Shape parameter for a non-axisymmetric isothermal dendrite

Cover of: Shape parameter for a non-axisymmetric isothermal dendrite |

Published by U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology in Gaithersburg, MD .

Written in English

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Subjects:

  • Russian-American Enterprise Shape -- Mathematical models,
  • Dendritic crystals -- Mathematical models,
  • Crystal growth -- Mathematical models,
  • Supercooled liquids -- Mathematical models

Edition Notes

Book details

StatementG.B. McFadden, S.R. Coriell, R.F. Sekerka
SeriesNISTIR -- 6347
ContributionsCoriell, S. R, Sekerka, R. F., National Institute of Standards and Technology (U.S.)
The Physical Object
FormatMicroform
Pagination7 p.
ID Numbers
Open LibraryOL13626233M
OCLC/WorldCa43429730

Download Shape parameter for a non-axisymmetric isothermal dendrite

These solutions provide self-consistent corrections through second order in a shape parameter ε to the Peclet number -- supercooling relation of the Ivantsov solution.

The parameter ε is proportional to the amplitude of the four-fold correction to the dendrite shape, as Author: Geoffrey B.

McFadden, Sam R. Coriell, R F. Sekerka. shape parameter non-axisymmetric isothermal dendrite peclet number parameter ffl cubic material growth direction four-fold axial symmetry dendrite shape dendritic growth good agreement form fl second order shape parameter ffl value ffl equilibrium shape ivantsov solution previous work four-fold correction ffl gamma0 ivantsov paraboloid.

Get this from a library. Shape parameter for a non-axisymmetric isothermal dendrite. [Geoffrey B McFadden; S R Coriell; R F Sekerka; National Institute of Standards and Technology (U.S.)]. Shape Parameter for a Non-Axisymmetric Isothermal Dendrite Article (PDF Available)   October   with  13 Reads  How we measure 'reads' A 'read' is.

Shape Parameter for a Non-Axisymmetric Isothermal Dendrite. By S. R These solutions provide self-consistent corrections through second order in a shape parameter e to the Peclet number-supercooling relation of the Ivantsov solution.

The parameter e is proportional to the amplitude of the four-fold correction to the dendrite shape, as. Shape Parameter for a Non-Axisymmetric Isothermal Dendrite.

By Non-axisymmetric Isothermal Dendrite, G.B. McFadden, S. Coriell and R. Sekerka. Abstract. In previous work, we found approximate solutions for paraboloids having perturbations with four-fold axial symmetry in order to model dendritic growth in cubic materials.

These solutions. 8. Discussion. We have obtained approximate solutions for dendrite shapes having three- and four-fold sinusoidal axial anisotropies of amplitude of order shapes lead to corrections of order ε 2 to the Ivantsov relationship between the Peclet number P and the Stefan number second order in ε, these solutions satisfy the flux condition at the surface of an assumed isothermal dendrite.

Analytic solution for a non-axisymmetric isothermal dendrite - Transport and Stability These solutions provide self-consistent corrections through second order in a shape parameter ε to the. The parameter ε is proportional to the amplitude of the four-fold correction to the dendrite shape, as measured from the Ivantsov paraboloid of revolution.

The equilibrium shape for anisotropic surface free energy to second order in the anisotropy is calculated. We investigate the three-dimensional morphology of the dendrite tip using the phase-field method. We find that, for low undercoolings, this morphology is ostensibly independent of anisotropy strength except for a localized shape distortion near the tip that only affects the value of the tip radius ρ (which is crudely approximated by ρ≈(1−α)ρIv where ρIv is the Ivantsov tip radius of.

Yet within the widely quoted model [J. Lipton, W. Shape parameter for a non-axisymmetric isothermal dendrite book and R. Trivedi, Acta Metall. 35, ()] for the calculation of dendritic growth velocities the kinetic and GibbsThomson undercoolings evaluated at the dendrite tip are assumed to apply equally over the whole dendrite surface, approximating the non‐isothermal dendrite as an isothermal.

The name dendrite derives from the treelike shape of the deposit, which can range from nearly linear and pointed (needle-like) to highly branched (bush-like).

Past work has primarily considered the propagation rate and morphology of dendrites. 5 Most early experiments rely on microscopy, but qualitative pictures resulting from computer.

where h is the number of handles, g is the genus and N is the number of fragments. The experimental results on fragmentation and coalescence under isothermal conditions are given in [].In this case, the number of handles per volume was seen to be an order of magnitude larger than the number of fragments per volume, indicating that the secondary Sn-rich dendrite arms preferentially coarsen by.

Stationary non-isothermal growth of a needle-like crystal is considered. When the undercooling parameter is very small, the dendrite will always be slender. Hence slender body theory is applicable. We obtain a self consistent uniformly valid asymptotic solution to the problems.

Isothermal coordinates on surfaces. Gauss () proved the existence of isothermal coordinates on an arbitrary surface with a real analytic metric, following results of Lagrange () on surfaces of revolution. Results for Hölder continuous metrics were obtained by Korn () and Lichtenstein ().Later accounts were given by Morrey (), Ahlfors ()), Bers () and Chern ().

The parameter e is proportional to the amplitude of the four-fold cor- rection to the dendrite shape, as measured from the Ivantsov paraboloid of revolution. Abstract: Coupling the force flow field with the phase field model for the isothermal growth of dendrite, Sola algorithm is used to calculate the flow speed and pressure of liquid metal, Using double grid numerical method to reduce the calculation amount of computer simulation, The space factor and time factor are introduced to improve the accuracy of double grid numerical calculation, Taking.

Axisymmetric drop-shape analysis-no apex (ADSA-NA) is a recent drop-shape method that allows the simultaneous measurement of contact angles and surface tensions of drop configurations without an apex (i.e., a sessile drop with a capillary protruding into the drop).

Although ADSA-NA significantly enhanced the accuracy of contact angle and surface tension measurements compared to that of. An experimental isothermal profile is applied to the solidification process of the experimental alloy to promote an isothermal coarsening process of the primary austenite dendrite network during solid and liquid coexistence.

Through interrupted solidification experiments, the primary austenite is preserved and observed at room temperature. Thermal Parameters: Anisotropic (U ij) Six parameters are used to describe anisotropic thermal motion.

They are diagonal and off diagonal terms of a three-by-three matrix. An isotropic ellipsoid would have all off-diagonal terms equal to zero, and all diagonal terms are the same.

The first attempt to find a shape of the steady-state dendrite growing in the undercooled melt was made by Ivantsov [11,12] (see also). He found the shape in the form of a parabolic crystal in the two-dimensional case and of a symmetric paraboloidal crystal in the three-dimensional case.

The present work derives closed form expressions for the drift and the migration velocity where the capillary stresses can be non-axisymmetric and along the axial or transverse direction. This would enable one to design parameter combinations to control the droplet migration for possible use in various applications.

K/min was imposed in the arc-shape molten pool. Figure 3(a) and Figure 3(d) show the simulated evolution of multi-dendrites growth. It is notable that all the dendrites grow along their crystallographic orientations at the beginning of solidification, and the primary trunks grow fast and the secondary dendrite arms begin emitting from the unstable solid/liquid interface of the primary trunks.

exact solution of the non-isothermal flow between finite coaxial parallel plates exist. Consequently, approximate techniques have been used to reduce the equations to more tractable forms. For example, in [2] Bird and Turian as-sumed a velocity profile of the form v h = rg(z), which satisfies the momentum equation only if the flow is.

The results show that the impact capacity and optimum value range of the process parameters vary in different indices, and that, to achieve the comprehensive optimum effect of a small forming force, high product quality, and high forming efficiency, the optimal process parameter combination is the up-beating mode, a spindle rotation speed of.

In general, the isothermal cross-section of a dendrite is initiated at the very first stage of solidification by the use of a four-fold shape function (table 3).

During further solidification, the morphology of dendrites is ruled by diffusion and element distribution (diffusion-limited growth). Otherwise, you might end up with surfaces like the plane, which cannot be put into global isothermal co-ordinates with domain the disc (although of course it admits local isothermal co-ordinates).

$\endgroup$ – macbeth Mar 22 '11 at The measurements include the steady dendrite tip velocity and radius, the non- axisymmetric amplitude coef“cient of the “ns near the tip, and the envelope width, projection area, and contour length of the sidebranch structure far from the tip.

The velocities of the [] dendrites are always equal to those by welding, regardless of the weld pool shape for the ()‖[] orientations (Rappaz et al.,), and average dendrite tip velocity in [] and [] is higher than that of the [] orientation along the rear part of the solid/liquid interface.

The average dendrite tip. The distribution of the order parameter in the bulk phases is Gaussian centered at μ with standard deviation σ. The definition of order parameter in the phase-field method is as follows: ϕ = 0 if q 6 q 6 b: = μ s + 2σ s and ϕ = (q 6 q 6 − a)/(b − a) otherwise.

Isothermal Titration Calorimetry: Thermodynamic Analysis of the Binding Thermograms of Molecular Recognition Events by Using Equilibrium Models, Applications of Calorimetry in a Wide Context - Differential Scanning Calorimetry, Isothermal Titration Calorimetry and Microcalorimetry, Amal Ali Elkordy, IntechOpen, DOI: / Results.

The BMG/dendrite composite has a composition of Zr Ti Nb Cu Ni Be in atomic percent (at. %) prepared by arc-melting a mixture of Zr, Ti, Nb, Cu, Ni, and Be with purity higher than % (weight percent) under an argon atmosphere This BMGMC system is known for its good ductility A dog-bone-shape specimen was prepared for the in-situ compression.

Close Drawer Menu Close Drawer Menu Menu. Home; Journals. AIAA Journal; Journal of Aerospace Information Systems; Journal of Air Transportation; Journal of Aircraft; Journal of. Isothermal parameters A Review of Complex Analysis. Let C be the complex plane. A C 1-function 7 f: C 3 D 2 z 7.

w = f (z) 2 C de ned on a domain D is said to be holomorphic if the derivative f 0(z):= lim h. 0 f (z + h) f (z) h exists for all z 2 D. Fact (The Cauchy-Riemann equation). A function f: C 3 D. C is holomorphic if and.

Dendrites The shape of the 3-D dendrite tip w as under considerable debate. 16Ð19 G.P. Ivantsov calculated analytically under the assumption of an isothermal interf ace, without anisotrop y and GibbsÐThom-son effect, that a possible steady-state solution of the go verning equations is a.

Intermediate shapes in closed-die forging by the backward deformation optimization method (BDOM) Journal of Materials Engineering and Performance, Vol.

3, No. 4 Design of optimal process parameters for non-isothermal forging. We investigate the three-dimensional morphology of the dendrite tip using the phase-field method. We find that, for low undercoolings, this morphology is ostensibly independent of anisotropy strength except for a localized shape distortion near the tip that only affects the value of the tip radius {rho} [which is crudely approximated by {rho}{approx_equal}(1-{alpha}){rho}{sub Iv} where {rho.

Isothermal titration calorimetry (ITC) is a physical technique used to determine the thermodynamic parameters of interactions in solution. It is most often used to study the binding of small molecules (such as medicinal compounds) to larger macromolecules (proteins, DNA etc.). It consists of two cells which are enclosed in an adiabatic jacket.

The compounds to be studied are placed in the. We find distinct regions of the parameter space associated with 〈 〉 and 〈 〉 dendrites, separated by a region where hyperbranched dendrites are observed. In simulations of directional solidification, we find similar behavior at the extrema, but in this case, the anisotropy parameters corresponding to the hyperbranched Title: managing director.

Measurements are carried out for dendrite tip growth of succinonitrile-acetone alloys solidifying freely in an undercooled current experimental investigation is conducted using the equiaxed dendritic solidification experiment (EDSE).

This setup allows for precise measurements of the dendrite tip velocity, radius and shape for a range. However, non-axisymmetric shapes are relevant both at the onset of the buckling instabil22 and for heavily deflated thin shells that undergo a secondary buckling transition. 13,30–33 Here, we aim for a classification of the transition from the spherical to the axisymmetric buckled shape under osmotic pressure, under mechanical pressure.A model for dendrite growths in polycrystalline Si films formed during laser/plasma deposition with a silane discharge and a pulsed KrF laser has been developed.

The model assumes a thin (less than 10 nm) amorphous silicon (a-Si) film is deposited on a substrate prior to phase transformation due to.This book highlights some recent advances in interfacial research in the fields of fluid mechanics and materials science at the beginning of the twenty-first century.

It is an extension of the presentations made during the conference “Interfaces for the 21st Century,” held on .

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