Interlamellar Spacing in Directionally Solidified Eutectic Thin Films

Fault-free lamellar structures were grown in eutectic thin films of Pb-Sn, Cd-Pb, and Al-Al₂Cu. The 2 μ thick films were directionally solidified by either a scanning laser or a quartz iodine lamp. A thermal gradient at the solid-liquid interface was estimated to be 8000°C/cm for the laser heat source compared to 200°C/cm for the lamp. In each alloy the lamellar spacing was larger than values estimated from previous experiments with bulk material. Defects in the films were observed to generate V-shaped waves of bent plates that provide a mechanism for increasing the lamellar spacing. Computer-simulated microstructures for two dimensional lamellar growth were made by calculating the diffusion in the liquid ahead of an irregular lamellar structure assuming a planar interface, finding the shape of the solid-liquid interface, and finding the trajectories of the three phase junctions. The mechanism of two-dimensional eutectic growth was discussed. This paper is based on a presentation made at the symposium “Establishment of Microstructural Spacing during Dendritic and Cooperative Growth” held at the annual meeting of the AIME in Atlanta, Georgia on March 7, 1983 under the joint sponsorship of the ASM-MSD Phase Transformations Committee and the TMS-AIME Solidification Committee     

A Review of the Data on the Interlamellar Spacing of Pearlite

After defining interlamellar spacing the various optical and electron optical methods for measuring spacing are outlined. It is clear for both isothermal and forced velocity transformation conditions that pearlite can grow at a constant velocity with a range of true spacings. The minimum true spacing and mean true spacing are not related by a constant factor, but this may vary from system to system and with temperature in a given system. The relationship between interlamellar spacing and temperature for isothermal growth conditions and between translation velocity and spacing for forced-velocity growth conditions is reviewed for a range of steels and nonferrous alloys. It is seen that the velocity-spacing relationship for the two modes of transformation is the same. For isothermal transformation a linear relationship between reciprocal spacing and temperature is generally observed, but for steels containing alloy additions there is little evidence of the predicted inflexion corresponding to a temperature at which alloy partitioning at the transformation front ceases. The lack of precise interfacial energy data makes it difficult to determine reliably the relationship between measured and critical spacings, although it seems likely to be in accord with the maximum growth rate or maximum rate of entropy production optimization criteria. This paper is based on a presentation made at the symposium “Establishment of Microstructural Spacing during Dendritic and Cooperative Growth” held at the annual meeting of the AIME in Atlanta, Georgia on March 7, 1983 under the joint sponsorship of the ASM-MSD Phase Transformations Committee and the TMS-AIME Solidification Committee.     

A Numerical Finite Difference Model of Steady State Cellular and Dendritic Growth

A theoretical model is developed to treat the steady state growth of an array of cells and dendrites in a positive temperature gradient using finite difference techniques. The coupled three dimensional heat and solute flow equations have been solved in a ‘half-cell’ repeat unit with radial symmetry using the conservation boundary conditions at the solid-liquid interface. As, however, the problem is a free boundary one, there is an additional condition to be satisfied at the solid-liquid interface. Using this ‘equilibrium’ condition, self-consistent cell shapes have been obtained. Calculations have been carried out at several different growth velocities for fixed values of alloy content and liquid gradient. At each velocity self-consistent shapes have been found up to a maximum value of the cell spacing. The effect of surface energy and the kinetic coefficient on growth behavior has also been examined. Formerly Research Fellow, Department of Metallurgy, Oxford University This paper is based on a presentation made at the symposium “Establishment of Microstructural Spacing during Dendritic and Cooperative Growth” held at the annual meeting of the AIME in Atlanta, Georgia on March 7, 1983 under the joint sponsorship of the ASM-MSD Phase Transformations Committee and the TMS-AIME Solidification Committee.     

Interdendritic Spacing: Part I. Experimental Studies

Directional solidification experiments have been carried out in a succinonitrile-5.5 mol pct acetone system to characterize dendrite tip radius and interdendrite spacings as functions of growth rate and temperature gradient in the liquid. A maximum in primary dendrite spacing as a function of growth rate is observed, and this maximum is found to occur at the dendrite-cellular transition velocity. A scaling law is shown to exist between the secondary dendrite arm spacing, λ₂, near the tip and the dendrite tip radius, p, which is λ₂/ρ = 2.2 ± 0.3. Experimental results on ρ have been found to agree with the theoretical model based on the marginal stability criterion. This paper is based on a presentation made at the symposium “Establishment of Microstructural Spacing during Dendritic and Cooperative Growth” held at the annual meeting of the AIME in Atlanta, Georgia on March 7, 1983 under the joint sponsorship of the ASM-MSD Phase Transformations Committee and the TMS-AIME Solidification Committee.     

Interdendritic Spacing: Part II. A Comparison of Theory and Experiment

The primary spacing data of Part I are compared to the existing theoretical models of Hunt and of Kurz and Fisher, and a significant disagreement is found. A theoretical model based on the Hunt model is developed, and it is found that the theory adequately explains the variation in primary spacing, λ₁, with the growth rate,V. A maximum in λ₁,vs V is predicted and the velocity at which the maximum occurs matches with the result obtained experimentally. It is shown that the maximum in λ₁ corresponds to the dendrite-to-cell transition, and cellular structures are found to grow with much smaller spacings than dendritic structures under identical growth conditions. This paper is based on a presentation made at the symposium “Establishment of Microstructural Spacing during Dendritic and Cooperative Growth” held at the annual meeting of the AIME in Atlanta, Georgia on March 7, 1983 under the joint sponsorship of the ASM-MSD Phase Transformations Committee and the TMS-AIME Solidification Committee.     

Dendritic solidification of alloys in low gravity

Gravity-driven convective flow influences dendrite morphology, interdendritic fluid flow, dendrite interface morphology, casting macrosegregation, formation of channel type casting defects, and casting grain structure. Dendritic solidification experiments during multiple parabolic aircraft maneuvers for iron-carbon type alloys and superalloys show increased dendritic spacing in low-gravity periods. Larger dendrite spacings for low-gravity solidification have also been reported for sounding rocket and space laboratory experiments for metal-model and binary alloys. Convection decreases local solidification time and increases the rate of interdendritic solute removal. The elimination of convection in low gravity is thus expected to increase dendritic spacing. Convection's effect on dendritic arm coarsening is expected to be dependent on the coarsening mechanism. Decreased coarsening in low gravity found for Al-Cu is indicative of coarsening predominately by arm coalescence. This paper is based on a presentation made in the symposium “Experimental Methods for Microgravity Materials Science Research” presented at the 1988 TMS-AIME Annual Meeting in Phoenix, Arizona, January 25–29, 1988, under the auspices of the ASM/MSD Thermodynamic Data Committee and the Material Processing Committee.     

Intrinsic ledges at interphase boundaries and the crystallography of precipitate plates

The structure of intrinsic ledges at interphase boundaries has been interpreted with extended O-lattice/DSC-lattice approaches. The distribution of structural ledges can be predicted if the spacing difference between parallel matrix and product planes is treated as a measure of the relaxed coincidence condition. A small rotation away from the low-index planar parallelism introduces a series of interfacial dislocations that cancels the spacing difference, resulting in a lattice invariant line. Misfit-compensating ledges at bcc: hcp interfaces are produced as a ledged interface intersects additional O-points that are recognized with the incorporation of previously omitted bcc atom positions into the O-lattice construction. Energetic consideration suggests that structural interfacial energy may decrease when a flat interface becomes ledged with misfit-compensating ledges. Burgers vectors associated with structural ledges and misfit-compensating ledges are displacement shift complete (DSC) lattice vectors. Precipitate and martensite crystallography may both include a lattice invariant line, but they are involved in different interphase boundary characteristics. Assumptions and implications in precipitate and martensite crystallography are discussed in the framework of the O-lattice theory and phenomenological theory of martensite crystallography. This article is based on a presentation made at the Pacific Rim Conference on the “Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products,” held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL’S Phase Transformations Committee.     

Eutectic Growth in Three Dimensions

Critical experimental studies have been carried out to examine the stability of eutectic morphology in three-dimensional (3-D) samples under diffusive growth conditions. By directionally solidifying capillary samples of the well-characterized Al-Cu eutectic alloy, it is shown that the observed minimum spacing agrees with the value predicted by the Jackson and Hunt (JH) model, but the range of stable spacing is reduced significantly in three dimensions. The ratio of the maximum to minimum eutectic spacing in three dimensions is found to be only 1.2 compared to the predicted value of 2.0 in two dimensions. The narrow range of stable spacing is shown to be due to the instabilities in the third dimension that forms when the local spacing becomes larger than some critical spacing value, which corresponds to the maximum stable spacing. A new mechanism of lamellar creation in the third dimension is observed in which lamella with a local spacing larger than the critical value becomes unstable and forms a sidewise perturbation that becomes enlarged at the leading front and then propagates parallel to the lamella to create a new lamella. Alternately, an array of sidewise perturbations form, which then coalesce at their leading fronts and then become detached from the parent lamella to form a new lamella. This article is based on a presentation made in the symposium entitled “Solidification Modeling and Microstructure Formation: In Honor of Prof. John Hunt,” which occurred March 13–15, 2006, during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the TMS Materials Processing and Manufacturing Division, Solidification Committee.     

Strain-induced self-organization of steps and islands in SiGe/Si multilayer films

It has recently been recognized that “stress management” may become a unique way of fabricating nanostructures, because structural self-assembly and self-organization can be strongly influenced by strain. In this article, we review recent studies of growth and ordering processes in multilayer films of alternating Si and SiGe layers with nanometer-layer spacing. The formation of ordered arrays, superlattices of step bunches, and three-dimensional (3-D) islands that exhibit remarkable spatial and size uniformity and very good long-range order, are demonstrated. Theoretical analyses and simulations based on elastic models are discussed to elucidate the lattice strain-induced formation and self-organization processes. The self-organized steps and 3-D islands provide a possible route for fabricating novel devices based on quantum wires and quantum dots. This article is based on a presentation made in the symposium “Kinetically Determined Particle Shapes and the Dynamics of Solid:Solid Interfaces,” presented at the October 1996 Fall meeting of TMS/ASM in Cincinnati, Ohio, under the auspices of the ASM Phase Transformations Committee.     

The growth kinetics of the discontinuous precipitation reaction in Mg−Al alloys

The extent, the growth rate and the interlamellar spacing of the discontinuous precipitation reaction in Mg−Al solid solutions with 5, 7, 9, and 11 at. pct Al are presented and analyzed by the theories of Turnbull, Cahn and Sundquist.K ₀λD ^B-values are computed with the aid of Turnbull's formula as well as Sundquist's solution of the diffusion problem. The activation energies confirm the assumption of grain boundary diffusion to be the rate controlling process. The thermodynamic of the reaction was treated on the base of the regular solution. The “maximum growth rate” criterion yields interlamellar spacings deviating clearly from the experimental values whether Turnbull's formula or Cahn's treatment was taken as a basis. The application of Sundquist's concept provides the boundary shape as a function of interlamellar spacing. The parameter ϑ', by which the boundary shape is determined, lies in the range -0.3 ⪯ ϑ' ⪯ 2 at the experimental spacing, which is the minimum true spacing. These ϑ'-values correspond to boundary shapes with no or moderate recesses. Observed boundary shapes are not in contrast to these results. The development of recesses by increasing interlamellar spacing is observed too and confirmed theoretically. Deep recesses guarantee the creation of new lamellae which reduce the enlarged spacings to such with more stable boundary shapes. This leads to the conclusion that the concept of unique interlamellar spacing must be abandoned in favor of a distribution of spacings according to the probability of nucleation of new lamellae.     

Microporosity Simulation in Aluminum Castings Using an Integrated Pore Growth and Interdendritic Flow Model

A new computational model for predicting microporosity in aluminum alloys is described. The model was calibrated against literature data for binary Al-7 pct Si alloys, and subsequently applied to a chill plate test casting in A356 alloy and to an engine block in 319 alloy. The new model allows spherical micropores to nucleate and grow by hydrogen diffusion from a material volume surrounding the pores. This differs from a conventional interdendritic flow computational model for calculating porosity that assumes spherical pores have a diameter proportional to the secondary dendrite arm spacing (SDAS). The new integrated pore growth and interdendritic flow model predicts larger pore diameters and a volume fraction of microporosity that is in better agreement with experimental observations than the interdendritic flow model. This article is based on a presentation made in the symposium “Simulation of Aluminum Shape Casting Processing: From Design to Mechanical Properties,” which occurred March 12–16, 2006, during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the Computational Materials Science and Engineering Committee, the Process Modeling, Analysis and Control Committee, the Solidification Committee, the Mechanical Behavior of Materials Committee, and the Light Metal Division/Aluminum Committee.     

Processing,microstructure, and mechanical properties of (Nb)/Nb<Subscript>5</Subscript>Si<Subscript>3</Subscript> two-phase alloys

It has been shown that a fine lamellar structure composed of Nb solid solution, (Nb), and Nb₅Si₃ is formed through eutectoid decomposition in the Nb-Si binary system and its ternary derivatives. Such alloys would exhibit a high strength at over 1400 K, yet showing room-temperature toughness of over 10 to 20 MPa m^1/2 if a proper lamellar spacing is chosen. In the present work, effects of processing on the microstructure evolution and mechanical properties are investigated on the Nb-18 at. pct Si alloys prepared by hot pressing (HP) and spark-plasma sintering (SPS). The powders used in the present work are of pure Nb and Nb₅Si₃ in order for the fabrication to become possible at temperatures higher than the melting point of Si and to reduce the formation of SiO₂. The results show that the SPS yields more uniform two-phase microstructure but the alloy fabricated through HP tends to provide higher elevated temperature strength. This article is based on a presentation made in the symposium entitled “Beyond Nickel-Base Superalloys,” which took place March 14–18, 2004, at the TMS Spring meeting in Charlotte, NC, under the auspices of the SMD-Corrosion and Environmental Effects Committee, the SMD-High Temperature Alloys Committee, the SMD-Mechanical Behavior of Materials Committee, and the SMD-Refractory Metals Committee.     

Void/pore distributions and ductile fracture

The dependence of ductile, microvoid fracture on the size and distribution of voids or pores has been modeled experimentally. Pores or voids have been physically modeled in two dimensions by both random and regular arrays of equi-sized holes drilled through the thickness of tensile specimens of 1100-0 Al sheet and 7075-T6 Al plate and sheet. Fracture strains as well as failure paths have been determined for different hole sizes, spacings, and area fractions. A statistical analysis of the data indicates that increasing the minimum hole spacing, which decreases the degree of hole clustering, increases both strength and ductility. Conversely, decreasing the hole size causes a minor increase in both strength and ductility. Increasing the rate of work hardening is beneficial to ductility in that a high strain hardening rate appears to increase the resistance to flow localization between holes. The results are discussed in terms of a fracture process which depends on shear localization between holes/voids and which is very sensitive to void/pore distributions. This paper is based on a presentation made at the symposium “Stochastic Aspects of Fracture” held at the 1986 annual AIME meeting in New Orleans, LA, on March 2-6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee.     

Microstructural evolution and mechanical properties of Cr-Ru alloys

In an effort to enhance ductility and strength of Cr-base alloys, a series of Cr-Ru alloys with Ru contents ranging from 3 to 30 at. pct were made to study their microstructure evolution and mechanical properties. The microstructure of the alloys with 6 to 20 at. pct Ru showed signs of a eutectic structure. However, no corresponding eutectic reaction is indicated in the published Cr-Ru phase diagram. The yield strength of the Cr-Ru alloys increased with increasing Ru content at both room temperature and 1200 °C. The tensile ductility of Cr-3 at. pct Ru is about 1.5 pct at room temperature, while the alloys containing 6 at. pct or more Ru showed zero tensile elongation. The deformation mechanisms of the Cr-Ru alloys are discussed in terms of the microstructure and fracture behavior. This article is based on a presentation made in the symposium entitled “Beyond Nickel-Base Superalloys,” which took place March 14–18, 2004, at the TMS Spring meeting in Charlotte, NC, under the auspices of the SMD-Corrosion and Environmental Effects Committee, the SMD-High Temperature Alloys Committee, the SMD-Mechanical Behavior of Materials Committee, and the SMD-Refractory Metals Committee.     

Modeling of local strains in ductile fracture

The concept of dividing microvoid coalescence (MVC) ductile fracture into three constituent processes, nucleation, growth, and coalescence, is discussed, with emphasis on needs for additional analytical and experimental work. Statistical and stochastic aspects of the problem are presented. Recent work on modeling of local strains during ductile fracture, and particularly as components of fracture toughness, is summarized and discussed in light of current knowledge of ductile fracture. Such local strain modeling is especially attractive because it permits micromechanisms of fracture to be explicitly included in the fracture model. This paper is based on a presentation made at the symposium “Stochastic Aspects of Fracture” held at the 1986 annual AIME meeting in New Orleans, LA, on March 2-6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee.     

Computational Modeling of Microstructure Evolution in Solidification of Aluminum Alloys

In this article, a front tracking (FT) model and a modified cellular automaton (MCA) model are presented and their capabilities in modeling the microstructure evolution during solidification of aluminum alloys are demonstrated. The FT model is first validated by comparison with the predictions of the Lipton–Glicksman–Kurz (LGK) model. Calculations of the steady-state dendritic tip growth velocity and equilibrium liquid composition as a function of melt undercooling for an Al-4 wt pct Cu alloy exhibit good agreement between the FT simulations and the LGK predictions. The FT model is also used to simulate the secondary dendrite arm spacing as a function of local solidification time. The simulated results agree well with the experimental data. The MCA model is applied to simulate dendritic and nondendritic microstructure evolution in semisolid processing of an Al-Si alloy. The effect of fluid flow on dendritic growth is also examined. The solute profiles in equiaxed dendritic solidification of a ternary aluminum alloy are simulated as a function of cooling rate and compared with the prediction of the Scheil model. The MCA model is extended to the multiphase system for the simulation of eutectic solidification. A particular emphasis is made on the quantitative aspects of simulations. This article is based on a presentation made in the symposium ”Simulation of Aluminum Shape Casting Processing: From Design to Mechanical Properties,” which occurred March 12–16, 2006, during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the Computational Materials Science and Engineering Committee, the Process Modeling, Analysis and Control Committee, the Solidification Committee, the Mechanical Behavior of Materials Committee, and the Light Metal Division/Aluminum Committee.     

The Influence of Fluid Flow on the Microstructure of Directionally Solidified AlSi-Base Alloys

To obtain a quantitative understanding of the effect of fluid flow on the microstructure of cast alloys, a technical Al-7 wt pct Si-0.6 wt pct Mg alloy (A357) has been directionally solidified with a medium temperature gradient under well-defined thermal and fluid-flow conditions. The solidification was studied in an aerogel-based furnace, which established flat isotherms and allowed the direct optical observation of the solidification process. A coil system around the sample induces a homogeneous rotating magnetic field (RMF) and, hence, a well-defined flow field close to the growing solid-liquid interface. The application of RMFs during directional solidification results in pronounced segregation effects: a change to pure eutectic solidification at the axis of the sample at high magnetic field strengths is observed. The investigations show that with increasing magnetic induction and, therefore, fluid flow, the primary dendrite spacing decreases, whereas the secondary dendrite arm spacing increases. An apparent flow effect on the eutectic spacing is observed. This article is based on a presentation made in the symposium entitled “Solidification Modeling and Microstructure Formation: in Honor of Prof. John Hunt,” which occurred March 13–15, 2006 during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the TMS Materials Processing and Manufacturing Division, Solidification Committee.     

The pearlite reaction

A critical appraisal of theory and experiments for both isothermal and forced velocity pearlite is presented. It is concluded for binary systems that both the theoretical models for volume diffusion and boundary diffusion control are well-advanced and adequate for the purposes of experimental test. However, some ambiguity remains in the boundary diffusion model with respect to the thermodynamics of the boundary ”phase” region, so it is still not possible to predict absolute rates of transformation. The theoretical problem for ternary pearlites is also well understood, although rigorous theory seems intractable. A new perturbation procedure for definition of the optimal steady-state spacing is presented and amplified for both isothermal and forced velocity pearlite, and for both volume and boundary diffusion models. In terms of the critical spacing S_c for isothermal pearlite and the spacing at minimum undercooling S_m for forced velocity pearlite the predicted stability points are as follows: {fx2777-1} For isothermal pearlite these perturbation results correspond closely to the state of maximum entropy production rate while for forced velocity pearlite the correspondence is also satisfactory. A detailed analysis of the data leads us to reaffirm the author’s conclusions that the eutectoid reactions in Cu-12 pct Al and some related ternary alloys reported by Asundi and West are controlled by volume diffusion and that the eutectoid reaction in Al-78 Zn reported by Cheetham and Ridley is controlled by boundary diffusion. We conclude further after careful analysis that the pearlite reaction in Fe-0.8 C is controlled for the higher temperatures by volume diffusion of carbon in austenite. We are also led to state that the pearlite transformations in Fe-C-Mn and Fe-C-Ni occur for the most part in a nopartition regime and are therefore controlled by volume diffusion of carbon in austenite, while the transformations in Fe-C-Cr and Fe-C-Mo, being forced by thermodynamics to sustain partition of chromium and molybdenum, are controlled by phase boundary diffusion of the latter elements. nt]mis|M. P. PULS, formerly Postdoctoral Fellow, Department of Metallurgy and Materials Science, McMaster University, Hamilton, Ontario, Canada This paper is based on a presentation made at a symposium on “The Cellular and the Pearlite Reactions,” held at the Detroit Meeting of The Metallurgical Society of AIME, October 20, 1971, under the sponsorship of the IMD Heat Treatment Committee.     

Numerical modeling of cellular/dendritic array growth: spacing and structure predictions

A numerical model of cellular and dendritic growth has been developed that can predict cellular and dendritic spacings, undercoolings, and the transition between structures. Fully self-consistent solutions are produced for axisymmetric interface shapes. An important feature of the model is that the spacing selection mechanism has been treated. A small, stable range of spacings is predicted for both cells and dendrites, and these agree well with experiment at both low and high velocities. By suitable nondimensionalization, relatively simple analytic expressions can be used to fit the numerical results. These expressions provide an insight into the cellular and dendritic growth processes and are useful for comparing theory with experiment. This article is based on a presentation made at the “Analysis and Modeling of Solidification” symposium as part of the 1994 Fall meeting of TMS in Rosemont, Illinois, October 2–6, 1994, under the auspices of the TMS Solidification Committee.     

Equal-channel angular extrusion of beryllium

The equal-channel angular extrusion (ECAE) technique has been applied to a powder metallurgy (P/M) source Be alloy. Extrusions have been successfully completed on Ni-canned billets of Be at approximately 425 °C. No cracking was observed in the billets, and significant grain refinement was achieved. In this article, microstructural features and dislocation structures are discussed for a single-pass extrusion, including evidence of 〈c〉 and 〈c+a〉 dislocations. Significant crystallographic texture developed during ECAE, which is discussed in terms of this unique deformation processing technique and the underlying physical processes which sustain the deformation. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.