Interface Kinetic Effects Research Articles

Origin of the Shanggong gold deposit, the southern margin of the North China Craton: Constraints from Rb-Sr ages of sericite, and trace elements and sulfur isotope of pyrite

The Shanggong Au deposit is a world-class Au deposit in the southern margin of the North China Craton. Pyrite, as the primary Au carrier in this deposit, is an ideal mineral for dissecting the complex ore-forming process and origin of this deposit. Four types of pyrite were identified by EPMA, SEM, LA-ICP-MS, and NanoSIMS analyses: the coarse-grained cubic, disseminated pyrite (Py1) in the early ore stage (S1) and three types of the fine-grained pentagonal dodecahedron, disseminated pyrite (Py2-1, Py2-2, and Py2-3) with zoning textures in the main ore stage (S2). Py1 is relatively depleted in most metals but enriched in Co and Bi compared with other types of pyrite in S2. On the other hand, both Py2-1 and Py2-3 contain relatively high contents of As, Au, and other metals, whereas Py2-2 contains highest Au, As, Ag, Cu, Sb, Te, Tl, and Pb. Oscillatory zoning in Py2-1 resulted from repeated local fluid phase separation at the near-surface of pyrite crystal due to sharp fluid pressure fluctuation. The Au and As-rich Py2-2 was probably formed under both extrinsic fluctuations in fluid pressure and composition and intrinsic local crystal-fluid interface kinetic effects (e.g., diffusion-limited self-organization, surface electrochemistry-driven adsorption). Crystallization of Py2-1 and Py2-2 has exhausted the metals in the residual fluids, wherein the trace element-poor Py2-3 crystallized and locally replaced Py2-2 through a dissolution-reprecipitation process. Our new data and previous results suggest the ore-forming fluids were likely initial produced by degassing of the concealed pluton, and the metals were sourced from both the crust (e.g., the Taihua complex and Xiong’er Group) and the mantle. The negative δ34S values for pyrite in the S2 stage might result from both the isotopic fractionation between sulfide and sulfate minerals via oxidation of the ore-forming fluid and the input of biogenic sulfur.

Development and validation of a semi-analytical framework for droplet freezing with heterogeneous nucleation and non-linear interface kinetics

We present a novel, semi-analytical framework which accurately predicts every stage of droplet freezing. Supercooling degree of the freezing droplet is computed by coupling the 1-D transient heat conduction equation in spherical coordinates with a modified heterogeneous nucleation model. The coupling connects atomic-scale thermodynamic properties with bulk thermophysical properties and yields interesting insights into the freezing process. The study also develops a novel dendritic growth model for crystal propagation that takes into account the effects of non-linear interface kinetics and surface curvature. This non-equilibrium phase-change formulation during the recalescence stage is coupled with quasi-steady phase change approximation using perturbation series for equilibrium freezing stage to yield an accurate closed form solution of freezing dynamics. The temperature curves, nucleation rates, dendritic growth velocities and mass fraction evolution from the model are validated or verified with the available experimental or numerical data in the literature. The analytical framework developed is a reduced-order freezing model that is fast to compute and yields accurate results. The framework presented can be useful as a subgrid model for high-fidelity crystal growth and spray freezing simulations.

Phase-field simulations of dendritic morphologies in hot-dip galvanized Zn-Al coatings

The growth morphologies of dendrites in thin Zn-0.2 wt% Al coating layers are investigated as a function of the inclination axis and angle of the Zn basal plane with respect to the coating plane using three-dimensional (3D) phase-field simulations under realistic process conditions. In addition to the well-known growth direction families of 〈101¯0〉 and 〈0001〉, we incorporate a third preferred growth direction family into interface kinetic anisotropy based on the recent suggestion by Kim et al. [Metall. Mater. Trans. A 50 (2019), 3186–3200]. When this interface kinetic anisotropy is combined with the isotropic interface energy in the phase-field model, the 3D simulations realistically reproduce most of the morphological characteristics of the dendrites observed in experiments. These include the asymmetric morphologies about the inclination axis, morphological changes with the inclination angle, and angular variations between the primary aims. However, simulations using the experimental estimates of the interface energy anisotropy fail to reproduce characteristic morphologies, such as the four- and eight-fold dendrites, even when combined with strong interface kinetic effects. The present study establishes the existence of a third preferred growth direction family, which is close to the directions normal to the 12¯11planes, and the importance of the interface kinetic anisotropy over the interface energy anisotropy in the dendritic solidification of Zn-rich alloys.

Combined molecular dynamics and phase field simulation investigations of crystal-melt interfacial properties and dendritic solidification of highly undercooled titanium

The effects of kinetic and capillary anisotropies on crystal morphology and growth rate during solidification of titanium are studied using atomistically-informed phase field simulations. Molecular dynamics (MD) is employed to calculate the anisotropic kinetic coefficient and crystal-melt interface free energy using the free solidification and capillary methods. The phase field simulation results for solidification velocity and interface temperature are in quantitative good agreement with experimental and analytical data for undercoolings below 150 K. As the role of interface kinetic effects increases with undercooling the use of a modified phase field model allowed the extension of its quantitative prediction capability to higher undercoolings. In addition, the effect of MD calculated kinetic and capillary anisotropy parameters on dendrite shape and tip and solidification velocity was investigated.

On the Nonequilibrium Interface Kinetics of Rapid Coupled Eutectic Growth

Nonequilibrium interface kinetics (NEIK) is expected to play an important role in coupled growth of eutectic alloys, when solidification velocity is high and intermetallic compound or topologically complex phases form in the crystallized product. In order to quantitatively evaluate the effect of NEIK on the rapid coupled eutectic growth, in this work, two nonequilibrium interface kinetic effects, i.e., atom attachment and solute trapping at the solid–liquid interface, were incorporated into the analyses of the coupled eutectic growth under the rapid solidification condition. First, a coupled growth model incorporating the preceding two nonequilibrium kinetic effects was derived. On this basis, an expression of kinetic undercooling (∆T k), which is used to characterize the NEIK, was defined. The calculations based on the as-derived couple growth model show good agreement with the reported experimental results achieved in rapidly solidified eutectic Al-Sm alloys consisting of a solid solution phase (α-Al) and an intermetallic compound phase (Al11Sm3). In terms of the definition of ∆T k defined in this work, the role of NEIK in the coupled growth of the Al-Sm eutectic system was analyzed. The results show that with increasing the coupled growth velocity, ∆T k increases continuously, and its ratio to the total undercooling reaches 0.32 at the maximum growth velocity for coupled eutectic growth. Parametric analyses on two key alloy parameters that influence ∆T k, i.e., interface kinetic parameter (μ i ) and solute distribution coefficient (k e ), indicate that both μ i and k e influence the NEIK significantly and the decrease of either these two parameters enhances the NEIK effect.

Effects of anisotropic interface kinetics and surface tension on deep cellular crystal growth in directional solidification

In this paper, we study the effects of anisotropic interface kinetics and surface tension on deep cellular crystal growth in directional solidification. The following assumptions are made: the process of solidification is viewed as a two-dimensional problem; the minor species in this binary mixture system is considered as an impurity; the solute diffusion in the solid phase is negligible; the thermodynamic properties other than the diffusivities are the same for both solid and liquid phases; there is no convection in the system; the anisotropic interface kinetics and the anisotropic surface tension are a four-fold symmetry function each; neither the preferred directions of the anisotropic interface kinetics nor the anisotropic surface tensions are necessarily the same as their counterparts for the solid and liquid phases respectively; the angle between the preferred directions of the two anisotropies is 0. By using the matched asymptotic expansion method and the multiple variable expansion method, we obtain the diagram of interface morphology for a deep cellular crystal in directional solidification. The results show that there exists a discrete set of the steady-state solutions subject to the quantization condition (35). The quantization condition yields the eigenvalue ???106801-20170033???* as a function of parameter and other parameters of the system, which determines the interface morphology of the cell. The results also show the variation of the minimum eigenvalue ???106801-20170033???*(0) with parameter . It is seen that when the preferred directions of the two anisotropies are the same, i.e., 0 = 0, the minimum eigenvalue ???106801-20170033???*(0) reduces with the increase of anisotropic surface-tension coefficient 4 , increases with the augment of parameter , and is unrelated to anisotropic interface kinetic coefficient 4 in the low order; when the angle 0 0 /4, as the 0 increases, the minimum eigenvalue ???106801-20170033???*(0) increases; when the angle /4 0 /2, as the 0 increases, the minimum eigenvalue ???106801-20170033???*(0) decreases. In addition, the results show the composite solution for the interface shape function B described on (X, Y) plane. It is seen that both of the anisotropy and the angle 0 have a significant effect on the total length and the root of deep cellular crystal, however, have little influence on the other solid-liquid interface, such as the top of deep cellular crystal. When the angle 0 is 0, as anisotropic coefficient increases, the total length of the finger increases, the curvature of the interface near the root increases or the curvature radius decreases. It is found that the influence of the anisotropic surface-tension coefficient on interface morphology is more remarkable than that of the anisotropic interface kinetics coefficient. when the angle 0 0 /4, as the 0 increases, the total length of the finger decreases, the curvature of the interface near the root decreases or the curvature radius increases; when the angle /4 0 /2, as 0 increases, the total length of the finger increases, the curvature of the interface near the root increases or the curvature radius decreases.

Morphological instability of a solid sphere of dilute ternary alloy growing by diffusion from its melt

The diffusion-limited growth of an initially spherical particle of dilute ternary alloy in contact with its melt has been studied from a theoretical point of view and the effects of interface kinetics and multicomponent diffusion have been characterized on the development of a shape perturbation of the sphere. When both concentrations of the diffusing species are imposed in the far-field, the different radii related to the absolute and relative stability of the particle with respect to the development of spherical harmonics have been determined when a linear kinetics law is considered for the solid/liquid interface. The development of the shape fluctuations of the sphere has been also characterized when the flux of both species are set in the far-field.

Interface kinetics in phase-field models: Isothermal transformations in binary alloys and step dynamics in molecular-beam epitaxy

We present a unified description of interface kinetic effects in phase-field models for isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy. The phase-field equations of motion incorporate a kinetic cross-coupling between the phase field and the concentration field. This cross-coupling generalizes the phenomenology of kinetic effects and was omitted until recently in classical phase-field models. We derive general expressions (independent of the details of the phase-field model) for the kinetic coefficients within the corresponding macroscopic approach using a physically motivated reduction procedure. The latter is equivalent to the so-called thin-interface limit but is technically simpler. It involves the calculation of the effective dissipation that can be ascribed to the interface in the phase-field model. We discuss in detail the possibility of a nonpositive definite matrix of kinetic coefficients, i.e., a negative effective interface dissipation, although being in the range of stability of the underlying phase-field model. Numerically we study the step-bunching instability in molecular-beam-epitaxy due to the Ehrlich-Schwoebel effect, present in our model due to the cross-coupling. Using the reduction procedure we compare the results of the phase-field simulations with the analytical predictions of the macroscopic approach.

Computational analysis of lateral overgrowth of GaAs by liquid-phase epitaxy

Two-dimensional computational analysis of lateral overgrowth of GaAs by liquid-phase epitaxy has been carried out. The evolution of the growth interfaces is obtained by using growth velocity calculated from solute concentration field in the vicinity of the growth layer. Effects of interface kinetics and crystal surface tension (Gibbs–Thomson effect) were taken into account. The shapes of grown epilayers are in good agreement with experimental observations. The comparison of numerical results under different growth conditions demonstrates the importance of interface kinetics and Gibbs–Thomson effects on shape and aspect ratio of epitaxial laterally overgrown (ELO) layers.

Effects of interface kinetics and anisotropy on the stability of the growing crystal face and dissolution face during crystallization from solution under microgravity

The stability of the shapes of the growing crystal face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied. Effects of the interface kinetics and anisotropy of crystallization and dissolution on the stability are also studied. It is proved that the stable shapes of crystal growth face and dissolution face do exist, which are of suitably shaped curves with their upper parts inclined backward properly no matter whether the interface kinetics and the anisotropy are taken into account or not. The stable shapes of the growing crystal faces and dissolution faces are calculated for various cases. The interface kinetics will make the inclination degree of stable crystal growth face reduce and that of stable dissolution face reduce slightly. The anisotropy of crystallization and dissolution may make the inclination degree of stable-growing crystal face smaller or larger, and that of the stable dissolution face varies very slightly.

Hybrid liquid phase epitaxy processes forYBa2Cu3O7 film growth

A number of liquid phase epitaxy (LPE) related growth methods have been investigated.These hybrid-LPE processes enable high rate ‘liquid assisted’ growth of epitaxialYBa2Cu3O7 films without the many disadvantages of classical LPE. Growth occurs by diffusive transport ofY through a thin liquid flux layer. This layer may be pre-deposited onto the substrate byvarious means including vacuum and non-vacuum techniques, or deposited at the growthtemperature. The composition of the liquid layer is maintained during film growth by feedingYBa2Cu3O7, or the separate components, either from the vapour or by a powder route. Growth rates up to10 nm s−1 have been demonstrated.Deposition of c-axisoriented epitaxial YBa2Cu3O7 is reported on both seeded and non-seeded substrates; the process is tolerant of a high substrate mismatch.Films 1–2 µm thick with K and a critical current densityJc>2 MA cm−2 have been grown on a range of single crystal substrates as well as on buffered texturedmetallic tapes. The mechanism of nucleation and growth from a thin liquid layer isdescribed within the general theoretical framework of crystal growth. Particular features ofthe growth are the short time constant for equilibration of transients in the depositionconditions, the wide range of relative supersaturation spanned by the process, anddominance of interface kinetic effects compared to volume diffusion in the liquid flux.

Computationally efficient phase-field models with interface kinetics.

We present a phase-field model of solidification which allows efficient computations in the regime when interface kinetic effects dominate over capillary effects. The asymptotic analysis required to relate the parameters in the phase field with those of the original sharp-interface model is straightforward, and the resultant phase-field model can be used for a wide range of material parameters.

Growth of needle and plate shaped particles: theory for small supersaturations, maximum velocity hypothesis

A solution to the diffusion controlled growth of needle and plate shaped particles is presented as their shape approaches respectively a paraboloid of revolution or a parabolic cylinder, under small supersaturation values, when capillarity and interface kinetic effects are present. The solutions show that as supersaturation decreases, the growth rate and needle tip radius approach a common value regardless of interfacial kinetics effects as capillarity is the main factor that retards particle growth. Simple asymptotic expressions are thus obtained to predict the growth rate and tip radius at low supersaturations, assuming a maximum velocity hypothesis. These represent the circumstances during solid state precipitation reactions which lead to secondary hardening in steels.

Nonequilibrium analysis of high gradient absolute stability during unidirectional solidification

Further analysis of the M-S interface stability theory predicts a new phenomenon, the high gradient absolute stability (HGAS); that is, when temperature gradient exceeds a critical value, the solidification interface becomes absolutely stable no matter how large solidification velocity is. The critical temperature gradient for HGAS is explicitly evaluated by incorporating mathematical deduction with numerical calculation. The critical conditions for HGAS of several typical alloys are modified by inserting a velocity-dependent partition coefficient and a velocity-dependent slope of the “kinetic liquidus” into the HGAS analysis. These nonequilibrium interface kinetic effects decrease the predicted critical temperature gradient for HGAS.

Monte Carlo studies of the interdependence of crystal growth morphology, surface kinetics and bulk transport

The evolution of crystal growth morphologies was explored using a Monte Carlo model. The model combines diffusive transport in the nutrient with thermally activated and local configuration-dependent steps for attachment, surface diffusion and detachment. The solid pair interaction energy, ϕ, temperature, T, and chemical potential difference between nutrient and surface, Δµ, were used as input parameters. For a given set of simulation parameters, we found that, due to the competing effects of bulk diffusion and interface kinetics, there is a critical size beyond which a crystal cannot retain its macroscopically faceted shape. This critical size scales linearly with the mean free path in the nutrient, a. The stabilization of the growth shape by anisotropies in the kinetics is reduced through thermal and kinetic roughening. Thus, further increases either in T or Δµ, and/or decreases in ϕ, cause successive transitions from faceted to compact dendritic and side-branched dendritic morphologies. On interfaces with emerging screw dislocations the spiral growth mechanism dominates at low Δµ. When a is comparable to the lattice constant, the combination of bulk and surface diffusion reduces the terrace width near the centre of a growth spiral. At elevated T and Δµ, 2D nucleation-controlled growth can dominate in the more readily supplied corner and edge regions of a facet, while spiral growth prevails in its centre.

Solidification of highly undercooled Fe-P alloys

Rapid solidification behavior of highly undercooled iron-phosphorus alloys was investigated by using a high-speed optical temperature measurement system. The experimental results on solidification rate as a function of bulk undercooling agree well with a model which includes a treatment of nonequilibrium effects during the solidification process. The model is based on an earlier analysis by Boettinger, Coriell, and Trivedi[81] (BCT) and employs temperature-dependent values of equilibrium liquidus slope, equilibrium solute distribution coefficient, and solute interdiffusion coefficient. Values of the kinetic parameters,a0 andV0, in the analysis which best fit the experimental results are 5 x 10-10 m and 600 m/s, respectively. Comparison of experimental results and theory suggests that a transition from local equilibrium to nonequilibrium solidification takes place with increasing undercooling and that interface kinetic effects become predominant at higher undercooling (or growth velocity).

Effect of nonequilibrium interface kinetics on cellular breakdown of planar interfaces during rapid solidification of Si-Sn

During rapid solidification, nonequilibrium interface kinetics alter the predictions of the Mullins-Sekerka theory for the stability of a planar interface against cellular breakdown. The velocity-dependence of the partition coefficient and of the Sn concentration at the onset of cellular breakdown have been measured during pulsed laser melting of Si-Sn alloys. The Mullins-Sekerka theory is modified by inserting a velocity-dependent partition coefficient and a velocity-dependent slope of the “kinetic liquids”, both of which are extracted from the continuous growth model for interface kinetics. These nonequilibrium interface kinetic effects increase the predicted critical concentration for cellular breakdown by two orders of magnitude for Sn in Si, and account fairly well for the experimental results.

The effects of interface attachment kinetics on solidification interface morphologies

The presence of an interface kinetic effect significantly influences microstructures that form during the solidification of alloys. In order to quantitatively evaluate the effect of interface kinetics on microstructure formation, critical directional solidification studies have been designed in the pivalic acid-ethanol (PVA-Eth) system, in which significant anisotropies in interface properties are present. The interface kinetic effect is studied in high-purity PVA by measuring the interface temperature of a planar interface which is growing under steady-state conditions. In a binary system of PV A-Eth, the interface kinetic effect is characterized by examining the variations in dendritic microstructural scales with velocity and composition and by examining the planar interface instability condition. The variations in the dendrite tip radius,R, the primary spacing, and the secondary arm spacing near the dendrite tip with velocity,V, as well as with composition, have been characterized. Experimental results at a given composition showedVR2. to be constant, and those at constant velocity showed δTsR2 to be constant, where δTs is the product of the liquidus slope and the concentration difference at the dendrite tip. In order to characterize the system properly, additional experiments were carried out to measure the liquidus temperatures of the system. These experimental results are then compared with the theoretical models of planar interface instability and of dendritic growth to evaluate the role of interface kinetics on microstructure formation. Based on the theoretical models for planar and dendritic growth in an anisotropic system, the results on the interface kinetic effects are analyzed to give an insight into the possible phenomena which contribute to the complex kinetic behavior that is observed experimentally in the PVA system.

Initial conditions implied by [formula omitted] solidification of a sphere with capillarity and interfacial kinetics

We explore the initial conditions implied by t 1 2 growth ofa spherical crystal solidifying from a pure, undercooled melt, including the effects of both capillarity and interface kinetics, and relate our findings to initial conditions that would be expected on the basis of classical nucleation theory. For crystal sizes near the nucleation radius, the calculated temperature profiles show a cold region ahead of the advancing interface that is even more undercooled than the undercooled bath. This cold region acts as a local heat sink that compensates for the reduced growth speed that would otherwise result from capillarity and kinetics, leading to precisely the same t 1 2 growth law that would have been obtained had both capillarity and kinetics been neglected. We submit that this t 1 2 solution should not be taken seriously in the context of the classical theory of nucleation of a crystal from an isothermal melt.

Anisotropic interface kinetics and tilted cells in unidirectional solidification

We derive a nonlinear evolution equation governing the cellular structure of a binary alloy having small segregation coefficient, including the effects of anisotropic interface kinetics. This equation, applicable to long-wave instabilities of a planar interface, describes the spatial pattern of the growing disturbances. The presence of anisotropy causes the cells to grow at an angle to the normal of the planar front. This transition to a cellular morphology is shown to be a subcritical instability.