Anisotropy Of Interfacial Energy Research Articles

The degenerate and non-degenerate Stefan problem with inhomogeneous and anisotropic Gibbs–Thomson law

The Stefan problem is coupled with a spatially inhomogeneous and anisotropic Gibbs–Thomson condition at the phase boundary. We show the long-time existence of weak solutions for the non-degenerate Stefan problem with a spatially inhomogeneous and anisotropic Gibbs–Thomson law and a conditional existence result for the corresponding degenerate Stefan problem. To this end, approximate solutions are constructed by means of variational problems for energy functionals with spatially inhomogeneous and anisotropic interfacial energy. By passing to the limit, we establish solutions of the Stefan problem with a spatially inhomogeneous and anisotropic Gibbs–Thomson law in a weak generalisedBV-formulation.

Noise Mechanisms in Small Grain Size Perpendicular Thin Film Media

In this paper, we present a set of systematic experimental investigations on possible noise mechanisms for current perpendicular thin film media of small grain sizes. In particular, we focus on intergranular exchange coupling and grain boundary surface anisotropy in the granular layer of the present continuous-granular-composite film structure. Micromagnetic modeling studies are conducted to study the impact of the observed experimental phenomenon. Modeled experiments show that significant intergranular exchange coupling may occur when oxide grain boundary thickness becomes less than 1 nm. If the grain boundary thickness has significant distribution below this critical value, the exponential dependence of the coupling strength on the oxide thickness would yield significant degradation of the medium signal-to-noise ratio. Carefully designed experiments have also been conducted to study possible grain boundary interfacial anisotropy. Co/Cr, CoPt/Cr, Co/SiO2, Co/Cr2O3, and Co/TiO 2 interfaces are investigated and the corresponding interfacial anisotropy strengths are quantitatively measured. Although Co/SiO2 interfacial anisotropy appears to be the weakest among them, the measured interfacial anisotropy energy strengths for all of them are significant fractions of the crystalline perpendicular anisotropy of the grains at present grain sizes. Finally, we investigated the impact of stacking faults in hcp Co-alloy grains. It is found that when the anisotropy strength of a small segment of a grain substantially reduces due to the existence of stacking faults, it will yield a switching field reduction disproportional to the volume ratio of the segment.

A cellular automaton model for the solidification of a pure substance

An improved cellular automaton model for describing the evolution of solidification morphology of a pure substance is presented. The mesh-induced anisotropy was investigated for the traditional capture rules such as Von Neumann’s and Moore’s capture rules. A random zigzag capture rule was developed, which can greatly reduce the mesh-induced anisotropy. The method for the calculation of solid/liquid (SL) interface curvature was also improved by using a bilinear interpolation method, which increased the accuracy of the calculation of the SL interface curvature. Based on these improvements, the effect of interfacial energy anisotropy on the dendritic growth behavior was analyzed.

An inhomogeneous, anisotropic, elastically modified Gibbs­Thomson law as singular limit of a diffuse interface model

AbstractWe consider the sharp interface limit of a diffuse phase‐field model with prescribed total mass taking into account a spatially inhomogeneous, anisotropic interfacial energy and an elastic energy. The main aim is to establish a weak formulation of an inhomogeneous, anisotropic, elastically modified Gibbs‐Thomson law in the sharp interface limit. To this end we pass to the limit in the weak formulation of the Euler‐Lagrange equation of the diffuse phase‐field energy. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A New Algorithm of Phase Field Approach to Polycrystalline Dendritic Solidification in Two and Three Dimensions

A new algorithm of phase field model is developed to simulate polycrystalline dendritic solidification growth in undercooled melts. The algorithm adopts a single phase field order parameter model incorporated with the anisotropy of solid-liquid interfacial energy and mobility. The model validation is performed by comparing the simulations with the theory analytical results and experimental information for both single and multi-grain dendritic growth, which demonstrates the quantitative capabilities of the proposed algorithm.

A Cellular Automaton Model with the Lower Mesh-Induced Anisotropy for Dendritic Solidification of Pure Substance

A modified cellular automaton model for describing the dendritic solidification of pure substance was developed. Instead of using the high mesh-induced anisotropy capture rules, such as Von Neumann’s and Moore’s method, a new capture rule---random zigzag method was developed, which greatly reduced the mesh-induced anisotropy in crystallographic orientation. The calculation method for the solid/liquid interface curvature was also improved. The effect of interfacial energy anisotropy on the dendritic growth behavior was analyzed.

Tailoring perpendicular magnetic anisotropy in ultrathin Co/Pt multilayers coupled to NiO

The nanomagnetism of ultrathin Co/Pt multilayer films is set largely by the microstructure and composition of the interface. To examine these finite-size effects on the Co/Pt magnetism, we have made different Co thickness multilayer films using an ion-beam deposition method with controlled ion energies via an End-Hall voltage VEH, and deposited a layer of NiO to examine the nature of the magnetic anisotropy by way of studying the in-plane and perpendicular magnetism. Examining different Co/Pt multilayers made using different VEH ion energies, we have ascertained that 1.2 nm of Co is the minimum thickness required to establish perpendicular magnetic anisotropy PMA and that no intermixing of Co and Pt at their interface is necessary for PMA to occur. First-principles calculations, consistent with the analysis of electron-energy-loss spectrometry with near atomic resolution, indicate that PMA is due to hybridization of Co and Pt at the interface which results in a perpendicular magnetization axis being set in the Co layer due to a significant lowering of the interfacial anisotropy energy. These results point toward an interesting way to tune PMA in ultrathin Co/Pt multilayers.

Mixed-phase solidification of thin Si films on SiO 2

Mixed-phase solidification (MPS) is a new beam-induced solidification method that can produce large-grained and highly (1 0 0)-surface textured polycrystalline Si films on SiO 2. The grains resulting from this mixed-phase solidification (MPS) method, which was conceived based on a well-known phenomenon of coexisting solid–liquid regions in radiatively melted Si films, are found to be essentially devoid of various intragrain defects that always plague, and subsequently degrade the utility of large-grained Si films previously obtained using other crystallization techniques. It is experimentally shown that multiple exposures are required in order to generate such a polycrystalline microstructure from an initial amorphous precursor. The observed trends are conceptually explained in terms of the melt being initiated primarily at grain boundaries in polycrystalline films, and melting and solidification subsequently proceeding laterally at interface-location specific rates as determined by the local thermodynamic factors, which include the anisotropic surface and interfacial energies of the grains, and the unusual local thermal profile—all transpiring within a near-equilibrium but nonisothermal and dynamic environment that needs to address the thermal and stability requirements associated with the coexisting solid–liquid regions.

Phase-Field Simulations of Dendritic Orientation Selection in Mg-Alloys with Hexagonal Anisotropy

A special feature of Mg solidification is the anisotropy of the hexagonal closed packed lattice, which under directional growth conditions causes a strong crystallographic texture. Although this primary growth texture is in technical processes masked by subsequent solid state processes, its understanding can be helpful for efficient microstructure optimization. The aim of the present work is to study the fundamental orientation selection mechanisms by numerical simulation. For this pur-pose, a phase-field model has been extended to allow for complex 3D anisotropic interfacial ener-gies and interfacial mobilities, calibrated by data from molecular dynamics studies. The model is first applied in 3D to Mg-6%Al, revealing two major stages of texture formation. Directly after nuc-leation, all grains with basal plane parallel to the gradient direction are selected. During further competitive growth, grains with <1120> closely aligned to the temperature gradient commonly pre-vail, but process dependent also other orientations of the basal plane (between <1120> and <1010>) may coexist. The latter phenomenon is investigated in detail in 2D for the ternary alloy AZ31.

Phase-Field Simulation of Three-Dimensional Dendritic Growth

Based on a thin interface limit 3D phase-field model by coupled the anisotropy of interfacial energy and self-designed AADCR to improve on the computational methods for solving phase-field, 3D dendritic growth in pure undercooled melt is implemented successfully. The simulation authentically recreated the 3D dendritic morphological fromation, and receives the dendritic growth rule being consistent with crystallization mechanism. An example indicates that AADCR can decreased 70% computational time compared with not using algorithms for a 3D domain of size 300×300×300 grids, at the same time, the accelerated algorithms’ computed precision is higher and the redundancy is small, therefore, the accelerated method is really an effective method.

The influence of solid–liquid interfacial energy anisotropy on equilibrium shapes, nucleation, triple lines and growth morphologies

The anisotropy of the solid–liquid interfacial energy plays a key role during the formation of as-solidified microstructures. Using the ξ-vector formalism of Cahn and Hoffman, this contribution presents the effect that anisotropy has on the equilibrium shapes of crystals and on surface tension equilibrium at triple lines. Consequences for heterogeneous nucleation of anisotropic crystals and for dendritic growth morphologies are detailed with specific examples related to Al–Zn and Zn–Al alloys.

The Effects of Structure Orientation on the Growth of Fe<SUB>2</SUB>B Boride by Multi-Phase-Field Simulation

A morphological evolution of the growth of Fe2B boride on steel substrate has been investigated using two dimensional (2D) multi-phase-field (MPF) simulations. In order to evaluate competitive growth between boride seeds during the coating process, variations on boride seed orientation have been implemented. In addition, in order to have anisotropy growth of boride, anisotropy of interfacial energy is considered on the evaluation of phase-field evolution. It was observed that boride seed with structure orientation of 90° shows a preferential growth as compared with the growth of boride seeds at other orientations. On the other hand, competitive growth between boride seeds at different crystal orientations can also be observed, where boride seeds approaching a preferential orientation angle grow faster and suppress the growth of boride seeds at the lower orientation angle. Both of these present observations agree with previous experimental observations that boride seeds tend to grow perpendicular to the substrate surface and the growth of boride seeds in this direction suppress growth in other directions. Additionally, it was observed that the preferential growth of boride is independent of the initial size of the boride seed.

Dendritic growth texture evolution in Mg-based alloys investigated by phase-field simulation

Under directional growth conditions, a strong crystallographic texture is observed in Mg-based alloys due to the anisotropy of the hcp-phase. The aim of the present work is to investigate the fundamental mechanisms of this growth texture evolution by microstructure simulations. For this purpose, a phase-field model has been extended to allow for complex 3D anisotropic interfacial energies and mobilities, calibrated by data from molecular dynamics studies. The model is first applied in 2D to AZ31 (Mg–3%Al–1%Zn). Bicrystal simulations are performed for a systematic study of grain interactions. Extended simulations are compared to experiments. Comprehensive texture evolution is investigated in 3D for Mg–6%Al. Texture is found to evolve mainly due to retarded growth in basal <0001> orientations. Grains with the fast growing <1120> orientation most closely aligned to the temperature gradient commonly prevail, but process dependent also other orientations of the basal plane (between <1120> and <1010>) may coexist.

Exsolution by spinodal decomposition I: Evolution equation for binary mineral solutions with anisotropic interfacial energy

Phase separation in a binary system that results from the uphill diffusion of chemical components is investigated theoretically. We reconsider the original spinodal decomposition model of Cahn and Hilliard taking into account possible intrinsic anisotropy of the underlying system. Specifically we address the effects of orientation dependent interfacial energy. Such anisotropy is of particular importance for mineral systems. The corresponding evolution equation is systematically derived. We show how the anisotropy affects the interfacial energy per unit area, the interface width, scaling laws, and the critical system size at which spinodal decomposition starts to develop. We further obtain numerical solutions and discuss coarsening dynamics for the case where the decomposition products have pronounced shape anisotropy.

Phase-field model study of the crystal morphological evolution of hcp metals

An expression for anisotropic interfacial energy of hexagonal close-packed metals has been formulated which is able to reproduce published data obtained using the modified embedded-atom method, covering the variation in interface energy as a function of orientation for a number of metals. The coefficients associated with the expression can be determined fully by measured or calculated interfacial energies of just three independent crystal planes. Three-dimensional phase-field model simulations using this representation of interfacial energy have been found to yield convincing crystal morphologies. The apparent rate of crystal growth as a function of orientation in the phase-field simulation agrees with predictions made by surface energy theory.

Microstructure and Microtexture Formation of AZ91D Magnesium Alloys Solidified in a Static Magnetic Field

In the present study, we solidified AZ91D magnesium alloys in a static magnetic field with a magnetic flux density up to 10 Tesla (T). Three different regions can be identified in a solidified alloy, according to their microtexture and microstructure; these regions are: (a) region (A), the central region with equiaxed dendrites, (b) region (B), the transitional region with directional dendrites grown from an unmelted region, and (c) region (C), the edge region with cellular dendrites grown from the substrate of the container. No detectable difference can be discerned with regard to the influence of the magnetic field on the microstructure in region (A). However, the microtexture evolution in the region shows a strong dependence on the magnetic field and the preferential orientation formation is briefly elucidated. Special attention is focused on the orientation development of the directional dendrites in region (B) as a function of the magnetic flux density B 0, when the electron backscatter diffraction (EBSD) technique is employed. It is shown that the directional dendrites exhibit a random orientation distribution at B 0 < 5 T, while they have a unique orientation at B 0 ≥ 5 T. Microstructure observation indicates that the crystallographic orientation selection completes at the interface of the melt/unmelted regions. A theoretical analysis reveals that the competition between the magnetization energy and the anisotropic interfacial energy difference of the crystals controls the crystallographic orientation selection. For the microstructure and microtexture in region (C), heterogeneous nucleation takes place from the polycrystalline Al2O3 substrate and thus enables a random crystallographic orientation distribution. The short growth interval may not be sufficient for the preferred growth direction to be selected near the chilling area; this applies to the cellular dendrites grown from the substrate at all levels of the magnetic field.

Effects of AlN layer thickness on magnetic anisotropy and transport phenomena of CoPt/AlN layered structure

The magnetic anisotropy was studied as a function of the AlN layer thickness in [AlN( x nm)/CoPt(2 nm)]5/AlN( x nm) layered structure ( x is AlN layer thickness, and 5 is the number of multilayer series). The multilayered film was deposited by a sputtering apparatus equipped with two pairs of facing targets. It was found that, in the range of AlN layer thickness below 30 nm, CoPt/AlN multilayers transform from an enhanced in-plane magnetic anisotropy to perpendicular magnetic anisotropy (PMA) through thermal annealing in vacuum, with an optimized AlN thickness of 10 nm for strong PMA. However, beyond this thickness range, the PMA did not occur, and thermal annealing only results in magnetic isotropy in both parallel and perpendicular directions. The related structure analysis revealed that smooth interface and good texture of CoPt (111) make positive contributions to interface anisotropy energy and magnetocrystalline anisotropy energy for producing PMA in CoPt/AlN layered structure. In addition, the transport phenomena were also studied by using a four-probe method.

Phase-field model study of the effect of interface anisotropy on the crystal morphological evolution of cubic metals

An expression is proposed for the anisotropy of interfacial energy of cubic metals, based on the symmetry of the crystal structure. The associated coefficients can be determined experimentally or assessed using computational methods. Calculations demonstrate an average relative error of <3% in comparison with the embedded-atom data for face-centred cubic metals. For body-centred-cubic metals, the errors are around 7% due to discrepancies at the {3 3 2} and {4 3 3} planes. The coefficients for the {1 0 0}, {1 1 0}, {1 1 1} and {2 1 0} planes are well behaved and can be used to simulate the consequences of interfacial anisotropy. The results have been applied in three-dimensional phase-field modelling of the evolution of crystal shapes, and the outcomes have been compared favourably with equilibrium shapes expected from Wulff’s theorem.

電析デンドライトのフェーズフィールド解析

Effect of the phase-boundary potential at the electrode-electrolyte interface and the anisotropy of interfacial energy on the morphology of the electrodeposits have been investigated by phase-field simulation. In equilibrium system, the change in the phase-boundary potential due to the interfacial curvature satisfies the Gibbs-Thomson effect. The stability analysis of the electrode-electrolyte interface reveals that the marginal wavelength is proportional to the inverse of the square root of the growth velocity of the interface. It is found that the linear relationship between the marginal wavelength and tip radius during electrodeposition satisfies the crystal growth theory confirmed by the dendrite growth in solidification process.

Numerical simulation of three-dimensional dendritic growth using phase-field method

Quantitative numerical simulation of three-dimensional dendritic growth in pure undercooled melt is carried out based on phase-field model of thin-interface limit and incorporating interfacial energy anisotropy which is solved by an accelerated algorithm of the dynamic computing regions, the dendritic growth is faithfully described. The dendritic tip is analyzed by cutaway view, indicating that the anisotropy of main branches’ section is not more obvious than that of main branches. The dendritic tip growth speed, tip radius, tip Peclet number as well as classic stability parameter σ* are simulated, compared with reported values under same condition,and they agree well with each other. Dendritic growth law that is in accordance with crystalline theroy is achieved, and it is proved that it is feasible and effective to simulate three-dimensional dendritic growth using phase-field method.