Directional solidification experiments have been carried out on different Al–Cu alloys as a function of solidification parameters, temperature gradient G, growth rate V, and composition C0. The specimens were solidified under steady state conditions with a constant temperature gradient (7.4 K mm−1) at a wide range of growth rates (9–490 μm s−1) and with a constant growth rate of 9.5 μm s−1 at a wide range of temperature gradients (1.0–7.4 K mm−1). Microstructural parameters, the primary dendrite arm spacing λ1, secondary dendrite arm spacing λ2, dendrite tip radius R, mushy zone depth d were measured and expressed as functions of solidification parameters, G, V and C0 by using a linear regression analysis. The results were in good agreement with previous experimental work and current theoretical models suggested for dendritic growth.

Directional solidification of aluminium -copper alloys

We present the results of a numerical study based on the boundary integral technique of interfacial pattern formation in directional solidification of thin-film lamellar eutectics at low velocity. Microstructure selection maps that identify the stability domains of various steady-state and nonsteady-state growth morphologies in the spacing-composition (λ –C
 0) plane are constructed for the transparent organic alloy CBr4-C2Cl6 and for a model eutectic alloy with two solid phases of identical physical properties. In CBr4-C2Cl6, the basic set of instabilities that limit steady-state growth is richer than expected. It consists of three primary instabilities, two of which are oscillatory, which bound the domain of the commonly observed axisymmetric lamellar morphology, and two secondary oscillatory instabilities, which bound the domain of the nonaxisymmetric (tilted) lamellar morphology. The latter is predicted to occur over a hypereutectic range of composition which coincides well with experiment. Moreover, the steady tilt bifurcation lies between but does not directly bound either of these two domains, which are consequentlydisjoint. Four stable oscillatory microstructures, at least three of which have been seen experimentally, are predicted to occur in unstable regimes. In the model alloy, the structure is qualitatively similar, except that a stable domain of tilted steady-state growth is not found, in agreement with previous random-walk simulations. Furthermore, the composition range of stability of the axisymmetric morphology decreases sharply with increasing spacing away from minimum undercooling but extends further off-eutectic than predicted by the competitive growth criterion. In addition, oscillations with a wavelength equal to two λ lead to lamella termination at a small distance above the onset of instability. The implications of these two features for the eutectic to dendrite transition are examined with the conclusion that in the absence of heterogeneous nucleation, this transition should be histeritic at small velocity and temperature gradient.

Morphological instabilities of lamellar eutectics

Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter1-6, non-equilibrium systems7-9, networks of neurons10,11, social groups with conformist and contrarian members12, directional interface growth phenomena13-15 and metamaterials16-20. Although wave propagation in non-reciprocal media has recently been closely studied1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points21. We describe the emergence of these phases using insights from bifurcation theory22,23 and non-Hermitian quantum mechanics24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.

Non-reciprocal phase transitions.

This is the first account of the history of our understanding of, and ability to model, solidification microstructures. Its objective is to retrace the scientific steps made, from the earliest obse...

Progress in modelling solidification microstructures in metals and alloys: dendrites and cells from 1700 to 2000

A binary liquid undergoes unidirectional solidification. The one-dimensional steady state is susceptible to morphological instability that causes the solid/liquid interface to change from a planar state to a cellular pattern. This paper examines the effects on this transition of volume-change convection, buoyancy-driven convection or forced flows. It emphasizes how flows alter stability limits, create scale and pattern changes in morphology, and create, through coupling, new instabilities. Emphasis is placed on the physical mechanisms of the interactions.

Hydrodynamic interactions in directional solidification

Directional solidification of metallic alloys: The nature of the bifurcation from planar to cellular interface

During directional solidification of thin layers (50 μm) of the transparent CBr4-C2Cl6 lamellar eutectic alloy, we observed tilt waves, a type of instability consisting in small domains of tilted lamellae moving transversely along the growth front. This instability is a way the system adjusts its wavelength after a small perturbation, without creating or destroying lamellae.

Solitary Tilt Waves in Thin Lamellar Eutectics

During directional solidification of alloys, a cellular structure can be observed above a critical pulling speed. Under certain conditions, the cusps behind the cells can present a secondary instability characterized by a periodic emission of liquid droplets. These droplets are transported by the solid, but also migrate towards the solid-liquid interface by temperature gradient zone migration. We study the conditions of appearance of the droplet instability and discuss the information concerning growth mechanisms that can be deduced from a study of the migration. J. Phys. France 50 (1989) 3007-3019 1er OCTOBRE 1989, Classification Physics Abstracts 61.50C 81.10F 81.30F

P. Kurowski

Papers

Directional solidification of metallic alloys: The nature of the bifurcation from planar to cellular interface

Solitary Tilt Waves in Thin Lamellar Eutectics

Cusp instability in cellular growth