Interphase Boundary Energy Research Articles

On the Effect of Interphase Boundary Energy Anisotropy on Morphologies: A New Type of Eutectic Grain Observed in a Three-Phase Eutectic System

Eutectic microstructures are dramatically affected by the anisotropy in interphase boundary energy. Depending on this anisotropy function, different eutectic grains may grow simultaneously at the same experimental conditions. In all reported quasi-isotropic and anisotropic two-phase and three-phase eutectic grains in thin samples, lamellar morphology is observed and the microstructure is essentially two dimensional (2D), since the interphase boundaries are perpendicular to the sample walls. Using the β(In)–In2Bi–γ(Sn) system and real-time solidification experiments in thin samples, we introduce a unique and new type of anisotropic three-phase eutectic grain, entitled here as “Laminated Matrix with Rods (LMR).” In this grain, due to the anisotropy in In2Bi/γ(Sn) interphase boundary, the evolving phases, and hence, the microstructures observed through the two glass plates of the thin sample are completely different, despite the strong confinement effect. During rotating directional solidification (RDS) experiments, the morphology or the aspect ratio of all phases changes periodically and drastically. Specifically, In2Bi, β(In), and γ(Sn) phases evolve from all being lamellar perpendicular to the sample walls to the matrix, elongated/trapezoidal rods, and a lamella parallel to the sample walls, respectively. Our experimental results show that these morphological transitions are due to change in the interphase boundary orientation with respect to the growth direction.Graphical abstract

Interphase Boundaries and Their Impact on Carrier Dynamics in Lead Halide Perovskites.

Interphase boundaries (IBs) are widely present in lead halide perovskites (LHPs) owing to their relatively low phase transition barriers. However, their atomic structures and electronic properties have rarely been investigated. In this study, various IB structures were constructed computationally, and their influences on the charge carrier transport properties of LHPs were studied by calculating the effective interphase boundary energy and analyzing the electronic structure. The results show that the presence of IBs plays a significant role in carrier transport and that they may be tuned to prolong carrier lifetimes. This study provides insights for improving the performance of LHPs by engineering IBs, primarily by their compositional phases and ratios.

A Mechanism of Double-Membrane Vesicle Formation from Liquid-Ordered/Liquid-Disordered Phase Separated Spherical Membrane.

Genome replication of coronaviruses takes place in specific cellular compartments, in so-called double-membrane vesicles (DMVs), formed from the endoplasmic reticulum (ER). An intensive production of DMVs is induced by non-structural viral proteins. Here, we proposed a possible mechanism of the DMV formation from ER-derived spherical vesicles where liquid-ordered and liquid-disordered lipid phases coexist. These vesicles are supposed to divide into two homogeneous liquid-ordered and liquid-disordered vesicles. The formation of two spherical vesicles constituting DMV requires a mechanical work to be performed. We considered the excess energy of the boundary between the coexisting lipid phases as the main driving force behind the division of the initial vesicle. Explicitly accounting for the energy of elastic deformations and the interphase boundary energy, we analyzed a range of physical parameters where the DMV formation is possible. We concluded that this process can principally take place in a very narrow range of system parameters. The most probable diameter of DMVs formed according to the proposed mechanism appeared to be approximately 220 nm, in an agreement with the average diameter of DMVs observed in vivo. Our consideration predicts the DMV size to be strongly limited from above. The developed analysis can be utilized for the production of DMVs in model systems.

On the Effect of Interphase Boundary Energy Anisotropy on Morphologies: A New Type of Eutectic Grain Observed in a Three-Phase Eutectic System

On the Effect of Interphase Boundary Energy Anisotropy on Morphologies: A New Type of Eutectic Grain Observed in a Three-Phase Eutectic System

Microstructure development and morphological transition during deposition of immiscible alloy films

Complex three-dimensional microstructural patterns arise during deposition of immiscible alloys and their morphologies depend sensitively on alloy composition, deposition rates and substrate temperatures. Using phase field simulations, we construct a microstructure morphology map in a multi-dimensional space of material properties and processing parameters. We consider simultaneous effects from temperature-dependent surface and bulk diffusivities and thermodynamic driving force for phase separation, temperature- and composition-dependent interphase boundary and surface energies, as well as alloy composition, substrate temperature and deposition rate. The microstructural patterns and morphological transition sequences in as-deposited films revealed by the microstructure map are validated using experimental data from sputtered Cu-Mo alloy films as well as from other systems. Such a microstructural map can guide synthesis of three-dimensional compositionally modulated nanostructures via self-organization during deposition of immiscible alloy films.

Dielectric relaxation in water of the adsorption layer on the surface of a solid

The influence of temperature and interphase boundary energy on the dielectric relaxation parameters in adsorbed water was investigated within the framework of thermodynamic consideration. It is shown that accounting for the interfacial boundary energy greatly increases the orientation dielectric relaxation time in adsorbed water. This allows us to determine the dispersion of the dielectric characteristics of adsorbed water using Debye’s relaxation theory.

Interphase boundary segregation and precipitate coarsening resistance in ternary alloys: An analytic phase-field model describing chemical effects

Many experimental and first principles studies on precipitation hardening alloys show that segregation of elemental species to the matrix-precipitate interphase boundary (IB) reduces the boundary’s energy. This segregation mechanism can thermally stabilize the microstructure against precipitate coarsening processes and allow for higher operating temperatures in structural applications. In this paper, we develop a phase-field modeling framework to describe IB solute segregation in ternary alloys. The interfacial thermodynamics is effectively described by defining an IB phase with a characteristic free energy-concentration dependence. Equilibrium for the IB phase is established via the parallel tangent plane construction, analogous to classical treatments for segregation to free surfaces and grain boundaries. Analytic steady-steady solutions elucidating the dependence of IB properties on bulk phase composition, temperature and model parameters are derived for a one-dimensional system. Analytic relations for the classical thermodynamic quantities–IB energy and relative solute excess–are derived and the Gibbs adsorption equation is shown to hold; therefore, predictions of the model can be compared with experiments and atomistic simulations. An application of the model is demonstrated for Zn segregation to Mg/Mg2Sn using representative IB parameters. A two-particle coarsening simulation of IB segregation is performed: the result demonstrates enhanced coarsening resistance of the ternary alloy relative to the binary alloy.

A phase-field approach for modeling equilibrium solute segregation at the interphase boundary in binary alloys

A number of experimental and theoretical findings in age hardening alloys suggest that specific solute elements preferentially segregate to and reduce the energy of the interphase boundary (IB). This segregation mechanism can stabilize the precipitation microstructure against coarsening, allowing higher operating temperatures in structural applications. Herein, we present a phase field model of solute segregation to IBs that separate matrix and precipitate phases in binary alloys. The proposed modeling framework is capable of capturing bulk thermodynamics and interfacial free energies, while also accounting for various mass transport mechanisms. Analytical equilibrium solutions of one-dimensional systems are presented, and excess IB quantities are evaluated independent of the Gibbs dividing surface convention. With the aid of the parallel tangent construction, IB segregation isotherms are established in terms of the alloy composition and the model parameters describing the free energy functions. Under the regular solution approximation, computational studies elucidating the dependence of the IB energy and segregation levels on temperature and free energy model parameters are presented. We show that the model is consistent with the Gibbs adsorption equation; therefore, it is possible to compare the adsorption behavior predicted by the model parameters with experiments and atomistic simulations. Future work on extending the model to ternary alloys, and incorporating the effect of elastic interactions on IB segregation is expected.

Interphase Boundary Segregation and Precipitate Coarsening Resistance in Ternary Alloys: An Analytic Phase-Field Model Describing Chemical Effects

Many experimental and first principles studies on precipitation hardening alloys show that segregation of elemental species to the matrix-precipitate interphase boundary (IB) reduces the boundary's energy. This segregation mechanism can thermally stabilize the microstructure against precipitate coarsening processes and allow for higher operating temperatures in structural applications. In this paper, we develop a phase-field modeling framework to describe IB solute segregation in ternary alloys. The interfacial thermodynamics is effectively described by defining an IB phase with a characteristic free energy-concentration dependence. Equilibrium for the IB phase is established via the parallel tangent plane construction, analogous to classical treatments for segregation to free surfaces and grain boundaries. Analytic steady-steady solutions elucidating the dependence of IB properties on bulk phase composition, temperature and model parameters are derived for a one-dimensional system. Analytic relations for the classical thermodynamic quantities--IB energy and relative solute excess--are derived and the Gibbs adsorption equation is shown to hold; therefore, predictions of the model can be compared with experiments and atomistic simulations. An application of the model is demonstrated for Zn segregation to Mg/Mg2Sn using representative IB parameters. A two-particle coarsening simulation of IB segregation is performed; the result demonstrates enhanced coarsening resistance of the ternary alloy relative to the binary alloy.

Nonisothermal immiscible compressible thermodynamically consistent two-phase flow in porous media

In this paper, we introduce a new model of the nonisothermal immiscible compressible thermodynamically consistent two-phase flow in a porous domain Ω. This model includes the term describing the skeleton and interphase boundary energies. In the framework of the model, we derive the equation for the entropy function in the whole Ω and then obtain the estimate of the maximal entropy of the system.

Mathematical models of two-phase flows’ interaction with a solid body

Expressions for supercooled droplets’ crystallization parameters are proposed according to experimental results’ interpolation. Estimation of interphase boundary energy fluxes generation were obtained. Mathematical models of the non-spherical particles motion were developed.

Stretch-Induced Interdigitation of a Phospholipid/Cholesterol Bilayer.

The interdigitated gel (LβI) phase is one of the membrane phases of phospholipid molecules in which the hydrophobic tails of the phospholipid molecules penetrate the opposite leaflet of the bilayer. Recent molecular dynamics (MD) simulations have shown that interdigitation can take place as a phase transition from the liquid-ordered (Lo) phase to the LβI phase under stretching. However, there is still no conclusive experimental evidence for this process, so its existence remains controversial. In this study, to explain the transition from energy balance, we propose a free-energy model. The model consists of three energy components: the elastic deformation energy, surface energy at the bilayer-water interface, and interphase boundary energy. To determine the parameters of the model, we perform MD simulations of a stretched 1,2-dipalmitoyl- sn-glycero-3-phosphocholine/cholesterol bilayer. The phase diagrams from our model are in good agreement with those obtained from MD simulations. The energy balance among the components in the stretched bilayer quantitatively explains the stretch-induced transition. In the model, increasing the system size to that used in experiments shows that interdigitation is favorable for rigid bilayers under stretching or in alcohol solutions. These results suggest that the stretch-induced interdigitation might be observed in microscopic experiments.

Influence of interphase boundary anisotropy on bulk eutectic solidification microstructures

The solidification of eutectic alloys generally produces two-phase microstructures. Their morphology is determined by the dynamics of the solid-liquid interfaces at the crystallization front. At the triple lines, where the liquid and the two solid phases meet, solid-liquid and solid-solid surface free energies are in local equilibrium. We perform three-dimensional phase-field simulations with a multi-phase-field model in which the surface free energies can be independently controlled. We find that an anisotropy of the interphase boundary (solid-solid) energy has a strong effect on the microstructural patterns. The lamellae tend to align with directions of minimal interphase boundary energy. For a two-fold anisotropy, as generally expected for interphase boundaries between two cubic crystals, regular lamellar arrays are formed, in strong contrast to the labyrinth patterns observed in isotropic systems. If two different grains compete, the one with the lowest interphase boundary energy always overgrows the other. These results are consistent with observations in bulk metallic eutectic samples, namely, the frequent occurrence of large regular lamellar arrays and the prevalence of grains with special orientation relationships.

Microstructure of NbTi superconducting alloy

A superconducting multifilament wire made of Nb-60 at.% Ti alloy was investigated by methods of atom probe/field ion microscopy (APFIM), three-dimensional atom probe (3DAP), high resolution electron microscopy (HREM) and computer simulation. The results of the APFIM and HREM analysis suggest, that the specimens contain two phases, a bcc structure (β-phase), and a hcp structure (α-phase). The mesascopic and nanoscale heterogeneities of element concentration in *-phase were observed. Atom probe analyses of annealed NbTi superconductors and a statistical processing of the chains of atoms, consistently registered by mass-analyses, indicated that no atomic clusters were formed in alloy prior to the onset of the second phase formation. The β-phase and niobium enriched phase have the configurations extended along the wire axis, the nanoscale heterogeneity inside the β-phases was nearly isotropic. An atomic structure of interphase boundaries has been determined using HREM and atomistic structure calculations. Interphase boundaries in Nb-Ti alloy are coherent or semi-coherent in spite of the existence of the irregular microprotrusions.The boundaries between α- and β-phases reveal the absence of the rigid-body translation and continuity of lattice planes across the interface. It was demonstrated that the method of simulation in reciprocal space is computationally efficient for investigations of the atomic structure and energy of coherent and non-coherent interphase boundaries. The extremely high critical current density in the optimized Nb-Ti can be due to the coherent structure of interphase boundaries.

Dependence of the specific energy of the β/α interface in the VT6 titanium alloy on the heating temperature in the interval 600–975°C

The specific energy of interphase boundaries is an important characteristic of multiphase alloys, because it determines in many respects their microstructural stability and properties during processing and exploitation. We analyze variation of the specific energy of the β/α interface in the VT6 titanium alloy at temperatures from 600 to 975°C. Analysis is based on the model of a ledge interphase boundary and the method for computation of its energy developed by van der Merwe and Shiflet [33, 34]. Calculations use the available results of measurements of the lattice parameters of phases in the indicated temperature interval and their chemical composition. In addition, we take into account the experimental data and the results of simulation of the effect of temperature and phase composition on the elastic moduli of the α and β phases in titanium alloys. It is shown that when the temperature decreases from 975 to 600°C, the specific energy of the β/α interface increases from 0.15 to 0.24 J/m2. The main contribution to the interfacial energy (about 85%) comes from edge dislocations accommodating the misfit in direction [0001]α || [110]β. The energy associated with the accommodation of the misfit in directions \({\left[ {\bar 2110} \right]_\alpha }\left\| {{{\left[ {1\bar 11} \right]}_\beta }} \right.\) and \({\left[ {0\bar 110} \right]_\alpha }\left\| {{{\left[ {\bar 112} \right]}_\beta }} \right.\) due to the formation of “ledges” and tilt misfit dislocations is low and increases slightly upon cooling.

Modeling of Microstructure Evolution in Metallic Multilayers with Immiscible Constituents

Thermal stabilities of Cu/Nb, Cu/Ag, and Cu/Mo multilayers are studied by a recently developed model for microstructure evolution in multilayers with immiscible constituents, which actually is an extension to the classic grooving theory. The experimentally evidenced zig–zag microstructure is found to form through grooving when grains are staggered in a “stair-like” fashion. Furthermore, stability maps for these systems are developed in terms of the aspect ratio of grain dimensions and the ratio of the distance between two nearest triple junctions to the in-plane grain size. A comparison of stability among the three systems shows that the ratio of the grain boundary energy to the interphase boundary energy is more important than the ratio of the two grain boundary energies in controlling the stability. A simple criterion is also proposed for a quick estimation of the stability. Both maps from the model and from the simple criterion are in good agreement with the experiments for multilayers.

Grain boundary complexion transitions in WO3- and CuO-doped TiO2 bicrystals

Several grain boundary complexions (grain boundary interfacial phases) have been identified in TiO2 bicrystals by high-resolution transmission electron microscopy (TEM) and aberration-corrected scanning TEM (STEM). An intrinsic grain boundary with no apparent impurity segregation was observed in an undoped TiO2 bicrystal. In a WO3-doped TiO2 bicrystal, WO3 second-phase particles formed along the boundary, with a nominally clean, intrinsic-type grain boundary in between the particles. In a CuO-doped bicrystal, a remarkable series of three distinct grain boundary complexions with abrupt structural transitions was discovered coexisting at the grain boundary, and the existence of a fourth equilibrium complexion at the annealing temperature was implied. Thus, the WO3- and CuO-doped TiO2 bicrystals exhibit dramatically different solute partitioning behavior which can be understood in terms of the relative interphase boundary energies of these two systems. STEM–electron energy loss spectroscopy and energy-dispersive X-ray spectroscopy analysis of the nanoscale lens-shaped films of amorphous material in the CuO-doped TiO2 bicrystal demonstrated an excess of CuO, as expected, yet also revealed the unintentional presence of SiOx. The multiple grain boundary complexions in CuO-doped TiO2 offer an explanation for the CuO-enhanced grain growth and sintering of TiO2 that has been reported in the literature. Conversely, the intrinsic grain boundary complexion observed in WO3-doped TiO2 is consistent with previous work showing that WO3 has no effect on grain boundary mobility in TiO2. A phenomenological thermodynamic model is proposed to explain the physical origin of these observed grain boundary complexions and the abrupt, first-order complexion transitions that are believed to occur upon cooling of the CuO-doped TiO2 bicrystal.

A theory of thin lamellar eutectic growth with anisotropic interphase boundaries

We present a semiempirical theory of the effects of an orientation dependence of the surface free energy of interphase boundaries (interphase boundary anisotropy) on lamellar eutectic growth in thin samples. We show that, to a good approximation, thin lamellar eutectic patterns with a strong interphase boundary anisotropy travel along the growth front at such a velocity – or, equivalently, at such an inclination angle of the lamellae left behind in the solid – that the surface tension force of the interphase boundary is nearly parallel to the applied thermal gradient. This explains, among other things, the crystallographic locking of lamellar eutectic patterns that occurs in those eutectic grains, which have cusp singularities in the Wulff plot of the interphase boundary. Based on this theory, we show that the rotating directional solidification method, by which a thin sample is rotated with respect to a fixed unidirectional thermal gradient, must yield eutectic lamellae whose trajectories are nearly homothetic to the two-dimensional Wulff form of the interphase boundary. This opens up new possibilities for the experimental study of interphase boundary anisotropy in eutectic alloys.

Interphase Energies and Nonequilibrium Growth of γ-precipitates in Al-Ag: A DFT Study

AbstractDensity-functional theory (DFT) calculations of interphase boundary energies provide useful input for many precipitate growth models in alloy systems [1]. One example is Al-Ag, where a rich variety of precipitate types exist, and the sizes and shapes are determined roughly by a Wulff construction, namely, minimizing surface free energies with respect to geometry. This is only a first approximation, however, as kinetic-considerations and crystallography do not allow for a uniform, isotropic growth. Consequently, a nonequilibrium growth model is developed for γ-plates [2], which attempts to connect semi-coherent (ledge) and incoherent (edge) interface growth rates in a way that incorporates shape and interface energies. Through this connection, we make a DFT model with approximate unit cells that mirror experimental conditions, which gives accurate predictions for precipitate aspect ratios and time-development of nonequilibrium shapes. Starting from an explicit calculation of Suzuki segregation of solute to stacking-faults, we find a mechanism for nucleation of nanoscale γ-plates on quenched defects, identify a bulk structure from a calculated phase diagram that gives the relevant HCP equilibrium precipitate structure occurring at 50 at.% Ag and calculate critical nucleation parameters for γ-precipitate formation. Applications to island-coarsening and lath morphology are also discussed.

Influence of interface energies on solute partitioning mechanisms in doped aluminas

The experiments described in this paper have been designed to understand how particular dopants in alumina (Ca, Mg, Si, and Y) affect microstructural development through the energetics of their associated precipitates. Specifically, the role of the interphase boundary energy and precipitation activation energy are considered to be in competition with grain boundary complexion (disorder) transitions for partitioning excess solute. The results reveal a relationship between the relative precipitation activation energy and the temperature at which grain boundary complexion transitions occur. The large differences in activation energy primarily derive from the interphase boundary energy. Precipitates that form lower interphase boundary energies tend to suppress complexion transitions, while systems that contain precipitates with high interphase boundary energies are more susceptible. Based on the findings, a new criterion for additive selection to control complexion transitions and abnormal grain growth is proposed that is based on interfacial energies between the host and precipitate.