An analytical geometrical model for secondary dendrite arm detachment

A simple geometrical model of a ripened secondary dendrite arm is used to investigate the curvature at the neck of the arm where it joins the primary trunk. It is found that the negative K-(1) component of the curvature does not fully balance the peak in the positive K-(2) component

Spontaneous deterministic side-branching behavior in phase-field simulations of equiaxed dendritic growth

The accepted view on dendritic side-branching is that side-branches grow as the result of selective amplification of thermal noise and that in the absence of such noise dendrites would grow without the development of side-arms. However, recently there has been renewed speculation about dendrites displaying deterministic side-branching [see, e.g., M. E. Glicksman, Metall. Mater. Trans A 43, 391 (2012)]. Generally, numerical models of dendritic growth, such as phase-field simulation, have tended to display behaviour which is commensurate with the former view, in that simulated dendrites do not develop side-branches unless noise is introduced into the simulation. However, here, we present simulations that show that under certain conditions deterministic side-branching may occur. We use a model formulated in the thin interface limit and a range of advanced numerical techniques to minimise the numerical noise introduced into the solution, including a multigrid solver. Spontaneous side-branching seems to be favoured by high undercoolings and by intermediate values of the capillary anisotropy, with the most branched structures being obtained for an anisotropy strength of 0.03. From an analysis of the tangential thermal gradients on the solid-liquid interface, the mechanism for side-branching appears to have some similarities with the deterministic model proposed by Glicksman

Effect of rapid solidification on the microstructure and microhardness of BS1452 grade 250 hypoeutectic grey cast iron

Containerless solidification of low alloyed commercial grey cast iron in two different cooling media (N2 and He) using a 6.5 m high vacuum drop-tube have been investigated. Both the conventionally cooled, as-cast alloy and the rapidly cooled drop-tube samples were characterized using SEM, XRD and Vickers microhardness apparatus. The estimated range of cooling rates are 200 K s−1 to 16,000 K s−1 for N2 cooled droplets and 700 K s−1 to 80,000 K s−1 for He cooled droplets (in each case for 850 μm and 38 μm diameter droplets respectively). Microstructural analysis reveals that the as-received bulk sample displayed a graphitic structure while the rapidly cooled samples display decreasing amounts of α-Fe as the cooling rate increases. At moderate cooling rates α is replaced with γ and Fe3C, while at higher cooling rates with α′. Microhardness increase with cooling rate but cannot be mapped uniquely onto cooling rate, suggesting undercooling also influences the mechanical properties

Evidence for an extended transition in growth orientation and novel dendritic seaweed structures in undercooled Cu-8.9 wt%Ni

A melt encasement (fluxing) technique has been used to systematically study the microstructural development and velocity-undercooling relationship of a Cu-8.9 wt%Ni alloy at undercoolings up to 235 K. A complex series of microstructural transitions have been identified with increasing undercooling. At the lowest undercoolings a 〈1 0 0〉 type dendritic structure gives way to an equiaxed grain structure, consistent with the low undercooling region of grain refinement observed in many alloys. At intermediate undercoolings, dendritic growth returns, consisting of dendrites of mixed 〈1 0 0〉 and 〈1 1 1〉 character. Within this region, 8-fold growth is first observed at low undercoolings, indicating the dominance of 〈1 0 0〉 character. As undercooling is increased, 〈1 1 1〉 character begins to dominate and a switch to 6-fold growth is observed. It is believed that this is an extended transition region between 〈1 0 0〉 and 〈1 1 1〉 dendrite growth, the competing anisotropies of which are giving rise to a novel form of dendritic seaweed, characterised by its containment within a diverging split primary dendrite branch. At higher undercoolings it is suggested that a transition to fully 〈1 1 1〉 oriented dendritic growth occurs, accompanied by a rapid increase in growth velocity with further increases in undercooling. At the highest undercooling achieved, a microstructure of both small equiaxed grains, and large elongated grains with dendritic seaweed substructure, is observed. It is thought that this may be an intermediate structure in the spontaneous grain refinement process, in which case the growth of dendritic seaweed appears to play some part

Estimation of cooling rates during close-coupled gas atomization using secondary dendrite arm spacing measurement

Al-4 wt pct Cu alloy has been gas atomized using a commercial close-coupled gas-atomization system. The resulting metal powders have been sieved into six size fractions, and the SDAS has been determined using electron microscopy. Cooling rates for the powders have been estimated using a range of published conversion factors for Al-Cu alloy, with reasonable agreement being found between sources. We find that cooling rates are very low relative to those often quoted for gas-atomized powders, of the order of 10 K s for sub-38 μm powders. We believe that a number of numerical studies of gas atomization have overestimated the cooling rate during solidification, probably as a consequence of overestimating the differential velocity between the gas and the particles. From the cooling rates measured in the current study, we estimate that such velocities are unlikely to exceed 20 m s

Rapid solidification morphologies in Ni3Ge: Spherulites, dendrites and dense-branched fractal structures

Single-phase β-Ni3Ge has been rapidly solidified via drop-tube processing. At low cooling rates (850–300 μm diameter particles, 700–2800 K s−1) the dominant solidification morphology, revealed after etching, is that of isolated spherulites in an otherwise featureless matrix. At higher cooling rates (300–75 μm diameter particles, 2800–25,000 K s−1) the dominant solidification morphology is that of dendrites, again imbedded within a featureless matrix. As the cooling rate increases towards the higher end of this range the dendrites display non-orthogonal side-branching and tip splitting. At the highest cooling rates studied (25,000 K s−1), dense-branched fractal structures are observed. Selected area diffraction analysis in the TEM reveals the spherulites and dendrites are a disordered variant of β-Ni3Ge, whilst the featureless matrix is the ordered variant of the same compound. We postulate that the spherulites and dendrites are the rapid solidification morphology and that the ordered, featureless matrix grew more slowly post-recalescence. Spherulites are most likely the result of kinetically limited growth, switching to thermal dendrites as the growth velocity increases. It is extremely uncommon to observe such a wide range of morphologies as a function of cooling rate in a single material

Evidence for dendritic fragmentation in as-solidified samples of deeply undercooled melts

The congruently melting, single phase intermetallic β-Ni3Ge has been subject to rapid solidification via drop-tube processing. We establish that the rapidly solidified material growing during the recalescence phase of solidification can be distinguished from the post-recalescence material in the as-solidified sample by the degree of chemical ordering displayed. This can in turn be used to visualize the material from the recalescence phase of solidification. At intermediate cooling rates this recalescence material consists of fragmented dendrites. The occurrence of fragmentation is compared against established theoretical models based on the growth of Rayleigh instabilities with excellent agreement being found. EBSD mapping is used to establish the relationship between these dendritic fragments and the final grain size distribution. The dendritic fragments are found to be poor nuclei for new grains and the fragmented dendrites do not consistently give rise to classical grain refined structures

Dynamics of core–shell particle formation in drop-tube processed metastable monotectic alloys

We examine the apparent size of the core and shell as a function of cooling rate in core–shell particles of the metastable monotectic alloy Co-50 at% Cu, finding that the volume fraction of the core systematically increases with cooling rate and hence undercooling. A model for this variation is proposed. A Monte-Carlo simulation is used to correct for sectioning effects allowing the true core:shell volume ratio to be estimated. From this, and the observation of a second, spinodal, episode of liquid phase separation we are able to estimate the undercooling at solidification. This permits a calculation of the time available following liquid phase separation for the migration giving rise to the observed core–shell structure to occur and hence the required Marangoni velocity required to such migration

Numerical and Experimental Investigations of the Effect of Melt Delivery Nozzle Design on the Open- to Closed-Wake Transition in Closed-Coupled Gas Atomization

The single-phase gas-flow behavior of a closed-coupled gas atomization was investigated with four different melt nozzle tip designs with two types of gas die. Particular attention was paid to the open- to closed-wake transition. Experimental Schlieren imaging and numerical modeling techniques were employed, with good agreement between the two being found in relation to the wake closure pressure. It was found that the melt nozzle tip design had a significant impact on the WCP, as did the type of die used, with a convergent–divergent gas die giving significantly high WCPs