Cellular precipitation

A theory of cellular precipitation is developed that assumes the interlamellar spacing to be controlled by the nucleation of new precipitate lamellae in recesses that develop in the advancing grain boundary at a sufficiently large interlamellar spacing. The theory also assumes a grain-boundary diffusion mechanism of mass transport, the maximum possible departure from local equilibrium across the grain boundary, and a grain-boundary model developed by Hillert. Application of the theory to all existing data that are sufficiently complet gives values for grain-boundary diffusivities that are both reasonable and in accord with existing diffusitivity data. It also suggests strongly that the velocity of grain-boundary migration is much more strongly dependent on driving force than the linear dependence given in most current theories. The interlamellar-spacing criterion proposed here is in reasonably good agreement with existing experimental data and with the experimental observation of Tu and Turnbull. BRUCE E. SUNDQUIST, formely with the U.S. Steel Corp., E. C. Bain Laboratory for Fundamental Research     

The coherency strain driving force for CIGM in non-cubic crystals: Comparison with in situ observations in calcite

Chemically induced grain boundary migration (CIGM) was observed in situ in calcite bicrystals in an optical microscope heat-stage. Three high-angle and two low-angle boundaries were observed. The solute was SrCO₃. Migration rates and solute concentrations were compared with boundary orientations. The coherency strain driving force was generalized for plane stress in any crystal system and applied to calcite. Because of the high anisotropy of lattice parameter expansion with Sr addition, a strong dependence of Sr concentration and migration driving force on crystallographic orientation was predicted. However, no correlation between SrCO₃ concentration and boundary orientation was observed, and little evidence for driving force dependence on orientation was found. Some evidence for a correlation between solute concentration and migration rate was found, but the nature of the correlation changed between bicrystals. Migration rates always decreased with time. Near-surface solute concentrations were depressed beneath values expected for stress-free equilibrium and plane stress modified equilibrium, but without obvious orientation dependence, which suggested that the coherency stress had a hydrostatic component. A PV driving force for migration might be present if solute diffusion fields around grain boundaries caused pressure gradients around the boundaries.     

Migration of liquid film and grain boundary in Mo-Ni induced by temperature change

Migration of liquid films and grain boundaries in liquid phase sintered 95Mo-5Ni (wt%) alloy occurs if the sintered specimens are heat-treated at temperatures above or below those of the initial sintering treatment. Behind the migrating boundaries, solid solutions in equilibrium at the heat-treatment temperature are deposited on the parent grains and the process is analogous to discontinuous precipitation and diffusion induced grain boundary migration (DIGM). The migration rate is varied by changing the sintering temperature while keeping the heat-treatment temperature constant; it increases parabolically with the expected composition difference between the initial and the final solid solutions. This result agrees with Hillert's proposal that the coherency strain energy in a diffusion layer in the retreating grain is the driving force. The observed migration rate and retardation effect due to the boundary curvature also agree in an order of magnitude with the coherency strain energy as the driving force. The results show that chemically induced migration of liquid films between the grains can be readily controlled experimentally and analyzed theoretically in terms of well known thermodynamic and kinetic laws.     

Migration Pinning and Roughening Transition of a Ni Grain Boundary

To date, much research has been conducted into the effect of migration pinning on the grain size in polycrystalline materials. However, effects of migration pinning on the grain-boundary structure and its transition have not been illuminated. Here, using transmission electron microscopy (TEM) we have explored the pinning effects for the grain boundary in a Ni bicrystal. During TEM specimen preparation, a hole was intentionally drilled in the middle of the grain boundary as a pinning point against grain-boundary migration. The specimen was heated to 600 °C. The grain boundary is driven to migrate by both the surface energy anisotropy and the total strain energy reduction. Grain-boundary facets with a plane orientation of {0 3 2}//{1 1 1} appear near the hole. The facets undergo a structural transition from atomically flat to rough with increasing distance from the hole. A pinning force exerted by the hole suppresses the migration of the grain boundary near the hole, indicating that the grain-boundary region away from the hole is subjected to a higher driving force. It certainly appears that the phenomenon originates from a change in driving force with the distance from the hole, being a signature of kinetic roughening.     

Chemical stresses induced by grain-boundary diffusion

Based on Whipple-Suzuoka solutions, the chemical stresses induced by grain-boundary diffusion under constant- and instantaneous-source concentrations are investigated. For a finite boundary, the chemical stress consists of both compression and tension fields, in the sequence of compression I-tension-compression II, with the compression I field near the diffusion interface. The magnitudes and distributions of these fields differ for different source concentrations and are strongly affected by the ratio of diffusivity in the grain boundary and diffusivity in the lattice (D′/D). As D′/D increases, the magnitude of the compression I field decreases and that of the tension and compression II fields increases. An increase in D′/D also increases the range of the compression I field. The trend is distinct in the case of constant-source diffusion, while in the case of instantaneous source diffusion, both the tension and compression II fields appear to be extremely small.     

Morphology and kinetics of discontinuous precipitation and dissolution in an Fe-8.5Al-27Mn-1.0Si-0.92C alloy

The morphology and growth kinetics of discontinuous precipitation (DP) and discontinuous dissolution (DD) in an Fe-8.5Al-27Mn-1.0Si-0.92C alloy are investigated. The results indicate that the solid-solution-treated austenite phase decomposes into lamellar DP after aging at temperatures ranging from 900 to 1050 K. After the specimens of a preaged DP structure go through further aging at temperatures ranging from 1118 to 1173 K, the lamellar DP falls into dissolution because of the DD reaction. The lamellar spacings of the DP structure, as well as the reaction-front migration rates during DP and DD reactions, are measured. Based on Aaronson and Liu’s simplified kinetics model, the grain-boundary diffusivities are estimated. They are found to be slightly lower than the grain-boundary diffusion data of Mn in Fe and Fe in Fe as reported by Aaronson and Liu.     

Chemically induced migration in low and high angle calcite grain boundaries

Chemically induced grain boundary migration (CIGM) occurs in the CaCO₃-SrCO₃ system at 680°C, producing microstructures similar to those observed in metals systems. Forty calcite bicrystals with varying misorientation were examined. CIGM was usually observed along the entire length of high angle boundaries, and along very small lengths of boundary with misorientation magnitudes (θ_m) as low as 0.7° ± 0.35°. Percentage of the boundary which migrated, migration rate, node spacing, and Sr concentration correlate with θ_m below ≈ 14–18°. Sr concentrations were heterogenous and well beneath values expected for chemical equilibrium, and were not measurable by electron microprobe or secondary ion mass spectroscopy when θ_m was below 3°. At θ_m ≈ 14–18° there may be a change in behavior associated with the transition to high angle boundary structure. Extrinsic factors probably complicate the experiments, but the observations suggest CIGM in calcite may be regarded as a two-stage process of nucleation and growth. Existing theories for CIGM do not explain many of the results.     

Specimen size effects in DIGM,DIR and RID

Specimen size effect in diffusion induced grain boundary migration (DIGM), diffusion induced recrystallization (DIR) and recrystallization induced diffusion (RID) was studied. The Fisher model of grain boundary diffusion was used, provided the total diffusive impurity flux is reflected from the lower side of film. The limits of grain-boundary migration rates, for which this model is valid, were estimated. The threshold character of DIGM, DIR and RID was shown. Manifestations of specimen size effect of DIGM, DIR and RID below some critical thickness were discussed.     

The effect of grain boundary precipitation on the stability of extrinsic grain-boundary dislocations in austenitic steel and aluminium alloy

The effect of grain boundary precipitation on the stability of extrinsic grain boundary dislocations (EGBD) was studied in alloys in which the occurence of depletion of definite alloy elements in grain boundary region is well documented, namely Cr-Ni-austenitic steel and Al-Zn-Mg alloy. It was found that depletion of grain boundaries of alloying elements that occurs in the process of precipitation on grain boundaries results in substantial decrease of EGBDs stability. Results are interpreted in terms of changes in grain-boundary diffusion coefficients.     

Defect structures in fatigued Al-6.5 at. pet Zn alloy

Lattice defects induced by cyclic straining in a homogenized and quenched Al-6.5 at. pet Zn alloy were investigated. Whereas homogeneously distributed dislocations were produced by cycling with a strain amplitude exceeding the elastic limit, dislocations produced by cycling with an amplitude below the elastic limit were limited to a zone adjacentto the grain boundary which prior to cycling was denuded of quench-induced dislocation loops. Cycling with an amplitude below the elastic limit caused the dislocations to accumulate at the grain boundary and continued cycling resulted in grain boundary migration and in enhanced precipitation of the equilibrium phase at the boundary. The driving force for the boundary migration was provided by the strain energy of the dislocations accumulated in the denuded zone and the precipitation took place mainly by diffusion of zinc atoms along the moving boundary.     

Pinning of grain boundaries by deformable particles

Interaction between a grain boundary and deformable particles has been modeled. It is shown that deformable particles pin the grain boundaries more effectively than rigid spherical particles. The required driving force to unpin a grain boundary increases with decreasing the interphase energy of the deformable particle. Deformable particles also reduce the rate of grain-boundary migration more effectively than rigid spherical particles. The rate of grain boundary migration decreases with the interphase energy of the deformable particle. The model allows the shape of a deformable particle to be determined as the particle is dragged by a grain boundary. The particle shape allows prediction of the force acting on the particle.     

Shrinkage and splitting of microcracks under pressure simulated by the finite-element method

The two-dimensional finite-element method is applied to analyze the shrinkage and splitting of microcracks regularly arranged on or perpendicular to a grain boundary under pressure. Grain-boundary and surface diffusions are coupled by the boundary conditions at the triple point of the microcrack surface and the grain boundary. The shrinkage and splitting processes for the two kinds of microcracks are revealed by detailed finite-element analyses. For the microcrack lying on a grain boundary, it first shrinks to a small void shape, then the void is split by the grain boundary and the two split voids assume a cylindrical shape under the capillary force of the surface. For the microcrack perpendicular to the grain boundary, it is split into two segments by the grain boundary during the early stage of shrinkage. Then, the split microcracks stop shrinking and evolve into two cylindrical channels with a circular section by the capillary force of the surface. These evolution processes are controlled by the applied pressure, microcrack spacing, ratio of grain-boundary diffusion to surface diffusion, and equilibrium dihedral angle, defined by surface and grain-boundary tensions. The influences of these controlled parameters on the evolution processes are numerically clarified based on a great number of finite-element analyses.     

A critical test for the coherency strain energy as the driving force for the discontinuous precipitation in MoNi alloy

When 90Mo-10Ni alloys prepared by liquid phase sintering are heat-treated at 1300°C, discontinuous precipitation of MoNi phase in the form of discrete particles or rods occurs in the MoNi grains. In order to test the diffusional coherency strain hypothesis as the driving force for the discontinuous precipitation, Fe has been added at varying concentrations to the matrix of the liquid phase sintered MoNi specimens before the heat-treatment at 1300°C. The discontinuous precipitation is observed to be suppressed by the grain boundary diffusion of Fe and does not occur at all when the Fe concentration in the solidified matrix is increased to a certain range, where the coherency strain energy is estimated to be close to the minimum value of 0. The result thus shows that the coherency strain energy is the driving force for the discontinuous precipitation in this alloy. When the Fe concentration in the matrix is high, the chemically induced grain boundary migration (commonly referred to as DIGM) occurs due to the predominant effect of Fe diffusion, producing a tensile coherency stress.     

Discontinuous precipitation at [001] twist boundaries in Cu-0.75 wt pct Be alloy bicrystals

The misorientation dependence of discontinuous precipitation (DP) at [001] twist boundaries in Cu-0.75 wt pct Be alloy bicrystals has been systematically investigated in the temperature range 523 to 723 K. A good correlation is found between both the incubation period, τ, to initiate DP and cell growth rate, ν, and the energy of boundaries. The maximum of τ and the minimum of ν occur where the cusps of the boundary energy exist. The formation and growth of DP are easier at higher-energy boundaries. The DP cells at [001] twist boundaries nucleate and grow less than those at [001] symmetric tilt boundaries in the same-alloy bicrystals. A kinetic analysis of DP using the models of Turnbull and Petermann and Hornbogen has yielded grain-boundary diffusion data. Although the activation energy, Q _b , of boundary diffusion changes with the models, the values of Q _b are smaller than the activation energy for volume diffusion of Be in Cu. The diffusivity in a boundary shows a close correlation with the energy of the boundary. A lower-energy boundary has a lower diffusivity with a larger activation energy and a larger pre-exponential factor.     

The effect of external stress on the discontinuous precipitation in an AlZn alloy at high and low temperatures

The effect of external tensile stress on continuous precipitation (DP) has been investigated in an Al21.8 at.% Zn alloy at high (215°C) and low (75 and 50°C) temperatures. The ratio of the macroscopic lattice diffusivity, D, to the DP boundary velocity, v, (D/v) is estimated to be larger than the interatomic spacing, λ, at the high temperature, and smaller than λ at the low temperatures. Under tensile stresses, the DP rates are enhanced at the grain boundary segments oriented transverse to the stress direction and suppressed at those oriented parallel to it at both high and low temperatures. Furthermore, Yi and Park show the DP rate changing continuously with temperature over the range where D/v increased from values much smaller than λ to those much larger. These results show that the diffusional coherency strain is the major driving force for DP even at low temperatures where, with D/v < λ, no solute diffusion is usually assumed to occur in front of the moving DP boundaries.     

Kinetics and Grain Boundary Selectivity of Discontinuous Precipitation in Binary Ni-Cr Alloy

A supersaturated Ni-Cr alloy (42 wt pct Cr) was subjected to a series of aging heat treatments in the two-phase region in the temperature range of 923 K to 1123 K (650 °C to 850 °C) for different time periods. The resultant microstructures were seen to be composed of varying volume fractions of continuous (CP) and discontinuous precipitation (DP). The DP dominated at lower temperatures, while CP dominated at higher temperatures and the expected DP termination temperature was estimated to be 1138 K (865 °C). The kinetics of DP followed the Turnbull model at lower temperatures and the Aaronson–Liu model at higher temperatures. The nucleation and growth of DP cells, which occurred via the ‘precipitate driven grain boundary migration,’ was seen to be a strong function of the nature of the participating grain boundaries.

     

The effect of hold time and waveform on the high-temperature, low-cycle fatigue properties of a Nb-A286 alloy

The effect of hold time and waveform on the high-temperature, low-cycle fatigue (HTLCF) of a Nb-modified A286 alloy was investigated at 650 °C. It was found that the fatigue life with strain hold was lower than that of continuous low-cycle fatigue, and this was due to the additive creep deformation during hold time. The apparent activation energy for the creep deformation during the tensile and compressive hold times was determined to be about 260 to 270 kJ/mole from stress-relaxation curves. This value is in good agreement with the apparent activation energy required for the formation of η phase at the grain boundary in the Nb-A286 alloy. Therefore, the grain-boundary precipitates and the corresponding cavitation along the grain boundary were estimated to be the main damage of the creep-fatigue interaction of the Nb-A286 alloy and to cause the intergranular failure. Also, the driving force for grain-boundary cavitation leading to intergranular failure under a compressive strain hold is reduced compared to the case of a tensile strain hold. This fact is known to be due to the healing effect of the grain-boundary cavitation. Therefore, the strain hold in compression leads to less reduction in fatigue life than that in tension.     

On theories of growth during discontinuous precipitation

Growth theories for the lamellar eutectoid transformation are reviewed from a free energy point of view in order to form a background for an examination of the various treatments of growth during discontinuous precipitation. The shortcomings of Cahn’s theory of discontinuous precipitation are pointed out and the treatment based upon the individual consideration of growth conditions for the two phases is discussed, with particular emphasis on how the total free energy available to drive the reaction is divided into many parts which are used for various purposes. New sets of calculations are presented in order to demonstrate the effect of free energy losses due to boundary friction and volume diffusion. The effect of coherency stresses in the parent grain is shown to decrease the free energy loss due to volume diffusion and may thus provide a driving force for grain boundary movement. This paper is based on a presentation made at a symposium on “The Cellular and the Pearlite Reactions,” held at the Detroit Meeting of The Metallurgical Society of AIME, October 20, 1971, under the sponsorship of the IMD Heat Treatment Committee.     

Grain-Boundary Precipitate in Aluminum-Magnesium Alloys

Abstract

An investigation has been made of grain boundaries in aluminum-magnesium alloys in the stress-corrosion-susceptible and non-susceptible conditions, to elucidate the structure of the type of boundary found in susceptible alloys; it appears after chemical etching as a continuous groove when viewed under the optical microscope.

Vacuum cathodic etching was used to reveal the boundaries, and carbon replicas were examined by electron microscopy. The boundaries were found to contain either a fine, discontinuous precipitate, or no precipitate at all. In no case was a continuous grain-boundary precipitate observed.

These observations were substantiated by an examination of similar boundaries in electrothinned samples by transmission electron microscopy.     

A Comparative Study of the Kinetics of Interface Diffusion Controlled Transformations In Fe-Zn Alloys

Abstract

A comparative study of the kinetics of discontinuous precipitation, coarsening and dissolution, diffusion induced grain boundary migration and grain growth has been carried out in Fe-Zn alloys. Except for cells of the discontinuous coarsening reaction, rates of migration of the cell boundaries of precipitation and dissolution and diffusion induced grain boundary migration (DIGM) rates lie within an order of magnitude of each other. The rate of cell boundary migration during discontinuous coarsening is two orders of magnitude smaller than those for the four transformation processes mentioned above. The kinetics (of minimum rate) of grain growth which occurs after long annealing times is comparable to the discontinuous precipitation and coarsening in the Fe-Zn alloy. The kinetics (of maximum rate) of grain growth, which corresponds to short annealing times, are comparable to the discontinuous dissolution and DIGM. The diffusivity values lie within an order of magnitude of the boundary diffusivity during grain growth when considered at the same temperature (extrapolated). Although the driving force differs by four orders of magnitude from as low as 0.08 Jmol^?1 for grain growth to 1420 Jmol^?1 for DIGM at 923 °K, the small difference in the diffusivity (kD_bδ) predicts that the conduit for solute transport is the same for the above transformations.

On a effectué une étude comparative de la cinétique de précipitation discontinue, de grossissement et de dissolution, de migration de joints de grain induite par diffusion (DIGM) et de croissance de grain, d'alliages de Fe-Zn. À l'exception des cellules de réaction de grossissement discontinu, le taux de migration des joints de cellules de précipitation, de dissolution ainsi que le taux de migration de joints de grain induite par diffusion se situent à un ordre de grandeur l'un de l'autre. Le taux de migration du joint de la cellule lors du grossissement discontinu est de deux ordres de grandeur plus petit que celui des quatre procédés de transformation mentionnés ci-dessus. La cinétique (taux minimum) de croissance de grain qui se produit après une longue durée de recuit est comparable à la précipitation discontinue et au grossissement de l'alliage Fe-Zn. La cinétique (taux maximum) de croissance de grain qui correspond à de courtes périodes de recuit est comparable à la dissolution discontinue et à “DIGM”. Les valeurs de diffusivité se situent à un ordre de grandeur de la diffusivité du joint lors de la croissance de grain lorsque considérée à la même température (extrapolée). Bien que la force directrice diffère par quatre ordres de grandeur, allant de 0.08 Jmol^?1 pour la croissance de grain jusqu'à 1420 Jmol^?1 à 923 °K pour “DGIM”, la petite différence de diffusivité (kD_bδ) prédit que le conduit pour le transport de soluté est le même pour les transformations ci-dessus.