Boundary Conditions for Momentum and Vorticity at an Interface between Two Fluids

Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes equation and the equation of vorticity transport. It has been shown first that a contribution of fluid molecules crossing over a conceptual surface moving with fluid velocity due to their fluctuating motion is essentially important to understanding transport phenomena of momentum and vorticity. A notion of surface layers, which are thin layers at both sides of an interface, has been introduced next to elucidate the transporting mechanism of momentum and vorticity from one phase to the other at an interface through which no fluid molecules are crossing over. A fact that a size of δV, in which reliable values of density, momentum, and velocity of fluid are respectively defined as a volume-averaged mass of fluid molecules, a volume-averaged momentum of fluid molecules and a mass-averaged velocity of fluid molecules, is not infinitesimal but finite has been one of the key factors leading to the boundary conditions for vorticity at an interface between two fluids. The most distinguished characteristics of the boundary conditions derived here are the zero-value conditions for a normal component of momentum flux and tangential components of vorticity flux, at an interface.

Alcohol-dispersed polymer complex as an effective and durable interface modifier for n-i-p perovskite solar cells

Abundant interfacial defects remain a significant challenge that hampers both the efficiency and stability of perovskite solar cells(PSCs).Herein,an alcohol-dispersed conducting polymer complex,denoted as PEDOT:F(Poly(3,4-ethylene dioxythiophene):Perfluorinated sulfonic acid ionomers),is introduced into the interface between perovskite and hole transporting layer in regular-structured PSCs.PEDOT:F serves as a multi-functional interface layer(filling grain boundaries and covering perovskite's grain-surface)to achieve a robust interaction with organic groups within perovskites,which could induce a structural transformation of PEDOT to increase its conductivity for the efficient hole-transport.Furthermore,the strong interaction between PEDOT and perovskites could promote an effective coupling of undercoordinated Pb~(2+)ions with the lone electron pairs near O&S atoms in PEDOT molecules,thereby enhancing defect passivation.Additionally,PEDOT:F with inherent hydrophobic properties prevents effectively moisture invasion into perovskites for the improved long-term stability of the PSCs.Consequently,the PEDOT:F-based PSCs achieved a champion efficiency of 24.81%,and maintained ca.92%of their initial efficiency after 7680 h of storage in a dry air environment,accompanied by the enhanced photothermal stability.

INTERFACE MORPHOLOGIES AND SOLUTE SEGREGATION OF Al-Li ALLOY 8090 DURING UNIDIRECTIONAL SOLIDIFICATION

The solid-liquid interface morphology and solute segregation behaviour of AI-Li alloy 8090 during unidirectional solidification were studied by the liquid metal quenehing method under varied processing conditions.When solidification rate,R<O.13 or>O.75 mm/min (temper- ature gradient,G_L=130℃/cm),the structure revealed of planar or dendritic interface respectively.With the increase of R,the interface morphology becomes cellular from planar gradually,within a narrow range.And the greater the R,the,finer the dendrite.Segregation of element Cu and impurity elements Fe and Si are quite severe,the interface morphology markedly influences on solute segregation.During solidification at coarse dendrite interface, their segregation ratios are rather great and solidified structure is coarse.

PHASE INTERFACE SEGREGATION OF Mg IN A Ni-BASE SUPERALLOY IN100

The segregation of Mg to phase interfaces in a nickel base superalloy IN 100 has been investi- gated using EPT(Electron Microprobe Technique).AES(Auger Electron Spectroscopy) and EDS analyses on thin TEM film.The results show that Mg segregates to the phase inter- faces of MC/γ and γ′/γ.The segregation concentration and layer thickness of Mg on MC/γ phase interface are larger than that on γ′/γ phase interface.Mg is not only a grain boundary segregation element,but also a phase interface segregation one.

Effects of Ca(Y)-Si modifier on interface morphology and solute segregation during directional solidification of an austenite medium Mn steel

The austenite medium Mn steel modified with controlled additions of Ca, Y, Si were directionally solidified using the vertical Bridgman method to study the effects of Ca（Y）-Si modifier on the solid-liquid （S-L） interface morphology and solute segregation. The interface morphology and the C and Mn segregation of the steel directionally solidified at 6.9 μtrn/s were investigated with an image analysis and a scanning electron microscope equipped with energy dispersive X-ray analysis. The 0.5wt% Ca-Si modified steel is solidified with a planar S-L interface. The interface of the 1.0wt% Ca-Si modified steel is similar to that of the 0.5wt% Ca-Si modified steel, but with larger nodes. The 1.5wt% Ca-Si modified steel displays a cellular growth parttern. The S-L interface morphology of the 0.5wt% Ca-Si＋1.0wt% Y-Si modified Mn steel appears as dendritic interface, and primary austenite dendrites reveal developed lateral branching at the quenched liquid. In the meantime, the independent austenite colonies are formed ahead of the S-L interface. A mechanism involving constitutional supercooling explains the S-L interface evolution. It depends mainly on the difference in the contents of Ca, Y, and Si ahead of the S-L interface. The segregation of C and Mn ahead of the S-L interface enhanced by the modifiers is observed.

Effects of Interface and Grain Boundary on the Electrical Resistivity of Cu/Ta Multilayers

The electrical resistivity of Cu/Ta multilayers deposited by radio-frequency magnetron sputtering on a polyimide substrate was investigated as a function of monolayer thickness. It is found that the resistivity of the multilayer increases with decreasing monolayer thickness from 500 nm to 10 nm. Two significant effects of layer interface scattering and grain boundary scattering were identified to dominate electronic transportation behavior in the Cu/Ta multilayers at different length scales. The electrical resistivity of the multilayer with monolayer thickness ranging from nanometer to submicron scales can be well described by a newly-proposed Fuchs-Sandheimair （F-S） and Mayadas-Shatzkes （M-S） combined model.

GRAIN BOUNDARY SEGREGATION AND INTERGRANULAR BRITTLENESS IN HIGH STRENGTH ALUMINIUM ALLOY

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Grain boundary segregation of minor arsenic and nitrogen at elevated temperatures in a microalloyed steel

Auger electron spectroscopy （AES） was used to investigate the grain boundary segregation of arsenic and nitrogen in a kind of microalloyed steel produced by a compact strip production （CSP） technology at 950 to 1100℃, which are similar to the hot working temperature of the steel on a CSP production line. It was discovered that arsenic segregated on grain boundaries when the steel was annealed at 950℃ for 2 h. When the annealing temperature increased to 1100℃, arsenic was also found to have segregated on grain boundaries in the early annealing stage, for instance, within the first 5 min annealing time. However, if the holding time of the steel at this temperature increased to 2 h, arsenic diffused away from grain boundaries into the matrix again. Nitrogen was not found to have segregated on grain boundaries when the steel was annealed at a relatively low temperature, such as 950℃. But when the annealing temperature increased to 1100℃, nitrogen was detected to have segregated at grain boundaries in the steel.

ANTIMONY GRAIN BOUNDARY SEGREGATION AND ITS SUPPRESSION BY CERIUM IN Fe-2%Mn-Sb STRUCTURAL STEELS

Antimony grain boundary segregation in Fe-2%Mn-Sb structure steels has been studied through measurements of the ductile-brittle transition temperature in conjunction with scanning electron microscopy, Auger electron spectroscopy and secondary ion mass spectroscopy. The research result reveals that during tempering or ageing after quenching at 980℃, Sb segregates to grain boundaries with both equilibrium and non-equilibrium natures and brings about temper embrittlement in the steels. Cerium can relieve temper embrittlement of the steels and its segregation to grain boundaries may play an important role in reducing this embrittlement.

An FEGSTEM Study of Grain Boundary Segregation of Phosphorus during Quenching in a 2.25Cr-1Mo Steel

Quenching-induced phosphorus segregation to prior austenite grain boundaries in a 0.077 wt pct P-doped 2.25Cr-2Mo steel is examined using field emission gun scanning transmission electron microscopy （FEGSTEM）. A phosphorus level of around 1.56 at. pct is observed for the water-quenched sample. In recognition of insufficiently high spatial resolution of the technique for grain boundary composition analysis, the measured results are corrected by an analytical convolution method. The corrected phosphorus segregation level may be up to about 4.7 at. pct. The quenchinginduced phosphorus segregation is nonequilibrium segregation and the migration of vacancy-phosphorus complexes plays an important role in the kinetic process. For such a reason, the mechanism for migration of the complexes is discussed in some detail.

NON-EQUILIBRIUM SOLUTE SEGREGATION TO AUSTENITIC GRAIN BOUNDARY IN FERRUM-NICKLE ALLOY

The development of non-equilibrium segregation of boron at grain boundaries in Fe-4 0%Ni alloy during continuous cooling process was experimentally observed with boron Particle Tracking Autoradiography (PTA) and Transmission Electron Microscopy (TEM,). The samples with 10ppm boron were cooled at 2℃/s to 1040, 980, 920, 860, 780 and 640℃ respectively after pre-heat treatment of 1150℃ for 15mm with a Gleeble-1500 heat simulating machine, then water quenched to room temperature. The width of segregation layer and boron depletion zone, rich factor and other parameters were measured by a special image analysis system. The experimental results of PTA show that the grain boundary segregation of boron during cooling process is a dynamic process and the development of the non-equilibrium segregation experiences three stages: first increases rapidly from 1150 to 1040℃, then gently from 1040 to 860℃, and rapidly again from 860℃ to 640℃. The width of boron depletion zone increases from about 11μm at 1040℃ to 26μm at 640℃. TEM observation shows that boron precipitates exist at grain boundaries when the samples are cooled to below 860℃. The experimental phenomena are briefly discussed.

Segregation of alloying atoms at a tilt symmetric grain boundary in tungsten and their strengthening and embrittling effects

We investigate the segregation behavior of alloying atoms （Sr, Th, In, Cd, Ag, Sc, Au, Zn, Cu, Mn, Cr, and Ti） near Z3 （ 111 ） [1]-0] tilt symmetric grain boundary （GB） in tungsten and their effects on the intergranular embrittlement by performing first-principles calculations. The calculated segregation energies suggest that Ag, Au, Cd, In, Sc, Sr, Th, and Ti prefer to occupy the site in the mirror plane of the GB, while Cu, Cr, Mn, and Zn intend to locate at the first layer nearby the GB core. The calculated strengthening energies predict Sr, Th, In, Cd, Ag, Sc, Au, Ti, and Zn act as embrittlers while Cu, Cr, and Mn act as cohesion enhancers. The correlation of the alloying atom＇s metal radius with strengthening energy is strong enough to predict the strengthening and embrittling behavior of alloying atoms; that is, the alloying atom with larger metal radius than W acts as an embrittler and the one with smaller metal radius acts as a cohesion enhancer.

Modelling of Equilibrium Grain Boundary Solute Segregation under Irradiation

Both radiation-induced excess vacancies and solute-interstitials may enhance solute diffusion. The radiation-enhanced solute diffusion promotes the kinetic process of equilibrium segregation. This effect is especially considerable in the low temperature range. As a complement to modelling of radiation-induced non-equilibrium segregation, the radiation-created vacancy and solute-interstitial-accelerated equilibrium grain boundary solute segregation were theoretically treated. The models were applied to phosphorus segregation in α-Fe subjected to neutron irradiation.

Determination of Neutron Irradiation-Induced Phosphorus Segregation on Grain Boundaries in a P-doped 2.25Cr1Mo Steel

Irradiation-induced impurity segregation to grain boundaries is one of the important radiation effects on materials. For this reason, phosphorus segregation to prior austenite grain boundaries in a P-doped 2.25Cr1Mo steel subjected to neutron irradiation is examined using field emission gun scanning transmission electron microscopy (FEGSTEM) with energy dispersive X-ray microanalysis (EDX). The steel samples are irradiated around 270 and 400℃, respectively. The irradiation dose rate and dose are -1.05×10-8 dpa/s and -0.042 dpa respectively for 270℃ irradiation, and 1.7×10-8 dpa/s and 0.13 dpa respectively for 400℃ irradiation. The FEGSTEM results indicate that there is no apparent phosphorus segregation during 270℃ irradiation but there is some during 400℃ irradiation.

THE BOUNDARY LAYER SOLUTIONS OF THE INTERFACE PROBLEM CONSIDERING THE STRAIN GRADIENT

Acoording to the classical elastic theory, there is always adiscontinuity of rotation angle on the interface different materials.This illogic result can be overcome by the strain gradient plasticitytheory. In the light of this theory, there is a group of boundarylayer solutions near the in- terface, which have made importantadjustment of the classical results.

AN EMBEDDED BOUNDARY METHOD FOR ELLIPTIC AND PARABOLIC PROBLEMS WITH INTERFACES AND APPLICATION TO MULTI-MATERIAL SYSTEMS WITH PHASE TRANSITIONS

The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.

Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuse-interface immersed boundary method

A novel method is proposed to combine the wall-modeled large-eddy simulation(LES) with the diffuse-interface direct-forcing immersed boundary(IB) method.The new developments in this method include:(i) the momentum equation is integrated along the wall-normal direction to link the tangential component of the effective body force for the IB method to the wall shear stress predicted by the wall model;(ii) a set of Lagrangian points near the wall are introduced to compute the normal component of the effective body force for the IB method by reconstructing the normal component of the velocity. This novel method will be a classical direct-forcing IB method if the grid is fine enough to resolve the flow near the wall. The method is used to simulate the flows around the DARPA SUBOFF model. The results obtained are well comparable to the measured experimental data and wall-resolved LES results.

The Role of Nd Solid-Solution and Grain-Boundary Segregation in Binary NiAl Intermetallic Compound

The role of Nd solid-solution and grain-boundary segregation in binary NiAl alloy was studied based on microhardness and compressive macrostrain. X-ray and Auger spectra studies indicate that Nd not only is soluble in grain interiors, but also segregates to the grain boundaries. Nd solid-solution induces an increase of the microhardness from 269 to 290 HV in grain interiors and segregation results in an enhancement of hardness from 252 to 342 HV on grain boundaries. Thus, the cohesion of grain boundaries is enhanced by Nd segregation, which make the alloy doped with 0.05 wt pct Nd exhibit more compressive microstrain, i.e. the higher the compressive ductility at room temperature, the better the final surface condition at elevated temperature. Finally, a discussion was made on the reason that Nd strengthens the grain boundaries in NiAl intermetallic alloy.

Effects of low-frequency magnetic field on grain boundary segregation in horizontal direct chill casting of 2024 aluminum alloy

Effects of low frequency electromagnetic field on grain boundary segregation in horizontal direct chill (HDC) casting process was investigated experimentally. The grain boundary segregation and microstructures of the ingots, which manufactured by conventional HDC casting and low frequency electromagnetic HDC casting were compared. Results show that low frequency electromagnetic field significantly refines the microstructures and reduces grain boundary segregation. Decreasing electromagnetic frequency or increasing electromagnetic intensity has great effects in reducing grain boundary segregation. Meanwhile, the governing mechanisms were discussed.

Direct characterization of boron segregation at random and twin grain boundaries

Boron distribution at grain boundaries in hot-deformed nickel is directly characterized by the time-of-flight secondary ion mass spectrometry. The segregations of boron are observed at both the random and twin grain boundaries. Two types of segregations at random grain boundaries are observed. The first type of segregation has a high intensity and small width. Its formation is attributed to the incorporating of dislocations into the moving grain boundaries. The second type of segregation arises from the cooling induced segregation at the dislocations associated with the grain boundaries. The segregation at twin boundary is similar to the second type of segregation at random grain boundaries.