Nucleation kinetics of proeutectoid ferrite at austenite grain boundaries in Fe-C-X alloys

The nucleation kinetics of proeutectoid ferrite allotriomorphs at austenite grain boundaries in Fe-0.5 at. Pct C-3 at. Pct X alloys, where X is successively Mn, Ni, Co, and Si and in an Fe-0.8 at. Pct C-2.5 at. Pct Mo alloy have been measured using previously developed experimental techniques. The results were analyzed in terms of the influence of substitutional alloying elements upon the volume free energy change and upon the energies of austenite grain boundaries and nucleus: matrix boundaries. Classical nucleation theory was employed in conjunction with the pillbox model of the critical nucleus applied during the predecessor study of ferrite nucleation kinetics at grain boundaries in Fe-C alloys. The free energy change associated with nucleation was evaluated from both the Hillert-Staffanson and the Central Atoms Models of interstitial-substitutional solid solutions. The grain boundary concentrations of X determined with a Scanning Auger Microprobe were utilized to calculate the reduction in the austenite grain boundary energy produced by the segregation of alloying elements. Analysis of these data in terms of nucleation theory indicates that much of the influence of X upon ferrite nucleation rate derives from effects upon the volume-free energy change,i.e., upon alterations in the path of theγ/(α + γ) phase boundary. Additional effects arise from reductions in austenite grain boundary energy, with austenite-forming alloying elements being more effective in this regard than ferrite-formers. By difference, the remaining influence of the alloy elements studied evidently results from their ability to diminish the energies of the austenite: ferrite boundaries enclosing the critical nucleus. The role of nucleation kinetics in the formation of a bay in the TTT diagram of Fe-C-Mo alloys is also considered. Formerly Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University     

Growth kinetics of grain boundary ferrite allotriomorphs in Fe-C-X alloys

Parabolic rate constants for the thickening (α) and lengthening (β) kinetics of grain boundary allotriomorphs of proeutectoid ferrite have been measured as a function of isothermal transformation temperature in several Fe-C-X’ alloys whereX = Si, Ni, Mn, and Cr. These constants have been corrected approximately for the growth inhibition produced by facets on the allotriomorphs. The corrected α values are compared with those calculated on the basis of three models: equilibrium at α:γ boundaries with partition ofX, local equilibrium with “pile-up” ofX rather than bulk partition, and paraequilibrium. Values calculated from both the paraequilibrium and the “pile-up” models were in order of magnitude or better agreement with the corrected experimental α’s. Similar levels of agreement were obtained for the equilibrium model in the Si and Cr alloys and also in one Ni alloy at lower reaction temperatures. However, an estimate of the maximum possible diffusion distance of alloying element into austenite during growth supported only the paraequilibrium model under nearly all conditions investigated. Even for this model, however, measured rate constants are significantly less than those calculated for Fe-C-Mn and Fe-C-Cr and greater for Fe-C-Si and the higher Ni, Fe-C-Ni alloy. The Mn and Cr discrepancies seem best explained at present by a solute drag-like effect; an accompanying paper indicates that interphase boundary precipitation of carbides is involved in the Si and Ni alloys, though an inverse solute drag-like effect may also be operative. Formerly graduate student, Department of Metallurgical Engineering, Michigan Technological University. Formerly Professor at Michigan Technological University.     

Effects of austenitizing temperature on the kinetics of the proeutectoid ferrite reaction at constant austenite grain size in an Fe-C alloy

Austenitizing an Fe-0.23 pct C alloy at 1300°C and further at 900°C prior to isothermal transformation was found to increase the growth kinetics of grain boundary ferrite allotriomorphs while decreasing their rate of nucleation. A scanning Auger microprobe was used to establish that sulfur segregates to the austenite grain boundaries and does so increasingly with decreasing austenitizing temperature. A binding free energy of sulfur to these boundaries of approximately 13 kcal/mole (54.4 kj/mole) was calculated from theMcLean adsorption isotherm. The kinetic results were explained in terms of preferential reduction of the austenite grain boundary energy decreasig nucleation kinetics, and adsorption of sulfur at α:γ boundaries increasing the carbon concentration gradient in austenite driving growth.     

Alloying Element Partition and Growth Kinetics of Proeutectoid Ferrite in Hot-Deformed Fe-0.1C-3Mn-1.5Si Austenite

Alloying element partition and growth kinetics of proeutectoid ferrite in deformed austenite were studied in an Fe-0.1C-3Mn-1.5Si alloy. Very small ferrite particles, less than several microns in size, were formed within the austenite matrix, presumably at twin boundaries as well as at austenite grain boundaries. Scanning transmission electron microscopy–energy-dispersive X-ray (STEM-EDX) analysis revealed that Mn was depleted and Si was enriched in the particles formed at temperatures higher than 943 K (670 °C). These were compared with the calculation of local equilibrium in quaternary alloys, in which the difference in diffusivity between two substitutional alloying elements was assumed to be small compared to the difference from the carbon diffusivity in austenite. Although the growth kinetics were considerably faster than calculated under volume diffusion control, a fine dispersion of ferrite particles was readily obtained in the partition regime due to sluggish growth engendered by diffusion of Mn and Si.     

Growth kinetics and morphology of grain boundary ferrite allotriomorphs in an Fe-C-V alloy

Grain boundary ferrite allotriomorphs in an Fe-0.12 pct C-0.11 pct V alloy reacted in the temperature range 800‡ to 870 ‡C develop in two morphologies: conventional allotriomorphs, with an aspect ratio of about one-half, and “snakes≓, whose aspect ratio approaches zero. Interphase boundary vanadium carbides (VC) precipitate densely in association with conventional allotriomorphs but not with “snakes≓. Thickening kinetics of “snakes≓ are about an order of magnitude slower than predicted by the paraequilibrium model. Conventional allotriomorphs, on the other hand, thicken with the kinetics predicted by paraequilibrium. These observations are considered in terms of the solute drag-like effect and of “wetting≓ of austenite grain boundaries by ferrite in the presence of V. Absence of a distinct change in the thickening kinetics of conventional allotriomorphs in the vicinity of 845 ‡C, the approximate upper temperature limit of interphase boundary carbide precipitation, strongly supports the view that such carbides can precipitate only on immobile,i.e., partially coherent areas of austenite : ferrite boundaries. Formerly Visiting Research Associate, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931 Formerly Republic Steel Corporation Fellow, Michigan Technological University, Houghton, MI 49931 Formerly Professor, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931     

Isothermal transformations in an Fe-9 pct Ni alloy

Isothermal transformation from austenite in an Fe-9.14 pct Ni alloy has been studied by optical metallography and examination by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). In the temperature range 565 °C and 545 °C, massive ferrite (α _q ) forms first at prior austenite grain boundaries, followed by Widmanst?tten ferrite (α _W ) growing from this grain boundary ferrite. Between 495 °C and 535 °C, Widmanst?tten ferrite is thought to grow directly from the austenite grain boundaries. Both these transformations do not go to completion and reasons for this are discussed. These composition invariant transformations occur below T ₀ in the two-phase field (α+γ). Previous work on the same alloy showed that transformation occurred to α _q > and α _W on furnace cooling, while analytical TEM showed an increase of Ni at the massive ferrite grain boundaries, indicating local partitioning of Ni at the transformation interface. An Fe-3.47 pct Ni alloy transformed to equiaxed ferrite at 707 °C ±5 °C inside the single-phase field on air cooling. This is in agreement with data from other sources, although equiaxed ferrite in Fe-C alloys forms in the two-phase region. The application of theories of growth of two types of massive transformation by Hillert and his colleagues are discussed. This article is based on a presentation made at the symposium entitled “The Mechanisms of the Massive Transformation,” a part of the Fall 2000 TMS Meeting held October 16–19, 2000, in St. Louis, Missouri, under the auspices of the ASM Phase Transformations Committee.     

On the growth kinetics of grain boundary ferrite allotriomorphs

Previous work has shown that the thickening kinetics of proeutectoid ferrite allotriomorphs in an Fe-0.11 pct C alloy are often more rapid than the kinetics calculated for volume diffusion-control from the Dube-Zener equation for the migration of a planar boundary of infinite extent, assuming the diffusivity of carbon in austenite,D, to be constant at that of the carbon content of the Ae3. Recalculating the thickening kinetics, using a numerical analysis of the infinite planar boundary problem previously developed by Atkinson in which the variation ofD with composition is taken fully into account, was found to increase this discrepancy. Measurements were then made of the lengthening as well as the thickening kinetics of grain boundary allotriomorphs in the same alloy. Application to these data of Atkinson’s numerical analysis of the growth kinetics of an oblate ellipsoid, in which the composition-dependence ofD is similarly considered, produced an acceptable accounting for nearly all of the data. It was concluded that the growth of ferrite allotriomorphs is primarily controlled by the volume diffusion of carbon in austenite; the presence of a small proportion of dislocation facets along one of the broad faces of the allotriomorphs, however, usually results in growth kinetics which are somewhat slower. An alternate treatment of the lengthening and thickening data upon the basis of the theory of interfacial diffusion-aided growth of allotriomorphs indicated that, in the temperature range investigated (735° to 810°C),the diffusivities of carbon along γ:γ and γ:α boundaries required for this mechanism to make a significant contribution to growth are too high to be physically plausible. Formerly with Scientific Research Staff Formerly with Scientific Research Staff, Ford Motor Company     

Nucleation,growth, and overall transformation kinetics of grain boundary allotriomorphs of proeutectoid alpha in Ti-3.2 At. Pct Co and Ti-6.6 At. Pct Cr alloys

The nucleation, growth, and overall transformation kinetics of grain boundary α allotriomorphs were measured in Ti-3.2 at. pct Co and Ti-6.6 at. pct Cr alloys with optical microscopy. Nucleation kinetics were interpreted with classical heterogeneous nucleation theory, using the pillbox model of the critical nucleus. Growth kinetics of allotriomorphs were significantly accelerated by the rejector plate mechanism, but much less so than allotriomorphs formed in fcc substitutional matrices at comparable homologous temperatures. Overall transformation kinetics were accounted for with a modified version of Cahn’s theory of grain boundary nucleated reactions. Formerly Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213     

The pearlite-austenite growth interface in an Fe-0.8 C-12 Mn alloy

The interphase boundary structure and interface processes at the pearlite-retained austenite growth interface in Fe-0.8 wt% C-12 wt% Mn alloy have been investigated by transmission electron microscopy. Facetting, misfit correcting dislocations, and ledge defects are all observed at the previously assumed disordered boundary. Hot stage electron microscopy revealed that the ledge defects are mobile, indicating the migration of the growth interface occurs by the lateral movement of steps. It is found that the growth ledges are continuous across the growth interfaces of the pearlitic ferrite and cementite. This provides a mechanism by which the interface processes of the two pearlite phases may be coupled.     

Growth kinetics of grain boundary allotriomorphs of proeutectoid ferrite in Fe-C-Mn-X2 alloys

The parabolic rate constant for the thickening of grain boundary ferrite allotriomorphs at the faces of austenite grain boundaries was measured as a function of isothermal transformation temperature in three Fe-C-X₁-X₂ alloys where X₁ is Mn and X₂ is successively Si, Ni, and Co. The results were compared with the predictions of the local equilibrium model for multi-component systems and with those derived from the theory of growth under paraequilibrium conditions. The distribution of Mn and Si in ferrite and austenite in the Fe-C-Mn-Si alloy was also measured as a function of reaction temperature with transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDX). The observed temperature below which alloying element partition ceased was in good agreement with the local equilibrium model. Whereas the parabolic rate constant for thickening was considerably larger than the amount predicted by this theory in the alloying element diffusion-controlled regime, the opposite was true in the carbon diffusion-controlled regime. Similarly, the calculated paraequilibrium constant was usually considerably larger than that measured experimentally. Synergistic enhancements of the effects of Mn and X₂ in diminishing thickening kinetics were observed for each X₂. The time-temperature-transformation (TTT) curves for the beginning of transformation were calculated from a modified Cahn analysis for the overall kinetics of grain-boundary-nucleated reactions using values of the nucleation rate and the parabolic growth rate constant computed from various models and compared with experimentally determined TTT curves. Substantial discrepancies between the calculated and measured curves were ascribed to synergistic effects of Mn and X₂ upon nucleation and growth kinetics. Formerly Graduate Student, Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA Formerly Mehl Professor Emeritus at Carnegie Mellon University.     

The kinetics of ferrite nucleation at austenite grain edges in Fe-C and Fe-C-X alloys

Nucleation kinetics of proeutectoid ferrite allotriomorphs at the edges of austenite grains in Fe-C and Fe-C-X alloys, where X is successively Mn, Ni, Co, and Si, have been measured using a modification of the techniques previously developed to study nucleation at grain faces. Analysis of these data with classical heterogeneous nucleation theory has shown that ferrite nuclei formed at grain edges have low energy interphase boundaries. An equivalent conclusion was reached during our previous studies of ferrite nucleation at austenite grain faces. The influence of alloying elements on nucleation rates was also found to follow a pattern similar to that demonstrated for grain face nucleation. Formerly Graduate Student with the Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University,     

Analysis of the Grain Size Evolution for Ferrite Formation in Fe-C-Mn Steels Using a 3D Model Under a Mixed-Mode Interface Condition

A 3D model has been developed to predict the average ferrite grain size and grain size distribution for an austenite-to-ferrite phase transformation during continuous cooling of an Fe-C-Mn steel. Using a Voronoi construction to represent the austenite grains, the ferrite is assumed to nucleate at the grain corners and to grow as spheres. Classical nucleation theory is used to estimate the density of ferrite nuclei. By assuming a negligible partition of manganese, the moving ferrite–austenite interface is treated with a mixed-mode model in which the soft impingement of the carbon diffusion fields is considered. The ferrite volume fraction, the average ferrite grain size, and the ferrite grain size distribution are derived as a function of temperature. The results of the present model are compared with those of a published phase-field model simulating the ferritic microstructure evolution during linear cooling of an Fe-0.10C-0.49Mn (wt pct) steel. It turns out that the present model can adequately reproduce the phase-field modeling results as well as the experimental dilatometry data. The model presented here provides a versatile tool to analyze the evolution of the ferrite grain size distribution at low computational costs.     

Effects of alloying elements upon austenite decomposition in Low-C steels

The kinetics of austenite decomposition were studied in high-purity Fe-0.1C-0.4Mn-0.3Si-X (concentrations in weight percent;X represents 3Ni, 1Cr, or 0.5Mo) steels at temperatures between 500 °C and 675 °C. The transformation stasis phenomenon was found in the Fe-C-Mn-Si-Mo and Fe-C-Mn-Si-Ni alloys isothermally transformed at 650 °C and 675 °C but not in the Fe-C-Mn-Si and Fe-C-Mn-Si-Cr alloys at any of the temperatures investigated. The occurrence of transformation stasis was explained by synergistic interactions among alloying elements. The paraequilibrium model was applied to calculate the metastable fraction of ferrite in each alloy. This fraction was shown to coincide with cessation of transformation in the Mo alloy transformed at 600 °C. Transformation stasis was found in both the Ni and the Mo alloys isothermally reacted at 650 °C and 675 °C. The interactions among Mn, Si, and Mo, as well as interactions among Mn, Si, and Ni, appear to decrease the threshold concentrations for transformation stasis in Fe-C-Mn-Si systems. Segregation of Mn and Mo to the α/yγ boundary, assisted by the presence of Si, was suggested to enhance the solute draglike effect (SDLE) and lead to transformation stasis. In the Ni alloy, a lower driving force for ferrite formation resulting from the Ni addition could be responsible for the occurrence of transformation stasis.     

Formation of austenite in 1.5 pct Mn steels

The formation of austenite from different microstructural conditions has been studied in a series of 1.5 pct Mn steels that had been heated in and above the intercritical (α+ γ) region of the phase diagram. The influence of variables such as cementite morphology, initial structural state of the ferrite and the carbon content has been assessed in terms of their respective effects on the kinetics of austenite formation and final microstructure. Austenite was found to form preferentially on ferrite-ferrite grain boundaries for all initial structures. The results of this study have shown that the 1.5 pct Mn has lowered both the AC₃ and AC₁, lines causing large amounts of austenite to form in low carbon steel. The kinetics of austenite formation at 725 °C were not only very slow but also were approximately independent of the amount formed. Austenite appeared to form slightly more rapidly from cold rolled ferrite than from recrystallized ferrite or ferrite-pearlite structures.     

On the critical nucleus composition of ferrite in an Fe-C-Mn alloy

The displacement of the capillarity-corrected nucleus composition of ferrite relative to the two compositions conventionally used to calculate the nucleation rate,i.e., the bulk equilibrium composition and the maximum volume free energy change composition, was evaluated in an Fe-0.5 at. Pct C-3 at. Pct Mn alloy in the regime of the classical nucleation theory. While the nucleus composition is very close to the one at maximum volume free energy change, it is very different from that of bulk equilibrium. The errors arising in the calculation of critical nucleus size and nucleation rate when using inappropriate nucleus compositions are discussed under both para- and orthoequilibrium conditions for the formation of ferrite. M. Enomoto, formerly Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University     

The formation mechanism(s), morphology,and crystallography of ferrite sideplates

The formation mechanism(s), morphology, and crystallography of secondary ferrite sideplates were investigated with transmission electron microscopy (TEM), scanning electron microscopy (SEM), electron backscatter pattern (EBSP) analysis, and optical microscopy in a high-purity Fe—0.12 wt pct C—3.3 wt pct Ni alloy isothermally transformed at temperatures of 550 °C, 600 °C, 650 °C, and 675 °C. The results indicate that two different mechanisms contribute to the formation of these sideplates at austenite grain boundaries. On the first mechanism, primary sideplates form initially, followed by rapid lateral impingement along their bases, resulting in a region along the grain boundary which very early in the growth process resembles an allotriomorphic film. On the second mechanism, sympathetic nucleation of ferrite sideplates occurs atop pre-existing ferrite allotriomorphs, resulting in ferrite:ferrite grain boundaries and significant crystallographic misorientations between the sideplates and the allotriomorphs with which they are associated. These results indicate that “secondary sideplates” and the allotriomorphs from which they evolve arenot composed of monolithic single crystals formed by a morphological instability mechanism but are instead composed of multiple crystals formed by individual nucleation events. Previous investigations in Ti-Cr alloys and a high chromium stainless steel suggest that the findings presented here may be applicable to a number of other alloy systems as well. 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.     

Kinetic transitions and substititional solute (Mn) fields associated with later stages of ferrite growth in Fe-C-Mn-Si

A low-carbon balloy steel with relatively high Mn and Si concentrations (0.04 wt pct C-3 wt pct Mn-1.9 wt pct Si) has been used to explore the effects of alloy chemistry and austenite grain size on ferrite growth. Even at high levels of supersaturation, the volume fraction of ferrite is found to increase slowly relative to the relaxation time for carbon diffusion. A series of scanning transmission electron microscopy (STEM) analyses for Mn indicates that initial unpartitioned ferrite growth is replaced by partitioned growth, accompanied by a dramatic drop in growth rate, and a persistent level of residual supersaturation in the remaining austenite. The results are interpreted in terms of a transition from an initial paraequilibrium interfacial condition to partitioned ferrite growth. This article is based on a presentation made in the “Hillert Symposium on Thermodynamics & Kinetics of Migrating Interfaces in Steels and Other Complex Alloys,” December 2–3, 2004, organized by The Royal Institute of Technology in Stockholm, Sweden.     

On the influence of carbide formation upon the growth kinetics of proeutectoid ferrite in Fe-C-X alloys

In the preceeding paper, the growth kinetics of grain boundary ferrite allotriomorphs in Fe-C-Si, Fe-C-Mn, Fe-C-Ni, and Fe-C-Cr alloys are reported to be best described by the paraequilibrium model. Significant differences are still observed, however, between the experimentally measured kinetics and those calculated from this model. A TEM study was conducted on these alloys to ascertain whether any of these differences could be attributed to carbide precipitation. In the Fe-C-Mn and Fe-C-Cr alloys, where the measured growth kinetics are low, carbides precipitate on dislocations within the ferrite and are effectively absent, respectively; hence carbide precipitation cannot be responsible for the deviations in these alloys. In the low Ni, Fe-C-Ni alloy, where calculated and measured kinetics agree, carbide precipitation was again found on dislocations in the ferrite. Faster than calculated growth kinetics in the Fe-C-Si and the high Ni, Fe-C-Ni alloys, on the other hand, are attributed in part to carbide precipitation at austenite:ferrite boundaries. Formerly Republic Steel Fellow, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931 and Visiting Graduate Student, Carnegie-Mellon University, Pittsburgh, PA 15213 Formerly Professor, Department of Metallurgical Engineering, Michigan Technological University Formerly Graduate Student, Department of Metallurgical Engineering, Michigan Technological University     

The influence of the Si and Mn concentrations on the kinetics of the bainite transformation in Fe-C-Si-Mn alloys

Five Fe-C-Si-Mn alloys were investigated by dilatometry, optical microscopy, and transmission electron microscopy (TEM) analysis to determine the effects of Si and Mn content and austenitizing temperatures on the kinetics of bainite transformation. Segregation of Mn at prior austenite grain boundaries at a temperature below B_s was detected by the scanning transmission electron microscopy + energy dispersive spectroscopy (STEM + EDS) and secondary ion mass spectroscopy (SIMS) techniques. The fraction of intragranular ferrite increases with Mn content. The time needed for the initiation of the bainite transformation tends to decrease as the austenitizing temperature decreases. The results obtained were compared with those from Fe-0.38C-1.73Si and Fe-0.38C-3.11Mn alloys. Equilibrium and nonequilibrium segregation of Mn at prior austenite grain boundaries and the effect of the interaction between Si and Mn on the segregation of Mn are used to explain the results obtained and the large difference between the kinetics of the two ternary alloys and those of the Fe-C-Si-Mn alloys. This paper is based on a presentation made in the symposium “International Conference on Bainite” presented at the 1988 World Metals Congress in Chicago, IL, on September 26 and 27, 1988, under the auspices of the ASM INTERNATIONAL Phase Transformations Committee and the TMS Ferrous Metallurgy Committee.