Diffusion driven grain boundary migration in iron during zincification

At temperatures where only grain boundary diffusion is active in a diffusion couple, solute diffusion along the boundary can cause the boundary to migrate, mixing solute into the lattice swept by the moving boundary. This phenomenon—diffusion driven boundary migration (DDBM) — was investigated in the iron-zinc system. The (∼40 μm) iron foils and zinc vapor sources were sealed together in evacuated Vycor tubes and annealed at 550 °C to 630 °C for different times. The migration rate of grain boundaries was nearly constant throughout the transformation of the foil to alloy. Migration rates were about the same in pure iron and decarburized steel sheet. The apparent activation energy of DDBM (269 kJ/mol) was well above that expected for boundary diffusion of zinc in iron and is felt to reflect the role of creep in accommodating the local expansion that accompanies the addition of zinc. This expansion is in the plane of the sheet and indicates that D′_Zn in the boundary greatly exceeds D′_Fe. Inbulk samples annealed under the same conditions boundaries did not move (in 16 hours). This is consistent with a marked difference in the boundary mobility of Zn and Fe.     

Discontinuous cellular precipitation in a high-refractory nickel-base superalloy

A discontinuous precipitation reaction has been investigated in a high-refractory content nickel-base alloy. The reaction transforms the two-phase γ-γ′ parent microstructure into a three-phase cellular structure with a γ′ matrix containing Re-rich P-phase and agglomerated γ lamellae. The reaction has been studied in polycrystalline material and in bicrystals with varying degrees of boundary misorientation at temperatures in the range of T/T _m =0.78 to 0.85. The early stages of the reaction are characterized by heterogeneous nucleation of P-phase precipitates and migration of the grain boundary. At low-angle, near-tilt boundaries misoriented by less than 10 deg, nucleation of P-phase particles was observed, but the cellular reaction did not occur, due to limited boundary mobility and diffusivity. The high degree of supersaturation of Re and W in the initial γ-γ′ alloy appears to be the primary driving force for the reaction. Small amounts of creep deformation did not significantly influence the extent of the transformation. The diffusivity of Re associated with the moving boundary was calculated to be 5×10⁻⁸ cm² s⁻¹ at 1093 °C, which is approximately four orders of magnitude greater than the bulk lattice diffusivity of tungsten.     

Diffusion of the tracers Cu67, Ni66, and Zn65 in copper-rich solid solutions in the system Cu-Ni-Zn

Tracer diffusion coefficients were determined for the three isotopes, Zn⁶⁵, Cu⁶⁷, and Ni⁶⁶, in homogeneous Cu-Ni-Zn binary and ternary alloys, to 30 pct Ni and Zn, and pure copper as a function of composition and as a function of temperature, within about 250°C of the solidus surface. Activation energies andD ₀ factors were determined as functions of composition from these measurements. It is found that as the composition plane is traversed in the general direction from high nickel compositions on the copper-nickel binary to high zinc concentrations on the copper-zinc binary,i.e., as nickel is replaced by zinc, the diffusivity of all three tracers increases, and the activation energy for diffusion decreases. The total change in diffusivity across the composition plane is about two orders of magnitude. The three diffusivities are always in the order:D*_Zn >D*_Cu >D*_Ni, with the ratio being 9∶3∶1 at 900°C for all compositions. The three activation energies are usually in the orderQ*_Ni >Q*_Cu >Q*_Zn. These results are shown to be consistent with atom size and electron-to-atom concentrations of the three species in this alloy system. K. J. ANUSAVICE, formerly Graduate Student, Department of Materials Engineering, University of Florida, Gainesville, Fla.     

Interdiffusion in Ni-Rich,Ni-Cr-Al alloys at 1100 and 1200 °C: Part I. Diffusion paths and microstructures

Interdiffusion in Ni-rich, Ni-Cr-Al diffusion couples was studied after annealing at 1100 and 1200 °C. Recession of γ′ (Ni₃Al structure), β (NiAl structure), or α (bcc) phases was also measured. Aluminum and chromium concentration profiles were measured in the γ (fcc) phase for most of the diffusion couples. The amount and location of Kirkendall porosity suggests that Al diffuses more rapidly than Cr which diffuses more rapidly than Ni in the γ phase of Ni-Cr-Al alloys. The location of maxima and minima in the concentration profiles of several of the diffusion couples indicates that both cross-term diffusion coefficients for Cr and Al are positive and that D_CrAl has a greater effect on the diffusion of Cr than does D_A1Cr on the diffusion of Al. The γ/γ + β phase boundary has also been determined for 1200 °C through the use of numerous γ/γ+ β diffusion couples.     

Freeze-off limits in transient liquid-phase infiltration

Transient liquid-phase infiltration (TLI) involves a powder-metal skeleton and an infiltrant with similar composition containing a melting-point depressant (MPD). Upon infiltration, the MPD diffuses into the skeleton, causing isothermal solidification and allowing a homogeneous final-part composition. Diffusional solidification of the infiltrant can restrict liquid flow and result in premature freeze-off if the liquid solidifies before filling the entire part. A capillary-driven fluid-flow model was developed to predict the infiltration rate and freeze-off limit using a variable skeleton permeability. Diffusional solidification was measured via quenching experiments, compared to theory, and used to define the change in permeability of the skeleton. The infiltration rate was measured via mass increase and compared to the flow model for various skeletons with powder sizes ranging from 60 to 300 μm. The predicted horizontal infiltration freeze-off limits were proportional to the square root of d ³ γ/μDβ ², where d is the average powder diameter, γ and μ are the infiltrant surface tension and viscosity, respectively, D is the solid diffusivity, and β is a function of the solidus and liquidus concentrations. These relations can be used for selection of processing parameters and for evaluation of new material systems.     

Effect of Zn concentration on diffusion induced grain boundary migration in Cu -Zn system

Cu-Zn alloy system with three different compositions has been chosen to study the time, temperature and composition dependence of the Diffusion Induced Grain boundary Migration (DIGM) in the temperature range of 277–427°C. The grain boundary migration follows parabolic rate law as a function of time. The diffusivity, D_bα, was calculated from concentration-distance profile using growth rate, v. The activation energy for diffusion is found to be 101kJ/mol which is nearly half of the activation energy required for volume diffusion indicating that preferential grain boundary diffusion is more favorable than volume diffusion leading to grain boundary migration in Cu-Zn system.     

The chemical diffusivity of oxygen in liquid iron oxide and a calcium ferrite

Measurements have been made of the chemical diffusion coefficient of oxygen in liquid iron oxide at temperatures from 1673 to 1888 K and in a calcium ferrite (Fe/Ca = 2.57) at temperatures from 1573 to 1873 K. A gravimetric method was used to measure the oxygen uptake during the oxidation of the melts by oxygen or CO₂-CO mixtures. The rate was shown to be controlled by mass transfer in the liquid melt. The chemical diffusivity of oxygen in liquid iron oxide at oxygen potential between air and oxygen was found to be 4.2±0.3 × 10⁻³ cm²/s at 1888 K. That in iron oxide at oxidation state close to iron saturation was established to be given by the empirical expression log D=−6220/T + 1.12 for temperatures between 1673 and 1773 K. For the calcium ferrite (Fe/Ca=2.57) at oxygen potential between air and oxygen, the diffusivity of oxygen was found to be given by log D=−1760/T−1.31 for temperatures between 1673 and 1873 K. This article is based on a presentation made in the “Geoffrey Belton Memorial Symposium,” held in January 2000, in Sydney, Australia, under the joint sponsorship of ISS and TMS.     

Solute redistribution during and after solidification of Ni-Al-Ta dendritic monocrystals

Dendritic Monocrystals of Ni-Al-Ta alloys were grown at 0.05, 0.25, and 2.00 m/h and in some cases at other intermediate rates, under thermal gradients of 8 × 10³ and 18 × 10³ K/m. The growth of such monocrystals provides a rapid and easy way for:a) establishing the distribution of solute during and after solidification, as well as its dependence on local cooling rate; b) determining the effect of dendritic coarsening on this distribution and; c) studying the solution kinetics of the nonequilibrium interdendritic γ′ phase. Back-diffusion in the solid rather than dendritic coarsening was found to control the evolution of the solute distribution profile across the dendritic structure during solidification. With increasing local cooling rate the maximum solute concentration,C _M, remained practically unchanged, the minimum solute concentration,C _m, slightly decreased, the segregation ratio,S = C _M/C_m, increased and so did the volume fraction of nonequilibrium interdendritic γ′ phase. This phase dissolved during crystal pulling much faster at higher crystal growth rates. Solution kinetics were found to depend on the dimensionless parameterDθ/L ², whereD is diffusivity of solute at a given temperature at which a given transverse cross-section of the crystal remains for a timeθ andL is half the primary dendrite arm spacing.     

Diffusion of managenese and silicon in liquid iron over the whole range of composition

The measurement of the diffusivities of manganese and silicon in molten binary ferroalloys over the whole range of composition was undertaken to clarify existing but conflicting data at lower concentrations, to present new data at higher concentrations and to indirectly confirm the behavior of both systems observed in thermodynamic studies. The experiments were carried out under argon atmosphere in a Tammann furnace. The diffusion couples were held in 5 mm ID alumina tubes (98 pct Al₂O₃). Electron probe microanalysis of the samples led to a diffusion-penetration curve for the system under consideration. Results obtained over the whole range of composition showed a slight negative deviation for the Fe−Mn system and a very large positive deviation for the Fe−Si system. At lower concentrations (0 to 4 pct Mn), the temperature dependence of managanese diffusivity for the Fe−Mn binary alloy in the temperature range 1550° to 1700°C is as follows:D _Fe−Mn=1.8×10⁻³ exp (−13,000/RT) cm²/sec The concentration dependence of manganese diffusivity for the same system at 1600°C may be expressed asD _Fe−Mn={5.48−0.0137 (%Mn)+0.000276 (%Mn)²}×10⁻⁵ cm²/sec The temperature dependence of silicon diffusivity for the Fe−Si binary system in the temperature range 1550° to 1725°C at various concentrations is as follows:D _Fe−Si=2.8×10⁻³ exp (−11,900/RT) cm²/sec at 20 pct SiD _Fe−Si=2.1×10⁻³ exp (−13,200/RT) cm²/sec at 12.5 pct SiD _Fe−Si=5.1×10⁻⁴ exp (−9,150/RT) cm²/sec at 2.2 pct Si FELIPE P. CALDERON, formerly Graduate Student. University of Tokyo, Tokyo, Japan. This paper is based on a portion of a thesis submitted by FELIPE P. CALDERON in partial fulfillment of the requirements for the degree of Doctor of Engineering at University of Tokyo.     

Contribution of grain boundary diffusion and capillarity forces to the diffusional creep of wires or fibers

Herring’s analysis of the Newtonian creep of wires with a bamboo grain structure is modified to include the effects of grain boundary diffusion and capillarity. The grain boundary contribution depends on the ratio σD _b/2DR _v whereR is the wire radius,D _b andD _v are the boundary and volume diffusion coefficients, and σ is the width of the grain boundary. Capillarity is introduced in a consistent fashion into the analysis and the classical result for equilibrium between the applied load and capillarity forces is found. The creep rate of single crystal fibers embedded in a plastically deformed matrix is considered for some simple geometries.     

The effects of segregation on the kinetics of irrtergranular cavity growth under creep conditions

Intergranular cavity growth under creep conditions is examined with particular reference to the potential effects of segregation on cavity growth. When cavities are present on all of the boundaries in a polycrystalline solid, they are able to grow in an unconstrained manner. Under these conditions the rate of cavity growth may be controlled by grain boundary diffusion (D _GB), surface diffusion (D _S), or power law creep, which in turn is controlled by lattice diffusion (D _L). When only isolated boundaries are cavitated, cavity growth is constrained and may be completely limited by creep flow of the surrounding grains. The segregation of solute to the grain boundary and the cavity surface can influence the kinetics of cavity growth in several different ways. The reduction in surface energy associated with segregation can increase the rate of cavity growth when the cavities are crack-like. The effects of segregation on grain boundary and surface diffusion can also influence the rate of cavity growth. A phenomenological relation proposed by Borisovet al indicates thatD _GB /D_L decreases with segregation, thus causing grain boundary diffusion controlled cavity growth to be slowed by segregation. In some cases solute additions increaseD _L, thus increasing the rate of creep controlled cavity growth. When these effects are sufficiently large,D _GB can increase with solute additions, in spite of the effect of segregation. In some alloysD _S increases with segregation by several orders of magnitude. Similar effects on cavity growth are not expected even for surface diffusion controlled cavity growth because the rate of cavity growth is limited by other factors whenD _S is very large. This paper is based on a presentation made at the symposium “The Role of Trace Elements and Interfaces in Creep Failure” held at the annual meeting of The Metallurgical Society of AIME, Dallas, Texas, February 14-18, 1982, under the sponsorship of The Mechanical Metallurgy Committee of TMS-AIME.     

Catalyzed precipitation in Al-Cu-Si

The work reported here concerns the effect of Si on the precipitation of θ′ phase (metastable Al₂Cu) during the isothermal aging of Al-2Cu-1 Si (wt pct). The binary alloys Al-2Cu and Al-1 Si were studied for comparison. Only two precipitate phases were detected: essentially pure Si in Al-1 Si and Al-2Cu-1 Si, and θ′ (metastable Al₂Cu) in Al-2Cu and Al-2Cu-1Si. On aging the ternary alloy at 225 °C, Si precipitates first and catalyzes the θ′ phase. The precipitates in the ternary alloy are smaller, are more densely distributed, have lower aspect ratios, and coarsen more slowly than those in the binary Al-2Cu aged at the same temperature. While the shapes of individual θ′ precipitates in binary Al-2Cu are strongly affected by the kinetic problem of nucleating growth ledges, which produces a significant scatter in the aspect ratio for samples of given thickness, the overall evolution of particle shape with size follows the predictions of the Khachaturyan-Hairapetyan (KH) thermoelastic theory, which reduces to κ=L/d ∞ √L at large sizes. The KH theory provides an estimate for the interfacial tension of the broad Al-θ′ interface of 85 to 96 mJ/m², which is near the values for other low-energy interfaces in Al, such as the twin boundary energy (100 mJ/m²) and the antiphase boundary energy in δ′ Al₃Li (70 mJ/m²). Si and θ′ precipitates in Al-2Cu-1 Si have a strong elastic interaction because of their compensating strain fields. This elastic interaction promotes the nucleation of θ′ precipitates on Si, decreases the expected aspect ratio of θ′, and inhibits coarsening. Finally, Si precipitation in ternary Al-2Cu-1 Si differs from that in binary Al-1 Si in that the Si precipitates are coarser, more equiaxed, and more extensively twinned. These changes appear to be effects of Cu, which increases the solubility of Si in Al and adsorbs on the Si-Al interface, promoting twinning by a “step-poisoning” effect at the interface.     

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.     

Analysis of an asymmetrical model for boundary diffusion

An asymmetrical version of the Fisher model, in which bulk diffusivities on both sides of the boundary are different, is analyzed. Five regimes of boundary diffusion (C,B₁, B₃ and B₄) are distinguished. They progressively change each other as the temperature or/and time of diffusion anneal increase. Asymptotic solutions corresponding to the regimes are obtained, three types of surface conditions (constant source, Suzuoka's conditions, fast surface diffusion) being considered. In B₂-regime, which is the most widely spread, only the product D′δ can be determined, while in B₁-regime the boundary diffusivity D′ and width δ can be determined separately. Due to introducing an effective bulk diffusion coefficient, analytical solutions for C, B₁ and B₂-regimens are applicable to interphase boundary diffusion. The results can be used in designing diffusion experiments and treating measured penetration curves.     

Interdiffusion behavior of Pt-modified <Emphasis Type="Italic">γ</Emphasis>-Ni + <Emphasis Type="Italic">γ</Emphasis>′-Ni<Subscript>3</Subscript>Al alloys coupled to Ni-Al-based alloys

The effect of platinum addition on the interdiffusion behavior of γ-Ni + γ′-Ni₃Al alloys was studied by using diffusion couples comprised of a Ni-Al-Pt alloy mated to a Ni-Al, Ni-Al-Cr, or Ni-based commercial alloy. The commercial alloys studied were CMSX-4 and CMSX-10. Diffusion annealing was at 1150 °C for up to 100 hours. An Al-enriched γ′-layer often formed in the interdiffusion zone of a given couple during diffusion annealing due to the uphill diffusion of Al. This uphill diffusion was ascribed to Pt addition decreasing the chemical activity of aluminum in the γ + γ′ alloys. For a given diffusion couple end member, the thickening kinetics of the γ′ layer that formed increased with increasing Pt content in the Ni-Al-Pt γ + γ′ alloy. The γ′-layer thickening kinetics in diffusion couples with Cr showed less of a dependence on Pt concentration. Inference of a negative effect of Pt and positive effect of Cr on the Al diffusion in this system enabled explanation of the observed interdiffusion behaviors. There was no or minimal formation of detrimental topologically close-packed (TCP) phases in the interdiffusion zone of the couples with CMSX-4 or CMSX-10. An overlay Pt-modified γ + γ′ coating on CMSX-4 showed excellent oxidation resistance when exposed to air for 1000 hours at 1150 °C. Moreover, the Al content in the coating was maintained at a relatively high level due to Al replenishment from the CMSX-4 substrate.     

The thermal stability of the fibrous copper-chromium eutectic

The elevated temperature stability of the fibrous copper-chromium eutectic was studied and found to depend strongly upon the extent of structural defects in the as-grown eutectic. Both highly branched and nearly “ideal,” or regular, fibrous structures were obtained by controlling the crystal growing conditions. The branched structure coarsens at a much faster rate than the regular structure. In the regular structure, the initial stage of coarsening is described by a simple two-dimensional Ostwald ripening mechanism modified to take into account the effects of fiber geometry and volume fraction. The coarsening rate is limited by volume diffusion of the chromium solute in the copper matrix. The activation energy for coarsening is approximately 298 kJ/mol. After long time annealing, the chromium-rich fibers begin to pinch off and three dimensional coarsening is initiated which leads to a rapid increase in the coarsening rate. Application of theoretical analyses to the observed coarsening rate yields the productDΣ as 1.3 × 10⁻¹³ J/s at 1000°C, whereD is the diffusivity of Cr in solid Cu and Σ the Cu-Cr interfacial energy. Using reported values ofD, Σ is bracketed between 0.27 and 2.5 J/m². The latter is quite high for a solid-solid interfacial energy, but is consistent with the rapid coarsening observed in this system.     

The rate of reaction of solid iron with oxidized “FeO”-CaO-SiO2-Al2O3 slags at 1360 °C—the chemical diffusivity of iron oxide

Measurements have been made of the rate of reduction of oxidized iron oxide-containing 41CaO-38SiO₂-21Al₂O₃ (wt pct) slags at 1360 °C by a rotating disc of solid iron. For initial total iron concentrations of between 1.8 and 13.4 wt pct and rotation speeds up to 1000 rpm, the rate is shown to be determined by mass transfer in the liquid phase. The chemical diffusivity of iron oxide (in cm² s⁻¹) is found to be given by the empirical expression log D = −6.11 + 0.08 (wt pct Fe). It is concluded that the values of the diffusivity are for melts at close to iron saturation. It is shown that the available measurements of the diffusivity of iron oxide in liquid slags are consistent with increasing diffusivity with increasing state of oxidation, with about a tenfold increase between melts in equilibrium with iron and those in equilibrium with oxygen at 1 atm.     

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     

Tracer diffusion of63Ni in Fe-17 wt pct Cr-12 wt pct Ni

The tracer diffusion of⁶³Ni in Fe-17 Cr-12 Ni by both volume and grain boundary transport has been studied from 600° to 1250°C. The use of an RF sputtering technique for serial sectioning allowed the determination of very small volume diffusion coefficients at the lower temperatures. Volume diffusion of nickel in this alloy was observed to be much slower than in pure iron or austenitic stainless steel at comparable temperatures. The volume diffusion coefficient is described byD _v =8.8 exp (−60,000/RT) cm²/s and grain boundary diffusion is described by σD _gb =3.7×10⁻⁹ exp (−32,000/RT) cm³/s. R. A. PERKINS, formerly Presidential Intern, Metals and Ceramics Division, Oak Ridge National Laboratory, Oak, Ridge, Tenn. 37830, is     

Calorimetric Studies of Precipitation and Dissolution Kinetics in Aluminum Alloys 2219 and 7075

Differential scanning calorimetry (DSC) was used to study the kinetics of precipitation and dissolution of metastable and stable phases in aluminum alloys 2219 and 7075. A comparison of DSC scans obtained at heating rates of 1, 5, 10, and 20 K per minute showed that, during a DSC scan, the rates of precipitation of θ′ and θ in 2219 and η′ and η in 7075 were limited by their reaction kinetics. Likewise, the rates of dissolution of GP zones, θ′ and η′, were found to be dominated by kinetics. In contrast, the dissolution of θ and η was dominated by the thermodynamic equilibrium between these phases and the matrix. Analysis of the kinetically dominated reaction peaks and their dependence on heating rate and particle size showed that the GP zone dissolution reaction could best be described by a three-dimensional volume diffusion limited rate expression with an activation energy equal to that for diffusion. The rate of formation of θ′ was best described by an Avrami expression withn = 1.1, indicating that nucleation was not the rate controlling step. A pronounced dependence of the θ′ formation rate on prior plastic deformation was observed and ascribed to the influence of the matrix dislocation density on diffusivity.