Orientation selection in dendritic evolution

Abstract

D endritic alloy microstructures are formed during a wide range of solidification processes from casting to welding. These microstructures result from a morphological instability of the solid-liquid interface that produces dendrites, which are highly hierarchical branched patterns with primary-, secondary-and higher-order branches. As alloy impurities segregate in the interdendritic liquid during solidification, the spatially inhomogeneous distribution of impurities in the completely solidified alloy is a direct footprint of the dendritic network that formed and coarsened during the solidification process. It also determines the formation and distribution of secondary phases, and thus has a profound influence on the properties of a wide range of technologically important structural materials, from light-weight aluminium alloys used in the automotive industry to nickel-based superalloys used for turbine blades. The study of dendritic growth 1,2 has also been of long-standing fundamental interest because of the ubiquity of branched structures exhibited by diverse interfacial pattern formation systems [3][4][5] .Major theoretical and computational advances over the past two decades have improved our fundamental understanding of dendrite growth, as well as new capabilities to simulate and predict dendritic microstructures on experimentally relevant length and timescales 6 and to elucidate new pattern formation mechanisms 7,8 that enlarge the scope of our understanding of these structures. The commonly accepted microscopic solvability theory of steadystate dendrite growth 9-12 , which builds on the earlier diffusive transport theory of Ivantsov 13 , has led to the understanding that crystalline anisotropy is a crucial parameter that uniquely determines the growth rate and tip radius of dendrites, which is the basic scaling length for the entire dendritic network. Predictions of this theory have been largely validated by phase-field simulations of dendritic evolution over the past few years for both small [14][15][16][17][18][19] and large 20 growth rate. Moreover, molecular dynamics (MD) simulation methods [21][22][23][24][25][26][27][28][29][30] as well as experimental techniques 31,32 have recently been developed to accurately compute anisotropic interfacial properties that control dendritic evolution.Despite this progress, dendrite growth theory remains limited to predicting the steady-state characteristics of dendrites growing along simple crystallographic directions, such as the 100 directions that correspond to the main crystal axes for materials with cubic symmetry, or the six directions in the basal plane of

Dendritic Growth Morphologies in Al-Zn Alloys—Part II: Phase-Field Computations

“…In order to further support this interpretation and to elucidate the growth mechanisms of the complex structures that form in the DOT region, a detailed phase-field study exploring anisotropy parameters' space is presented in this paper. For equiaxed growth, our results essentially recapitulate those of Haxhimali et al [1] in simulations for pure materials. We find distinct regions of the parameter space associated with h100i and h110i dendrites, separated by a region where hyperbranched dendrites are observed.…”

“…[1] are normalization constants, which Chan et al [6] chose such that each K i has unit amplitude in the polar direction in spherical coordinates. The choice of coefficients is not unique.…”

“…Haxhimali et al [1] and Gonzales and Rappaz [3,4] attributed the DOT to a modification of the weak anisotropy of the solid-liquid interfacial energy c s' of Al by the addition of Zn, an element with very high interfacial energy anisotropy in its pure state. Haxhimali performed phase-field simulations in which the anisotropy parameters were systematically varied to explore the role of these parameters on the resulting microstructures, but only for pure materials solidifying as equiaxed crystals in an undercooled melt.…”

Growth directions in directionally solidified Al–Zn and Zn–Al alloys near eutectic composition

“…This change of dendrite orientation in fcc Al-Zn was interpreted as a modification of the solid-liquid interfacial energy of aluminum c s' ðc Zn Þ as c Zn increases [1,3]. Indeed, dendrite growth directions are dictated by the anisotropy of c s' ; more precisely they are given by minima of the so-called interface stiffness S s' .…”

Orientation selection of equiaxed dendritic growth by three-dimensional cellular automaton model

“…Phase-field simulations [10] have showed that dendritic preferred growth directions vary continuously from <100> to <110>, when the anisotropy parameter 1 is reduced from 0.15 to 0.0 while the anisotropy parameter 2 is fixed to -0.02. However, for a large region sandwiched between the <100> and <110> regions (0.05< 1 <0.12,  2 =-0.02), the phase-field results are not as expected from the minimum stiffness criterion.…”