Interfacial steps and growth mechanism in ferrous pearlites

The role of steps at the growth and interlamellar interfaces in ferrous pearlites is examined. The direction steps at the ferrite/cementite interlamellar interface (FCI) first characterized by Hackney and Shiflet (HS)^1-5 are quantified by relating the degree of macroscopic curvature to step height and spacing using lattice imaging techniques. These interlamellar steps associated with alloy curvature are demonstrated to result directly from pearlite growth ledges. Interphase boundary carbide precipitation in an Fe-C-V alloy is employed to further demonstrate that the pearlite growth mechanism occurs through the migration of steps laterally across the growth front and that the reported mechanism is not specific to the high Mn-containing alloy. Analysis is based within the context of the dynamics of the phase transformation, with the argument made that the static interpretation of interphase boundary structure can be misleading. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Ledgewlse vaporization

Ledge formation and migration during evaporation were investigated for cleaved single crystals of alkali halides. The dependence of ledge velocity on ledge separation was determined, providing direct confirmation for the Burton, Cabrera, and Frank⁶ (BCF) theory for the case of evaporation. The effect of an externally applied electric field on the velocity of ledges is discussed, and the influence of impurities on the surface topography of evaporated crystals is shown. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

The crystallography and atomic structure of line defects in twin boundaries in hexagonal-close-packed metals

The crystallographic analysis of line defects in interfaces is discussed and applied to the particular case of twinning dislocations in hexagonal-close-packed (hop) metals, which have been studied here by atomistic simulation. Two crystallographic approaches are used; first, the concept of bicrystal structure maps is developed for the case of interfaces between crystals having multiple-atom bases, and second, the topological theory of line defects based on symmetry theory is used. On the basis of the atomistic calculations, some general conclusions concerning the relative contribution to the total energy of dislocations made by their elastic fields and core structures are presented. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Kinetic equations for concurrent size and shape coarsening by the ledge mechanism

The kinetic equations describing concurrent size and shape coarsening of plate-and rod-shaped particles having shapes that deviate from equilibrium are presented. In the derivations, the assumption is made that some of the interfaces are fully or partially coherent and migrate by the ledge mechanism. Three different interfacial character combinations are considered. The analysis also assumes a small and constant volume fraction of particles so that the average matrix composition can be estimated from knowledge of the particle size distribution, the surface area available for atomic attachment/detachment, and the diffusion distance. The resultant flux equations are then used in a computer model to predict the coarsening behavior of an ensemble of nonequilibrium-shaped particles. Comparison of these results with those obtained from the traditional coarsening theory of Lifshitz and Slyosov¹ and Wagner² (LSW) show significant discrepancies. These differences are attributed to the invalidity of many assumptions made in the LSW theory when applied to solid:solid coarsening systems. Formerly Graduate Student, Michigan. Technological University. Formerly Graduate Student, University of Utah. Formerly Graduate Student, University of Utah, Salt Lake City, UT. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Interface dislocations and ledges in oxidation and diffusional phase transformations

The origin of ledge concepts in growth from the vapor is reviewed. The ideas are extended to solid-state phase transformations with the added effects of strain and misorientation. Types of ledges and dislocations are classified. The concepts are illustrated for the example of oxidation of a metal. Further extensions to diffusional phase transformations are briefly discussed. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

The use of transmission electron microscopy for the assessment of interphase boundaries

The relative merits of the different ways in which the transmission electron microscope (TEM) has been commonly used to examine the form of interphase boundaries are assessed, and the potential application of the newly developed Fresnel Method is discussed. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Diffusion-controlled kink motion

A simple model for the growth of kinks by volume diffusion is discussed, and singular perturbation methods, valid for supersaturations much less than one, are used to derive coupled integral equations for the motion of trains of (well-spaced) kinks. Numerical results are presented for the motion of two-and three-kink trains. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Observations of the formation and kinetics of surface steps during evaporation and condensation

Surface step patterns produced by crystal growth or evaporation can be observed, e.g., on NaCl, AgBr, Ag, and Si, by means of the electron microscopic method of decoration. These observations give insight into the mechanisms (random two-dimensional (2-D) nucleation, formation of hills or pits by spirals or repeated preferential 2-D nucleation, kinematic step interaction, orientation dependence of step motion, light-influenced evaporation, and stage of coalescence of thin films) and molecular processes (surface and edge diffusion) of crystal and thin film growth. Combining the decoration and platinum-carbon replica techniques enables an interesting insight into the step kinetics during the process of faceting. The pinning of moving steps at impurities and their piling up are decisive particulars. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Electron microscopy of transformation dislocations at interphase boundaries

The concept of structural units (SU’s) developed in order to describe the atomic structures of twin boundary facets is also used for interphase boundary (IB) facets quasi-parallel to small near-coincident planar cells of the two adjacent lattices. These facets, which have their own SU’s, are separated by transformation dislocations (TD’s), the cores of which are often related to ledges having heights equal to several interplanar spacings. It is shown that the Somigliana dislocation (SD) concept is a good tool for the computation of elastic displacement fields of these TD’s in anisotropic elasticity. Applications are presented concerning the following IB’s observed in high-resolution transmission electron microscopy (HRTEM): Si/TiSi₂, Si/CoSi₂, and Ni₃Al/Ni₃Nb. The identification of the atomic rows around some TD’s at Si/CoSi₂ and Ni₃Al/Ni₃Nb has been obtained by careful comparisons of experimental and calculated images. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Computer simulation of the effect of coherency strain on cluster growth kinetics

To understand clustering behavior under the influence of a coherency strain, Monte Carlo simulations were carried out for both two-dimensional (2-D) square and three-dimensional (3-D) simple cubic lattices. In the Monte Carlo model, each solute was assumed to exert coherency stress owing to a tetragonal misfit strain and to have surface energy when in contact with solvent atoms. To account for the coherency strain of a cluster whose morphology continuously changes during aging, exact expressions for both the self-strain energy and elastic interaction term for rectangular parallelepipeds were derived. Strong elastic interactions among platelike clusters are shown to develop a stabilized structure with a tendency for bridging the clusters at a right angle. In the early stage of evolution, solute atoms were found to diffuse into regions of stress concentration. Morphological changes revealed step movements on the edge of a cluster, and some steps were moving in the direction of dissolution (rather than growth) for the cluster, thus displaying a dynamic nature of step movement. When an initial shape was an elastically unstable one, a large cluster was found to dissolve into its solid solution, while, in the same environment, a cluster of the same size with a stable morphology sustained growth. During dynamic evolution, some clusters showed concave, instead of convex, surfaces, even though the former are highly nonequilibrium shapes. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

The geometry and properties of ledges in interfaces

This paper is an overview of work on the structure and properties of line defects in crystalline interfaces. Emphasis is placed upon the treatment of the dislocation and step nature of the defects in a unified manner and upon the correct accounting for the step nature in topological analyses. It is also shown that consideration of the step character leads to predictions of behavior that are not always consonant with predictions based upon dislocation concepts alone. Much of the previous work on this subject has been developed for grain boundaries in cubic metals, and the means of extension to less simple cases is indicated. It is shown that results often depend upon the choice of a particular reference frame. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Real-Time atomic-level observations of in situ chemical reactions and transformations utilizing high-resolution electron microscopy

Three studies ofin situ chemical reactions or transformations utilizing real-time video recording of high-resolution microscopic images to reveal atomic resolution details are reported. In one study, the removal of a twin plane separating a surface promontory consisting of several hundreds of atoms from the main body of a TbO_x crystal is observed. In another study of a leached TbO_x specimen, the decomposition of a Tb(OH)₃ surface impurity is followed as the oxide product is accreted to the main body of the TbO₂ crystal. In a third example, a crystal of modified PbO2 grown from acid solution displays, in high resolution, rapid cooperative movement of scores to hundreds of atoms over the crystal surface before finally decomposing, presumably with loss of hydrogen, toβ-PbO₂. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

On the role of elastic interactions in the nucleation and growth of ledges

Elastic interactions among ledges on transformation interfaces have noticeable consequences when chemical and interfacial tension (capillary) forces are small, namely, near equilibrium. This occurs just at nucleation (unstable equilibrium) or during the slow coarsening regime. When the interface lies perpendicular to the misfit strain (as do the large faces of misfits in Al-Cu alloys), ledges of like sign repel one another, and nucleation of new ledges occurs as far as possible from existing ones. However, when the interface lies parallel to the misfit strain, ledges of like sign attract one another. We then expect the formation of superledges. Essentially, such an interface with ledges is elastically unstable. Expressions are derived for the kinetics of ledge amaleamation. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformation Committee of the Materials Science Division, ASM INTERNATIONAL.     

Growth kinetics of solid-liquid Ga interfaces: Part I. Experimental

A technique based on the Seebeck effect was used to determine directly the solid-liquid (S/L) interface supercooling and toin situ monitor the interfacial conditions during growth of high-purity Ga single crystals from a supercooled melt. Using this nonintrusive technique, the growth kinetics of faceted (111) and (001) interfaces were studied as a function of the interface supercooling in the range of 0.2 to 4.6 K, corresponding to bulk supercoolings of about 0.2 to 53 K. In addition, the growth kinetics have been determined as a function of crystal perfection related to the emergence of dislocations at the S/L interface. The results show that at low super-coolings, the faceted interfaces grow with either of the lateral growth mechanisms: two-dimensional nucleation-assisted (2DNG) or screw dislocation-assisted (SDG), depending on the perfection of the interface. At increased interfacial supercoolings, however, both growth rates (2DNG and SDG) become a linear function of the supercooling. Application of the existing growth theories to the experimental results gives only qualitative agreement and fails to predict the observed deviation in the kinetics at high supercoolings. A theoretical treatment of the growth of faceted interfaces will be given in Part II of this series.¹ Formerly Research Assistant with the Department of Materials Science and Engineering, University of Florida. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

The role of ledges in vapor/solid phase transformations observed by low-energy electron microscopy and photoemission electron microscopy

Adsorption at monatomic ledges was observedin situ, in real time, during the epitaxial growth of Cu deposited from the vapor phase onto Mo{110}. Migration of monatomic ledges of Cu was followed during both growth and sublimation near equilibrium conditions and was independent of crystallographic direction in accord with fundamental theories of crystal growth. Evidence is presented showing that the two-dimensional (2-D) vapor pressure of Cu Actatoms on the terraces near curved ledges differs from that near straight ledges. Formerly with the Technical University of Clausthal.This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Bainitelike transformations in some oxide ceramics

The authors show two examples of “bainitelike” transformations in some oxide ceramics. A bainitelike transformation means that a shear (martensitic) mechanism is controlled by, or together with, ionic diffusion in the lattice as well as the case of lower bainite in steel. The first example is a tetragonal-to-monoclinic transformation in ZrO₂-Y₂O₃ ceramics, where the bainitelike transformation must be characterized by (1) the increase in concentration of oxygen vacancies caused by the substitution of Zr⁴⁺ ions by Y³⁺ ions, (2) a fairly high mobility of oxygen ions through their vacancies, and (3) the formation of clusters composed of oxygen vacancies and oxygen ions. The second case is an inverse spinel to corundum structural change observed in γ Fe₂O₃ to α Fe₂O₃, in which the bainitelike transformation may be explained by cooperative movements of oxygen and ferric ions, which are sandwiched between oxygen layers. 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.     

Nonequilibrium effects during the ledgewise growth of a solid-liquid interface

Directional solidification studies have been carried out in the napthalene-camphor system in which the interface advances through the formation and motion of ledges. Growth conditions have been varied so as to characterize both the planar interface growth and the condition for the instability of the planar interface. It is found that the mechanisms of planar interface instability and the subsequent morphological development of the interface depend significantly on the crystallographic orientation of the interface. Appreciable interface kinetics effects are present during the growth of a planar interface, and experimental studies have been designed to quantitatively evaluate the nonequilibrium conditions at the interface. These nonequilibrium effects for the napthalene-camphor system have been determined experimentally and have been characterized by two response functions that describe the interface temperature and the interface composition in the liquid under nonequilibrium conditions. The interface kinetic law is found to be exponential, indicating that the growth of the interface occurs through the process of nucleation of new layers. Formerly with Ames Laboratory. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Recent trends and developments with rapidly solidified materials

Excellent progress is being made in demonstrating the significant improvements in metallic structures and properties through rapid solidification (RS) and rapid solid-state quenching. A number of atomization techniques are able to achieve solidification rates of the order of 10⁵ K/s at economical production rates, yielding excellent refined microstructures with resultant outstanding mechanical, physical, and chemical properties. Powder production rates need to be significantly improved, and several techniques offer realistic promises in this area. The spray deposition processes, which bypass the powder production phase, achieve excellent solidification and solid-state cooling rates and offer high tonnage rates for preforms with outstanding hot, warm, and cold working response and with excellent physical and mechanical properties. This invited critical overview paper is based on a presentation made in the symposium “Structure and Properties of Fine and Ultrafine Particles, Surfaces and Interfaces” presented as part of the 1989 Fall Meeting of TMS, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Structures Committee of ASM/MSD.     

The role of ledges in the proeutectoid ferrite and proeutectoid cementite reactions in steel

The influence of interphase boundary ledges on the growth and morphology of proeutectoid ferrite and proeutectoid cementite precipitates in steel is examined. After reviewing current theoretical treatments of growth by the ledge mechanism, investigations that clearly document the presence and motion of ledges with thermionic emission electron microscopy (THEEM) and transmission electron microscopy (TEM) are reviewed. A fundamental distinction is made between two types of ledges: (1) mobile growth ledges whose lateral migration displaces the inter-phase boundary and (2) misfit-compensating structural ledges. Both types of ledges strongly affect the apparent habit plane and aspect ratio of precipitate plates. Agreement between measured growth rates of proeutectoid ferrite and cementite (plates and allotriomorphs) and predicted growth kinetics assuming volume diffusion-controlled migration of ledge-free disordered boundaries is shown to be consistently poor. Physically realistic growth models should incorporate the ledge mechanism. More accurate comparisons of the growth models with experimental data will need to account for observed ledge heights, interledge spacings, and ledge velocities. In this vein, the sluggish growth kinetics of cementite allotriomorphs observed in an Fe-C alloy are shown to be quantitatively consistent with a strong increase in interledge spacing with time. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Thickening of grain-boundary α allotriomorphs in a Ti-Cr alloy by multiple sets of ledges

A computer model is developed to simulate the growth of grain-boundary allotriomorphs having more than one set of growth ledges at their interfaces. The growth is controlled by the volume diffusion of solute to or from the riser of a ledge. The time dependence of the growth rate of two orthogonal sets of ledges is found to be somewhat different from that of a single set of ledges. However, the operation of multiple sets of ledges is unlikely to alter significantly the growth kinetics of grain-boundary allotriomorphs from those predicted from the disordered growth theory, except at small ledge spacings or at short reaction times. Faster growth kinetics of proeutectoid α allotriomorphs than those of either planar or ellipsoidal disordered boundaries which have been reported in a Ti-6.6 at. pet Cr alloy are not likely to be accounted for with the heights and spacings of double sets of ledges actually observed on the interfaces of allotriomorphs. Hence, the grain-and interphase-boundary diffusion-assisted growth of precipitates, (rejector plate mechanism, RPM) appears to be operative during the growth of a allotriomorphs, as previously proposed on the basis of growth-rate measurements. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.