Ternary diffusion in the α and γ phases of the Fe-Ni-P system

Ternary diffusion coefficients have been determined in the α-bcc and γ-fcc phases of the Fe-Ni-P system and at four temperatures 1200, 1100, 1000, and 900°C. At 1100°C the ratio ofD _NiNi ^Fe /D _PP ^Fe in the α phase is 0.3 to 0.4 and the ratio of the cross coefficientD _PNi ^Fe /D _PP ^Fe is 0.03 to 0.05. m the γ phase the corresponding ratios are 0.01 to 0,02 and 0.0015 to 0.0025. The other cross coefficientD _NiP ^Fe could not be evaluated because of experimental uncertainties. Estimates of the ratioD _NiP ^Fe /D _NiNi ^Fe using the interaction parameter ε₁₂ are 0.004 to 0.01 in the α phase and 0.02 to 0.04 in the γ phase. The addition of P in both the α and γ phase increases the major ternary coefficients up to as much as a factor of ten at one temperature. This is consistent with the fact that P lowers the melting point of FeNi in the ternary system, up to 500°C. Isodiffusion coefficient contours obtained at 1100°C plot approximately parallel to the α and γ solidus boundaries and are similar in shape to the α and γ solidus boundaries as a function of temperature. Activation energies andD ₀ values were computed at selected compositions in both α and γ phases forD _PP ^Fe andD _NiNi ^Fe and are given below: Formerly Graduate Student, Department of Metallurgy and Materials Science, Lehigh University, Bethlehem, Pennsylvania     

Thermodynamics of carbon in austenite and Fe-Mo austenite

A Cahn Electrobalance has been used to determine directly and very accurately the carbon content of iron, iron-0.48 wt pct molybdenum and iron-1.16 wt pct molybdenum specimens which were equilibrated with a series of methane-hydrogen gas mixtures of constant composition. The equilibria investigated involved the austenite phases of the alloys at 783, 813 and 848‡C. The experimental results permit direct calculation of the activities of carbon in the samples, relative to graphite as unity, and of the enthalpy and entropy of solution of carbon. The results are compared with the experimental measurements of a number of other investigators. The results are in excellent agreement with those of Smith and Schenck and Kaiser for the Fe-C system at 800‡C, and indicate -H _C ^/M values of 9700 ± 500 cal/mole for pure Fe, 10,030 ± 500 cal/mole for an Fe-0.48 wt pct Mo alloy, and 10,150 ± 500 cal/mole for an Fe-1.16 wt pct Mo alloy. The effect of molybdenum in austenite is to decrease the activity coefficient of carbon in austenite.     

Thermodynamics of carbon in austenite and Fe-Mo austenite

A Cahn Electrobalance has been used to determine directly and very accurately the carbon content of iron, iron-0.48 wt pct molybdenum and iron-1.16 wt pct molybdenum specimens which were equilibrated with a series of methane-hydrogen gas mixtures of constant composition. The equilibria investigated involved the austenite phases of the alloys at 783, 813 and 848‡C. The experimental results permit direct calculation of the activities of carbon in the samples, relative to graphite as unity, and of the enthalpy and entropy of solution of carbon. The results are compared with the experimental measurements of a number of other investigators. The results are in excellent agreement with those of Smith and Schenck and Kaiser for the Fe-C system at 800‡C, and indicate -H _C ^/M values of 9700 ± 500 cal/mole for pure Fe, 10,030 ± 500 cal/mole for an Fe-0.48 wt pct Mo alloy, and 10,150 ± 500 cal/mole for an Fe-1.16 wt pct Mo alloy. The effect of molybdenum in austenite is to decrease the activity coefficient of carbon in austenite.     

The thermodynamics of stress-induced martensites in Cu Al Ni alloys

Stress-induced martensitic transformations have been studied in Β₁ Cu Al Ni single crystals in which two martensite crystal structures can form, Β _i ^′ and γ′. By straining specimens at one temperature and releasing the strain at either the same temperature or a different temperature, stresses corresponding to the transitions Β₁ ⇌ Β _i ^′ ,Β ₁ ⇌ γ′,Β _i ^′ ⇌ γ′ could all be measured. This enabled a quantitative stress-temperature diagram to be drawn, giving the stability ranges of the Β₁,Β _i ^′ and γ′ phases. The slope of the stress-temperature lines separating the different phases enabled the value of the entropy changes for the transformations to be calculated. This was very small for theΒ _i ^′ → γ′ transformation (0.08 J/mole K) and much larger for the Β₁ →Β _i ^′ and Β₁ → γ′ transformations (-1.21 and -1.4 J/mole K, respectively). The hysteresis between the forward and reverse transformations enabled evaluation of the critical free energy for transformation. This was small for the Β₁ → Β _i ^′ transformation (-2.9 J/mole), and large for the Β₁ → γ′ and Β _i ^′ → γ′ transformations (-28 and -29 J/mole respectively). Formerly Post Doctoral Fellow, Department of Metallurgy, University of British Columbia     

Deformation mechanisms in commercial Ti (0.5 at. pct oineq) at intermediate and high temperatures (0.3 - 0.6 tinm)

The plastic flow of the commercial titanium material Ti-50A (0.5 at. pct O_eq) of 22 μm grain size was investigated over the temperature range of 600 to 1150 structure) and strain rates of 3 x 10^-5 to 3 x 10^-2 per s employing both constant strain rate and strain rate cycling tests. Dynamic strain aging occurred in the temperature range of 600 to 850 (0.31 to 0.44T_m) with an activation energy of 50 kcal per mole derived from the start of serrations in the stress-strain curves, maxima in strain hardening and minima in ductility. This value is in accord with that for the diffusion of oxygen in titanium. At temperatures above 850 (0.46 to 0.59T_m) the data were very well represented by Weertman’s glide and climb high temperature creep mechanism, giving ε_skT/Dμb= 1.1 x 10⁶ (σ/μ)^4.55 withD = 1.0 x exp (- 57,800/RT). The value of 57.8 kcal per mole is in accord with available self-diffusion data for titanium.     

The high-temperature creep behavior of nickel-rich Ni-W solid solutions

The steady-state creep behavior of four nickel-rich Ni-W solid solutions (1, 2, 4, and 6 wt pct W) was investigated in the temperature range 850° to 1050°C. Constant stress tensile creep tests were performed in vacuum in the stress range 3000 to 7000 psi. Activation energies for creep were observed to be 71.4 ± 2.0, 74.4 ± 3.0, and 75.8 ±2.0 kcal per mole, after correcting temperature dependence of the elastic modulus, for alloys containing 2,4, and 6 pct W respectively. These values closely approximate the activation energies for the weighted diffusion coefficient, =D _Ni D _W/(X _W D _Ni) whereX _Ni andX _w are the atom fractions of nickel and tungsten respectively, andD _Ni andD _w are the diffusion coefficients of nickel and tungsten in the alloy. The steady-state creep rates exhibit a power law stress dependence with an exponent,n, equal to 4.8 ±0.2 for all of the alloys studied. For tests conducted at temperatures and stresses such that both the diffusivity, , and the ratio of the applied stress to the elastic modulus, σ/E, are. held constant, the steady-state creep rate, , was found to vary with the stacking fault energy, γ, according to the empirical relation ∼ γ^{4 2±4} over the range of creep rates studied. W. R. Johnson, formerly Graduate Student, Stanford Univeristy, Stanford, Calif.     

Kinetics of the carbon-oxygen reaction in molten iron

The kinetics of carbon monoxide absorption by stagnant liquid iron has been investigated over the first 10 min or so of gas-liquid metal contact. On the basis of experiments conducted at temperatures ranging between 1580° and 1700°C (PCO= 1 atm) and carbon monoxide pressures ranging between 0.1 and 1.5 atm (at 1600†C), it was concluded that the absorption kinetics of CO in liquid iron was diffusion controlled. Mass transfer equations developed to describe the process were adapted to define an “apparent diffusion coefficient” of carbon monoxide. This coefficient is a function of carbon and oxygen binary diffusion coefficients, and also depends on the initial bulk oxygen and carbon concentrations, and on the equilibrium constant for the reaction. CO = C + O Experimental D_COvalues averaged at 9.8 10−⁵cm²s−¹, while binary carbon and oxygen diffusivities were computed to be 41.2 10−⁵ and 5.2 10−T⁵cm²s−¹ respectively. Using the data obtained, the relative influence of carbon and oxygen diffusion on the kinetics of carburization and decarburization reactions is quantitatively considered. Formerly Graduate Student, McGill University, Montreal, Quebec, Canada     

Grain-boundary penetration of type 316 stainless steel exposed to cesium or cesium and tellurium

When 20 pct cold-worked Type 316 stainless steel is exposed to Cs at 700°C under controlled oxygen-chemical potential environment, Cs penetration into the stainless steel grain boundaries occurs at oxygen potentials ΔG_o2 ≥ -96 kcal per mole. At lower oxygen potentials (~ΔG_o2 ≤ —110 kcal per mole), no corrosion occurs. Under the same experimental conditions, when the stainless steel is exposed to Cs:Te (2:1, atomic), corrosion occurs and penetration morphology appears to depend strongly on the oxygen-potential environment. The stainless steel suffers intergranular corrosion by Te (in the presence of Cs-Te) under conditions where chromium oxidation is not expected to occur. The kinetics of grain-boundary penetration by Te have been studied at temperatures between 550 and 700°C. The depth of the penetrated zone varies as (time)^1/2, and the process has an activation energy of 34 kcal per mole. The results are discussed, and the effects of stainless steel microstructure and externally applied stress on corrosion reactions are also described.     

Analysis of low-temperature intermetallic growth in copper-tin diffusion couples

A multiphase diffusion model was constructed and used to analyze the growth of the ε- and η-phase intermetallic layers at a plane Cu-Sn interface in a semi-infinite diffusion couple. Experimental measurements of intermetallic layer growth were used to compute the interdiffusivities in theε andη phases and the positions of the interfaces as a function of time. The results suggest that interdiffusion in the ε phase(≈D _ε) is well fit by an Arrhenius expression with D₀ = 5.48 × 10⁻⁹ m²/s andQ = 61.9 kJ/mole, while that in the η phase (≈D_η) has D₀ = 1.84 × 10⁻⁹ m²/s andQ = 53.9 kJ/mole. These values are in reasonable numerical agreement with previous results. The higher interdiffusivity in theη phase has the consequence that theη phase predominates in the intermetallic bilayer. However, the lower activation energy for interdiffusion in theη phase has the result that theε phase fills an increasing fraction of the intermetallic layer at higher temperature: at 20 °C, the predicted ε-phase thickness is ≈10 pct of that ofη, while at 200 °C, its thickness is 66 pct of that ofη. In the absence of a strong Kirkendall effect, the original Cu-Sn interface is located within theη-phase layer after diffusion. It lies near the midpoint of theη-phase layer at higher temperature (220 °C) and, hence, appears to shift toward the Sn side of the couple. The results are compared to experimental observations on intermetallic growth at solder-Cu interfaces.     

Recrystallization behavior of a heavily cold-rolled Ni3Al(B,Zr) alloy

The present article describes the microstructural changes during recrystallization annealing of a 73 pct cold-rolled Ni₃Al(B,Zr) alloy along with a study of the recrystallization kinetics. The deformed γ regions, mostly within and near the shear bands, appear to recrystallize first. The recrystallization front leaves behind a lamellar discontinuous precipitation within the newly formed strain-free γ grains, when annealing is done at lower temperatures. At higher annealing temperatures, the precipitates within γ assume a globular morphology. This precipitate is presumably made up of γ′ particles. When γ recrystallization is nearly complete, the γ′ regions start to recrystallize. The two-stage recrystallization process is also corroborated from the kinetics results, which show that the activation energy up to 50 pct recrystallization of the material is only 117 kJ/mole, whereas beyond 50 pct until the completion of recrystallization, an activation energy of ∼274 kJ/mole is obtained.     

Kinetics of pearlite spheroidizations

A study of the kinetics of pearlite spheroidization under static annealing conditions was carried out in two materials — AISI 1080 steel and pure Fe-C alloy. A stereological “shape factor”,F, defined asF =S _v ^p/3• K_m, was introduced for the kinetic study. The significance of this shape factor in relation to the geometrical characters of lamellar structures is discussed. For constant temperature a linear relation betweenF and the logarithm of time was obtained. Analysis of the time and temperature dependencies for a constant shape factor gave an activation energy of 70 kcal/mole for AISI 1080 steel and 58 kcal/mole for Fe-C alloy which indicates that volume diffusion of Fe in ferrite is the rate-controlling mechanism. The modified fault migration theory, which was developed from the mechanism study of this research, was applied to predict the kinetics of the pearlite spheroidization. For both the AISI 1080 and the Fe-C alloy experimental results have a good match with the theoretical prediction.     

Henrian activity coefficient of As in Cu-Fe mattes and white metal

A transpiration method was used to evaluate the Henrian activity coefficient of As (γ _As ^o ) in Cu-Fe mattes and white metal. Values for the activity coefficient of As (γ _As) have been evaluated as a function of the Cu/Fe molar ratio from 1 to ∞, as a function of the sulfur deficiency (defined as SD=X _s−1/2X _Cu−X _Fe, where X _i is the mole fraction of the ith species) from −0.02 to +0.02 and at temperatures between 1493 and 1573 K. The activity coefficient for arsenic in the matte was found to have a weak dependence on both temperature and the Cu/Fe molar ratio, but a strong dependence on SD. Analysis of γ _As as a function of the trace-element concentration reveals that the activity coefficient is highly dependent on the As content, even at trace concentrations where Henrian behavior is expected. That dependency is attributed to uncertainty in the reported value of the saturation pressure of monatomic arsenic (P _As ^o ) and highlights problems in comparing results and specifying Henrian values for the activity coefficient. A method is presented whereby the impact of P _As ^o on computed values of γ _As is significantly reduced to obtain an approximate Henrian value of the activity coefficient.     

The interaction between oxygen and bismuth in dilute solution in copper at 1300 °C

The activities of bismuth (in the range 0.0021 < X_Bi< 0.0053) and oxygen (in the range 3 X 10⁻⁴ < X_o < 0.044) in liquid copper at 1300 ° have been measured by equilibrating pure copper specimens with gaseous atmospheres of known oxygen potential and partial pressure of bismuth. The value of γ_Bi^o in liquid copper at 1300 ° was obtained as 3.09 and the variation of γ_Bi with mole fraction of oxygen was obtained as log γ_Bi = −0.91X_o + 0.49, which yields ɛ_O^Bi = −2.1. The observed variation of log γ_o with mole fraction of bismuth is widely scattered but is in fair agreement with the thermodynamically-consistent expression, log γ_o = −0.9LY_Bi − 0.51.     

A study of stacking faults in deformed austenitic stainless steel by X-ray diffraction

Making use of the data obtained already in our laboratory on elongated, quenched samples of austenitic steel lCrl8Ni9, such as the effective domain size D_eff, the average dislocation density-ρ, the average dislocation configuration parameter, -M, the range of strain field -R_e, the elastic energy density 〈E/V〉,etc., some exact and clear expressions for the relation of intrinsic stack-ing fault (SF) density α′, extrinsic SF density α″, twin fault density β, SF energy γ, true particle size D₀, minimum value of the fault width T_min, and maximum particle size D_max are given.     

Solute diffusion in alpha- and gamma-iron

The diffusion rates of chromium, vanadium, and hafnium in α- and γ-Fe have been determined by radiotracer techniques. The results are (in sq cm sec⁻¹): α-Fe γ-Fe ChromiumD = 8.52 exp (−59,900/RT)D = 10.80 exp(−69,700/RT) VanadiumD = 3.92 exp (−57,600/RT)D = 0.25 exp (−63,100/RT) HafniumD = 1.31 exp (−69,300/RT)D = 3600 exp (−97,300/RT) The differences in diffusion rates are discussed in terms of the compressibility of the diffusing atom. Diffusion of chromium in γ-Fe was also measured by a microprobe analysis technique. The result is:D = 4.08 exp (−68,500/RT) Comparison is made between diffusion analysis by tracer techniques and by electron probe microanalysis. Formerly with Department of Metallurgy, University of Manchester, Manchester, England     

A melting and solidification study of alloy 625

The melting and solidification behavior of Alloy 625 has been investigated with differential thermal analysis (DTA) and electron microscopy. A two-level full-factorial set of chemistries involving the elements Nb, C, and Si was studied. DTA results revealed that all alloying additions decreased the liquidus and solidus temperatures and also increased the melting temperature range. Terminal solidification reactions were observed in the Nb-bearing alloys. Solidification microstructures in gastungsten-arc welds were characterized with transmission electron microscopy (TEM) techniques. All alloys solidified to an austenitic (γ) matrix. The Nb-bearing alloys terminated solidification by forming various combinations of γ/MC(NbC), γ/Laves, and γ/M₆C eutectic-like constituents. Carbon additions (0.035 wt pct) promoted the formation of the γ/MC(NbC) constituent at the expense of the γ/Laves constituent. Silicon (0.4 wt pct) increased the formation of the yJLaves constituent and promoted formation of the γ/M₆C carbide constituent at low levels (<0.01 wt pct) of carbon. When both Si (0.4 wt pct) and C (0.035 wt pct) were present, the γ/MC(NbC) and γ/Laves constituents were observed. Regression analysis was used to develop equations for the liquidus and solidus temperatures as functions of alloy composition. Partial derivatives of these equations taken with respect to the alloying variables (Nb, C, Si) yielded the liquidus and solidus slopes t(m _L , m _S ) for these elements in the multicomponent system. Ratios of these liquidus to solidus slopes gave estimates of the distribution coefficients (k) for these same elements in Alloy 625.     

Electrotransport and diffusion of Co,Fe, and Ag in γ-Cerium

Electrotransport mobilities and diffusion coefficients were obtained for radiotracer impurities of Fe, Co, and Ag in Ce. The iron and cobalt moved toward the anode with mobilities of ～10^?3 cm²/v-s in the range of 550° to 650°C. The silver moved to the cathode with mobilities of ～10^?5 cm²/v-s in the range of 600° to 700°C. The, diffusion coefficients obtained fit an Arrhenius equationD=D _o e ^?ΔH/RT with the following parameters: Fe:D _o=3.3×10^?4, ΔH=4.6 kcal/mole Co:D _o=10^?2, ΔH=11 kcal/mole Ag:D _o=1.4, ΔH=28 kcal/mole The results are compared with other rare-earth diffusion data, and the possibility of a substitutional-interstitial diffusion mechanism, is considered.     

A re-examination of the thermodynamics of the proeutectoid ferrite transformation in Fe-C alloys

Three models of the statistical thermodynamics of interstitial solid solutions have been used to reevaluate the thermodynamics of the proeutectoid ferrite reaction. The models of Kaufman, Radcliffe and Cohen and of Lacher, Fowler and Guggenheim, which were em-ployed in a previous study of this type, together with the model recently developed by McLellan and Dunn are used in conjunction with the extensive experimental data of Ban-ya, Elliott and Chipman, of Lobo and Geiger and of Dunn and McLellan on the activities of carbon in austenite and ferrite. Application of the McLellan and Dunn model and that of Lacher, Fowler and Guggenheim to carbon in austenite yields activities of carbon which are numerically indistinguishable and activities of iron which are mathematically identi-cal. However, the new activity data have revealed important differences between the pres-ent calculations and those of Aaronson, Domian and Pound. An average carbon-carbon repulsion energy in austenite of 1925 cal/mole (8054 J/mole) was determined from the CO/CO₂ data of Ban-yaet al. However, the C-C interaction energy in ferrite was found to be opposite in sign but exhibited erratic variations with temperature despite the large amount of activity data available. The γ/(α + γ) phase boundary calculated from the new data differs significantly, at lower temperatures, from the best curves reported by Aaron-sonet al. The calculateda/(α +γ) phase boundary also differs appreciably from the pre-vious results and exhibits only limited agreement with the experimentally determined phase boundary. Calculation of the free energy change associated with the proeutectoid ferrite reaction andT ₀- composition curves differs little from previous results; internal agreement among the new sets of curves, however, is much improved.