Explicit Dynamics of Diffuse Interface in Phase‐Field Model

Abstract

Interfaces play an important role during phase transition and interfacial chemical reactions. In this paper, three different methods are introduced to analyze the explicit dynamics of the diffuse interface by means of phase-field model, and these methods are based on three independent perspectives: non-dispersive propagation of the interfacial waveform, the flux density and sources/sinks analysis of continuity equation, and the moving interfacial coordinate transformation. These theoretical derivations not only present the relationship between the diffuse interfacial velocity and the effect of driving force and interfacial curvature, but also clarify the equivalent method between the phase-field dynamics and the sharp-interfacial dynamics, which reveals the physical meaning of the diffuse interfacial dynamical equation from different perspectives. The present study advances the understanding of the interfacial phase transition and provides theoretical insights for the phase-field model and numerical simulation.

Phase-Field Simulation of a Dynamic Protective Layer for the Inhibition of Dendrite Growth in Zinc Metal Batteries

“…The displacement of the protective layer induced by Zn metal surface movement is described by the evolution of the order parameter ξ 2 , ∂ ξ 2 ∂ t = − L ξ 2 { ∂ f ch ∂ ξ 2 − κ 2 true( ∇ 2 ξ 2 true) } − D f where L ξ 2 is the interfacial mobility of the protective layer, κ 2 is the gradient energy coefficient, and D f is the driving force term for the protective layer displacement due to the Zn metal surface movement during deposition. Based on the relationship between diffuse interface velocity and effective driving force, we defined D f as, D f = max [ − h ’ false( ξ 1 false) × h ’ false( ξ 2 false) × Δ G ] × b × ∂ ξ 2 ∂ x where normalΔ G = { exp true[ α z F η R T true] − C Zn 2 + exp true[ − β z F η R T true] } is the Butler–Volmer expression taken from eq , and the driving force constant b is selected to guarantee that no interfacial delamination between Zn metal and the protective la...…”

“…The displacement of the protective layer induced by Zn metal surface movement is described by the evolution of the order parameter ξ 2 , where L ξ 2 is the interfacial mobility of the protective layer, κ 2 is the gradient energy coefficient, and D f is the driving force term for the protective layer displacement due to the Zn metal surface movement during deposition. Based on the relationship between diffuse interface velocity and effective driving force, we defined D f as, where is the Butler–Volmer expression taken from eq , and the driving force constant b is selected to guarantee that no interfacial delamination between Zn metal and the protective layer would occur (the value of “ b ” can be found in Table ). The “max” function takes the maximum value of the product h ′ (ξ 1 ) × h ′ (ξ 2 ) × Δ G , where h ′ (ξ 1 ) × Δ G is the driving force acting at the surface of the order parameter ξ 1 , so that the same force would be applied on both surfaces of ξ 2 .…”

Strain Engineering of Energy Storage Performance in Relaxor Ferroelectric Thin Film Capacitors

“…Equations are numerically solved by semi-implicit Fourier-spectral method. [37][38][39][40] The simulation size is 128 × 128 × 16 discrete grid points with each grid space of 1 nm in real space and the thickness of films is 10 nm. A thin film mechanical boundary condition is adopted in this simulation, the top film surface is assumed to be traction-free, while the interface between the thin film and the substrate is mechanically coherent.…”

The diffuse interface phase‐field model for in situ interlayer phase formations in low‐temperature reaction bonding of alumina laminates—A theoretical and experimental comparison

“…Therefore, in this study, the diffusion bonding of alumina laminates with slip casted alanate mixtures (AlMeH, Me: Sr/Mg) interlayers at low temperatures and moderate pressures was designed. The possible phase evolution, based on diffusion interface approach 20,21 and solution mass transport processes, 22,23 was modeled by a phase‐field model. The structure, orientation, and composition of microstructure grains were estimated by reduction in bulk energy, 24 decrease in interfacial energy, 25 and solid‐state phase transformations 26 .…”