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.     

A mathematical method for the calculation of ledge growth kinetics

A method outlined in a recent paper by Atkinson and Wilmott¹ is applied here to the transient motion of a finite train of steps, particular attention being given to two-and three-step trains where the steps are sufficiently far apart. The resulting integro-differential equations which govern the step motions are solved numerically for some model situations, and some qualitative agreement with the extensive numerical calculations of Enomoto^2,3 is found. Equations are also derived for the case when two steps come close together, but numerical implementation of this case is still to be made. 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.     

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.     

Forced velocity pearlite in high purity Fe-C alloys: Part II. Theoretical

The forced velocity pearlite data of Part I is compared to the Zener-Hillert treatment and shown to fit the volume diffusion model but requires aD value higher than that of the Wells’et al.¹⁶ data by a factor of 3 to 4. It is postulated that the highD value is due to a strain in the austenite phase at the growth front. It is found that inclusion of a mobility term, μ, in the Zener-Hillert analysis requires a quadratic form,V = μΔ², in order to fit the data. Additional experiments have shown that the degenerate pearlite found at high growth velocities results from coarsening of fine pearlite as it cools from the growth front temperatures. Finally, some speculations are offered to explain the various interesting growth features of pearlite presented in Part I. This paper is based on a presentati on 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.     

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.     

Forced velocity pearlite in high purity Fe-C alloys: Part 1. Experimental

An experimental technique was developed to measure the interface temperature of directionally transformed pearlite. It was shown that the growth temperature of such forced velocity pearlite is the same as the growth temperature of isothermally formed pearlite which grows at the same velocities. It was also shown that forced velocity pearlite is kinetically limited to maximum growth rates of around 100 μm per second. It was demonstrated that a small but significant fraction of prior austenite grain boundaries interferes with pearlite growth by halting the growth of the cementite lamellae. Velocityvs spacing data were found to fit an equation of the formV ∝ S ^-n withn = 2.07. Arguments are presented which indicate that previous literature values ofn = 2.4 and 2.7 may be high due to experimental difficulties. 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.     

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.     

Effect of Aluminum Content on the Microstructure and Mechanical Properties of Hypereutectoid Steels

Hypereutectoid steels with 0, 0.69, 1.29, and 1.95 wt pct aluminum were prepared. The samples were hot rolled at 1100 °C followed by cooling in air. The microstructure of the as-rolled samples was characterized using field emission–scanning electron microscopy (FE-SEM). The electron backscattered diffraction (EBSD) technique was used to identify the grain boundary phases. The steels have a pearlitic microstructure with different amounts of grain boundary cementite. A continuous grain boundary cementite network is present in the 0 wt pct Al steel. Grain boundary cementite formation is completely suppressed in the 1.29 wt pct Al steel. Phase diagram calculations show that aluminum increases the eutectoid temperature. However, the interlamellar spacing and pearlite colony size decrease with increase in aluminum content. Dilatometry measurements show that aluminum addition increases the undercooling below the eutectoid temperature. The yield strength increases with the decrease in interlamellar spacing and colony size. Very high ultimate tensile strengths (1200 to 1400 MPa) and improved elongations to failure (7 to 9 pct) are achieved in the as-rolled condition.     

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.     

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.     

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.     

Eutectoid decomposition in Ag-Ga

The kinetics and mechanisms of eutectoid decomposition in alloys near Ag-15.3 wt pct Ga (Ag-21.8 at. pct Ga) were investigated. Isothermal decomposition of the parent β phase exhibits C-shaped time-temperature-transformation (TTT) curves below the eutectoid temperature. Pearlite forms from the eutectoid temperature (380 °C) to at least 85 °C below this temperature. Two distinct types of pearlite form: a coarse lamellar structure at higher reaction temperatures and a fine lamellar structure with characteristically faceted boundaries. The fine pearlite forms in compctition with coarse pearlite below 315 °C, and the interlamellar spacings of the two pearlites differ by an order of magnitude. The constituents of coarse pearlite are the equilibrium α and β phases with fcc and hP9 crystal structures, respectively. Fine pearlite is composed of α and a metastable phase, β′', with a crystal structure identified as 9R (structure type hR3). Both types of pearlite undergo coarsening by a discontinuous, or cellular, reaction. Formerly Graduate Student, Materials Science and Engineering Department, Virginia Tech Formerly Undergraduate Student, Materials Science and Engineering Department, Virginia Tech, is This article is based on a presentation made during TMS/ASM Materials Week in the symposium entitled “Atomistic Mechanisms of Nucleation and Growth in Solids,” organized in honor of H.I. Aaronson’s 70th Anniversary and given October 3–5, 1994, in Rosemont, Illinois.     

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.     

Fatigue Initiation Study of TMT Eutectoid Steel

Eutectoid steel and 1060 steel samples were given a variety of thermomechanical treatments (TMT), described in Table I, which varied the pearlite interlamellar spacing, the cementite and inclusion orientation, the degree of cold-work in the ferrite matrix, and (for 1060 steel only) the proeutectoid grain boundary ferrite network. These samples were then evaluated as to resistance to fatigue crack initiation. The TMT designated, G, involves a subcritical anneal and results in a partially recrystallized condition which shows not only excellent resistance to fatigue crack initiation in the near threshold region but is second only to a fine pearlite microstructure, B, in fatigue crack propagation threshold value. It is believed that the excellent properties of the TMT, G, are related to the formation of subgrains in the interlamellar ferrite. On a scale normalized to tensile strength,(ΔK/√ρ)/σ_u, fine oriented pearlite in a soft ferrite matrix (rapid up-quench TMT such as E, F) shows the best resistance to fatigue crack initiation. A proeutectoid ferrite grain boundary network is poor at resisting fatigue crack initiation but good at resisting fatigue crack propagation. It should be emphasized that the combined high resistance of the subcritical TMT (G) toboth fatigue crack initiation and propagation, coupled with its much easier implementation relative to similar microstructures produced by difficult rapid up-quench TMT's (E, F) make it a very promising approach to improving overall fatigue resistance.     

The effect of alloying elements and microstructure on the strength and fracture resistance of pearlitic steel

The processes of ductile and brittle fracture in fully pearlitic steel and their relation to both the scale of the microstructure and the presence of substitutional alloy elements have been investigated at room temperature using smooth tensile and over a range of temperatures using V-notched Charpy impact specimens. The results show that the early stages of cracking, revealed in both types of specimen, are largely the result of shear cracking of the pearlite lamellae. These cracks grow and can reach a size when they impinge upon the prior austenite boundary; afterward the character of fracture can be either microvoid coalescence or cleavage, depending on test conditions and metallurgical variables. Further, the carbide plates of the pearlite lamellae can act as barriers to the movement of dislocations as is the case normally with grain boundaries. For pearlite an optimum spacing of approximately 0.2 μm resulting from a balance between carbide plate thickness and interlamellar spacing was found to enhance toughness, although such changes are much smaller than corresponding changes due to varying alloy elements. Specific alloy elements used herein strengthened the lamellar ferrite in pearlite, inhibiting the movement of dislocations while also usually decreasing the lamellar cementite plate thickness for the same spacing. This dual behavior results in enhanced resistance to the initiation and propagation of microcracks leading to an improvement in strength, ductility, and toughness. The most effective alloy elements for the composition ranges studied in fully pearlitic steels are Si and Ni for strength improvement, and Ni and Mn for toughness.     

Deformation of pearlite

Pearlite with its lamellae oriented mainly parallel to the longitudinal direction was prepared by Bolling's method of transformation in a steep temperature gradient. The Fe-0.7 pct Mn-0.9 pct C pearlite was drawn into wire and also into strip in dies designed to minimize macroscopically nonuniform deformation. Cross sections of the drawn wires and strip were examined by conventional and high-voltage transmission electron microscopy and were analyzed by quantitative metallography for a) average interlamellar spacing, b) distribution of interlamellar spacings, and c) orientation relationship between the cementite lamellae and the slip systems in the ferrite. The strength of pearlite is proportional to the reciprocal square root of the average interlamellar spacing, and the proportionality constant analogous to the Hall-Petch constant (k) is related to the strength of the cementite lamellae. If the stress for the propagation of slip through the cementite is assumed constant, a Hall-Petch type of equation can be derived for the strengthening of the pearlite against slip in the ferrite by piled-up groups of dislocations. Evidence for the plastic deformability of cementite is presented; sufficiently thin cementite plates were fully plastic. The exponential strain hardening of drawn pearlitic wires and of rolled pearlite is explained in terms of locally inhomogenous deformation revealed by the lack of fragmentation of the lamellae. This paper is based on a presentation made at a symposium on “Mechanical-Thermal Processing and Dislocation Substructure Strengthening,” held at the Annual Meeting in Las Vegas, Nevada, on February 23, 1976, under the sponsorship of the TMS/IMD Heat Treating Committee.     

Estimation of nucleation rate and growth rate from time dependence of global microstructural properties during phase transformations

An approach has been developed for calculating nucleation and growth rates from the time variation of the volume fraction, surface area, and integral mean curvature of the product phase during a phase transformation. The local growth rate of the product phase can be estimated without any assumption or knowledge regarding the nucleation behavior. The approach is applicable over the complete range of volume fractions(i.e., from zero to one). Practical feasibility of the approach has been demonstrated by deducing the nucleation and growth rates of austenite during austenitization of pearlite in an Fe-0.83 wt pct C alloy at 730 ‡C, 740 ‡C, and 750 ‡C. It is concluded that the local growth rate and nucleation rate of austenite remain constant during an isothermal austenitization of pearlite. Formerly with the Department of Metallurgical Engineering, Indian Institute of Technology, Kanpur, India     

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.     

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.     

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.