Modelling of microstructure formation and evolution during solidification

A comprehensive probabilistic model for simulating microstructure formation and evolution during solidification has been developed, based on coupling a Finite Differential Method (FDM) for macroscopic modelling of heat diffusion to a modified Cellular Automaton (mCA) for microscopic modelling of nucleation, growth of microstructures and solute diffusion. The mCA model is similar to Nastac's model for handling solute redistribution in the liquid and solid phases, curvature and growth anisotropy, but differs in the treatment of nucleation and growth. The aim is to improve understanding of the relationship between the solidification conditions and microstructure formation and evolution. A numerical algorithm used for FDM and mCA was developed. At each coarse scale, temperatures at FDM nodes were calculated while nucleation-growth simulation was done at a finer scale, with the temperature at the cell locations being interpolated from those at the coarser volumes. This model takes account of thermal, curvature and solute diffusion effects. Therefore, it can not only simulate microstructures of alloys both on the scale of grain size (macroscopic level) and the dendrite tip length (mesoscopic level), but also investigate nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies. The calculated results are compared with values of grain sizes and solidification morphologies of microstructures obtained from a set of casting experiments of Al-Si alloys in graphite crucibles.

Impact of casting parameters and chemical composition on the solidification behaviour of Al-Si-Cu hypoeutectic alloy

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2010

An approximate mathematical model for solidification of a flowing liquid in a microchannel

A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the ice shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close.

One-dimensional solidification of supercooled melts

In this paper a one-phase supercooled Stefan problem, with a nonlinear relation between the phase change temperature and front velocity, is analysed. The model with the standard linear approximation, valid for small supercooling, is first examined asymptotically. The nonlinear case is more difficult to analyse and only two simple asymptotic results are found. Then, we apply an accurate heat balance integral method to make further progress. Finally, we compare the results found against numerical solutions. The results show that for large supercooling the linear model may be highly inaccurate and even qualitatively incorrect. Similarly as the Stefan number β → 1&sup&+&/sup& the classic Neumann solution which exists down to β =1 is far from the linear and nonlinear supercooled solutions and can significantly overpredict the solidification rate.

Feedback control of unstable cellular solidification fronts

We present a feedback control scheme to stabilize unstable cellular patterns during the directional solidification of a binary alloy. The scheme is based on local heating of cell tips which protrude ahead of the mean position of all tips in the array. The feasibility of this scheme is demonstrated using phase-field simulations and, experimentally, using a real-time image processing algorithm, to track cell tips, coupled with a movable laser spot array device to heat the tips locally. We demonstrate, both numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable with uniform spacing through the feedback control which is maintained with minimal heating.

Fusion weld metal solidification:Continuum from weld interface to centerline

We present a brief résumé of the history of solidification research and key factors affecting the solidification of fusion welds. There is a general agreement of the basic solidification theory, albeit differing - even confusing - nomenclatures do exist, and Cases 2 and 3 (the Chalmers' basic boundary conditions for solidification, categorized by Savage as Cases) are variably emphasized. Model Frame, a tool helping to model the continuum of fusion weld solidification from start to end, is proposed. It incorporates the general solidification models, of which the pertinent ones are selected for the actual modeling. The basic models are the main solidification Cases 1…4. These discrete Cases are joined with Sub-Cases: models of Pfann, Flemings and others, bringing needed Sub-Case variables into the model. Model Frame depicts a grain growing from the weld interface to its centerline. Besides modeling, the Model Frame supports education and academic debate. The new mathematical modeling techniques will extend its use into multi-dimensional modeling, introducing new variables and increasing the modeling accuracy. We propose a model: melting/solidification-model (M/S-model) - predicting the solute profile at the start of the solidification of a fusion weld. This Case 3-based Sub-Case takes into account the melting stage, the solute back-diffusion in the solid, and the growth rate acceleration typical to fusion welds. We propose - based on works of Rutter & Chalmers, David & Vitek and our experimental results on copper - that NEGS-EGS-transition is not associated only with cellular-dendritic-transition. Solidification is studied experimentally on pure and doped copper with welding speed range from 0 to 200 cm/min, with one test at 3000 cm/min. Found were only planar and cellular structures, no dendrites - columnar or equiaxed. Cell sub structures: rows of cubic elements we call "cubelettes", "cell-bands" and "micro-cells", as well as an anomalous crack morphology "crack-eye", were detected, as well as microscopic hot crack nucleus we call "grain-lag cracks", caused by a grain slightly lagging behind its neighbors in arrival to the weld centerline. Varestraint test and R-test revealed a change of crack morphologies from centerline cracks to grainand cell boundary cracks with an increasing welding speed. High speed made the cracks invisible to bare eye and hardly detectable with light microscope, while electron microscope often revealed networks of fine micro-cracks.

Dispersive liquid-liquid microextraction based on solidification of floating organic drop for simultaneous separation/preconcentration of nickel, cobalt and copper prior to determination by electrothermal atomic absorption spectrometry

A dispersive liquid-liquid microextraction based on solidification of floating organic drop for simultaneous extraction of trace amounts of nickel, cobalt and copper followed by their determination with electrothermal atomic absorption spectrometry was developed. 300 µL of acetone and 1-undecanol was injected into an aqueous sample containing diethyldithiocarbamate complexes of metal ions. For a sample volume of 10 mL, enrichment factors of 277, 270 and 300 and detection limits of 1.2, 1.1 and 1 ng L-1 for nickel, cobalt and copper were obtained, respectively. The method was applied to the extraction and determination of these metals in different water samples.

A NOVEL METHOD FOR THE DETERMINATION OF TRACE THORIUM BY DISPERSIVE LIQUID-LIQUID MICROEXTRACTION BASED ON SOLIDIFICATION OF FLOATING ORGANIC DROP

In this study, dispersive liquid-liquid microextraction based on the solidification of floating organic droplets was used for the preconcentration and determination of thorium in the water samples. In this method, acetone and 1-undecanol were used as disperser and extraction solvents, respectively, and the ligand 1-(2-thenoyl)-3,3,3-trifluoracetone reagent (TTA) and Aliquat 336 was used as a chelating agent and an ion-paring reagent, for the extraction of thorium, respectively. Inductively coupled plasma-optical emission spectrometry was applied for the quantitation of the analyte after preconcentration. The effect of various factors, such as the extraction and disperser solvent, sample pH, concentration of TTA and concentration of aliquat336 were investigated. Under the optimum conditions, the calibration graph was linear within the thorium content range of 1.0-250 µg L-1 with a detection limit of 0.2 µg L-1. The method was also successfully applied for the determination of thorium in the different water samples.

Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Simultaneous solidification of two catalyst wastes and their effect on the early stages of cement hydration

Two catalyst wastes (RNi and RAI) from polyol production were considered as hazardous, due to their respective high concentration of nickel and aluminum contents. This article presents the study, done to avoid environmental impacts, of the simultaneous solidification/stabilization of both catalyst wastes with type II Portland cement (CP) by non-conventional differential thermal analysis (NCDTA). This technique allows one to monitor the initial stages of cement hydration to evaluate the accelerating and/or retarding effects on the process due to the presence of the wastes and to identify the steps where the changes occur. Pastes with water/cement ratio equal to 0.5 were prepared, into which different amounts of each waste were added. NCDTA has the same basic principle of Differential Thermal Analysis (DTA), but differs in the fact that there is no external heating or cooling system as in the case of DTA. The thermal effects of the cement paste hydration with and without waste presence were evaluated from the energy released during the process in real time by acquiring the temperature data of the sample and reference using thermistors with 0.03 A degrees C resolution, coupled to an analog-digital interface. In the early stages of cement hydration retarding and accelerating effects occur, respectively due to RNi and RAl presence, with significant thermal effects. During the simultaneous use of the two waste catalysts for their stabilization process by solidification in cement, there is a synergic resulting effect, which allows better hydration operating conditions than when each waste is solidified separately. Thermogravimetric (TG) and derivative thermogravimetric analysis (DTG) of 4 and 24 h pastes allow a quantitative information about the main cement hydrated phases and confirm the same accelerating or retarding effects due to the presence of wastes indicated from respective NCDTA curves.

Characterization of the Al-3wt.%Si alloy in unsteady-state horizontal directional solidification

The main purpose of this paper is to investigate both the columnar to equiaxed transition and primary dendritic arm spacings of Al-3wt.%Si alloy during the horizontal directional solidification. The transient heat transfer coefficient at the metal-mold interface is calculated based on comparisons between the experimental thermal profiles in castings and the simulations provided by a finite difference heat flow program. Simulated curve of the interfacial heat transfer coefficient was used in another numerical solidification model to determine theoretical values of tip growth rates, cooling rates and thermal gradients that are associated with both columnar to equiaxed transition and primary dendritic arm spacings. A good agreement was observed between the experimental values of these thermal variables and those numerically simulated for the alloy examined. A comparative analysis is carried out between the experimental data of this work and theoretical models from the literature that have been proposed to predict the primary dendritic spacings. In this context, this study may contribute to the understanding of how to manage solidification operational parameters aiming at designing the microstructure of Al-Si alloys.