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.     

Diffusion and Growth of the <Emphasis Type="Italic">μ</Emphasis> Phase (Ni<Subscript>6</Subscript>Nb<Subscript>7</Subscript>) in the Ni-Nb System

Incremental diffusion couple experiments are conducted to determine the average interdiffusion coefficient and the intrinsic diffusion coefficients of the species in the Ni₆Nb₇ (μ phase) in the Ni-Nb system. Further, the tracer diffusion coefficients are calculated from the knowledge of thermodynamic parameters. The diffusion rate of Ni is found to be higher than that of Nb, which indicates higher defect concentration in the Ni sublattice.     

Phase Constituents and Microstructure of Interaction Layer Formed in U-Mo Alloys <Emphasis Type="Italic">vs</Emphasis> Al Diffusion Couples Annealed at 873 K (600 °C)

U-Mo dispersion and monolithic fuels are being developed to fulfill the requirements for research reactors, under the Reduced Enrichment for Research and Test Reactors program. In dispersion fuels, particles of U-Mo alloys are embedded in the Al-alloy matrix, while in monolithic fuels, U-Mo monoliths are roll bonded to the Al-alloy matrix. In this study, interdiffusion and microstructural development in the solid-to-solid diffusion couples, namely, U-15.7 at. pct Mo (7 wt pct Mo) vs pure Al, U-21.6 at. pct Mo (10 wt pct Mo) vs pure Al, and U-25.3 at. pct Mo (12 wt pct Mo) vs pure Al, annealed at 873 K (600 °C) for 24 hours, were examined in detail. Scanning electron microscopy (SEM), transmission electron microscopy (TEM), and electron probe microanalysis (EPMA) were employed to examine the development of a very fine multiphase interaction layer with an approximately constant average composition of 80 at. pct Al. Extensive TEM was carried out to identify the constituent phases across the interaction layer based on selected area electron diffraction and convergent beam electron diffraction (CBED). The cubic-UAl₃, orthorhombic-UAl₄, hexagonal-U₆Mo₄Al₄₃, and cubic-UMo₂Al₂₀ phases were identified within the interaction layer that included two- and three-phase layers. Residual stress from large differences in molar volume, evidenced by vertical cracks within the interaction layer, high Al mobility, Mo supersaturation, and partitioning toward equilibrium in the interdiffusion zone were employed to describe the complex microstructure and phase constituents observed. A mechanism by compositional modification of the Al alloy is explored to mitigate the development of the U₆Mo₄Al₄₃ phase, which exhibits poor irradiation behavior that includes void formation and swelling.     

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.     

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.     

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.     

Interdiffusion Study in the Fe–Nb System

The diffusion characteristics of the Fe–Nb system were investigated using the diffusion couple technique. The average interdiffusion coefficient was calculated for the Fe₂Nb Laves and the FeNb μ phases. The possible diffusion mechanism was predicted by using the calculated values of the activation energy for diffusion. Kirkendall marker experiments were conducted to determine the relative mobilities of the species. Fe was found to have a faster diffusion rate than Nb in both phases.     

Experimental Study of Ferrous Calcium Silicate Slags: Phase Equilibria at {\text{P}}_{{{\text{O}}_{2} }} Between 10?5?atm and 10?7?atm

Ferrous calcium silicate slags, whose principal components are “FeO _x ”-CaO-SiO₂, are widely used in copper smelting and converting operations. In the current study, high-temperature equilibration and rapid quenching techniques were used to study the phase equilibria of the ferrous calcium silicate slags. The compositions of phases in the slags were measured accurately using electron probe X-ray microanalysis (EPMA). The phase equilibria of the system have been characterized at oxygen partial pressures between 10⁻⁵ atm and 10⁻⁷ atm at selected temperatures between 1473 K and 1623 K (1200 °C and 1350 °C). The effects of oxygen partial pressure and temperature on the compositions of phases in the slags are presented.     

Ternary Diffusion: Restrictions on the (2D) Matrix

An analysis has been made of ternary diffusing systems to determine the possibility that individual diagonal interdiffusion coefficient elements of the_k(²D) (k = 1,2,3) interdiffusion coefficient matrices can be negative. It is shown that in ternary diffusing systems, in which the concentration-penetration curves are monotonic, as many as three of the six diagonal coefficients can be negative. It is further shown that several ternary diffusing systems having a negative diagonal interdiffusion coefficient matrix element have already in fact been determined experimentally.     

Structure, Properties, and Glass Forming Ability of Melt-Spun Fe-Zr-B-Cu Alloys with Different Zr/B Ratios

Melt-spun ribbons of Fe_99–x–y Zr _x B _y Cu₁ alloys with x + y = 11 and x + y = 13 were prepared under similar experimental conditions and characterized for structure and soft magnetic properties. Substitution of Zr by B changes the structure of as-spun ribbons from completely amorphous to cellular bcc solid solution coexisting with the amorphous phase at intercellular regions and then to completely dendritic solid solution. The glass forming ability (GFA) of the Fe-Zr-B-Cu system, evaluated from thermodynamic properties such as enthalpy of mixing and mismatch entropy, is found to be in good agreement with the experimental observations. Annealing of all ribbons leads to the precipitation of nanocrystalline bcc α-Fe phase from both amorphous phase and already existing bcc solid solution. A window of alloy compositions that exhibit the best combination of soft magnetic properties (high saturation magnetization and low coercivity) was identified.     

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 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.     

Formation and Stability of Equiatomic and Nonequiatomic Nanocrystalline CuNiCoZnAlTi High-Entropy Alloys by Mechanical Alloying

Nanocrystalline equiatomic high-entropy alloys (HEAs) have been synthesized by mechanical alloying in the Cu-Ni-Co-Zn-Al-Ti system from the binary CuNi alloy to the hexanary CuNiCoZnAlTi alloy. An attempt also has been made to find the influence of nonequiatomic compositions on the HEA formation by varying the Cu content up to 50 at. pct (Cu _x NiCoZnAlTi; x = 0, 8.33, 33.33, 49.98 at. pct). The phase formation and stability of mechanically alloyed powder at an elevated temperature (1073 K [800 °C] for 1 hour) were studied. The nanocrystalline equiatomic Cu-Ni-Co-Zn-Al-Ti alloys have a face-centered cubic (fcc) structure up to quinary compositions and have a body-centered cubic (bcc) structure in a hexanary alloy. In nonequiatomic alloys, bcc is the dominating phase in the alloys containing 0 and 8.33 at. pct of Cu, and the fcc phase was observed in alloys with 33.33 and 49.98 at. pct of Cu. The Vicker’s bulk hardness and compressive strength of the equiatomic nanocrystalline hexanary CuNiCoZnAlTi HEA after hot isostatic pressing is 8.79 GPa, and the compressive strength is 2.76 GPa. The hardness of these HEAs is higher than most commercial hard facing alloys (e.g., Stellite, which is 4.94 GPa).     

Growth of silicides and interdiffusion in the Mo-Si system

Solid-solid diffusion couples assembled with disks of Mo and Si were annealed at selected temperatures, over the temperature range from 900 °C to 1350 °C, for the development of diffusion structure and determination of interdiffusion coefficients for the silicides of Mo. Layers of MoSi₂ and Mo₅Si₃ were observed to form in the diffusion zone; the MoSi₂ layer was one to two orders of magnitude larger in thickness than the Mo₅Si₃ layer. The MoSo₂ layer developed a columnar microstructure with evidence of texture and preferential growth of grains in the direction of diffusion. The Si-to-Mo ratio, determined by microprobe analysis across the thickness of the MoSi₂ layer, varied within the approximate range from 1.9 to 2.0. From the concentration profiles, integrated interdiffusion coefficients as well as energies of activation for interdiffusion were determined for the silicide layers. On the basis of the observed stoichiometric range for the MoSi₂ phase, average values of the interdiffusion coefficients were also estimated. Relations are derived between the growth-rate constant and the integrated interdiffusion coefficient for the MoSi₂ phase. The evaluated activation energies for interdiffusion in the MoSi₂ and Mo₅Si₃ phases are 130±20 and 210±10 kJ/mol, respectively.     

Structure of Zr<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Pt<Subscript>100−<Emphasis Type="Italic">x</Emphasis></Subscript> (73 ≤ <Emphasis Type="Italic">x</Emphasis> ≤ 77) Metallic Glasses

The structure of hyper-eutectic Zr _x Pt_100−x (73 ≤ x ≤ 77) metallic glasses produced by melt spinning was examined with high-energy synchrotron X-ray diffraction (HEXRD) and fluctuation electron microscopy. In addition, details of the amorphous structure were studied by combining ab initio molecular dynamics and reverse Monte Carlo simulations. Crystallization pathways in these glasses have been reported to vary dramatically with small changes in compositions; however, in the current study, the structures of the different glasses were also observed to vary with composition, particularly the prepeak in the total structure factor that occurs at a Q value of around 17 nm⁻¹. Results from simulations and fluctuation electron microscopy suggest that the medium-range order of the amorphous structure is characterized by extended groups of Pt-centered clusters that increase in frequency, structural order, or spatial organization at higher Pt contents. These clusters may be related to the Zr₅Pt₃ structure, which contains Pt-centered clusters coordinated by 9Zr and 2Pt atoms. This article is based on a presentation given in the symposium entitled “Bulk Metallic Glasses IV,” which occurred February 25–March 1, 2007 during the TMS Annual Meeting in Orlando, Florida under the auspices of the TMS/ASM Mechanical Behavior of Materials Committee.

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