Moving Phase Boundary Research Articles

Self-consistent sharp interface theory of active condensate dynamics

Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active biomolecules which, after transient binding via molecular interactions, catalyze reactions among their substrates. Thereby, biomolecular condensates provide a spatial template for nonuniform concentration profiles of substrates. In turn, the concentration profiles of substrates, and their molecular interactions with enzymes, drive enzyme fluxes which can enable novel nonequilibrium dynamics. To analyze this generic class of systems, with a current focus on self-propelled droplet motion, we here develop a self-consistent sharp interface theory. In our theory, we diverge from the usual bottom-up approach, which involves calculating the dynamics of concentration profiles based on a given chemical potential gradient. Instead, reminiscent of control theory, we take the reverse approach by deriving the chemical potential profile and enzyme fluxes required to maintain a desired condensate form and dynamics. The chemical potential profile and currents of enzymes come with a corresponding power dissipation rate, which allows us to derive a thermodynamic consistency criterion for the passive part of the system (here, reciprocal enzyme-enzyme interactions). As a first-use case of our theory, we study the role of reciprocal interactions, where the transport of substrates due to reactions and diffusion is, in part, compensated by redistribution due to molecular interactions. More generally, our theory applies to mass-conserved active matter systems with moving phase boundaries. Published by the American Physical Society 2024

Weak Pinning and Long-Range Anticorrelated Motion of Phase Boundaries in Driven Diffusive Systems.

We show that domain walls separating coexisting extremal current phases in driven diffusive systems exhibit complex stochastic dynamics with a subdiffusive temporal growth of position fluctuations due to long-range anticorrelated current fluctuations and a weak pinning at long times. This weak pinning manifests itself in a saturated width of the domain wall position fluctuations that increases sublinearly with the system size. As a function of time t and system size L, the width w(t,L) has a scaling behavior w(t,L)=L^{3/4}f(t/L^{9/4}), with f(u) constant for u≫1 and f(u)∼u^{1/3} for u≪1. An Orstein-Uhlenbeck process with long-range anticorrelated noise is shown to capture this scaling behavior. The exponent 9/4 is a new dynamical exponent for relaxation processes in driven diffusive systems.

First principles calculation of composition dependence tracer and interdiffusion with phase change in γ/γ′ superalloy: A case study of Ir/Ir3Nb

In this work, the composition dependent tracer and interdiffusion coefficient with phase change in γ/γ′ Ir/Ir3Nb superalloy are studied by means of first-principles calculation together with nudged elastic band, and quasi−harmonic thermodynamics. The formulae scattered in the literature for composition dependence tracer diffusion coefficient are summarized and executed using first principles calculation. Each term in the newly derived formulae, such as energy barrier, jump frequency, defect concentration, correlation, solvent enhancement factor, effective escape frequency, etc. is meticulously calculated. We find the composition dependent tracer diffusion coefficient of Nb in L12 γ′-Ir3Nb phase is contributed mainly from the antisite bridge rather than five-frequency model proposed in FCC γ-Ir dilute solid solution. The faster diffuser is Nb in γ-Ir, while Ir in γ′-Ir3Nb. Based on the tracer diffusion coefficient, the interdiffusion coefficient is obtained using Darken-Manning equation. The composition profile and phase boundary movement of γ/γ′ Ir/Ir3Nb superalloy are evaluated through an analytical solution of Matano-Boltzmann equations. The calculated diffusion coefficients and composition profile are in good agreement with experiments. Our findings not only serve as a successful example for the quantitative calculation of composition dependent tracer diffusion coefficient, but also shed lights on the physics behind the diffusion in intermetallics.

Introducing a Novel Light Scattering Technique for Visualising Operando State-of-Charge Changes Within Individual Active Particles and Across the Electrode

In our presentation we will demonstrate the application of a recently developed operando optical microscopy technique to mechanistic studies of lithium-ion battery electrodes and active material characterisation. Our technique probes state-of-charge (SoC) changes in the active particles within the electrode during battery operation, based on the intensity variation of scattered light across each active particle. This enables detailed spatially resolved data on an individual particle level to be utilised for furthering mechanistic understanding of battery capability and degradation, and it also allows global statistics to be established for the optimisation and screening of new electrode materials. The technique is agnostic to the underlying battery chemistry, so in principle can be applied to study any battery electrode.In this talk, we will demonstrate how our technique can be used in the study of two key dynamic processes, solid-state ion transport and mechanical degradation. The ability to quantify ion transport during battery operation helps to provide insights into how lithium-ion dynamics affect the (de)lithiation mechanisms and degradation mechanisms of battery electrodes, which is crucial to improving their electrochemical performance. Using lithium cobalt oxide (LCO) as a case study, we will show how ion-transport mechanisms can be deduced by observing moving phase boundaries within particles during cycling.We will then demonstrate how local SoC changes within Ni-rich nickel manganese cobalt oxide (NMC) active particles can be visualised during operation, and how the intra-particle ion gradients identified can be used to determine the mechanistic origins of first-cycle capacity losses. Building on this, we will highlight how variation in the rates of (dis)charge between a population of active particles could be used to characterise the performance of new electrode compositions.In addition, we will highlight how lithium-ion concentration gradients can also be identified in high-rate niobium tungsten oxide (NWO) anode materials during initial lithiation and under initial rapid delithiation conditions and demonstrate how this can lead to particle cracking. Expanding on this, we illustrate how the proportion of cracked particles within an electrode can be quantified and then monitored over successive cycles as a potential metric for screening the stability of new electrode materials.

Framework for a chemo‐mechanical model of the breathing effect in lithium–silicon batteries

AbstractWe present a chemo‐mechanical finite element method model for the breathing effect of the silicon anode during lithiation and delithiation. The model is based on the framework for gradient extended standard dissipative solids. It couples diffusion of lithium ions, phase transformation with a moving phase boundary, and the related volume changes, which lead to mechanical stresses in the material. The driving force for diffusion is given by the gradient of the electrochemical potential. Phase transformation and phase boundary movement are described by the Allen–Cahn equation in combination with a constrained double obstacle potential. To shift the constraint from the nodes to the Gauss points, the model makes use of the micromorphic approach.

Hot deformation mechanisms of dual phase high entropy alloys

The microstructure of high entropy alloys can finally be designed via thermomechanical treatments to tune the mechanical properties. This work investigates the modification of the microstructure after treatments at 1100 °C for three hypo-eutectic high entropy alloys. Two phases were indexed according to the BCC and FCC crystal structures using electron backscattered diffraction. Their microstructure is investigated for three hot deformation tests: at a constant strain rate of 0.001s−1, at a strain rate jumps from 0.001s−1 to 1s−1 and from 1s−1 to 0.001s−1. The BCC size and fraction strongly influence the deformation of the FCC matrix. Due to its typical semi-interconnected hypo-eutectic structure, the BCC phase carries the load at the beginning of the deformation. Progressively, the FCC phase deforms to accommodate the plastic strain due to the bending and fragmentation of the BCC phase. Fine particles of the BCC phase are formed within the FCC matrix at high temperatures, and they pin the high-angle grain boundaries formed by continuous dynamic recrystallisation. The fragmentation of the BCC phase occurs faster for thinner eutectic BCC particles, and it is a consequence of I) the formation of boundaries during plastic deformation via dynamic recovery followed by continuous dynamic recrystallisation; II) the movement of phase boundaries consuming the formed boundaries within the BCC phase, fragmenting them. A fine substructure with a high density of high-angle grain boundaries is formed at 1100 °C for the alloy with initial fine BCC eutectic particles.

Kinetic Modeling of Grain Boundary Cementite Evolution

Prediction of grain boundary cementite growth kinetics in hypereutectoid steels is necessary to control its thickness. It is a question of major industrial importance but has remained unresolved to date. This paper presents and compares two different and new modeling approaches. The first one relies on diffusion-based nucleation and growth of cementite precipitates using a modified SFFK model with short-circuit grain boundary diffusion and accounting for heterogeneous nucleation site energy during isothermal treatments and continuous cooling. It is compared to previously published simulations of diffusion-controlled reaction with moving phase boundaries and a similar simulation using the software Dictra. The second approach implies that cementite thickening is driven by the nucleation of ledges at the stepped austenite/cementite interface, controlled by a structure barrier to ledge formation previously assumed in the literature.[1] We suggest a semi-empirical formulation of this barrier to ledge nucleation during isothermal transformation. Both approaches lead to an excellent match to experimental data for an almost pure Fe–C system. This implies that modeling the stepped structure of the austenite/cementite interface is not imperative for simulation of thickening kinetics, but also that understanding the governing physics of ledge formation allows for a comprehensive description of secondary cementite formation.

High piezoelectricity in PFN–PNN–PZT quaternary ceramics achieved via composition optimization near morphotropic phase boundary

To analyze the effect of PFN content on the microstructure and electrical properties of xPb(Fe0.5Nb0.5)O3–(0.57−x)Pb(Ni1/3Nb2/3)O3–0.43Pb(Zr0.3Ti0.7)O3, the doping of xPFN–PNN–PZT) were systematically studied with 0.015 ≤ x ≤ 0.075. XRD patterns and Raman spectra analysis reveal that PFN diffuses into PNN–PZT perovskite lattice and forms new quaternary solid solution. With the increase of PFN content x, the proportion of rhombohedral (R) phase decreases gradually, whereas the proportion of tetragonal (T) phase displays a contrary trend. In particular, R–T coexistence near MPB was observed at x = 0.045. Meanwhile, optimized electrical properties of d33 = 961 pC/N, kp = 0.716, εr = 6298, and tanδ = 3.1% are achieved for the 0.045PFN–PNN–PZT ceramics. Moreover, the ceramics at MPB showed larger remnant polarization Pr = 24.55 μC/cm2, smaller coercive field Ec = 0.36 kV/mm, and lower dielectric relaxor degree γ = 1.813. All these results reveal that the enhanced electrical properties could be attributed to synergistic phase boundary motion, dielectric relaxor behavior and ferroelectric hysteresis effect.

TinyLev acoustically levitated water: Direct observation of collective, inter-droplet effects through morphological and thermal analysis of multiple droplets

HypothesisUnderstanding the crystallization of atmospheric water can require levitation techniques to avoid the influence of container walls. Recently, an acoustic levitation device called the TinyLev was designed, which can levitate multiple droplets at room temperature. Proximal crystallization may affect droplet phase change and morphological characteristics. MethodologyIn this study, acoustically levitated pure water droplets were frozen individually and in pairs or triplets using a TinyLev device. Nucleation, bulk crystal growth, and melting were observed using digital and infrared cameras concurrently. FindingsInitially, the acoustic field forced the droplets into an oblate spheroid shape, though the counteracting force of the cooling stream caused them to circularize. Droplet geometry was thus the net result of streaming forces and surface tension at the acoustic boundary layer/air–liquid interface. Nucleation was determined to be neither homogeneous nor heterogeneous but secondary, and thus dependent on the cooling rate and not on the degree of supercooling. It was likely initiated by aerosolized ice particles from the air or from droplets that had already nucleated and broken up. The latter secondary ice production process resulted in multi-drop systems with statistically identical nucleation times. Notably, this meant that the presence of interfacial rupture at an adjacent droplet could influence the crystallization behaviour of another. After the formation of an initial ice shell around the individual droplets, dendritic protrusions grew from the droplet surface, likely seeded by the same ice particles that caused nucleation, but at a quasi-liquid layer. When freezing was complete, it was determined that the frozen core had undergone a volumetric expansion of 30.75%, compared to 9% for pure, sessile water expansion. This significantly greater expansion may have resulted from entrained air bubbles at the inner solid–liquid interface and oscillations at the moving phase boundary caused by changes in local acoustic forces. Soon after melting began, acoustic streaming, the buoyancy of the remaining ice, and convective currents caused by both an inner thermal gradient and thermocapillary effects along the air–liquid interface, all contributed to the droplet spinning about the horizontal axis.

Wave propagation in a non-linearly elastic bar with phase transformations

There exist considerable difficulties in studying the wave propagation problems of the kind of phase transforming materials with non-monotone material responses due to the lack of uniqueness of solution for a moving phase boundary. An admissibility condition, which is named the Maxwell equal-area criterion, was established from a three-dimensional (3D) internal-variable formulation in the previous study to supplement the one-dimensional (1D) dynamical system of the bars/rods made of the special materials to determine the phase boundary uniquely. In this paper, we employ this criterion to investigate the wave propagation in the bar made of the special kind of phase transforming materials, which are associated with trilinear non-monotone stress–strain responses. The Riemann problem for different boundary states that arises from wave encounters are analyzed by the method of wave curves. Based on the construction of the Riemann solution, we explicitly study the wave propagation in a semi-infinite bar under an impulsive stress impact to explore the dynamical features of the special materials. The wave structures in the entire spatial and temporal domain for two different impact levels are obtained, as well as the state profiles. Detailed analyses and discussions of the wave patterns and wave encounters occurring during the wave propagation process are given for a deep understanding of dynamical phase transitions of the materials. These results are further compared with those obtained using the artificially adopted maximal dissipation rate criterion. The similarities and differences are discussed. The comparisons further confirmed that the special phase transforming material can be used for designing wave-absorption/impact-protection devices.

Temperature evolution associated with phase transition from quasi static to dynamic loading

Thermo-mechanical coupling is an intrinsic property of first order martensitic transformation. In this paper, we study the temperature evolution during phase transition at a wider strain rates from quasi static to impact loading to reveal the thermodynamic nature of the strain rate effect of phase transition materials. Based on the laws of thermodynamics and the principle of maximum dissipated energy, a thermal-mechanically coupled model was proposed. The model shows that, in the quasi static case, the temperature profile grades around the moving phase boundary, while for the dynamic case, thermal response of the specimen can be reached homogeneously due to random nucleation. The predicted results of the model are in good agreement with the experimental results, suggesting that the interaction between the self-heating effect and the temperature dependence of phase transition behavior plays a leading role in the process of the transformation deformation mechanism associated with the loading rate.

The M Waves Emitted by an Expanding Phase Boundary Create a “Lacuna”

Abstract The M waves introduced by Burridge and Willis (1969, “The Self-Similar Problem of the Expanding Crack in an Anisotropic Solid,” Math. Proc. Cambridge Philos. Soc., 66(2), pp. 443–468) are emitted by the surface of a self-similarly expanding elliptical crack, and they give Rayleigh waves at the corresponding crack speed. In the analysis for the self-similarly expanding spherical inclusion with phase change (dynamic Eshelby problem), the M waves are related to the waves obtained on the basis of the dynamic Green’s function containing the contribution from the latest wavelets emitted by the expanding boundary of phase discontinuity, and they satisfy the Hadamard jump conditions for compatibility and linear momentum across the moving phase boundary of discontinuity. In the interior of the expanding inclusion, they create a “lacuna” with zero particle velocity by canceling the effect of the P and S. It is shown that the “lacuna” and Eshelby properties are also valid for a Newtonian fluid undergoing phase change in a self-similarly expanding ellipsoidal region of a fluid with different viscosity.

Phase boundary propagation mode in nano-sized electrode materials evidenced by potentiostatic current transients analysis: Li-rich LiFePO4 case study

Phase boundary propagation dynamics in phase-transforming battery nanomaterials is widely studied due to high practical relevance of the boundary propagation patterns to the rate performance and degradation of metal-ion batteries. In this work, we decipher the complex interplay between the kinetic limitations in the course of phase boundary movement, which can be controlled by slow diffusion, interfacial charge transfer and nucleation. Employing nanosized Li-rich LiFePO4 materials as model systems, we consistently analyze the effect of each of the possible limiting factors on the evolution of potentiostatic current transients’ shape. Our results conclusively demonstrate that under the experimental conditions all three rate-controlling factors contribute to the rate-limitations of an intercalation material. We used numerical modeling to provide illustrative examples of current transients under different limiting regimes, which can be employed for the rapid and accurate diagnostics of the control factors during phase transformations. The derived conclusions allow rationalizing both the phase-transformation pathways in multiparticle electrodes (particle-by-particle or concurrent intercalation) and phase-growth morphologies (intercalation wave or shrinking core) based on easily accessible experimental estimates of kinetic parameters. These results are of high diagnostic value for the development of physically adequate battery models.

A Study on the Kinetics of the Phase Transformation in Silicon Anodes in Lithium Ion Batteries - in-Situ Experiments and a Computational Model

Being one of the major incentives in advancing technologies, characterizing the phase transformation in materials is yet far from reaching a fully comprehended subject. Understanding the mechanics, thermodynamics, and kinetics of the phase transformation serves a significant role in modeling the performance of materials. In this talk, we introduce a non-destructive in situ method for monitoring the advancement of the reaction front with a resolution of ~10 nm. We combine Picosecond Ultrasonics with Atomic Force Microscopy to study the velocity of the phase boundary propagation and the corresponding volumetric strain. Picosecond Ultrasonics is a pump and probe technique that can measure the thickness of the internal layers of material using ultrasounds that are generated and detected optically. Crystalline silicon is chosen as our model system due to its characteristic phase transformation behavior during its reaction with lithium. Using this technique, we have examined the diffusion of lithium atoms through different crystallographic orientations under various galvanostatic and potentiostatic conditions. Based on these experimental results, we have calibrated a modified Cahn-Hilliard type of phase field model of a moving phase boundary problem. In contrast to the classical formulation, the mobility of the interface can be determined using this modified Cahn-Hilliard model. The relevant thermodynamic and kinetic parameters for the phase transformation due to diffusion of Li in crystalline Si for the two crystallographic orientations are extracted. The extracted model parameters can facilitate the simulation of phase transformation in more complex structures with multiple crystallographic facets.

Motion of phase boundary during antiferroelectric–ferroelectric transition in a PbZrO3 -based ceramic

The in situ biasing transmission electron microscopy technique is employed to investigate the nucleation and growth of the ferroelectric phase during the electric field-induced phase transition in ${\mathrm{Pb}}_{0.99}{{\mathrm{Nb}}_{0.02}{[{({\mathrm{Zr}}_{0.57}{\mathrm{Sn}}_{0.43})}_{0.94}{\mathrm{Ti}}_{0.06}]}_{0.98}}{\mathrm{O}}_{3}$, a ${\mathrm{PbZrO}}_{3}$-based antiferroelectric ceramic. The first-order displacive phase transition is found to be highly reversible with the initial antiferroelectric domain configuration almost completely recovered upon removal of the applied field. In the forward transition from the antiferroelectric to ferroelectric phase, ${{100}}_{\mathrm{c}}$ facets are dominant on the phase boundary; while in the reverse transition from the ferroelectric to antiferroelectric phase during bias unloading, the phase boundary is segmented into ${{101}}_{\mathrm{c}}$ and ${{121}}_{\mathrm{c}}$ facets. The motion of the phase boundary is nonuniform, taking the form of sequential sweeping of facet segments. The elastic distortion energy and the depolarization energy at the antiferroelectric/ferroelectric phase boundary is suggested to dictate the facet motion.

Improved phase-field models of melting and dissolution in multi-component flows.

We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretizations that track the moving phase boundary. However, standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework, we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid-solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.

Non-isothermal decomposition kinetics of nano-scale CaCO3 as a function of particle size variation

We report the synthesis of nanocrystalline calcium carbonate with varying particle sizes by precipitation techniques from an aqueous solution of calcium nitrate and sodium carbonate at controlled pH. The particle size of the carbonate powder was precisely controlled by changing the precursor concentration. The synthesized carbonate powders were characterized by using scanning electron microscopy, X-ray diffraction technique, and transmission electron microscopy. The particle size, along with the crystallite size of as-synthesized carbonate powder, decreases with increasing precursor concentration. The non-isothermal decomposition kinetics of the carbonate powder was also evaluated by using near to the modified Arrhenius equation's exact solution. The experimental results were best fitted at n = 0.5, and the one-dimensional diffusion-controlled transport process mechanism (D1) and one-dimensional phase boundary movement mechanism (R1) was found to be very close fit of the corresponding evaluated g(α) value. The apparent activation energy of the nano calcium carbonate decomposition was found in the range of 120–175 kJ/mol, which is also inherently functioning with the average particle size. The apparent activation energy of decomposition of CaCO3 found to be decreased with decreasing average particle size of nanocrystalline calcium carbonate.

B-Axis Phase Boundary Movement Induced (020) Plane Cracking in LiFePO4.

Phase boundary movement accomplishing reversible LiFePO4/FePO4 biphasic transition is a fundamental Li-ion intercalation/deintercalation mechanism for LiFePO4 cathode. Phase boundary energetically favors crack nucleation and propagation; thus, postmortem observation on cracks becomes a feasible approach to investigate the phase-transition behavior and the Li-ion diffusion mechanism. The previously observed (200) plane cracks facilitate the "domino" diffusion model. Herein, our microscopic observations reveal another type of cracks along the (020) planes in a commercial LiFePO4 cathode cycled at moderate rates (0.1C, 0.33C, and 1C). Such (020) plane cracks are more detrimental to electrochemical performance because they can cut off the Li-ion diffusion pathway, causing inactive segments of LiFePO4. The (020) plane cracks indicate the LiFePO4/FePO4 phase boundary is along the (020) plane and moving along the b-axis during battery operation, which is a typical bulk diffusion-limited Li-ion diffusion behavior. Our observations stress that large LiFePO4 primary particle (>200 nm) not only aggravates cracking degradation but also switches the Li-ion diffusion mode to a slow bulk diffusion mechanism, plunging the overall battery performance.

Structure Preserving Discretization of Allen–Cahn Type Problems Modeling the Motion of Phase Boundaries

We study the systematic numerical approximation of a class of Allen–Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an associated energy functional along solution trajectories. We first study the discretization in space by a conforming Galerkin approximation of a variational principle which characterizes smooth solutions of the problem. Well-posedness of the resulting semi-discretization is established and the energy decay along discrete solution trajectories is proven. A problem adapted implicit time-stepping scheme is then proposed and we establish its well-posed and decay of the free energy for the fully discrete scheme. Some details about the numerical realization by finite elements are discussed, in particular the iterative solution of the nonlinear problems arising in every time-step. The theoretical results are illustrated by numerical tests which also provide further evidence for asymptotic expansions of the interface velocities derived by Alber et al. and support the observation that their hybrid Allen–Cahn model avoids the problem of mesh-locking to a large extent.

Tuning ferroelectricity by manipulating the global and local structure in a lead-free Sr-doped Ba(Ti1-x Snx)O3ceramics

The effect of 5% Sr substitution at the Ba site in Ba(Ti1-x Snx)O3 (BTSnx) system is investigated for , 0.075, and 0.12 compositions. The phase transition studies were carried out using dielectric, high-resolution X-ray diffraction, and PE hysteresis loop measurements. Rietveld refinements, along with dielectric studies on strontium-doped BTSnx reveal that the inter-ferroelectric phase boundaries observed in pure BaTiO3 approach the Tc line, with morphotropic phase boundary like behaviour. The PE hysteresis loops show enhanced polarization (≈ 190%) in Sr-doped BTSn5, which is attributed to the inter-ferroelectric phase instability (which facilitates polarization rotation, phase boundary motion, and domain wall motion), enhanced tetragonality (c/a), and increased unit-cell polarization evident from the amplitude of frozen phonon mode corresponding to the zone center of the cubic Brillouin zone. The ferroelectric polarization observed in the average-cubic-structure state of Sr-doped BTSn12 is attributed to the cooperative polar off-centre displacements of A (Ba2+/Sr2+) and B (Ti4+/Sn4+) site cations along and directions, respectively. Further, Sr-doped BTSn12 has high dielectric constant and low loss which makes this material an important composition for various technological applications.