Dendritic Spacing Research Articles

Remarkable dendritic effect in the polymer-supported catalysis of the Heck arylation of olefins.

[reaction: see text] Phosphine-palladium complexes, immobilized on polystyrene, demonstrated a remarkable increase in catalytic activity and selectivity in the Heck reaction upon the introduction of a dendritic spacer between the support and phosphine. For some reactions an up to 5-fold increase in yield is observed.

Quasi-steady-state modeling of dendritic growth

A new method of the moving-boundary problem analysis is developed. After proposed coordinate transformation, the quasi-steady-state differential equation was reduced to equivalent Laplace equation. Transformed boundary conditions of a rescaled field distribution reflect the presence of rate-dependent sources on interface. Taking into account the local rate-dependence of the Neumann's boundary conditions, non-equilibrium pattern formation was considered. The problem of dendrite fractal growth was reduced to one of interaction of conformal to tips charged particles. Conditions of the quasi-steady growth and the recurrence formula for k-order dendrite spacing were derived. Theoretically obtained scaling laws for interface shape, dendrite spacing, critical sidebranch distance are confirmed by available experimental data.

Evaluation of effects of niobium and manganese addition on nickel base weldments

The present work investigates the influence of different concentrations of Nb (from 0.1 to 3.35 wt-%) or Mn (from 0.78 to 3.32 wt-%) on the microstructure and mechanical properties of an Inconel 690 weldment. Welding electrodes are produced by coating Inconel filler metal 52 with a flux containing various percentages of Nb or Mn. Weldments with a bevel edge are butt welded via a manual shielded metal arc welding process, using identical parameters and procedures. The microstructure and mechanical properties of the resulting weldments are then analysed. The experimental results indicate that the subgrain structures of the welds are primarily dendritic. Under tensile testing, it is found that each specimen ruptures in the fusion zone and that the fracture surfaces exhibit entirely ductile features. It is noted that as the content of Nb increases, the welds tend to show a finer subgrain structure, i.e. having smaller dendritic spacing. Consequently, the tensile strength and microhardness of the fusion zone increase slightly and the tensile rupture mode changes from slant to flat fracture. It is determined that the interdendritic precipitates are mainly Nb rich eutectic type and Nb rich type constituents. The presence of these precipitates increases with higher concentrations of Nb in the flux and results in a significant decrease in the ductility of the weldment. Regarding the relative influence of the Mn additions, there appears to be no significant change in the subgrain structure as the percentage of Mn increases. However, the ductility tends to increase and it is also found that the tensile strength and microhardness of the fusion zone also increase slightly. Accordingly, the tensile rupture mode exhibits a slight tendency to change from flat to slant fracture. Although the interdendritic precipitates identified in the Mn series are similar to those in the Nb series, it should be noted that the precipitates appear in lower numbers and are smaller than their Nb counterparts.

Effects of Gravitational orientation on the microstructural evolution of gas tungsten arc welds in an Al-4 wt% Cu alloy

Gas tungsten arc (GTA) welds on Al-4 wt% Cu alloys were investigated to determine effects of gravitational orientation on the weld solidification behavior. A bead-on-plate welding was performed by varying the relation between the arc translation direction and gravity vector, e.g., parallel-up, parallel-down, and perpendicular orientations. A solidification rate (VS) was calculated from the measured grain orientation, and a thermal gradient (GL) was estimated from the observed weld pool shape following a linear relation. A primary dendrite spacing (λ1) decreased continuously from the s-l boundary to the weld pool surface regardless of the gravitational orientations. Larger λ1 for the parallel-up weld was observed near the boundary and surface than that of the perpendicular and parallel-down welds, which is believed to be associated with a smaller GL due to larger weld pool dimension and with different solidification morphology. A solidification morphology and orientation in the perpendicular and parallel-up welds was comparable with a loss of columnar directionality near the weld surface and a continuous grain orientation. However, the parallel-down weld exhibited more columnar structure near the surface, which might be associated with the larger GL and relatively mild convection flows. Outward convection flows in the parallel-down weld might be inhibited because of its reverse direction with respect to the gravity vector. This resulted in abnormal ‘S’ shape of the trailing s-l interface and the VS, which was receded toward the weld pool center. Based on these findings, significant influence of gravitational orientation resulted in the variation on the weld pool shape associated with convection flows, which in turn affected solidification orientation/morphology and the primary dendrite spacing.

The Effect of Solidification Rates and Thermal Gradients on Directionally Solidified Microsturucture in the Ni-Base Superally GTD111M

Morphological evolution and growth mechanism at the solid/liquid interface during solidification were investigated in the Ni-base superalloy GTD111M by directional soldification and quenching(DSQ) technique. The experiments were conducted by changing solidification rate(V) and thermal gradient(G) which are major solidification process variables. High thermal gradient condition could be obtained by increasing the furnace temperature and closely attaching the heating and cooling zones in the Bridgeman type furnace. The dendritic/equiaxed transition was found in the G/V value lower than <TEX>$0.05<TEX>$\times$</TEX>10{^3}^{\circ}C$</TEX>s/<TEX>$\textrm{mm}^2$</TEX>, and the planar interface of the MC-<TEX>${\gamma}$</TEX> eutectic was found under <TEX>$17 <TEX>$\times$</TEX> 10{^3}^{\circ}C$</TEX> s/<TEX>$\textrm{mm}^2$</TEX>. It was confirmed that the dendrite spacing depended on the cooling rate(GV), and the primary spacing was affected by the thermal gradient more than solidification rate. The dendrite lengths were decreased as increasing the thermal graditne, and the dendrite tip temperature was close to the liquidus temperature at <TEX>$50 \mu\textrm{m}$</TEX>/s.

Cellular/dendritic transition during unsteady-state unidirectional solidification of Sn–Pb alloys

Structural parameters such as grain size, dendritic and cellular spacings, segregated products, porosity and other phases are strongly influenced by the thermal behavior of the metal/mold system during solidification, imposing a close correlation between this and the resulting microstructure. Numerous unidirectional solidification studies have been carried out with the objective of characterizing cellular and dendritic spacings and most of the published work has involved solidification in steady-state heat flow conditions. The objective of this article is to determine the thermal solidification parameters affecting the cellular/dendritic transition as well as to compare theoretical models that predict cellular and primary dendritic spacings with experimental results for unsteady-state solidification. Experiments were carried out in a water cooled unidirectional solidification apparatus and dilute alloys of the Sn–Pb system have been used (Sn 1.5 wt.% Pb, Sn 2.5 wt.% Pb and Sn 5 wt.% Pb).

Theoretical - Experimental Analysis of Cellular and Primary Dendritic Spacings during Unidirectional Solidification of Sn-Pb Alloys

Structural parameters as grain size, dendritic and cellular spacings, segregated products, porosity and other phases are strongly influenced by the thermal behavior of the metal/mold system during solidification, imposing a close correlation between this and the resulting microstructure. Several unidirectional solidification studies with the objective of characterizing cellular and dendritic spacings have been developed in large scale involving solidification in steady-state heat flow. The main objective of this work is to determine the thermal solidification parameters during the cellular/dendritic transition as well as to compare theoretical models that predict cellular and primary dendritic spacings with experimental results for solidification situations in unsteady-state heat flow. Experiments were carried out in a water cooled unidirectional solidification apparatus and dilute alloys of the Sn-Pb system were used (Sn 1.5wt%Pb, Sn 2.5wt%Pb and Sn 5wt%Pb). The upper limit of the Hunt-Lu cellular growth model closely matched the experimental spacings. The lower limit calculated with the Hunt-Lu dendritic model best generated the experimental results. The cellular/dendritic transition was observed to occur for the Sn 2.5wt%Pb alloy over a range of analytical cooling rates from 0.28 K/s to 1.8 K/s.

Rigid dendritic donor-acceptor ensembles: control over energy and electron transduction.

Several generations of phenylenevinylene dendrons, covalently attached to a C(60) core, have been developed as synthetic model systems with hierarchical, fine-tuned architectures. End-capping of these dendritic spacers with dibutylaniline or dodecyloxynaphthalene, as antennas/electron donors, yielded new donor-bridge-acceptor ensembles in which one, two, or four donors are allocated at the peripheral positions of the well-defined dendrons, while the electron accepting fullerene is placed at the focal point of the dendron. On the basis of our cyclic voltammetry experiments, which disclose a single anodic oxidation and several cathodic reduction processes, we rule out significant, long-range couplings between the fullerene core and the end-standing donors in their ground-state configuration. Photophysical investigations, on the other hand, show that upon photoexcitation an efficient and rapid transfer of singlet excited-state energy (6 x 10(10) to 2.5 x 10(12) s(-1)) controls the reactivity of the initially excited antenna portion. Spectroscopic and kinetic evidence suggests that yet a second contribution, that is, an intramolecular electron-transfer, exists, affording C(60)(.-) -dendron(.+) with quantum yields (Phi) as high as 0.76 and lifetimes (tau) that are on the order of hundreds of nanoseconds (220-725 ns). Variation of the energy gap modulates the interplay of these two pathways (i.e., competition or sequence between energy and electron transfer).

Characteristics of TiC dendrites in as solidified Ti–Al–C alloys

Results are reported on the dendrite secondary arm spacing of a series of as cast Ti–C and Ti–Al–C alloys in the composition range up to 10 at.-%C and 15 at.-%Al. The presence of Al leads to a significant decrease in the dendrite spacing, an effect of potential interest for improving mechanical properties. The structural refinement is attributed mainly to the slower diffusion of Al as compared with carbon, in the solute partitioning required for coarsening of dendrite arms.

Modeling of primary spacing selection in dendrite arrays during directional solidification

By analyzing the competitive growth in a dendrite array, an analytical model is proposed to describe the characteristic features in dendrite spacing selection. Nominal spacing, according to scale law at steady state, is defined as the baseline for spacing variation. Variation in dendrite spacing is attributed to the creation of new dendrites or to the elimination of existing dendrites. Newly formed spacing is equated to current nominal spacing factored by a kinetic factor. Critical velocities are proposed for the initiation of dendrite creation/elimination during increasing/decreasing velocity, thus yielding the length of incubation periods during which the spacing remains unchanged. The evolution of spacing distribution between its upper and lower limits, and thus weighted average spacing, can be calculated in the process of dendrite creation/elimination. Quantitative calculations have been performed for a model alloy succinonitrile-2.5 wt pct ethanol and compared with the experimental data reported in the literature. The results show that this model provides a reasonable description of the characteristic features of dendrite spacing selection, such as the wide range in spacing distribution, the delayed response in spacing variation, and its history dependence.

A real-scale anatomical model of the dentate gyrus based on single cell reconstructions and 3D rendering of a brain atlas

As a first step towards the creation of a cellular model of dentate gyrus (DG) anatomy, we distributed 1,000,000 digitized granule cells (gcs) in 3D in a virtual reality reconstruction of Swanson's brain atlas. DG coronal sections were assembled into 3D surfaces using implicit function generation. The resulting file included hilar, granular, and molecular boundaries. 20,000 replicas of each of 50 reconstructed gcs were added to the model by packing the somata in the appropriate layer and then radially orienting the dendritic tree axes. The model can be used to evaluate stereologic parameters such as dendritic overlap probability, space occupancy, and exposure to incoming fibers.

History effects during the selection of primary dendrite spacing. Comparison of phase-field simulations with experimental observations

The paper describes numerical experiments to investigate the selection of primary dendritic spacing λ under transient conditions. The phase field method coupled to solutal diffusion is combined with a moving frame algorithm to enlarge the total calculation domain. For constant growth conditions of an Al–7%Si alloy, a range of λ has been achieved depending on initial conditions. Quasistationary decrease of the solidification velocity leads to extinction of redundant trunks. Increasing the velocity leads to the formation of new trunks from ternary arms, but a striking incubation delay suggests a history-dependent spacing assignment. The results are compared to experimental and theoretical results.

Preparation of a ribonucleic acid-(polyamidoamine)-(zirconia-urea-formaldehyde resin) high-performance liquid affinity chromatographic stationary phase.

A preparative method for a high-performance liquid affinity chromatographic (HPLAC) stationary phase is described. The 3- to 5-microm nonporous composite spherical microparticles of zirconia and urea-formaldehyde (UF) resin are synthesized through the reaction of zirconyl chloride with hexamethylene tetra-amine and urea, and then it is used as the matrix of the HPLAC stationary phase of which the diameter and structure are determined by scanning electron microscopy. In a methanol medium, the polyamidoamine (PAMAM) starburst dentritic spacer arms are linked with the imido-groups on the surface of the matrix by the Michael addition reaction with methyl acrylate and the amination reaction with ethylene diamine. After repeating these steps in triplets, amine-terminated dentritic spacer arms with a generation of 3 are obtained. The topological structure of the spacer arms is examined by solid-state 13C NMR. The Br-substituted ribonucleic acid (RNA) ligand is obtained by the reaction of liquid bromine with RNA and bonded to the dendritic spacer arms of the matrix in a solution of NaOH (pH 9-11). The binding capacity of RNA is measured by UV spectrophotometry. A new type of stationary phase--RNA-(PAMAM)-(zirconia-UF resin--for HPLAC, which possesses starburst dendritic spacer arms, is synthesized and used for the separation of biological macromolecules.

Hydrogen porosity in directionally solidified aluminium–copper alloys: a mathematical model

A combined continuum and stochastic model of diffusion-controlled growth was developed to simulate the formation of porosity during the solidification of aluminium alloys. The whole population of pores was tracked, rather than just the average values. A finite difference solution of the diffusion equations was used, combined with a stochastic model of nucleation. The growth of each individual pore was simulated, assuming the shape to be spherical until it impinged on the developing dendrites, at which point the growth was modelled as a hemispherically capped segmented cone, with the growth radius limited by the liquid space between the dendrites. A previously published model by one of the authors was used to predict the dendritic spacing as a function of the thermal conditions. The model was compared with in situ observations of the formation of porosity during the solidification of aluminium–copper alloys, where the size, distribution and morphological evolution of pores were measured as a function of temperature/time. The predicted development of the porosity, including the distribution in size and morphology, compared well with that observed experimentally. The qualitative agreement between the model predictions and experimental results supports the hypothesis that the effect of hydrogen and its diffusion must be incorporated into any accurate model of pore formation in aluminium alloys.

Structure and properties of Al–Nb alloys produced by laser surface alloying

Al–Nb alloys present considerable strength and hardness, being promising materials for structural applications and for coatings. This paper reports results of a study of the structure and properties of Al–Nb surface alloys produced by laser alloying. Surface alloys were produced by a two-step process: firstly, commercial purity Al substrates were alloyed with Nb by injecting an Al–25 wt.% Nb powder mixture into the melt pool generated using a CO 2 laser, and, secondly, the microstructure was refined by laser melting. In the first step, Nb concentrates near the surface of the melt pool during solidification, resulting in the production of surface layers about 700 μm thick of Al–37.6 (±3) wt.% Nb alloy. These alloys are heterogeneous and present porosity and undissolved Nb particles for all the processing parameters used. Their microstructure is formed of large dendrites of Al 3Nb and interdendritic α-Al solid solution. Laser melting of the alloyed layers results in complete elimination of defects and homogenisation of the material. Previously undissolved Nb particles dissolve, raising the Nb concentration in the alloy and increasing the volume fraction of Al 3Nb. The microstructure still consists of Al 3Nb and α-Al solid solution but the dendrites are finer and the volume fraction of interdendritic α is less than 5%. The Vickers microhardness of the surface alloys is high owing to the large amount of this intermetallic compound. It varies from 480 to 650 HV, depending on the volume fraction and dendrite spacing of Al 3Nb. Despite the brittleness of Al 3Nb no cracks were observed, probably because of the presence of the thin interdendritic film of ductile Al solid solution, which enables better accommodation of the generated stresses.

A mechanism for the equalisation of primary spacing during cellular and dendritic growth

The Hunt and Lu [Metall. Mater. Trans. A27A (1996) 611] model for the selection of primary spacing, λ, during cellular and dendritic growth predicts a range of spacings falling between minimum and maximum values of λmin and λmax respectively. Within the model λmax/λmin will be at least 2 and may, under certain circumstances, be significantly greater. In this paper we use a free boundary model of solidification within an array to demonstrate that interaction between the tips of the cells or dendrites leads to a transverse adjustment mechanism that will tend to equalise the spacing as growth proceeds. This transverse adjustment mechanism is shown to be rapid for the spacings characteristic of cellular growth but much more gradual for the spacings characteristic of dendritic growth. These findings are consistent with observations of the primary spacing of dendrites grown in alloys of the transparent casting analogue, succinonitrile.

Correlation between unsteady-state solidification conditions, dendrite spacings, and mechanical properties of Al-Cu alloys

The wide range of operational conditions existing in foundry and casting processes generates as a direct consequence a diversity of solidification microstructures. Structural parameters such as grain size and interdendritic spacings are strongly influenced by the thermal behavior of the metal/mold system during solidification, imposing, as a consequence, a close correlation between this system and the resulting microstructure. Mechanical properties depend on the microstructural arrangement defined during solidification. Expressions correlating the mechanical behavior with microstructure parameters should be useful for future planning of solidification conditions in terms of a determined level of mechanical strength, which is intended to be attained. In the present work, analytical expressions have been developed describing thermal gradients and tip growth rate during one-dimensional unsteady-state solidification of alloys. Experimental results concerning the solidification of Al-4.5 wt pct Cu and Al-15 wt pct Cu alloys and dendritic growth models have permitted the establishment of general expressions correlating microstructure dendrite spacings with solidification processing variables. The correlation of these expressions with experimental equations relating mechanical properties and dendrite spacings provides an insight into the preprogramming of solidification in terms of casting mechanical properties.

Associative memory model with temporal spike coding and active dendrite

We propose a neuron model whose internal state is integrated on a two dimensional phase space composed of time and dendritic space. Here, the postsynaptic potential is given as a curved surface on the phase space. Using the proposed neuron model, we introduce a continuous-time associative memory model with spike propagation delay and multiple synaptic sites on the dendrite. We show by numerical simulation that the memory capacity is doubled due to the effects of temporal spike coding and active dendrite compared to the sparse coding associative memory model.

Mushy zone morphology during directional solidification of Pb-5.8 wt pct Sb alloy

The Pb-5.8 wt pct Sb alloy was directionally solidified with a positive thermal gradient of 140 K cm−1 at a growth speed ranging from 0.8 to 30 µm s−1, and then it was quenched to retain the mushy zone morphology. The morphology of the mushy zone along its entire length has been characterized by using a serial sectioning and three-dimensional image reconstruction technique. Variation in the cellular/dendritic shape factor, hydraulic radius of the interdendritic region, and fraction solid along the mushy zone length has been studied. A comparison with predictions from theoretical models indicates that convection remarkably reduces the primary dendrite spacing while its influence on the dendrite tip radius is not as significant.

Influence of heat input and travel speed on microstructure and mechanical properties of double tandem submerged arc high strength low alloy steel weldments

An evaluation is presented of the microstructural characteristics and mechanical properties of welds in 20 mm thickness high strength low alloy steel HSLA 80, of Australian manufacture. In total, nine butt joints were prepared using the double tandem (four wire) submerged arc welding process in which both heat input and travel speed were varied. The inclusion size distribution was determined for selected welds and showed that heat input had a major effect. Colour etching techniques were used to reveal the solidification structure, which in turn correlated with welding parameters. As the heat input increased, the cooling rate decreased resulting in a larger cellular dendritic cell spacing, decreased acicular ferrite content, and coarser acicular ferrite laths. The effect of travel speed on delta ferrite cell spacing and prior austenite grain size was found to be co-dependent on the heat input and the thermal profile resulting from multiple electrode welding. These results show that increased deposition rates can be achieved by increasing the travel speed and current density without sacrificing joint quality.