Quantitative phase field simulations of polycrystalline solidification using a vector order parameter.

A vector order parameter phase field model derived from a grand potential functional is presented as an alternative approach for modeling polycrystalline solidification of alloys. In this approach, the grand potential density is designed to contain a discrete set of finite wells, a feature that naturally allows for the growth and controlled interaction of multiple grains using a single vector field. We verify that dendritic solidification in binary alloys follows the well-established quantitative behavior in the thin interface limit. In addition, it is shown that grain boundary energy and solute back-diffusion are quantitatively consistent with earlier theoretical work, with grain boundary energy being controlled through a simple solid-solid interaction parameter. Moreover, when considering polycrystalline aggregates and their coarsening, we show that the kinetics follow the expected parabolic growth law. Finally, we demonstrate how this vector order parameter model can be used to describe nucleation in polycrystalline systems via thermal fluctuations of the vector order parameter, a process that cannot be treated consistently with multiphase or multi-order-parameter based phase field models. The presented vector order parameter model serves as a practical and efficient computational tool for simulating polycrystalline materials. We also discuss the extension of the order parameter to higher dimensions as a simple method for modeling multiple solid phases.

Electrical Stressing Induced Monolayer Vacancy Island Growth on TiSe2.

To ensure practical applications of atomically thin transition metal dichalcogenides, it is essential to characterize their structural stability under external stimuli such as electric fields and currents. Using vacancy monolayer islands on TiSe2 surfaces as a model system, we have observed nonlinear area evolution and growth from triangular to hexagonal driven by scanning tunneling microscopy (STM) subjected electrical stressing. The observed growth dynamics represent a 2D departure from the linear area growth law expected for bulk vacancy clustering. Our simulations of monolayer island evolution using phase-field modeling and first-principles calculations are in good agreement with our experimental observations, and point toward preferential edge atom dissociation under STM scanning driving the observed nonlinear area growth. We further quantified a parabolic growth rate dependence with respect to the tunneling current magnitude. The results could be potentially important for device reliability in systems containing ultrathin transition metal dichalcogenides and related 2D materials subject to electrical stressing.

Simulation and analysis of γ-Ni cellular growth during laser powder deposition of Ni-based superalloys.

Cellular or dendritic microstructures that result as a function of additive manufacturing solidification conditions in a Ni-based melt pool are simulated in the present work using three-dimensional phase-field simulations. A macroscopic thermal model is used to obtain the temperature gradient G and the solidification velocity V which are provided as inputs to the phase-field model. We extract the cell spacings, cell core compositions, and cell tip as well as mushy zone temperatures from the simulated microstructures as a function of V. Cell spacings are compared with different scaling laws that correlate to the solidification conditions and approximated by G-mV-n. Cell core compositions are compared with the analytical solutions of a dendrite growth theory and found to be in good agreement. Through analysis of the mushy zone, we extract a characteristic bridging plane, where the primary γ phase coalesces across the intercellular liquid channels at a γ fraction between 0.6 and 0.7. The temperature and the γ fraction in this plane are found to decrease with increasing V. The simulated microstructural features are significant as they can be used as inputs for the simulation of subsequent heat treatment processes.

Incorporating Noise Quantitatively in the Phase Field Crystal Model via Capillary Fluctuation Theory.

A tacit assumption underlying most phase field models of nonequilibrium phase transformations is that of scale separation. Stochastic order parameter field theories utilize noise to separate atomic-scale fluctuations from the slowly varying fields that describe microstructure patterns. The mesoscale distribution of such stochastic variables is generally assumed to follow Gaussian statistics, with their magnitude following fluctuation-dissipation relations. However, there is still much debate about how atomic-scale fluctuations map onto the mesoscale upon coarse graining of microscopic theories. This Letter studies interface fluctuations in the phase field crystal (PFC) model and proposes a self-consistent method for relating how the effective noise strength and spectral filtering of the noise in the PFC model, and similar types of microscopic models, should be defined so as to attain the spectrum of mesoscale capillary fluctuations quantitatively.

Calculating the role of composition in the anisotropy of solid-liquid interface energy using phase-field-crystal theory.

This work uses Ginzburg-Landau theory derived from a recent structural phase-field-crystal model of binary alloys developed by the authors to study the roles of concentration, temperature, and pressure on the interfacial energy anisotropy of a solid-liquid front. It is found that the main contribution to the change in anisotropy with concentration arises from a change in preferred crystallographic orientation controlled by solute-dependent changes in the two-point density correlation function of a binary alloy, a mechanism that leads to such phenomena as solute-induced elastic strain and dislocation-assisted solute clustering. Our results are consistent with experimental observations in recent studies by Rappaz et al. [J. Fife, P. Di Napoli, and M. Rappaz, Metall. Mater. Trans. A 44, 5522 (2013)]. This is the first PFC work, to our knowledge, to incorporate temperature, pressure, and density into the thermodynamic description of alloys.

Phase-field-crystal model of phase and microstructural stability in driven nanocrystalline systems.

We present a phase-field-crystal model for driven systems which describes competing effects between thermally activated diffusional processes and those driven by externally imposed ballistic events. The model demonstrates how the mesoscopic Enrique and Bellon [Phys. Rev. Lett. 84, 2885 (2000)] model of externally induced ballistic mixing can be incorporated into the atomistic phase-field-crystal formalism. The combination of the two approaches results in a model capable of describing the microstructural and compositional evolution of a driven system while incorporating elastoplastic effects. The model is applied to the study of grain growth in nanocrystalline materials subjected to an external driving.