlighting recent advances to incorporate phononic and heat transport mechanisms. To simulate laser heating, energy is deposited onto a number of polycrystalline, two-dimensional samples through the application of initial stochastic fluctuations. We first demonstrate the ability of the model to simulate plasticity and recrystallization events that follow laser heating in the isothermal limit. Importantly, we also show that sufficient kinetic energy can cause voiding, which serves to suppress shock propagation. We subsequently employ a newly developed thermo-density PFC theory, coined thermal field crystal (TFC), to investigate laser heating of polycrystalline samples under non-isothermal conditions. We observe that the latent heat of transition associated with ordering can lead to long lasting metastable structures and defects, with a healing rate linked to the thermal diffusion. Finally, we illustrate that the lattice temperature simulated by the TFC model is in qualitative agreement with predictions of conventional electron-phonon two-temperature models. We expect that our new TFC formalism can be useful for predicting transient structures that result from rapid laser heating and re-solidification processes.

Simulation of TSV Protrusion in 3DIC Integration by Directly Loading on Coarse-Grained Phase-Field Crystal Model

As thermal management in 3DIC integration becomes increasingly important in advanced semiconductor node processes, novel experimental and modeling approaches are in great demand to reveal the critical material issues involving multiscale microstructures that govern the behavior of through-silicon-via (TSV) protrusion. Here, a coarse-grained phase-field crystal model properly coupled with mechanics through the atomic density field is used to simulate the formation of polycrystalline structures and protrusion of nano-TSVs from the atomic scale. TSVs with different grain structures are directly loaded, and protrusion/intrusion profiles are obtained along with displacement, stress, and strain fields. Thermodynamic driving forces from external loadings and the mismatch of Young’s modulus between adjoining grains as well as detailed displacement and strain distributions are ascribed to control the complex deformation in TSVs. TSVs with sizes up to around 30 nm and an aspect ratio of 4 are successfully investigated, and a further increase in the size and aspect ratio to cover the micrometer range is feasible, which lays down a solid basis toward a multiscale material database for simulation inputs to the design of TSV-based 3DIC integration and relevant electronic design automation (EDA) tools.

Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres

The velocity of dislocations is derived analytically to incorporate and predict the intriguing effects induced by the preferential solute segregation and Cottrell atmospheres in both two-dimensional and three-dimensional binary systems of various crystalline symmetries. The corresponding mesoscopic description of defect dynamics is constructed through the amplitude formulation of the phase-field crystal model, which has been shown to accurately capture elasticity and plasticity in a wide variety of systems. Modifications of the Peach-Koehler force as a result of solute concentration variations and compositional stresses are presented, leading to interesting new predictions of defect motion due to effects of Cottrell atmospheres. These include the deflection of dislocation glide paths, the variation of climb speed and direction, and the change or prevention of defect annihilation, all of which play an important role in determining the fundamental behaviors of complex defect network and dynamics. The analytic results are verified by numerical simulations.

Spontaneous shrinkage of droplet on a wetting surface in the phase-field model

Phase-field theory is widely used to model multiphase flow. The fact that a drop can shrink or grow spontaneously due to the redistribution of interface and bulk energies to minimize the system energy may produce ill effects on the simulation. In this Rapid Communication, the spontaneous behavior of a drop on a partially wetting surface is investigated. It is found that there exists a critical radius dependent on the contact angle, the domain size, and the interface width, below which the drop will eventually disappear. In particular, the critical radius can be very large when the surface becomes very hydrophilic. The theoretical prediction of the critical radius is verified numerically by simulating a drop on a surface with various contact angles, the domain sizes, and the interface widths.

Landau-Type Theory of Planar Crystal Plasticity

We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as a Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group GL(2,Z). Quasistatic loading can be then handled by athermal dynamics, while lattice-based discretization can play the role of regularization. As a proof of principle, we study dislocation nucleation in a homogeneously sheared 2D crystal and show that the global tensorial invariance of the elastic energy foments the development of complexity in the configuration of collectively nucleating defects. A crucial role in this process is played by the unstable higher symmetry crystallographic phases, typically thought to be unrelated to plastic flow.

Mechanical relaxation and fracture of phase field crystals

A computational method is developed for the study of mechanical response and fracture behavior of phase field crystals (PFC), to overcome a limitation of the PFC dynamics which lacks an effective mechanism for describing fast mechanical relaxation of the material system. The method is based on a simple interpolation scheme for PFC (IPFC) making use of a condition of the displacement field to satisfy local elastic equilibration, while preserving key characteristics of the original PFC model. We conduct a systematic study on the mechanical properties of a sample nanoribbon system with honeycomb lattice symmetry subjected to uniaxial tension, for numerical validation of the IPFC scheme and the comparison with the original PFC and modified PFC methods. Results of mechanical response, in both elasticity and fracture regimes, show the advantage and efficiency of the IPFC method across different system sizes and applied strain rates, due to its effective process of mechanical equilibration. A brittle fracture behavior is obtained in IPFC calculations, where effects of system temperature and chirality on the fracture strength and Young's modulus are also identified, with results agreeing with those found in previous atomistic simulations of graphene. The IPFC scheme developed here is generic and applicable to the mechanical studies using different types of PFC free-energy functionals designed for various material systems.