Diffusion of titanium in copper

Interdiffusion coefficients in copper-titanium alloys have been determined by Matano's method in the temperature range between 973 and 1283 K on (pure Cu)-(Cu-1.98 at. pct Ti alloy) and (pure Cu)-(Cu-2.91 at. pct Ti alloy) couples. Temperature dependence of the impurity diffusion coefficient of titanium in copper, determined by extrapolation of the concentration dependence of the interdiffusion coefficient to zero mole fraction of titanium, is expressed by the following Arrhenius equation along with the probable errors:D _Ti/Cu=(0.693 _−0.135 ^+0.169 )×10⁻⁴exp[−(196±2)kJ mol⁻¹/RT] m²/s. The difference in the activation energies for the impurity diffusion of the 3d-transition metals and self-diffusion in copper has been calculated by applying LeClaire's model with the oscillating potential of the impurity atom in copper. The calculated values agree well with the experimental values including the present one. Kazutomo Hoshino, formerly Graduate Student, Tohoku University     

Diffusion in β2 Fe-Ni-Al alloys

Diffusion in the β(bcc) phase field of the Fe-Ni-Al system was investigated at 1004°C with solid-solid diffusion couples assembled with β₂ alloys of selected composition. Experimental diffusion paths were determined for all couples and interdiffusion coefficients calculated at composition points corresponding to intersections of diffusion paths and maxima and minima of concentration profiles. The dependence of interdiffusion coefficients on composition was most clearly presented in terms of the parameter Fe/(Fe + Ni). The diffusive interactions between aluminum and nickel as represented by the cross coefficients were either positive or negative depending on the ternary composition. The Fe/(Fe + Ni) ratio appeared to be a significant parameter since iron and nickel atoms behave differently in affecting the degree of ordering in nonstoichiometric (Fe, Ni)Al alloys with less than 50 at. pct aluminum.     

A new analysis for the determination of ternary interdiffusion coefficients from a single diffusion couple

Concentration profiles that develop in a ternary diffusion couple during an isothermal anneal can be analyzed directly for average ternary interdiffusion coefficients. A new analysis is presented for the determination of average values for the main and cross-interdiffusion coefficients over selected regions in the diffusion zone from an integration of interdiffusion fluxes, which are calculated directly from experimental concentration profiles. The analysis is applied to selected isothermal diffusion couples investigated with α (fcc) Cu-Ni-Zn alloys at 775 °C, β (bcc) Fe-Ni-Al alloys at 1000 °C, and γ (fcc) Ni-Cr-Al alloys at 1100 °C. Average ternary interdiffusion coefficients treated as constants are calculated over composition ranges on either side of the Matano plane and examined for the diffusional interactions among the diffusing components. The ternary interdiffusion coefficients determined from the new analysis are observed to be consistent with those determined by the Boltzmann-Matano analysis at selected compositions in the diffusion zone. The ternary interdiffusion coefficients are also employed in analytical solutions based on error functions for the generation of concentration profiles for the selected diffusion couples. The generated profiles are a good representation of the experimental profiles including those exhibiting uphill diffusion or zero-flux plane (ZFP) development for the individual components. Uncertainties in the values of the interdiffusion coefficients calculated on the basis of the new analysis are found to be minimal.     

Multiphase diffusion in Fe−Ni−Al system at 1000°C: II. Interdiffusion coefficients for β and γ alloys

Ternary interdiffusion coefficients were determined at 1000°C at several Fe−Ni−Al alloy compositions with multiphase β(bcc)vs γ (fcc) diffusion couples which developed planar β/γ-interfaces. The coefficients, (i,j=Al or Ni) were calculated at compositions corresponding to points of intersections of diffusion paths with Fe taken as the dependent component. These coefficients varied with composition by 1 to 2 orders of magnitude in the β-phase but relatively little in the γ-phase. Empirical relations were derived to describe the composition dependence of the main coefficients. and . Interdiffusion coefficients with either Al or Ni as the dependent component were also evaluated. The relative diffusivities of the elements increase in the order, Fe, Ni, Al for both β- and γ-alloys. The ternary diffusion data were consistent with binary interdiffusion coefficients for Fe−Al and Fe−Ni alloys. G. H. CHENG, formerly a Graduate Student at Purdue University     

Effects of microstructure on the erosion

The effects of microstructure on the erosion of Al-Si alloys by 40 μm Al₂O₃ particles were investigated. The impact angle dependence of the erosion rate of Al and the Al-Si alloys exhibited the ductile signature, whereas that for pure Si showed the brittle signature. The eroded surface of pure Al was characterized by craters, lips, overlaps and folds, and platelets; that for pure Si exhibited complex radial and lateral cracking at the impact site. At shallow impact angles these features were elongated in the direction of the tangential component of the velocity in both materials. The measured erosion rates of the Al-Si alloys were found to be in accord with an inverse rule of mixtures based on pure Al and pure Si; better agreement was, however, obtained if pure Al and the eutectic were taken as the two constituents for the hypoeutectic alloys, and pure Si and the eutectic for the hypereutectic alloys. The microstructure size had two effects: (a) scaling with respect to the impact damage zone size and (b) an influence on the physical and mechanical properties which govern material removal. The present results are considered in terms of current models for the erosion of ductile and brittle materials. Formerly with the Department of Materials Engineering, Formerly with the Department of Materials Engineering,     

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.     

Interdiffusion in the Mg-Al System and Intrinsic Diffusion in β-Mg2Al3

Solid-to-solid diffusion couples were assembled and annealed to examine the diffusion between pure Mg (99.96?pct) and Al (99.999?pct). Diffusion anneals were carried out at 573?K, 623?K and 673?K (300?°C, 350?°C and 400?°C) for 720, 360, and 240?hours, respectively. Optical and scanning electron microscopes were used to identify the formation of the intermetallic phases, ??-Mg₁₇Al₁₂, and ??-Mg₂Al₃, as well as the absence of the ??-Mg₂₃Al₃₀ in the diffusion couples. The thicknesses of the ??-Mg₁₇Al₁₂ and ??-Mg₂Al₃ phases were measured and the parabolic growth constants were calculated to determine the activation energies for growth. Concentration profiles were determined with electron microprobe analysis using pure elemental standards. Composition-dependent interdiffusion coefficients in Mg-solid solution, ??-Mg₁₇Al₁₂, ??-Mg₂Al₃, and Al-solid solutions were calculated based on the Boltzmann-Matano analysis. Integrated and average effective interdiffusion coefficients for each phase were also calculated, and the magnitude was the highest for the ??-Mg₂Al₃ phase, followed by ??-Mg₁₇Al₁₂, Al-solid solution, and Mg-solid solution. Intrinsic diffusion coefficients based on Huemann??s analysis (e.g., marker plane) were determined for the ~ Mg-62 at. pct Al in the ??-Mg₂Al₃ phase. Activation energies and the pre-exponential factors for the interdiffusion and intrinsic diffusion coefficients were calculated for the temperature range examined. The ??-Mg₂Al₃ phase was found to have the lowest activation energies for growth and interdiffusion among all four phases studied. At the marker location in the ??-Mg₂Al₃ phase, the intrinsic diffusion of Al was found to be faster than that of Mg. Extrapolations of the impurity diffusion coefficients in the terminal solid solutions were made and compared with the available self-diffusion and impurity diffusion data from the literature. Thermodynamic factor, tracer diffusion coefficients, and atomic mobilities at the marker plane composition were approximated using the available literature values of Mg activity in the ??-Mg₂Al₃ phase.     

Measurement of solid solubility of germanium in aluminum

The solid solubility of Ge in aluminum was determined by resistivity measurement at 77 K of Al-Ge alloys annealed at various temperatures for times sufficient to complete the precipitation of the equilibrium Ge phase. The solid solubility of Ge in aluminum was found to vary from 0.252 at. pct at 533 K to 1.82 at. pct at 693 K. From the temperature dependence of the solid solubilities, the excess entropy of mixing ΔS and heat of mixing ΔH associated with the formation of solid solution of Ge in aluminum were calculated to be 2.77 R and 38.5 kJ mol^-1, respectively. Using these values of ΔS and ΔH, the maximum solid solubility of Ge in aluminum was calculated to be 2.08 at. pct at the eutectic temperature 697 K. The magnitude Δρ _Ge ⁷⁷ /Δc due to 1 at. pct impurity was determined to be 8.60 nΩm/at. pct Ge. The resistivity of Al-1.32 at. pct Ge alloys aged at 573 and 623 K was measured at 77 K to determine the time variation of the average concentrationc of the solute in the matrix during coarsening of the Ge precipitates. The value ofc, calculated using the value of Δρ _Ge ⁷⁷ /Δc, decreased linearly in accordance with the t^-1/3 law. The concentration of the solute in the matrix, in equilibrium with the Ge particle of infinite size, was determined by extrapolating thec vs t^-1/3 plot to infinite time, in excellent agreement with the above solid solubility. Formerly Graduate Student, Department of Materials Science, Tohoku University     

Diffusion studies in the β (B2), β′ (bcc), and γ (fcc) Fe-Ni-Al alloys at 1000 °C

Diffusion studies were carried out in the Fe-Ni-Al system at 1000 °C with solid-solid diffusion couples assembled with β (B₂), β′ (bcc), and γ (fcc) single-phase alloys for the development of diffusion structures, diffusion paths, and for the determination of interdiffusion and intrinsic diffusion coefficients. The diffusion structures were examined by optical and scanning electron microscopy, and the concentration profiles were determined by electron microprobe analysis. Diffusion couples included several series of β vs γ and β′ vs γ diffusion couples characterized by a common terminal alloy bonded to several terminal alloys with varying compositions. The development of planar and nonplanar interfaces, as well as two-phase layers, as observed in various couples, were related to the diffusion paths. The interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the diffusional interactions among components were examined in the light of zero-flux planes (ZFPs) and flux reversals, which were identified in several couples. Ternary interdiffusion coefficients ( (i, j = Al, Ni)), with Fe considered as the dependent concentration variable, were evaluated at composition points of the intersection of diffusion paths of single-phase couples and of multiphase couples that developed planar interfaces. The interdiffusion coefficients were the largest in magnitude for the β′ alloys, especially near the β/β′ miscibility gap, and decreased for the β and γ alloys. In the β and γ phases, the main interdiffusion coefficient for Al was larger than those for Ni and Fe. Also, Fe interdiffused faster than Ni in the Fe-rich β and β′ phases. The cross-interdiffusion coefficients ( and ) were negative in all three phases. In general, the coefficients were larger in magnitude than the coefficients; however, the magnitude of was greater than that of near the β/(β + γ) phase boundary on the ternary isotherm. In the β phase, the magnitude of (i, j=Al, Ni) coefficients increased over 1 to 2 orders of magnitude with a decrease in the Al concentration and increase in the Fe/Ni concentration ratio. Interdiffusion coefficients, extrapolated from the ternary coefficients for binary alloys, were consistent with those in literature. Intrinsic diffusion coefficients were also determined at selected compositions. In addition, tracer diffusion coefficients were estimated for the binary Fe-Al and Ni-Al alloys at selected compositions, from an extrapolation of ternary interdiffusion coefficients.     

Effects of microstructure on the erosion of Al-Si alloys ny solid particles

The effects of microstructure on the erosion of Al-Si alloys by 40 μm Al₂O₃ particles were investigated. The impact angle dependence of the erosion rate of Al and the Al-Si alloys exhibited the ductile signature, whereas that for pure Si showed the brittle signature. The eroded surface of pure Al was characterized by craters, lips, overlaps and folds, and platelets; that for pure Si exhibited complex radial and lateral cracking at the impact site. At shallow impact angles these features were elongated in the direction of the tangential component of the velocity in both materials. The measured erosion rates of the Al-Si alloys were found to be in accord with an inverse rule of mixtures based on pure Al and pure Si; better agreement was, however, obtained if pure Al and the eutectic were taken as the two constituents for the hypoeutectic alloys, and pure Si and the eutectic for the hypereutectic alloys. The microstructure size had two effects: (a) scaling with respect to the impact damage zone size and (b) an influence on the physical and mechanical properties which govern material removal. The present results are considered in terms of current models for the erosion of ductile and brittle materials.     

Diffusion of Zn in Nanostructured Aluminum Alloys Produced by Surface Mechanical Attrition Treatment

After surface nanocrystallization of pure Al and a cast Al-Si alloy through surface mechanical attrition treatment (SMAT), 200- to 300-??m-thick Zn coatings were deposited on the nanostructured surface using the clod spray technique. Subsequently, diffusion of Zn into the Al substrate was induced by postspray annealing treatment at various temperatures for different times. The diffusion kinetics of Zn in the nanostructured surface layers was studied in terms of the Zn concentration profile in the substrate by using scanning electron microscopy (SEM) and electron probe microscopy analysis (EPMA). Experimental results show that not only the diffusivity of Zn in the nanocrystalline grains is significantly increased compared with the diffusion in the coarse grained counterpart, but the temperature at which noticeable Zn diffusion in Al alloys occurs is also reduced from 573?K (300?°C) in coarse-grained Al alloys to 523?K (250?°C) in nanostructured alloys. In addition, because the nanocrystalline grains produced by SMAT in Al-Si alloys are much smaller than those in pure Al due to the effect of eutectic Si, the diffusion of Zn in the SMATed Al-Si alloy is much faster than that in the SMATed pure Al. It is believed that the high diffusivity of Zn in the nanocrystalline Al grains is attributed to the large fraction of grain boundaries that act as fast diffusion channel. The effect of thermal stability of the nanocrystalline grains on Zn diffusion in the SMATed Al alloys is also discussed.     

Thermodynamic properties of α Nickel-Indium Alloys

The vapor pressure of indium over α Ni-In alloys was measured by atomic absorption. The thermodynamic activity of indium was calculated from the vapor pressure, and the partial and integral entropy and enthalpy were calculated from temperature coefficients. It was found that the excess chemical potential of indium increases with atom fraction of indium at low temperatures, in the manner generally observed with similar alloys, but that the slope changes sign, causing ΔG _In ^xs to decrease with increasingx _In at high temperatures. An analysis of the components of the excess entropy indicated that the excess entropy, which has a large negative value, has a major contribution which can be attributed to the conduction electrons. Such an electronic contribution to ΔS^xs is in accord with the band structure thought to characterize nickel-base alloys.     

A theory for solute impurity diffusion, which considers engel-brewer valences, balancing the fermi energy levels of solvent and solute, and differences in zero point energy

A theory that assumes the Engel-Brewer valence of elements (one for bcc structures, two for cph structures, and three for fcc structures) and considers the effects of balancing the solute and solvent Fermi energy levels and differences in zero point energy between solvent and solute atoms to calculate an “effective” relative valence for solute impurities is presented. The calculated values of relative valence and the experimental values of the differences in diffusional activation energy between solute and solvent atoms, ΔQ, are compared to the values of ΔH ₂ + ΔE calculated from the Lazarus-LeClaire theory for several solute impurities in ten solvent metals. The calculated results agree very well with the experimental values for the large majority of solutes. The theory presented adequately describes solute impurity diffusion in both α-Fe and γ-Fe, Al, Ni, and the noble metals. In particular, the low activation energies for impurity diffusion of the alkali metals (ground state valence of one) in Al (ground state valence of three) are accounted for by the theory. It is shown that the diffusion of the electronegative solute impurities (Cr, Mn, Fe, and Co) in Al is not anomalous when the relative valence is calculated by the proposed theory. The diffusion of electronegative solute impurities in the noble metals, which has been problematic in the past, is also well described by the proposed theory. The proposed theory introduces a simple method of estimating the effective electron densities of solute impurities and illustrates that the Lazarus-LeClaire theory adequately describes solute impurity diffusion in the ten solvent metals studied. It is expected that more accurate calculations of effective electron density for solute impurities would result in even better agreement between experimental and calculated results.     

Chemical diffusion in the β phase of the Zr-Ti alloy system

Interdiffusion studies have been carried out in the bcc phase of the Zr-Ti alloy system using diffusion couples of zirconium and Zr-Ti alloys. Geoscan electron microprobe was employed to establish the concentration-penetration profiles in the diffusion zones, and the interdiffusion coefficients were evaluated by Boltzmann-Matano analysis. The concentration and temperature dependence of the diffusivity have also been examined. Present studies further showed that the diffusivity in the Zr-Ti system in theβ-phase could be expressed by an equation similar to that given by Vignes and Birchenall for vacancy-controlled interdiffusion in fee solid solutions.     

Intrinsic diffusion coefficients and the vacancy flow factor in Dilute Cu-Zn Alloys

Interdiffusion coefficients in copper-rich copper-zinc solid solutions containing up to 8 at. pct of Zn at 1168 K have been determined by Matano's analysis using semi-infinite diffusion couples consisting of pure copper and Cu-Zn alloys with Kirkendall markers. From the marker shift and Darken's relation, intrinsic diffusion coefficients, D_Zn and D_Cu, in the alloys containing 3.2 and 4.7 at. pct of Zn have been determined. Further, using thin plate couples, D_Zn and D_Cu in Cu alloys containing 0.9, 2.3, 3.5, and 4.6 at. pct of Zn at 1168 K have been determined by Heumann's method. The ratio of the intrinsic diffusion coefficients, D_Zn/D_Cu, has been found to be about two for all the compositions examined. Using the values of the intrinsic diffusion coefficient of copper at infinite dilution of zinc obtained by extrapolating the concentration dependence of D_Cu, and the self- and impurity diffusion coefficients in pure copper, the vacancy flow factor has been estimated to be - 0.22_-0.15 ^+0.06 at 1168 K. By combining this value of the vacancy flow factor with the solute enhancement factor of solvent diffusion determined by Peterson and Rothman, the correlation factor for impurity diffusion of Zn in Cu at 1168 K has been evaluated to be 0.5, which is in good agreement with the value of 0.47 determined by Peterson and Rothman based on the isotope effect measurement. KAZUTOMO HOSHINO, formerly Graduate Student, Tohoku University is now with Materials Science Division, Argonne National Laboratory, Argonne, IL 60439. YOSHIAKI IIJIMA, Instructor, and KENICHI HIRANO, Professor, are both with the Department of Materials Science, Faculty of Engineering, Tohoku University, Sendai 980, Japan.     

Magnetic contribution to the interdiffusion coefficients in bcc (<Emphasis Type="Italic">α</Emphasis>) and fcc (<Emphasis Type="Italic">γ</Emphasis>) Fe-Ni alloys

The interdiffusion coefficients in bcc (α) and fcc (γ) Fe-Ni alloys below their Curie temperatures have been calculated based on the magnetic contribution to the free energy for interdiffusion. The free energy for interdiffusion due to magnetic ordering in bcc Fe-Ni alloys is positive. The calculated interdiffusion coefficients in bcc Fe-Ni alloys fit the experimental data quite well. In fcc Fe-Ni alloys, the magnetic contribution to interdiffusion depends on both temperature and composition and is abnormal for Ni compositions in the Invar region. The free energy of vacancy formation is positive and the free energy of vacancy migration is negative, due to the effect of magnetic ordering. The interdiffusion coefficient in the ferromagnetic phase is lower than that extrapolated from the paramagnetic phase for Ni compositions of 50 at. pct and greater and is higher than that extrapolated from the paramagnetic phase for Ni compositions of 40 at. pct and lower.     

Metallurgical factors influencing the corrosion of aluminum,Al-Cu,and Al-Si alloy thin films in dilute hydrofluoric solution

The corrosion behavior of sputter-deposited Al, Al-Cu, and Al-Si alloy thin films in dilute hydrofluoric (HF) acid solution was investigated. These materials maintain a thin aluminum oxide film in dilute HF solutions and, consequently, are susceptible to localized corrosion. Pit densities increase for the alloys with Cu and, to a lesser extent, Si additions. Open circuit potentials (OCP) are more positive for such alloys relative to the OCP of pure Al. Metastable pits in Al-Cu alloys are formed in Cu-depleted zones at grain boundaries which are galvanically coupled to adjacent θ-Al₂Cu precipitates. Metastable pits in Al-Si alloys are formed in the Al matrix which is galvanically coupled to adjacent elemental Si nodules. θ-Al₂Cu has different electrochemical characteristics than Al, even though both maintain a thin Al oxide in dilute HF solutions. θ-Al₂Cu has a more positive OCP than pure Al and facilitates cathodic reactions at enhanced rates relative to pure Al. Hence, its presence raises the potential of the adjacent pure Al grain boundary to potentials which increase the probability of metastable pitting. Evidence is also presented which suggests that metastable pit growth may be cathode limited. A new hypothesis describing one mechanism by which θ-Al₂Cu supports cathodic electron transfer re-actions is discussed.     

Diffusional and thermodynamic interactions in the Cu-Ni-Zn system at 775°C

Diffusion was investigated in both α(fcc) and β(bcc) phase regions of the Cu-Ni-Zn system at 775°C with solid-solid diffusion couples and interdiffusion coefficients were determined at several compositions. Intrinsic and interdiffusion coefficients were also estimated from available data on thermodynamic activities and tracer diffusivities for α Cu-Ni-Zn alloys; and the estimated coefficients were consistent with those experimentally determined. Large off-diagonal coefficients indicating strong interactions among the diffusing species were observed and could be appreciated in terms of the compositional dependence of the thermodynamic activities of the components.     

Interdiffusion in the Ni-Cr-Co-Mo system at 1300 °C

Interdiffusion was investigated with solid-solid diffusion couples in theα (fcc) region of the quaternary Ni-Cr-Co-Mo system at 1300 °C for the determination of diffusion paths and diffusional interactions among the components. The concentration profiles for a given couple exhibited a common cross-over composition, Y_c, which reflected the relative depths of diffusion in the terminal alloys. Interdiffusion fluxes were calculated directly from the concentration profiles, and the quaternary interdiffusion coefficients were calculated at selected compositions. Ni and Co exhibited uphill diffusion against their individual concentration gradients in a direction opposite to the interdiffusion of Cr. Quaternary diffusion paths were presented as a set of partial diffusion paths on the basis of relative concentration variables.