Three-dimensional dendrite-tip morphology at low undercooling (original) (raw)

Three-dimensional dendrite-tip morphology

Physical Review E, 1995

We investigated the morphology of dendrite tips through the growth and measurement of pure succinonitrile dendrites at a fixed supercooling of 0.46 K. Many current theories of dendritic growth rely on the assumption that the tip region can be approximated by a paraboloid of revolution. The evidence presented here suggests that this assumption becomes invalid in regions only slightly removed from the tip and well before the appearance of side branches. Characterization of dendrites using a fourth-order polynomial, with fourfold rotational symmetry, provides a useful description of the dendrite extending to regions up to eight radii from the tip. This has also enabled a more precise determination of the shape and size of a dendrite tip than was heretofore possible. This includes information about the anisotropy of the interface morphology.

Study of the twinned dendrite tip shape II: Experimental assessment

Acta Materialia, 2011

The favorable growth kinetics of twinned dendrites can be explained by their complex morphology, multiple side branching mechanisms, growth undercooling and tip morphology. Three models were proposed for the twinned dendrite tip shape: (i) a grooved tip [1] satisfying the Smith condition at the triple line; (ii) a doublon [2], i.e. a double-tip dendrite that grows with a narrow and deep liquid channel in its center; and (iii) a pointed (or edgy) tip [3], with consideration of the solid-liquid interfacial energy anisotropy. In the first part of this work, phase field simulations of half a twinned dendrite with an appropriate boundary condition to reproduce the Smith condition supported the doublon conjecture, with a narrow liquid channel ending its solidification with the formation of small liquid droplets. In this part, experimental observations of twinned dendrite tips reveal the presence of a small, but well-defined, groove, thus definitely eliminating the edged tip hypothesis. Focused ion beam nanotomography and energy-dispersive spectroscopy chemical analysis in a transmission electron microscope reveal the existence of a positive solute gradient in a region localized within 2 lm around the twin plane. In Al-Zn specimens, small particles aligned within the twin plane further support the doublon conjecture and the predicted formation of small liquid droplets below the doublon root.

Crystal anisotropy and dendritic crystal growth

Acta Crystallographica Section A Foundations of Crystallography, 1992

Observation of selected low-symmetry crystals growing in the dendritic morphology indicates the importance of crystal structure in determining not only the sidebranch spacing but also the very existence of sidebranching. This evidence provides a perspective which supplements the view of sidebranching as being governed by the continuum dynamics of a moving solid-liquid interface. Direct evidence is presented for a parabolic diffusion field surrounding growing dendrite tips. The existence of this field is consistent with the theoretical analysis which leads to the needlecrystal model of dendritic growth.

The shape of dendritic tips: a test of theory with computations and experiments

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2021

This article is devoted to the study of the tip shape of dendritic crystals grown from a supercooled liquid. The recently developed theory (Alexandrov & Galenko 2020Phil. Trans. R. Soc. A378, 20190243. (doi:10.1098/rsta.2019.0243)), which defines the shape function of dendrites, was tested against computational simulations and experimental data. For a detailed comparison, we performed calculations using two computational methods (phase-field and enthalpy-based methods), and also made a comparison with experimental data from various research groups. As a result, it is shown that the recently found shape function describes the tip region of dendritic crystals (at the crystal vertex and some distance from it) well.This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Theoretical modeling of crystalline symmetry order with dendritic morphology

The European Physical Journal Special Topics, 2020

The stable growth of a crystal with dendritic morphology with n-fold symmetry is modeled. Using the linear stability analysis and solvability theory, a selection criterion for thermally and solutally controlled growth of the dendrite is derived. A complete set of nonlinear equations consisting of the selection criterion and an undercooling balance (which determines the implicit dependencies of the dendrite tip velocity and tip diameter on the total undercooling) is formulated. The growth kinetics of crystals having different lattice symmetry is analyzed. The model predictions are compared with phase field modeling data on ice dendrites grown from pure undercooled water.

Heat diffusion anisotropy in dendritic growth

Journal of Crystal Growth, 1998

An anisotropic heat diffusion coefficient is introduced in order to study some interfacial growth phenomena. This anisotropy has been incorporated in a phase field model which has been studied numerically to reproduce some fundamental solidification situations (needle crystal growth) as well as the dynamics of a nematic-smectic-B interface. As a general result, we find that dendrites grow faster in the lower heat diffusion direction. Simulation results are compared with experiments with remarkable qualitative agreement.

Selected mode for rapidly growing needle-like dendrite controlled by heat and mass transport

Acta Materialia, 2017

The boundary integral method is developed for fast anisotropic interfaces. A general integro-differential equation for curved interfaces controlled by heat and mass transport is derived and applied to the problem of rapid dendritic growth. A selection criterion for the steady-state mode of growing parabolic interfaces is obtained and, in common solution with the undercooling balance, it is compared with experimental data on rapid dendritic solidification of deeply supercooled liquid droplets. In this comparison, transitions from solute diffusion-limited to thermo-solutal regime and, finally, to pure thermally controlled regime of the anisotropic dendrite are discussed and revealed. Limiting cases of known selection criteria for anisotropic dendrites growing at small and high growth P eclet numbers are provided.

Computations of Dendrites in 3-D and Comparison with Microgravity Experiments

2003

The phase field model is used to compute numerically the temporal evolution of the interface for solidification of a single needle crystal of succinonitrile (SCN) in a three dimensional cylindrical domain with conditions satisfying microgravity experiments. The numerical results for the tip velocity are (i) consistent with the experiments, (ii) compatible with the experimental conclusion that tip velocity does not increase for larger anisotropy (e.g., for pivalic acid), (iii) different for 3D versus 2D by a factor of approximately 1.76, (iv) strongly dependent on physical value of the kinetic coefficient in the model. Also, as indicated by theory and the laboratory experiments, the results obtained for single needle crystal show that the growth velocity approaches a constant value in large time.

Maximal curvature and crystal orientation on directionally solidified dendrites

Physical Review E, 2010

We experimentally address the locations of maximal curvature on crystalline cellular or dendritic interfaces that directionally grow in a thin sample of a transparent material. Local curvatures are determined on the whole dendrite tips by considering the intersection of nearby normals. It is found that, at the location of the curvature maximum, the interface normal points toward a particular direction solely set by the crystal lattice and equal in practice to the dendrite growth direction at large pulling velocity. This property is independent of the growth conditions ͑thermal gradient, velocity, dendrite spacing, and crystal orientation͒. It enables crystal orientations to be recovered from dendrite shapes and provides a bridge to understand the implications of anisotropy on the forms and orientations of directionally solidified dendrites.