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.     

Growth kinetics of grain boundary ferrite allotriomorphs in Fe−C alloys

The kinetics of lengthening and thickening of grain boundary allotriomorphs of proeutectoid ferrite were measured at several temperatures in high purity Fe−C alloys containing 0.11 pct, 0.23 pct and 0.42 pct C. These measurements were conducted by measuring the length of the longest and the width of the widest allotriomorph in each specimen. All specimens were austenitized so as to make the grain boundaries perpendicular to the plane of polish. This measurement technique appreciably reduced the scatter in the parabolic rate constant data previously encountered in thermionic emission microscopy measurements. Parabolic rate constants for lengthening and thickening were calculated, using the experimental aspect ratio, by means of the Atkinson analysis for oblate ellipsoids. The ratio of the measured to the calculated constants was in all cases less than unity. The previously made suggestion that these slow growth kinetics are due to faceting was supported through the observation of facets on allotriomorphs by means of scanning and transmission electron microscopy. The aspect ratio of ferrite allotriomorphs was shown to beca 1/3, independent of reaction time temperature and carbon content. The dihedral angle of the allotriomorphs was found to be 100±5 deg, as compared with a published angle for recrystallized and equilibrated specimens ofca 115 deg. Several possible explanations for the aspect ratio and dihedral angle findings are considered. M. RIGSBEE, formerly Postdoctoral Research Associate with Michigan Technological University     

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     

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.     

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

The steady-state nucleation rates of ferrite allotriomorphs at the “faces” of austenite grain boundaries were measured in Fe-C-X₁-X₂ alloys, where X₁ was Mn and X₂ was successively Si, Ni, and Co, using techniques previously developed for counterpart studies on Fe-C and Fe-C-X alloys. The results were compared with the predictions of the classical nucleation theory, using the pillbox-shaped critical nucleus model. The volume free energy changes associated with nucleation in Fe-C-X₁-X₂ quaternary systems were evaluated from the central atoms model (CAM) for both para- and orthoequilibrium modes of transformation. The nucleation process was assumed to be controlled by volume and/or grain boundary diffusion of alloying elements. The so-called synergistic effects of alloying elements were considered in terms of the volume free energy change and interfacial energies on the basis of the results of the nucleation rate measurements. Formerly Graduate Student, Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh,PA Formerly R.F. Mehl Professor Emeritus at Carnegie Mellon University, is with GEO-Centers, Inc., Ft. Washington, MD,     

The stereology of grain boundary allotriomorphs

Grain boundary allotriomorphs have been modeled as two abutting spherical caps of equal radius. The effects of the distance from the center of the allotriomorph, х, and the angle with respect to the plane normal to the grain boundary, ψ, at which a plane of polish sections the allotriomorph have been investigated. Expressions were derived relating the apparent to the true thickness, length, aspect ratio and dihedral angle. The effects of х and ϕ upon measurements of the lengthening and thickening kinetics of allotriomorphs were found to be significant, particularly at larger values of ψ. Analysis of published high-temperature measurements of allotriomorph growth kinetics indicated that an appreciable portion of the scatter in this data may have been due to nonzero values of х and ψ. A room temperature technique for making these measurements which minimizes such effects is concluded to be stereologically more reliable.     

Crystallography of grain boundary proeutectoid ferrite

A study has been made of the crystallography of proeutectoid ferrite precipitated at high angle austenite grain boundaries in an Fe-0.47 pct C alloy, isothermally transformed above the eutectoid temperature. Using the Kossel X-ray microdiffraction technique, ferrite orientations have been determined in relation to the orientations of both matrix grains at the grain boundary; the austenite orientations were derived indirectly. It has been observed that the ferrite, irrespective of morphology, possessed an orientation relationship with respect to at least one matrix grain which approximated to the Kurdjumov-Sachs and, to a lesser extent, the Nishiyama relationships. At several of the boundaries the ferrite was allowed to possess an orientation relationship with both matrix grains and it has been shown that the ferrite orientation at these boundaries was often influenced by the orientation of both matrix grains. Several instances have been observed in which preferential growth occurred into the austenite grain with which the precipitate did not have a specific orientation relationship. The results have been compared with the work of Ryder, Pitsch and Mehl,5 and factors governing the observation of Widmanstatten sideplates have been discussed.     

Crystallography of grain boundary proeutectoid ferrite

A study has been made of the crystallography of proeutectoid ferrite precipitated at high angle austenite grain boundaries in an Fe-0.47 pct C alloy, isothermally transformed above the eutectoid temperature. Using the Kossel X-ray microdiffraction technique, ferrite orientations have been determined in relation to the orientations of both matrix grains at the grain boundary; the austenite orientations were derived indirectly. It has been observed that the ferrite, irrespective of morphology, possessed an orientation relationship with respect to at least one matrix grain which approximated to the Kurdjumov-Sachs and, to a lesser extent, the Nishiyama relationships. At several of the boundaries the ferrite was allowed to possess an orientation relationship with both matrix grains and it has been shown that the ferrite orientation at these boundaries was often influenced by the orientation of both matrix grains. Several instances have been observed in which preferential growth occurred into the austenite grain with which the precipitate did not have a specific orientation relationship. The results have been compared with the work of Ryder, Pitsch and Mehl,5 and factors governing the observation of Widmanstatten sideplates have been discussed.     

Development and application of growth models for grain boundary allotriomorphs of a stoichiometric compound in ternary systems

A model for the isothermal growth of grain boundary allotriomorphs of a stoichiometric phase, (M, N)_aI_b, with a nonsingular interface in a ternary M-N-I matrix is developed. The element I is assumed to diffuse orders of magnitude faster than element N. The growth model assumes two initial no-partition growth stages and a subsequent partition growth stage with respect to element N. Both planar and spherical film geometries of allotriomorphs are considered. Strict mass balance conditions are taken into account so that the model can be used in rigorous computer simulations. A method to correct the allotriomorph thickness for the specific volume difference of the matrix and the precipitate is also shown. The growth of cementite allotriomorphs in Fe-Cr-C austenite is computer-simulated with the developed growth model. Interfacial concentration terms were calculated by programming the Sharma-Purdy-Kirkaldy regular solution model for the Fe-Cr-C system. Formerly Research Assistant at the Colorado School of Mines, is Senior Researcher, Toyo Kohan Ltd.     

On the kinetics of the spreading of extrinsic grain boundary dislocations

The kinetics of the disappearance (spreading) of extrinsic grain boundary dislocations (EBGDs) at random grain boundaries has been investigated in a low-carbon austenitic stainless steel (0.01C-19Cr-18Ni) by measuring in TEM their disappearance times at the temperature range 360 to 450 °C. Experimental results fit most satisfactorily to a kinetic equation of the general form:t _d =AT _d exp(ΔH _b /RT _d ) derived by Johannesson and Thölen10 and Lojkowski and Grabskiⁱⁱ¹² assuming either a dissociation into discrete structural grain boundary dislocation or the core spreading, respectively. Additional spreading experiments performed on commercial 316 austenitic stainless steel also support this general equation. Calculations employing experimental results indicate that the spreading time of a parallel component of the EGBD's Burgers vector is negligible and does not play any role during the process. Johannesson and Thölen¹⁰ and Lojkowski and Grabskiⁱⁱ¹² models are practically indistinguishable assuming that in the J & T model an EGBD dissociates into an array of grain boundary dislocations with the magnitude of the Burgers vectorb _b ? 0.07 nm. The TEM photographic documentation of the spreading clearly indicates that some grain boundaries exhibiting fine lines (not Moiré fringes) behave during spreading as random (general) boundaries. On the other hand, some grain boundaries free of any fine lines exhibit very high spreading temperature indicating a special behavior.     

On the chemistry of grain boundary segregation and grain boundary fracture

This paper considers the problem of impurity segregation in metals and the effect of these impurities on grain boundary cohesion. The primary goal of this paper is to provide a physical model that will allow us to think about these two processes. We describe both of them in chemical terms. Segregation is treated as a distribution of a solute between two phases. In this way, it is a typical example of heterogeneous equilibrium. We also consider the various driving forces for solute segregation and find that the correlation between decreased solubility and increased segregation, first proposed by Hondros and Seah,^[9] is still an adequate one. We introduce the discussion of grain boundary fracture by pointing out that as the impurity enters the boundary, it establishes chemical bonds with the structural units of the boundary. The segregated boundary can then be thought of as a string of molecular units with bonds of different types. Some of these bonds will be weaker than others, and they will be the ones that eventually fracture when a stress is applied. We consider the cause of these weak bonds and suggest that the primary reason for them is the transfer of electronic charge from the metal atoms to the impurity, as proposed in previous work.^[3] However, some of the ideas in the earlier models should be amended based on new results obtained from the quantum mechanical analysis of bonding in metals presented by McAdon and Goddard.^[10,11] We also suggest that intergranular brittleness of intermetallic compounds such as Ni₃Al, which occurs in the absence of impurity segregation, can be explained by the charge distribution present at the grain boundary. Finally, we provide a critique of other models that have been used to describe grain boundary fracture and segregation. This paper is based on a presentation made in the symposium “Interface Science and Engineering” presented during the 1988 World Materials Congress and the TMS Fall Meeting, Chicago, IL, September 26–29, 1988, under the auspices of the ASM-MSD Surfaces and Interfaces Committee and the TMS Electronic Device Materials Committee.     

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 kinetics of ferrite nucleation at austenite grain boundaries in Fe-C alloys

The nucleation kinetics of grain boundary allotriomorphs of proeutectoid ferrite at austenite grain faces have been measured in three high purity Fe-C alloys as a function of isothermal reaction time and temperature. Several correction techniques, including discrimination between different nucleation sites and the effect of carbon diffusion fields on further nucleation of ferrite, were incorporated into a stereological procedure utilizing the SchwartzJSaltykov size distribution analysis. This analysis enabled the number of ferrite particles per unit unreacted grain boundary area to be obtained as a function of isothermal reaction time, and thus the time-dependent nucleation kinetics to be obtained as a function of temperature and carbon concentration. These rates were then compared with those predicted by classical heterogeneous nucleation theory using various models for the critical nucleus. It was concluded that viable critical nuclei must have predominately low energy interphase boundaries. Only a very small fraction of the austenite grain face area appears to be capable of supporting nucleation. Formerly Graduate Student, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931 Formerly Professor at Michigan Technological University     

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     

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     

Cavity growth on a sliding grain boundary

Cavity growth on a sliding grain boundary to which a normal stress is applied is found to be faster than that on a stationary grain boundary. The morphology of the cavity contains an asymmetric crack-like tip which prompts surface diffusion locally when the sliding is dominant, and the growth rate becomes proportional to the third power of the normal stress independent of the sliding rate. Since the sliding rates of all grain boundaries are statistically comparable, only the normal stress dependence remains important. The conditions which favor the present mechanism are examined and shown to be in good agreement with the experimental evidence in creep cavitation.     

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,     

Growth mechanisms of grain boundary allotriomorphs in Al-4Pct Cu at high homologous temperatures: Interfacial vs direct volume diffusion

The lengthening and thickening kinetics of θ allotriomorphs in Al-4 pet Cu were measured at 350°, 400°, and 450°C. Three different analyses all indicated that interfacial diffusion (i.e., a right angle collector plate mechanism) was the predominant growth mechanism at 350° and 400°C, but that volume diffusion directly to the growing allotriomorphs made a significant contribution to growth at 450°C. Using the data of this and previous investigations one may conclude that volume diffusion of solute directly to the allotriomorph does not contribute noticeably to growth belowT/T (solidus) = 0.78, plays a substantial but still a minority role atT/T (solidus) = 0.84 and 0.90 and becomes the major contributor atT/T (solidus) ≥ 0.91 when the matrix is fee.