Tertiary Arms Research Articles

Study on the dendritic growth and grain boundary formation in the suddenly expanded cross-section of single crystal superalloy during directional solidification process

The dendritic growth behavior at the suddenly expanded cross-section of single crystal blades dramatically affects the defects formation. In this work, the dendrite growth mechanism is deeply investigated in the rectangular platform by analyzing the quasi-three-dimensional microstructures via the continuous image shooting and orientation scanning, combined with simulating the thermal fields at different furnace temperatures. As the solidification proceeds to the platform, the secondary branches at the connection between the primary zone and the expansion zone grow outwardly. Some secondary branches growth direction deflects the preferred orientation. The well-developed tertiary arms would develop on some secondary branches. The different generation dendrites with the different growth directions converge and form the boundary angles. The tertiary proportion and the dendrite boundary lengthes/angles show the decrease tendency as the temperature increases. The undercooling in the platform edges and corners from the concave/convex degree of isothermal surface should be responsible for the formation and convergence of the different generation dendrites the matrix dendrite expanding behavior towards the platform edge and their subsequent upward directional growth. The nonuniformity of thermal gradient at the isothermal surface should affects the inconsistency of the growth directions of the different dendrites, which provides the more opportunity for the dendrite deviation. This study sheds light on the dendrite growth behavior when the single crystal blade directionally solidifies through the suddenly expanded platform.

Primary-dendrite-pattern regulation by secondary branch during the directional solidification of the single crystal superalloy

The dendrite array by directional solidification determines the mechanical properties of the single crystal superalloy. Achieving precise and effective control over the directional dendrite array has been challenging due to a lack of understanding the underlying mechanism. The study found that secondary branches with specific orientations play a significant role in determining the arrangement pattern of primary dendrites on the transverse section. These secondary branches induce either a unidirectional or bidirectional aligned pattern in the primary dendrite array. The proportion of aligned dendrites increases with the solidification distance, but decreases with the withdrawal velocity. The competitive growth coefficient of secondary branch was proposed based on the effectiveness components of thermal gradient. This coefficient is determined by the convexity of the liquid-solid interface, the angle between the primary arm and the vertical direction, and the orientations angle of secondary branch. The presence of a large competitive coefficient at the liquid-solid interface edge near the crucible gives secondary branches an advantage in growth. This leads to the development of tertiary arms which further grow into the main trunks, aligning parallel to the primary dendrites and forming the aligned pattern. Additionally, based on the competitive coefficient, the formation criterion and distribution law of dendritic pattern transitions were summarized. This provides effective guidance not only for controlling dendrite arrangement but also for estimating the single crystal orientation through visual inspection by back-calculating the formation criterion.

Columnar dendritic solidification of TiAl under diffusive and hypergravity conditions investigated by phase-field simulations

Based on 2D phase-field simulations including fluid flow driven by natural convection, columnar dendritic growth of the β -solidifying Ti-48 at.%Al alloy is characterised for different gravity levels ranging from 0 to ± 15 g. Depending on the direction of the gravity g with respect to the growth direction, different flow regimes emerge which show stable or unstable dendritic growth dynamics. When gravity and growth directions are parallel, the dendrite tips experience downward melt flow and individual dendrites grow in a stable manner with a rather small modification of the operating state. When gravity and growth directions are antiparallel, the impact on the operating state is larger. Eventually, at higher gravity levels the upward melt flow around the dendrite tips “destabilises” the dendritic morphology resulting in tip splitting, branching and local changes in the apparent dendrite growth direction which is an alternative mechanism for the adjustment of the primary dendrite arm spacing in addition to tertiary arm formation.

In situ studies revealing dendrite and eutectic growth during the solidification of Sn-0.7Cu-0.5Ag Pb-free solder alloy

Low-Ag Sn-0.7Cu-0.5Ag Pb-free solder solidifies into βSn dendrite and coupled eutectics structures. In this study, a range of solidification events in Sn-0.7Cu-0.5Ag solder alloy, such as primary βSn dendrite growth, binary eutectics and ternary eutectics growth, have been studied using in situ time-resolved synchrotron X-ray radiography. It was found that primary βSn dendrite arms showed accelerated growth, whilst secondary dendrite arms competitive growth/coarsening was strongly influenced by neighboring arms. Axial remelting of tertiary arms of βSn dendrite also occurred during coarsening. Most importantly, simultaneous growth of invariant binary βSn-Ag3Sn eutectic/ternary βSn-Cu6Sn5-Ag3Sn eutectic were observed.

Blobs, spiral arms, and a possible planet around HD 169142

Context. Young planets are expected to cause cavities, spirals, and kinematic perturbations in protostellar disks that may be used to infer their presence. However, a clear detection of still-forming planets embedded within gas-rich disks is still rare. Aims. HD 169142 is a very young Herbig Ae-Be star surrounded by a pre-transitional disk, composed of at least three rings. While claims of sub-stellar objects around this star have been made previously, follow-up studies remain inconclusive. The complex structure of this disk is not yet well understood. Methods. We used the high contrast imager SPHERE at ESO Very large Telescope to obtain a sequence of high-resolution, high-contrast images of the immediate surroundings of this star over about three years in the wavelength range 0.95–2.25 μm. This enables a photometric and astrometric analysis of the structures in the disk. Results. While we were unable to definitively confirm the previous claims of a massive sub-stellar object at 0.1–0.15 arcsec from the star, we found both spirals and blobs within the disk. The spiral pattern may be explained as due to the presence of a primary, a secondary, and a tertiary arm excited by a planet of a few Jupiter masses lying along the primary arm, likely in the cavities between the rings. The blobs orbit the star consistently with Keplerian motion, allowing a dynamical determination of the mass of the star. While most of these blobs are located within the rings, we found that one of them lies in the cavity between the rings, along the primary arm of the spiral design. Conclusions. This blob might be due to a planet that might also be responsible for the spiral pattern observed within the rings and for the cavity between the two rings. The planet itself is not detected at short wavelengths, where we only see a dust cloud illuminated by stellar light, but the planetary photosphere might be responsible for the emission observed in the K1 and K2 bands. The mass ofthis putative planet may be constrained using photometric and dynamical arguments. While uncertainties are large, the mass should be between 1 and 4 Jupiter masses. The brightest blobs are found at the 1:2 resonance with this putative planet.

Planet-driven Spiral Arms in Protoplanetary Disks. I. Formation Mechanism

Abstract Protoplanetary disk simulations show that a single planet can excite more than one spiral arm, possibly explaining the recent observations of multiple spiral arms in some systems. In this paper, we explain the mechanism by which a planet excites multiple spiral arms in a protoplanetary disk. Contrary to previous speculations, the formation of both primary and additional arms can be understood as a linear process when the planet mass is sufficiently small. A planet resonantly interacts with epicyclic oscillations in the disk, launching spiral wave modes around the Lindblad resonances. When a set of wave modes is in phase, they can constructively interfere with each other and create a spiral arm. More than one spiral arm can form because such constructive interference can occur for different sets of wave modes, with the exact number and launching position of the spiral arms being dependent on the planet mass as well as the disk temperature profile. Nonlinear effects become increasingly important as the planet mass increases, resulting in spiral arms with stronger shocks and thus larger pitch angles. This is found to be common for both primary and additional arms. When a planet has a sufficiently large mass (≳3 thermal masses for (h/r) p = 0.1), only two spiral arms form interior to its orbit. The wave modes that would form a tertiary arm for smaller mass planets merge with the primary arm. Improvements in our understanding of the formation of spiral arms can provide crucial insights into the origin of observed spiral arms in protoplanetary disks.

Experimental Investigation of Ternary Al-Si-Cu Alloy Solidified with Unsteady-State Heat Flow Conditions

Ternary Al-9.0wt%Si-4.0wt%Cu alloy was solidified in a vertical directional solidification system under unsteady-state heat flow conditions. The resulting dendritic morphology and microsegregation were investigated. A more detailed analysis was dedicated to the microsegregation phenomena where a multielement interaction was observed. The solidification parameters such as: solidification speed (VL) and cooling rate (T˙) were determined from the cooling curves obtained during the solidification process. The thermal variables effect on the dendritic morphology is presented. The measurements of tertiary dendrite arm spacing (λ3) and microsegregation were performed for different positions along the casting. The experimental curves for microsegregation were obtained for Si and Cu from the center of dendritic tertiary arm to the next nearest tertiary arm. The solidification speed (VL) influence is built the effective partition coefficient (Kef_Cu and Kef_Si) that has been determined for the range of VL and microsegregation curves are calculated by Scheil's equation for comparison with experimental data. Good agreements of the Scheil's equation with experimental data on microsegregation curves of the Si and Cuwere obtained when effective partition coefficient (Kef_Cu and Kef_Si) is taken into consideration. The multielement interaction effect on the Si microsegregation is investigated. Experimental results show that, Cu-rich dendrites were accompanied by minute amounts of Si. The concentration profiles obtained experimentally point to a strong negative correlation between Si and VL on ternary Al-9.0wt%Si-4.0wt%Cu alloy.

On the Formation of Multiple Concentric Rings and Gaps in Protoplanetary Disks

Abstract As spiral waves driven by a planet in a gaseous disk steepen into a shock, they deposit angular momentum, opening a gap in the disk. This has been well studied using both linear theory and numerical simulations, but so far only for the primary spiral arm: the one directly attached to the planet. Using 2D hydrodynamic simulations, we show that the secondary and tertiary arms driven by a planet can also open gaps as they steepen into shocks. The depths of the secondary/tertiary gaps in surface density grow with time in a low-viscosity disk ( ), so even low-mass planets (e.g., super-Earth or mini-Neptune-mass) embedded in the disk can open multiple observable gaps, provided that sufficient time has passed. Applying our results to the HL Tau disk, we show that a single 30 Earth-mass planet embedded in the ring at 68.8 au (B5) can reasonably well reproduce the positions of the two major gaps at 13.2 and 32.3 au (D1 and D2), and roughly reproduce two other major gaps at 64.2 and 74.7 au (D5 and D6) seen in the mm continuum. The positions of secondary/tertiary gaps are found to be sensitive to the planetary mass and the disk temperature profile, so with accurate observational measurements of the temperature structure, the positions of multiple gaps can be used to constrain the mass of the planet. We also comment on the gaps seen in the TW Hya and HD 163296 disk.

Helmintos de peces del Pacífico mexicano. XXIX. Descripción de dos monogéneos nuevos de la familia Capsalidae Baird, 1853, subfamilia Benede­niinae Johnston, 1931, de Baja California

Two new monogenea of the family Capsalidae Baird. 1853, subfamily Benedeniinae Johnston, 1931, are described from fishes taken in Baja Califor­nia. The first, Neobenedenia pacifica sp. n., comes from the gills of Mugil cephalus L., from La Paz; it is considered a new species because of the sagittate form of the first pair of humuli of the opisthohaptor. The second, N. longi­prostata sp. n., from the gills of an undetermined serranid from Isla Rasa, differs from all known species in the extremely lengthened prostate ducts, which follow along the primary, secondary, and tertiary caecal arms and reach the caudal end of the body.

Numerical Simulation of Three-Dimensional Dendritic Growth of Alloy: Part II—Model Application to Fe-0.82WtPctC Alloy

In the second part (Part II) of the present simulation work, the three-dimensional (3D) dendritic growth of Fe-0.82wtpctC alloy is investigated with the 3D CA-FVM cellular automaton-finite volume method model developed in Part I. The influences of the melt undercooling, the interfacial anisotropy, and the forced flow on the equiaxed dendritic growth, especially the formation of secondary arms, are discussed. The comparisons of equiaxed dendritic growth in 3D and two-dimensional (2D) are also carried out. Finally, the columnar dendritic growth under different cooling conditions is investigated including the morphology and the secondary dendrite arm spacing (SDAS). The results show that the high undercooling can promote the formation of secondary arms as the anisotropy parameter is 0.04. With the increase of the anisotropy parameter, the secondary arms first reduce and then well develop again; meanwhile the tertiary arms are gradually developed. However, the secondary arms vanish at the undercooling of 5 K as the anisotropy parameter increases to 0.04. With the introduction of the forced flow with the inlet velocity of 0.001 m/s along the x axis, the secondary arms at the left (upstream) arm become more developed. However, they become slightly less developed with the forced flow intensifying. Secondary arms at the left side (upstream) of the perpendicular arms and in the y-z symmetrical plane become more and more developed as the inlet velocity increases. The competition of the secondary arms at the right side (downstream) of the perpendicular arms and at the right (downstream) arm becomes significant as the undercooling increases from 10 to 15 K. The solute-enriched envelope in 2D is much thicker than in the 3D case, so that the dendritic growth in 2D is influenced more by the melt flow and the undercooling; moreover, the secondary arms in 2D are hard to form even at the undercooling of 15 K and with the forced convection in the present article. Meanwhile, the variation tendency of the movement of columnar dendritic tip and the decrement of the average SDAS with every 0.025-MW/m2 increment of the heat flux are quite different.

Influence of processing parameters on laser metal deposited copper and titanium alloy composites

The laser metal deposition (LMD) was conducted on copper by varying the processing parameters in order to achieve the best possible settings. Two sets of experiments were conducted. The deposited composites were characterized through the evolving microstructure, microhardness profiling and mechanical properties. It was found that the evolving microstructures of the deposited composites were characterized with primary, secondary and tertiary arms dendrites, acicular microstructure as well as the alpha and beta eutectic structures. From the two sets of experiments performed, it was found that Sample E produced at a laser power of 1200 W and a scanning speed of 1.2 m/min has the highest hardness of HV (190±42) but exhibits some lateral cracks due to its brittle nature, while Sample B produced at laser power of 1200 W and a scanning speed of 0.3 m/min shows no crack and a good microstructure with an increase in dendrites. The strain hardening coefficient of the deposited copper composite obtained in this experiment is 3.35.

Microstructural evolution of laser surface remelting remolten Ni-28 wt%Sn alloy under liquid nitrogen cooling

The substrate of as-cast Ni-28 wt% Sn hypoeutectic alloy immersed in liquid nitrogen is rapidly remolten and solidified by laser surface remelting with a scanning velocity of 10 mm/s and the laser power of 1950 W. The microstructure of the substrate and its effect on the microstructure of the molten pool are investigated by scanning electron microscope carefully. It is found that the substrate of the Ni-28 wt%Sn ingot is composed of coarse primary α-Ni dendrites and the interdendritic (α-Ni+Ni3Sn) eutectic. The growth orientations of α-Ni dendrites and the interdendritic eutectic are distributed nearly randomly in the as-cast substrate. There are three kinds of microstructure characterstic zones from the top to the bottom of melted pool. The growth directions of α-Ni dendrites with the primary dendritic spacings ranging from 4.19 to 6.91 μm are approximately parallel to the laser scanning direction at the top of the molten pool due to the fact that the temperature gradient at the interface between the molten pool and substrate tends to be parallel to the laser scanning direction. In the middle of the molten pool, the epitaxial α-Ni columnar dendrites are found to be inclined to grow in the direction vertical to the bottom of the molten pool due to the fact that the temperature gradients in most zones of the molten pool are perpendicular to the bottom of the molten pool. The formation of new primary dendrites by the growth of the tertiary arm results in the decrease of primary dendritic spacing in comparison with that at the bottom of the molten pool. There are a small quantity of residual α-Ni primary phase and a large amount of (α-Ni+Ni3Sn) eutectic at the bottom of the molten pool. The microstructure of laser remolten zone is greatly influenced by the substrate microstructure, and the growth direction of the α-Ni dendrite in the molten pool is also affected remarkably by both the heat flux and the preferred crystal orientations for dendritic growth. Compared with the mixed lamella, rod and divorced (α-Ni+Ni3Sn) eutectic microstructures in the substrate, the eutectic structure in the molten pool is completely composed of the refined lamellar eutectic, which grows epitaxially in the direction perpendicular to the interface between the molten pool and the substrate at the bottom of molten pool. The eutectic lamellar spacing increases from the top (0.23 μm± 0.01 μm) to the bottom (0.42 μm± 0.02 μm) of the molten pool due to the interface growth velocity decreasing from the top to the bottom. The Kurz-Giovanola-Trivedi model for rapid dendritic growth and the Trivedi-Magnin-Kurz model for eutectic growth are used to estimate the growth undercooling of the microstructure in the molten pool respectively. It is found that the growth undercooling of dendrites and the eutectic in the molten pool should be between 50.4 K and 112.5 K, which is much larger than the critical undercooling for anomalous eutectic growth found in the high undercooled solidification in the previous researches. This phenomenon means that the critical undercooling for anomalous eutectic growth reported in the previous literature may be not the sufficient condition for generating the anomalous eutectic.

Additive manufacturing of nickel-based superalloy Inconel 718 by selective electron beam melting: Processing window and microstructure

Abstract

An Evaluation of Primary Dendrite Trunk Diameters in Directionally Solidified Al-Si Alloys

The primary dendrite trunk diameters of Al-Si alloys that were directionally solidified over a range of processing conditions have been evaluated. The empirical data are analyzed with a model that is an extension of one used to describe the ripening of dendrite arms. The analysis, based primarily on an assessment of secondary dendrite arm dissolution in the mushy zone, fits well with the experimental data. It is suggested that the primary dendrite trunk diameter is a useful metric that correlates well with the actual solidification processing parameters, and complements the conventionally used primary, secondary, and tertiary arm spacings.

Tertiary dendritic instability in late stage solidification of Ni-based superalloys

Derivatives of the commercial alloy CMSX-4 were directionally solidified and characterized with respect to their final dendrite microstructure. The results indicate that Ni-based superalloys with high segregation levels show significant instability in secondary dendrite arms and an increased tendency for tertiary arm formation, respectively. Phase-field simulations were used to explore the impact of chemical composition on morphological instability and tertiary arm formation during the directional solidification of Ni-based superalloys. It is found that an increase in specific alloying elements in the overall alloy composition leads to pronounced segregation at the end of solidification. This causes strong growth restriction of the secondary arms and triggers tertiary arm formation. The proposed mechanism explains experimental microstructures found in modifications of the base alloy CMSX-4.

Effect of solidification conditions on fractal dimension of dendrites

Dendrites are complex, three-dimensional structures that have conventionally been characterized by measuring the secondary dendrite arm spacing or the primary spacing in a dendritic network, but these global measures do not adequately describe the branched appearance of secondary and tertiary arms. This work focuses on the integral measurement of fractal dimension, a measure of complexity relatively unexplored in dendrites, in addition to specific surface area. Measurements were made on aluminum dendrites in directionally solidified Al–Si alloys of varying composition and solidification velocity, with and without induced convection currents. Contrary to expectations, average fractal dimension was found to be relatively insensitive to changes in solidification velocity and fluid flow within the ranges observed, compared to the variation in fractal dimension measured within any individual data set. Specific surface area was found to increase linearly with solidification velocity.

The Morphological Evolution of Low Volume Fraction Tin Dendrites During Coarsening

Tin dendrites tend to grow in closely spaced, parallel sheets; thus, within a certain range of solid volume fraction, it is possible to obtain samples with both dense dendritic regions and dendrite-free regions of liquid. Such samples were produced by directionally solidifying Pb-69.1 wt pct Sn, allowing us to compare tin dendrite structure and coarsening in a traditional dense mushy zone with the same dendrites in much lower volume fraction solid regions. The morphology of the dendrites, both in the dense and less-dense regions is analyzed using three-dimensional reconstructions obtained by serial sectioning. Quantitative measurements of these complex structures were obtained by calculating interfacial curvature and interfacial normal distributions, and the spatial correlations of interfacial curvature. We find that the spatial correlation measurement can be used to determine average secondary or tertiary arm length. We find also that coarsening proceeds in this system by both welding of secondary arms and dissolution and growth via long-range diffusional interactions and that the microstructure becomes more morphologically anisotropic as coarsening proceeds.

Observation of Misoriented Tertiary Dendrite Arms During Controlled Directional Solidification in Aluminum-7 Wt pct Silicon Alloys

Electron backscattered diffraction (EBSD) examination of transverse cross sections from a directionally solidified aluminum-7 wt pct silicon alloy revealed tertiary dendrite arms that appeared in place but in reality had orientations that significantly differed from their parent arm. The maximum extent of spuriously orientated arms occurred at an intermediate growth velocity and was more pronounced at subgrain boundaries that separated uniquely oriented dendritic arrays. Mechanisms for tertiary arm misorientations are discussed, and attention is called to the practical consequences of these in-situ defects.

Phase field modeling the selection mechanism of primary dendritic spacing in directional solidification

Selection mechanisms of primary dendritic spacing in directional solidification are investigated by the phase field method. Results show that the lower and upper limits of primary spacing are determined by the interdendritic solutal interactions and the interdendritic undercooling respectively. The upper limit of primary spacing resulting from overgrowth of the tertiary arm could be about four times as large as the lower limit. The microstructural evolution from the onset of planar instability during directional solidification with a constant pulling velocity can be divided into three stages: an initial competition stage, a submerging stage and a lateral adjustment stage. Simulation results also demonstrate that the final primary spacing with a constant pulling velocity is very close to the lower limit due to the dendrite submerging mechanism.

The Influence of Gravity on the CET in Diluted Zn-Al Alloys

In a solidification process, the microstructure depends on the alloy characteristics and is a function mainly of the temperature evolution ahead the solid/liquid interphase. Among the several phenomena occurring during solidification, like solute segregation and morphology stability, one of the most important is dendritic growth. The most important dendrite parameters are the primary, secondary and tertiary arm spacings due to their influence on mechanical properties. An efficient method of examining the evolution of dendrite arms is to apply steady-state directional solidification with an imposed growth rate, V, and a thermal gradient, G, at the solid/liquid interphase. In this work, experiments were performed under unidirectional solidification in a device cooled with water, and Zn-1%Al and Zn-2%Al (wt%) alloys were solidified in a vertical upward (0¼), inclined at 30¡ and 45¡ to the vertical and horizontally upward (90¼ to the vertical).The position of the transition from columnar-to-equiaxed structure (CET) through macro- and micro-analysis was determined, and significant thermal parameters by recording temperature-time data. The results show that the direction of growth of dendrites is about the direction of heat extraction and that the angle of inclination of the columnar grains with the longitudinal axis of the alloy sample coincides fapproximately with the angle of inclination of the furnace.