A SIMS investigation of impurity diffusion in amorphous Fe40Ni40B20

The diffusion coefficients of Be and Si in the amorphous alloy Fe₄₀Ni₄₀B₂₀ were measured in the temperature range 575–643 K by using the technique of secondary ion mass spectrometry (SIMS). The measurements were carried out on the pre-relaxed alloy specimens and the diffusion coefficients D were found to lie in the range 1.0 × 10⁻²³−2.0 × 10⁻²⁰ m² s⁻¹. The temperature dependence of the measured diffusion coefficients was found to be Arrhenius in nature yielding the values of the activation energy Q as 2.16 ± 0.19 eV atom⁻¹ and 3.39 ± 0.30 eV atom⁻¹ for the diffusion of Be and Si respectively. The corresponding values of the pre-exponential factors (D₀) were 9.4×10^{(−4.0±1.57)}m²s⁻¹ and 7.0 × 10^{5.0 ± 2.42} m² s⁻¹. An overall comparison of all the available data on diffusion in amorphous Fe₄₀Ni₄₀B₂₀ clearly shows that the previously reported correlations for the diffusion coefficient D, the activation energy Q, and the pre-exponential factor D₀ for amorphous alloys are seen in this alloy also. It is suggested that the mechanism of diffusion possibly involves a cooperative movement of a group of atoms.     

Diffusion studies in the metallic glass Zr61 Ni39 by Auger electron spectroscopy

The diffusion coefficients (D) of Cu and Al in the metallic glass Zr₆₁Ni₃₉ were measured in the temperature range 551–621 K by using the Auger depth profiling technique. The D values for Cu were observed to be higher than the corresponding values for Al by about an order of magnitude in this temperature range. The faster diffusion of Cu was consistent with the observed dependence, in this amorphous alloy, of diffusivity on the atomic size of the diffusing species. The values of the activation energy for diffusion (Q), evaluated on the basis of the observed Arrhenius type temperature dependence of D, were found to be 1.33 ± 0.17 eV for Cu and 1.68 ± 0.13 eV for Al. The corresponding values of the pre-exponential factor (D₀) were 10^{−7.57 ± 1.46} m² s⁻¹ and 10^{−5.35 ± 1.15} m² s⁻¹ respectively. No significant effect of structural relaxation of the glass on diffusivity could be observed from measurements on specimens subjected to a relaxation heat treatment prior to diffusion annealing.     

Diffusion and electrotransport of some transition elements in (b.c.c.) thorium

Diffusion and electrotransport parameters of the transition elements molybdenum, rhenium, tungsten and zirconium in β thorium were measured, for the temperature range 1660–1945 K. For each solute element, except zirconium, the measurement was made at four different temperatures, where as for zirconium, studies were performed for only two temperatures 1770 and 1870K. Our results indicate that all four solute elements migrate to the anode in b.c.c. thorium with mean Z¹ values of −6.6 for Mo, −4.6 for Re, −8.2 for W and about −2.5 for Zr. The results also indicate that molybdenum, rhenium and tungsten diffuse much faster in β thorium than zirconium which suggests a correlation between solute atom electric mobility and diffusivity with the atomic sizes of both the solute and matrix atom. Results of the diffusion studies yield the following equations of diffusion for Molybdenum: D_Mo = 15.1 exp(−51,500/RT) Renium: D_Re = 4.04 × 10⁻³ exp(−20,100/RT) Tungsten: D_W = 0.103 exp(−38,100/RT) Zirconium: D_Zr = 1.70 × 10⁴ exp(−91,700/RT).     

Self-diffusion in α-iron: The influence of dislocations and the effect of the magnetic phase transition

Self-diffusion in dislocated α-iron single crystals has been studied with the radioactive tracer ⁵⁹Fe in the temperature range 754–1163 K. Serial sectioning was performed either by microtome cutting or by sputtering. Based on systematic studies of diffusion along dislocations in the same material by the present authors [in DIMETA 88—Diffusion in Metals and Alloys (edited by F. J. Kedves and D. L. Beke). Defect and Diffusion Forum 66–69, 591 (1989)] lattice diffusion coefficients have been selected by considering the influence of dislocations on the apparent diffusivities measured in dislocated crystals. The temperature dependence of the lattice self-diffusion coefficient shows a deviation from the Arrhenius behaviour due to the magnetic order-disorder transition. The general relations and several semi-empirical models which describe this magnetic diffusion anomaly are discussed. From fits of the respective models to a set of lattice diffusion coefficients activation parameters for self-diffusion in the ferromagnetic state (D_f⁰ and Q_f) and in the completely disordered paramagnetic state (D_p⁰ and Q_p) are obtained: D_f⁰ = 6.8–27.7 · 10⁻⁴ m² s⁻¹, Q_f = 2.95–3.10 eV, D_p⁰ = 6.8–12.3 · 10⁻⁴ m² s⁻¹, and Q_p = 2.57–2.68 eV. Independent of the details of these models the parameters fall within fairly narrow limits.     

Diffusion along migrating and stationary grain boundaries in the CuAg system

The diffusion along a migrating random grain boundary of a Cu-3.8 at.% Ag bicrystal has been investigated by discontinuous precipitation and dissolution. The measurements have been carried out over an extensive temperature range. The reaction front velocities varied between 1.8 × 10⁻¹⁰ and 2.7 × 10⁻⁶ m/s. The values of sδD_b (s = segregation factor, δ = grain boundary width and D_b = grain boundary diffusion coefficient) have been determined from the precipitation data according to different models. All of the four models applied yield sδD_b values which are of the same order of magnitude as the sδD_b values of stationary grain boundaries. The best correspondence is given by the model of Turnbull resulting in the following Arrhenius parameters: pre-exponential factor (sδD_b)₀ = 5.80 × 10⁻¹¹ m³/s and effective activation energy Q^ef_b = 144.1 kJ/mol. Based on the numerous available data which permit a relevant comparison, we conclude that the diffusivities of migrating, sliding and stationary grain boundaries in the CuAg system are of the same order of magnitude. This conclusion is in accord with the general behavior of other binary systems.     

Low temperature volume diffusion of zinc in aluminium

The low temperature volume diffusion coefficients of zinc in aluminium have been measured over the temperature range from 180° to 235° C by determining the zinc concentraton profiles across grain boundaries more or less perpendicular to the surface of the extending across thick foils of aluminium which were chemically coatted with zinc and anneleed for times greater than that necessary to attain a steady state flow of zinc along the boundaries from one side of the foils to the other. The zinc concentrations were determined by energy dispersive X-ray analysis of thin foils in a transmission electron microscope and were fitted with the constant source of the diffusion equation in order to determine the diffusion coefficients. The diffusivities obtained agreed well with an extrapolation of the high temperature values of Hilliard et al. and yielded values of 0.018 cm²·s⁻¹ and 112 kJ·mol⁻¹ for the preexponential factor D₀ and the activation energy Q, respectively.     

Diffusion coefficients of 63Ni in Fe40Ni40B20 metallic glass

Self-diffusion coefficients of ⁶³Ni tracer atoms in the metallic glass Fe₄₀Ni₄₀B₂₀ were measured in the temperature range 575–645 K by using the secondary ion mass spectrometry (SIMS) technique. The values of the diffusion coefficients were measured on the “air-side” as well as on the “wheel-side” of the ribbon and were found to lie between 5.6 × 10⁻²³ m²/s and 11.2 × 10⁻²¹ m²/s. In the quenched specimens, the diffusion was found to decrease considerably with increasing annealing time until a well-relaxed amorphous state of the material is reached. The diffusion coefficients in the relaxed state were found to obey an Arrhenius type temperature dependence with an activation enthalpy of 2.14 ± 0.16eV for the “airside” and of 2.29 ± 0.16eV for the “wheel-side”. The corresponding values of the pre-exponential factors were 4 × 10⁻⁴ m²/s and 8 × 10⁻³ m²/s, respectively. The time dependence of measured diffusivity during structural relaxation is interpreted in terms of elimination of excess free volume via quasi-vacancies annealing out at the specimen surface which leads to an additional transport of the tracer atoms. The activation enthalpy governing this relaxation process was estimated to be about 1 eV.     

Mass diffusion in polycrystalline copper/electroplated gold planar couples

The Au/Cu system is common to electrical connectors and recent trends toward higher ambient temperatures and thinner gold electroplates focuses attention on a new failure mode. This mode is degradation of thin gold electroplates by mass diffusion of the base metal (copper) to the surface of the electroplate at low temperatures (less than 250°C). Therefore, diffusion experiments were conducted for polycrystalline copper/electroplated gold planar couples over the temperature range of 50° to 750°C. The chemical interdiffusion coefficients, ~D, were calculated using the Boltzmann-Matano solution on the concentration-distance profiles which were determined using an electron microprobe. Results of this study show that ~D is a small function of concentration, generally with a variation of less than a factor of 3 to 5. The correlation of the temperature dependence of ~D between 250° and 750°C with existing data is excellent. The data conform to an Arrhenius equation: ~D= 1.5×10⁻⁵ e^−23,600/RT At temperatures below 250°C the values of ~D deviate from this equation and below 150°C are significantly greater than would be predicted by extrapolating the high temperature Arrhenius equation. No correlation was found between electroplate thickness and diffusion rate.     

Influence of the crystalline microstructure on the diffusivity of hydrogen in palladium galvanostatic permeation and X-ray diffraction measurements

The influence of crystalline microstructure upon the apparent diffusion coefficient of hydrogen in Pd samples are reported. The apparent diffusion coefficient was measured by the galvanostatic permeation method (at 20°C), while the structure was characterized by X-ray diffraction measurements. Pd membrane electrodes of different thicknesses, l = 5 × 10⁻³cm and l = 10⁻²cm, were used. The structure of Pd membrane electrodes was changed by successive annealing and sequences of absorption and desorption of hydrogen accompanied by the α⇌β phase transition. Both the irreversible and reversible traps affect the mobility of hydrogen in Pd. The irreversible traps manifest in the variation of the apparent diffusion coefficient as a function of the average stationary bulk concentration of hydrogen, while the diffusion coefficient of the free hydrogen does not depend on the actual concentration of hydrogen in Pd. This is true provided that the average stationary bulk concentration of hydrogen is higher than the irreversible trap concentration. The diffusion coefficient of free hydrogen depends on the specific internal surface area according to McNabb-Foster-like equation. The value of the diffusion coefficient of hydrogen in single crystal of palladium was estimated, D₀ = (4.2 ± 0.3) × 10⁻⁷ cm²s⁻¹ (20°C).     

Fast diffusion of cobalt along stationary and moving grain boundaries in niobium

⁵⁷Co diffusion along grain boundaries (GBs) in high-purity Nb has been studied in the temperature range 823–1471 K by the serial sectioning technique. As it was not possible to fully stabilize the grain size by any pre-diffusion annealing, part of the GBs could migrate during the diffusion anneals. Using the earlier proposed method [Z. Metallk. 84, 584 (1993)], the product P = sD_GBδ [s being the 7GB-segregation factor, D_GB the GB-diffusion (GBD) coefficient, δ the GB width] for stationary GBs and the velocity V of moving GBs were deduced from the diffusion profiles. The P-values follow an Arrhenius dependence P = (4.84_−2.68^5.99) × 10⁻¹³ exp[-(14.5 +- 7.2) kJ mol⁻¹/RT] m³ s⁻¹ and are 4–2 orders of magnitude higher in the measured temperature range than the expected P-values for GB self-diffusion in Nb. This observation is well consistent with the known fact of fast lattice diffusion of Co in Nb and provides evidence for a combined vacancy-interstitial GBD mechanism. From the temperature dependence of V an activation enthalpy of GB motion in Nb H_m ≅ 182 kJ mol⁻¹ is estimated.     

Diffusion in the titanium-nickel system: II. calculations of chemical and intrinsic diffusion coefficients

Diffusion coefficients in the Ti-Ni system have been calculated by the aid of equations given by Sauer and Freise, and Wagner. Values for the TiNi (50 at. pct Ni) phase were found to be:D ^u (cm²/s) = 0.0020 exp - 142,000/R for the temperature range between 650 and 940°C. The heat of activation, expressed in J/mol, has an accuracy of ±6000. For the β-Ti(Ni) phase containing 6 at. pct Ni the temperature dependence of the diffusion coefficient is expressed by:D ^u (cm²/s) = 0.0688 exp - 141,000/RT. The uncertainty in the energy of activation is ±12000 J/mol. No clear variation of the diffusion coefficient with concentration could be detected. It was found that Ni is by far the fastest moving component in β-Ti(Ni), Ti₂Ni and TiNi (at least in the composition range between 50 and 53 at. pct Ni). Values ofD _Ni/D _Ti have been calculated with an equation derived by van Loo. The significance of the calculated values is critically examined. By means of a practical example it is shown that the calculated ratio of the intrinsic diffusion coefficients can be extremely sensitive to slight variations in the position of the marker interface.Diffusion coefficients in the Ti-Ni system have been calculated by the aid of equations given by Sauer and Freise, and Wagner. Values for the TiNi (50 at. pct Ni) phase were found to be:D ^u (cm²/s) = 0.0020 exp - 142,000/R for the temperature range between 650 and 940°C. The heat of activation, expressed in J/mol, has an accuracy of ±6000. For the β-Ti(Ni) phase containing 6 at. pct Ni the temperature dependence of the diffusion coefficient is expressed by:D ^u (cm²/s) = 0.0688 exp - 141,000/RT. The uncertainty in the energy of activation is ±12000 J/mol. No clear variation of the diffusion coefficient with concentration could be detected. It was found that Ni is by far the fastest moving component in β-Ti(Ni), Ti₂Ni and TiNi (at least in the composition range between 50 and 53 at. pct Ni). Values ofD _Ni/D _Ti have been calculated with an equation derived by van Loo. The significance of the calculated values is critically examined. By means of a practical example it is shown that the calculated ratio of the intrinsic diffusion coefficients can be extremely sensitive to slight variations in the position of the marker interface. This paper is based on a Thesis submitted by G. F. BASTIN in fulfillment of requirements for the degree of Doctor in Technological Sciences.     

Electrochemical behavior of cerium ion in molten LiCI-KCI

The electrode process of cerium(Ⅲ) on the Mo electrode in eutectic LiCl-KCl melt was investigated by electrochemical transient techniques in the temperature range of 673-783 K,respectively.These results unanimously indicated that the reduction process of cerium(Ⅲ) to cerium metal was a single step exchanging three electrons which was controlled by diffusion of cerium(Ⅲ).Diffusion coefficients(D Ce(Ⅲ)) in eutectic LiCl-KCl melt were determined by cyclic voltammetry,chronopotentiometry and square wave voltammetry.An empirical diffusion coefficient function depending on temperature was proposed:lnD Ce(Ⅲ) =-2.129-5704/T.The formal potentials(Eθ’ Ce(Ⅲ)/Ce(0) versus Ag/AgCl reference electrode) at different temperatures were obtained from chronopotentiometry,which were-2.10 V(673 K) and-2.07 V(733 K),respectively.     

Interdiffusion in the body cubic centered β-phase of titanium-hafnium alloys

Interdiffusion in the β-phase of Ti-Hf alloys has been studied between 1000 and 2000°C. The concentration dependence of the interdiffusion coefficients is small. With temperature, they show an “anomalous” behavior, caracteristic of the diffusion in b.c.c. metals and alloys: the high temperature activation energy (~ 175 kJ/mol) is greater than the low-temperature one, near the β → α transformation (~ 120 kJ/mol). Diffusion coefficients at infinite dilution D^o_Hf(Ti) and D^o_ti(hf) and the influence of zirconium impurities are specified. No Kirkendall effect was seen during experiments of diffusion in these alloys.     

Diffusion along [001] tilt boundaries in the Au/Ag system—I. Experimental results

The parameter, δ_bD_b^Ag, for the chemical diffusion of Ag along the tilt axes of a series of [001] symmetric tilt boundaries in the Au/Ag system, was measured as a function of temperature and tilt angle at relatively lowtemperatures. (D_b^Ag = boundary diffusivity; δ_D = boundary thickness) Sixteen boundaries were studied using a newly developed surface accumulation method. δ_bD_b^Ag was found to vary quite smoothly with tilt angle (i.e. no sharp minima or cusps at low-Σ misorientationswere observed) in a manner consistent with the structural unit model. The activation energies were found to be smooth functions of the tilt angle and to lie in the range 0.70–0.85 eV. The pre-exponential factors in the Arrhenius expression for δ_bD_b were ∼3 orders of magnitude smaller than many of those reported in the literature for diffusion at higher temperatures.     

High-temperature deformation of MnO

Steady-state flow stresses have been measured for {100}-oriented MnO single crystals for temperatures from 900 to 1400°C and strain rates from 2 × 10⁻⁶to 2 × 10⁻³s⁻¹. The crystals were equilibrated in oxygen partial pressures ranging from 10¹¹ to 10²Pa, which induced deviations from stoichiometry of 4 × 10⁻⁴to 9 × 10⁻². Deformation rates are controlled by oxygen diffusion. Pipe diffusion along dislocation cores is predominant for T ≤ 1000°C; volume diffusion is predominant for T ≥ 1200dgC. In general, the primary diffusing oxygen species are singly charged vacancies for low Po₂ and neutral interstitials for high Po₂. At 1400°C, ionization states decrease for the oxygen point defects.     

A Method for the Estimation of the Interface Temperature in Ultrasonic Joining

Ultrasonic joining of copper foil to 1100 aluminum sheet at nominal joining temperatures of 298 K to 413 K (25 °C to 140 °C) for 1.25 second caused significant copper diffusion into the aluminum sheet, indicating very high diffusivity (D) values of 1.54 × 10^?13 to 2.22 × 10^?13 m²/s. The D values reflect high excess vacancy concentrations caused by the rapid plastic deformation in the joining surfaces. A method is presented to estimate the actual values of interface temperature from the diffusion data and expected values of vacancy concentrations. The estimated values of interface temperature were about 390 to 410 deg below the equilibrium melting point of aluminum, and in agreement with reported experimental values.     

Radiochemical measurement of diffusion in the cesium chloride-tin and barium-sodium systems

Diffusion coefficients for cesium chloride in molten tin from 308 to 396°C and for barium in liquid sodium from 290 to 396°C were measured radiochemically. Cesium chloride coefficients were determined by measurement of nonsteady state surface concentrations of cesium chloride deposited on the surface of cylindrical specimens. Cesium chloride traced with cesium-137 was deposited on the specimens from a supersaturated solution dispersed in the molten tin and measured by gamma spectroscopy after removal of the specimen from the solution. Diffusion coefficients for barium in sodium were measured by a unique method in which radioactive cesium-137 (half-life of 33 yrs) dissolved in the sodium served as a volumetric source for its short-lived barium-137 daughter (half-life of 2.6 min). Since barium deposited on the surface of the specimen, measurement of the equilibrium barium-137m gamma activity on the specimen surfaces after removal from the solution yielded barium diffusion coefficients. The equations for these diffusion coefficients with 95 pct confidence limits are: Cesium chloride in tin (308 to 396°C):D=[(4.84±0.14)×10^?4] exp [?6720±6400)/RT] Barium in sodium (290 to 496°C):D=[(4.27±0.05)×10^?4] exp [?4600±990)/RT]     

Cyclic strain hardening in polycrystalline copper

Polycrystals of pure copper were cyclically deformed, at room temperature under symmetric tension-compression fatigue at constant total strain amplitude control with an approximate constant plastic strain rate of 10⁻⁴. The relationship between the saturation stress amplitude and strain amplitude over a range of plastic strain from 2 × 10⁻⁷ to 10⁻² reveals three regions of cyclic hardening. A quasi-plateau, where the stresses show a slow constant increase, was observed in the intermediate region extending in the plastic strain range γ_pl, of 1.5 × 10⁻⁵ to 7.5 × 10⁻⁴. In this region, persistent slip bands (PSBs) which consist of “ladder” structures, similar to the case of single crystals, were found in the bulk of the fatigued polycrystals. The fatigue limit was found to be Δσ_s/2 = 73 MPa which corresponds to the plastic strain Δϵ_pl/2 = 1.5 × 10⁻⁵ where PSBs do not form.     

Diffusion of hydrogen in iron

A mass spectrometer was used to study hydrogen diffusion and trapping phenomena in fullyannealed and slightly cold-worked pure iron specimens which were in contact with distilled water or dilute acidic Buffer solutions. In the case of fully-annealed iron and slightly coldworked iron, hydrogen can diffuse into iron only when the iron contacts water directly. This diffusion phenomenon of hydrogen increased markedly with temperature and was accelerated by abrasion and hydrogen ion concentration in dilute acid. Abrasion and hydrogen ions in a dilute acidic Buffer solution did not affect the diffusion coefficient of hydrogen,D, but increased the hydrogen concentration at the iron surface contacting water or Buffer solution,C _s . The permeability of hydrogen in fully-annealed iron in contact with distilled water and the diffusion coefficient of hydrogen in fully-annealed and slightly cold-worked iron for the temperature range 10° to 100°C were measured. Trapping parameters in the slightly cold-worked iron were calculated.     

A simultaneous analysis of segregation and diffusion of impurities in the grain boundary of a bicrystal. Application to sulphur segregation and diffusion in nickel bicrystals

A new technique is described to study diffusion and segregation in a bicrystal; it is based on a radiochemical microanalysis through a narrow slit, slowly moving on the surface. It is used to study sulphur (³⁵S) behaviour in a Ni bicrystal at 700°C (〈100〉 tilt grain boundary; angular desorientation: 20°). The segregation coefficient (α = 7000), the bulk diffusion coefficient (D_b = 4.10⁻¹²cm² · s⁻¹) and the grain boundary diffusion parameter αδD_gb are obtained from one sole experiment in one sample.