Masato Enomoto

Analysis of γ′/γ equilibrium in Ni−Al−X alloys by the

Various characteristics of γ′/γ phase equilibrium in ternary Ni−Al-X alloys are analyzed by the cluster variation method (CVM) with the phenomenological Lennard-Jones pair potential. Among the eleven alloy elements studied, three types of substitution behavior in γ′,i.e., the preferential substitution for Ni sites (Co and Cu), the almost entire substitution for Al sites (Ti, Nb, Mo, Hf, Ta, and W), and the substitution for both (Cr, Mn, and Fe), are recognized depending upon the relative magnitude of the Ni−X and Al−X interactions. In the last type, the substitution site appears to depend remarkably upon the Al and/or X concentrations in γ′: while X atoms enter preferentially, the Al sublattice in the case that the sum of the two concentations is less than the stoichiometry composition (0.25), they begin to enter the Ni sublattice as the sum exceeds it. The predicted substitution behavior is in good agreement with direct and indirect experimental evidences thus far reported. The direction of γ′/γ equilibrium phase boundaries, the equilibrium partition coefficient of X, and the effects of alloying upon the order-disorder transformation temperature from metastable γ′ to γ all appear to be closely related to substitution behavior. Also, the variation of lattice constants of γ′ and γ with the alloy element concentration may be better understood by collation with the substitution sites or the short range order in each phase.

Influence of solute drag on the growth of proeutectoid ferrite in Fe–C–Mn alloy

The diffusion-controlled growth of proeutectoid ferrite (α) from austenite (γ) in an Fe–C–Mn alloy was simulated incorporating the possible drag effect of Mn on the migration of α:γ interphase boundaries. The magnitude of drag force or the dissipation of free energy by drag was evaluated by means of Cahn and Purdy–Brechet models. The growth rate of ferrite was calculated from the flux balance equation for carbon taking into account the fact that the carbon concentration at the boundary in austenite varied with time. Whereas the time exponent of growth deviated from one-half at each moment, the overall time dependence was dictated by carbon volume diffusion in austenite. The reported differences of experimental growth rates from those calculated assuming paraequilibrium were reduced considerably by incorporating the drag of Mn, although simulation results may largely depend on the shape and depth of solute interaction potential with α:γ boundaries and Mn diffusivity within the boundary, etc.

Discrete lattice plane analysis of Baker-Nutting related B1 compound/ferrite interfacial energy

Abstract The interfacial energy of B1 (NaCl)-type carbides and nitrides (designated ξ) having Baker–Nutting orientation relationship with ferrite (α), i.e. (001)α//(001)ξ and [110]α//[100]ξ, was studied by discrete lattice plane, nearest neighbor broken bond method. The carbide (or nitride) lattice was contracted along the [001] direction so as to make the two lattices isomorphous and coherent at all interface orientations. The chemical interfacial energy of this hypothetical compound is highly anisotropic due to the difference in the M (metal atom)–I (non-metallic atom) coordination number between, for example, (001)- and (100)-type interfaces that would be equivalent in a cubic lattice. As a result, the equilibrium shape is a square plate with (001) broad faces. The anisotropy of the strain energy arising out of a large misfit along the [001] direction may override the anisotropy of chemical energy and dictate the observed square plate morphology of carbides and nitrides in ferrite.

Partition of Mn during the growth of proeutectoid ferrite allotriomorphs in an Fe-1.6 at. pct C-2.8 at. pct Mn alloy

A STEM analysis is made of the Mn distribution around grain boundary allotriomorphs of proeutectoid ferrite in an Fe-1.6 at. Pct C-2.8 at. Pct Mn alloy. Whereas the Mn enriched region is readily observed to extend along the austenite grain boundary, no substantial build-up or depletion of Mn near the ferrite : austenite interface is detected, consistent with the electron probe microanalysis previously reported. In the temperature range where the partition-local equilibrium (P-LE) mode has been proposed to prevail, measured parabolic growth rate constantsfall 1 to 2 orders of magnitude above that predicted from this model, but also below that calculated from the paraequilibrium (PE) model by roughly the same amount. A modification of the theory of grain boundary diffusion-aided growth of precipitates,i.e., the collector/rejector plate mechanism, on the other hand, accounts fairly well for the observed growth kinetics of ferrite allotriomorphs. However, only a slightly better accounting than the P-LE model is provided by this mechanism for the temperature dependence of Mn partition. Data on Ni partition, obtained in an Fe-0.5 at. Pct C-3.1 at. Pct Ni alloy, are also analyzed with the rejector plate model.

Three-dimensional morphology of degenerate ferrite in an Fe–C–Mo alloy

Abstract The three-dimensional morphology of degenerate ferrite formed below the bay of the TTT diagram in an Fe–C–Mo alloy was observed by serial sectioning and computer-aided reconstruction. The degenerate ferrite apparently consists of rod-like subunits, each several micron in length and 1–2 μm in diameter.

A DISCRETE LATTICE PLANE ANALYSIS OF COHERENT F.C.C./B1 INTERFACIAL ENERGY

Abstract A discrete lattice plane, nearest neighbor, broken bond model with constant bond energies, which had been used to calculate the energy of coherent interphase boundaries in substitutional alloys, was extended to a ternary substitutional–interstitial system to study the chemical interfacial energy between a f.c.c. solid solution and a B1(NaCl) compound. When the regular solution interaction coefficient of substitutional (metal) atoms is positive, interstitial (non-metallic) atoms which have different bond energies with the two metal atoms tend to increase both the composition difference and the interfacial energy. Even when the interaction coefficient of metal atoms is negative, a miscibility gap and a gradual composition change across the interface occur. The anisotropy of the interfacial energy varies widely according to the magnitude of interaction between the metal and the non-metallic atoms.

Alloying element accumulation at ferrite/austenite boundaries below the time–temperature–transformation diagram bay in an Fe–C–Mo Alloy

Abstract A scanning transmission electron microscope (STEM)-energy dispersive X-ray (EDX) analysis was made of the Mo concentration at boundaries between degenerate ferrite and austenite in an Fe–0.28mass%C–3mass%Mo alloy isothermally reacted below the bay temperature of the time–temperature–transformation (TTT)-diagram. The measured Mo concentration scattered widely from one boundary to another and varied considerably along the individual boundaries. The enrichment factor of Mo corrected for the sampling volume (beam diameter) to boundary thickness ratio showed an increasing tendency with isothermal holding time and reached as large as 15 when the alloy entered the transformation stasis. The amount of Mo in the boundary is compared with that calculated under the assumption of quasi-steady state diffusion that is used to analyze the solute drag effects on the motion of interphase boundaries.

Kinetics of ferrite transformation in an Fe-0.28mass%C-3mass%Mo alloy

The morphology and the kinetics of ferrite transformation below the TTT-diagram bay were studied in an Fe-0.28mass%C-3mass%Mo alloy. The three-dimensional reconstruction of the transformed microstructure revealed that the highly irregular morphology of ferrite observed on the polished specimen surface is formed due to extensive impingement and coalescence of thin rod-like crystals. The transformation stasis was observed consistently with previous observations. The fractions of ferrite achieved by fast carbon diffusion-controlled growth (followed by sluggish alloying element-partitioned growth) were calculated under paraequilibrium and local equilibrium. The calculated fractions of ferrite varied with temperature qualitatively in the same manner as those experimentally observed at the stasis. It is likely that above the bay the ferrite growth falls in the low velocity regime of Cahns solute drag theory, whereas below the bay it may fall initially in the high velocity regime, climb up the peak of the drag and enter the stasis. In alloys of lower C and Mo content the growth stasis does not occur presumably because the carbon diffusion-controlled growth can overcome the drag peak.

Computer simulation of ledge migration under elastic interaction

The diffusional growth of a phase by the motion of disconnections (ledges which contain transformation or misfit dislocations) was studied by a finite difference computer model. The elastic stress of these dislocations is considered to alter the (local equilibrium) solute concentration at the riser of ledges and cause a complex diffusion field interaction among ledges as they migrate. In some cases, however, the ledges forming a train can migrate all at the same speed in the presence of elastic interaction. The condition under which ledges overcome the elastic barrier and form a multipleheight ledge was determined. The model was applied to the migration of ledges/Shockley partial dislocations at γ′-plate interfaces in Al-Ag alloys.

Thermodynamics and kinetics of the formation of widmanstätten ferrite plates in ferrous alloys

Experimental data on the formation of Widmanstätten/bainitic ferrite in ferrous alloys(i.e., the Widmanstätten start temperature, partition of alloying elements, incomplete transformation, lengthening kinetics,etc.) are examined on the basis of thermodynamic calculations and kinetic analyses. A morphological change of ferrite from grain-boundary allotriomorph to Widmanstätten plate occurs well above theT0 temperature, except in high Mn and Ni alloys, but does so in the regime of carbon diffusion control in all alloys. Under the assumption that the plate tip consists of a pair of ledges of the height equal to the tip radius, the reported lengthening kinetics of ferrite plates can be accounted for very well by the diffusion-controlled motion of these ledges in a wide range of carbon supersaturation. It is also shown that the transformation stasis (incomplete transformation) observed below the kinetically definedBs in some iron alloys cannot be unequivocally attributed to either the completion of the precipitation of no-partitioned ferrite or the loss of the driving force for subsequent shear transformation.