Diffusion Multiple Technique Research Articles

Magnetization\u2013structure\u2013composition phase diagram mapping in Co-Fe-Ni alloys using diffusion multiples and scanning Hall probe microscopy

Transition metal alloys are essential for magnetic recording, memory, and new materials-by-design applications. Saturation magnetization in these alloys have previously been measured by conventional techniques, for a limited number of samples with discrete compositions, a laborious and time-consuming effort. Here, we propose a method to construct complete saturation magnetization diagrams for Co–Fe–Ni alloys using scanning Hall probe microscopy (SHPM). A composition gradient was created by the diffusion multiple technique, generating a full combinatorial materials library with an identical thermal history. The composition and crystallographic phases of the alloys were identified by integrated energy dispersive X-ray spectroscopy and electron backscatter diffraction. “Pixel-by-pixel” perpendicular components of the magnetic field were converted into maps of saturation magnetization using the inversion matrix technique. The saturation magnetization dependence for the binary alloys was consistent with the Slater-Pauling behavior. By using a significantly denser data point distribution than previously available, the maximum of the Slater-Pauling curve for the Co–Fe alloys was identified at ~ 32 at% of Co. By mapping the entire ternary diagram of Co–Fe–Ni alloys recorded in a single experiment, we have demonstrated that SHPM—in concert with the combinatorial approach—is a powerful high-throughput characterization tool, providing an effective metrology platform to advance the search for new magnetic materials.

High-throughput determination of high-quality interdiffusion coefficients in metallic solids: a review.

Accurate interdiffusion coefficients of composition and temperature dependence are significantly important for understanding different materials processes. However, the high-throughput determination of high-quality interdiffusion coefficients, especially in multicomponent systems, has been sustaining as a challenge in materials community. This review dealt with a comprehensive summarization of the recent progress in this field, aiming at advancing a scientific routine for realizing the high-throughput determination of high-quality interdiffusion coefficients in metallic solids. First, an introduction of traditional Matano-based approaches and their recent development was given. Second, the numerical inverse methods were described, with a focus on the recently developed pragmatic numerical inverse method and related public toolkits. Potential strategies for resolving the problems about accuracy and uniqueness of the solutions to the numerical inverse methods were highlighted. The combination of numerical inverse method and diffusion multiple technique was highly proposed for high-throughput determination of interdiffusion coefficients in metallic solids with any number of components. After that, the case studies on the high-throughput determination of interdiffusivity matrices in the real Ni-based, high-entropy/high-entropy superalloys were demonstrated. Discussion on the substitution of Re in Ni-based single-crystal superalloys and the sluggish diffusion in high-entropy/high-entropy superalloys was also carried out. Fourth, the general idea for the uncertainty quantification was proposed in order to obtain high-quality interdiffusion coefficients, followed by the introduction of recent progress on the uncertainty quantification in both Matano-based methods and numerical inverse methods. Finally, the conclusions were drawn, and the future trends in diffusion community were also pointed out.

High-throughput determination of interdiffusivity matrices in Ni-Al-Ti-Cr-Co-Mo-Ta-W multicomponent superalloys and their application in optimization of creep resistance

The creep resistance of nickel-based superalloys at elevated temperature is inheritably correlated with interdiffusivity matrices, which are still difficult to be determined nowadays. In this work, the interdiffusion coefficient matrices of multicomponent nickel-based superalloys with seven alloying elements (i.e., Al, Ti, Cr, Co, Mo, Ta and W) at 1553 K were determined in a high-throughput way by employing the diffusion multiple technique and HitDIC software. The results showed that the main interdiffusion coefficients D∼AlAlNi and D∼WWNi over the investigated composition space were the highest and lowest, respectively. Moreover, it was found that Al + Ti is correlatedly accelerate the diffusion processes, while Mo + Ta + W has the tendency of decelerate the diffusion activities. Thereafter, the creep merit index of the concerned superalloys was evaluated using the measured interdiffusion coefficients, and the results showed the noticeable deviation from the experimental data in commercial superalloys. A great improvement can be then achieved by considering the effect of Re and Ru in the creep model. With the modified creep model, the composition of the superalloy with the optimal creep resistance can be finally chosen. It was proposed that increasing the contents of Ti, W and Mo to some extent may enhance the creep resistance of superalloys.

On diffusion behaviors in face centered cubic phase of Al-Co-Cr-Fe-Ni-Ti high-entropy superalloys

Owning the excellent high temperature properties, low cost and density, Al-Co-Cr-Fe-Ni-Ti high-entropy superalloys (HESAs) represent a potential substitute for Ni-based superalloys. In this paper, the composition-dependent interdiffusivity matrices of face centered cubic (fcc) Al-Co-Cr-Fe-Ni-Ti HESAs at 1473 K were first determined via a combination of diffusion multiple technique and HitDIC software based on the numerical inverse method. The correlations between the main interdiffusivities and the components suggest that alloying elements play great impact on diffusion in HESAs. After that, comprehensive comparisons of the interdiffusivities and tracer diffusivities in present fcc HESAs with the literature data in fcc-based pure elements, lower-order alloys and traditional high-entropy alloys were conducted. The results indicate that the sluggish diffusion effect exists for only some of the components in the present HESAs. Moreover, comparisons of the diffusion coefficients between the HESAs and traditional Ni-based superalloys with refractory elements show that the interdiffusivities in the present HESAs are lower than the Ni-based superalloys with most refractory elements, but higher than those with Ir, Re and Os. Furthermore, it is also found that refractory elements need to be added in order to further improve the creep resistance of the HESAs.

Experimental Investigations on the Quaternary Interdiffusion Coefficients, Young’s Modulus and Hardness in bcc Ti-Nb-Ta-Zr Quaternary Alloys

Accurate interdiffusion coefficient, Young’s modulus and hardness are essential for precisely controlling the production of a homogeneous bio-metallic alloys with excellent properties. In this work, we utilized a combinational approach by combining the advanced diffusion multiple technique and the pragmatic numerical inverse method to efficiently determine the composition–dependent interdiffusion coefficient matrices in bcc quaternary Ti-Nb-Ta-Zr alloys at 1373 K. Moreover, the composition-dependent Young’s modulus and hardness of bcc Ti-Nb-Ta-Zr alloys were obtained by means of the nanoindentation technique.

High-Throughput Determination of Interdiffusivities for Ni-Al-Cr Alloys at 1173 K through a Combination of Diffusion Multiple and Numerical Inverse Method

In this report, a combination of the diffusion multiple technique and the recently developed numerical inverse method was employed for a high–throughput determination of interdiffusivity matrices in Ni–Al–Cr alloys. A face–centered cubic (fcc) quinary Ni–Al–Cr diffusion multiple at 1173 K was carefully prepared by means of the hot–pressing technique. Based on the composition profiles measured by the field emission electron probe micro analysis (FE–EPMA), the composition–dependent interdiffusivity matrices in ternary Ni–rich Ni–Al–Cr system at 1173 K were then efficiently determined using the numerical inverse method.

On Sluggish Diffusion in Fcc Al–Co–Cr–Fe–Ni High-Entropy Alloys: An Experimental and Numerical Study

High-throughput measurement using the numerical inverse method combined with the diffusion multiple technique was employed to determine the composition-dependent interdiffusion coefficients in fcc Al–Co–Cr–Fe–Ni high-entropy alloys at 1273, 1323, and 1373 K. The reliability of the obtained interdiffusion coefficients was confirmed by comparing the model-predicted composition/interdiffusion flux profiles with the experimental data. The tracer diffusivities of the components were then predicted based on the obtained interdiffusion coefficients and the simplified thermodynamic description. The diagonal interdiffusion coefficients in the present high-entropy alloys were comprehensively compared with those in conventional fcc alloys. Therefore, the sluggish diffusion effect does not apply for all the elements in the present fcc Al–Co–Cr–Fe–Ni high-entropy alloys. A similar result was also observed for the evaluated tracer diffusivities.

High-Throughput Determination of Interdiffusion Coefficients for Co-Cr-Fe-Mn-Ni High-Entropy Alloys

In this report, a combination of the diffusion multiple technique and the recently developed pragmatic numerical inverse method was employed for a high-throughput determination of interdiffusivity matrices in Co-Cr-FeMn-Ni high-entropy alloys (HEAs). Firstly, one face-centered cubic (fcc) quinary Co-Cr-Fe-Mn-Ni diffusion multiple at 1373 K was carefully prepared by means of the hot-pressing technique. Based on the composition profiles measured by the field emission electron probe micro analysis (FE-EPMA), the composition-dependent interdiffusivity matrices in quinary Co-Cr-Fe-Mn-Ni system at 1373 K were then efficiently determined using the pragmatic numerical inverse method. The determined interdiffusivities show good agreement with the limited results available in the literature. Moreover, the further comparison with the interdiffusivities in the lower-order systems indicates the sluggish diffusion effect in Co-Cr-Fe-Mn-Ni HEAs, which is however not observed in tracer diffusivities. In order for the convenience in further analysis, a generalized transformation relation among interdiffusivities with different dependent components in multicomponent systems was finally derived.

Intermetallic Layer Growth Kinetics in Sn‐Ag‐Cu System using Diffusion Multiple and Reflow Techniques

A diffusion multiple (DM) technique was applied to the Sn‐Ag‐Cu ternary system with the aim to determine the kinetics of formation of Cu‐Sn intermetallic compounds (IMCs) and to predict properties of the interface in the solder joints. The formation and growth of the Cu‐Sn intermetallics at the interface between the Cu as a base material and Sn‐Ag‐(Cu) solder was additionally studied during a standard reflow soldering process. Based on the experimental data, the kinetic rate constants and the respective activation energies of the Cu‐Sn IMCs in the temperature range between 150 and 200 °C were calculated and compared with experimental data from the literature. In this way, the mechanism of the pure solid‐state reaction (DM technique) and liquid phase reaction (reflow soldering) were studied. The limitations of DM techniques for the prediction of the IMCs growth during reflow soldering process are discussed as well.

Determination of α/γ phase boundaries in the Fe–Cr–Ni–Mn quaternary system with a diffusion-multiple method

The phase relationships between the ferrite phase (α) and the austenite phase (γ) were investigated in the iron-rich corner of the Fe–Cr–Mn–Ni quaternary system at 1000°C. Phase boundaries were determined using a diffusion-multiple technique. In this technique, three end members, Fe–Cr, Fe–Cr–Mn and Fe–Cr–Ni alloys, were coupled inside a metal tube, and then heat treated at 1300°C for 24h to create a microstructural state with a composition gradient of Cr, Ni and Mn within the composition range of the end members. This was followed by long time heat treatment at 1000°C for periods of up to 1000h to obtain phase equilibrium states between the γ and α phase in the composition range. The γ+α two-phase field shifts in a way to expand the γ single phase field when the Mn content is increased from 0 up to 17wt.%. Ni equivalent of Mn (NieqMn) is highly dependent on the Cr and Mn contents. A maximum NieqMn value of 0.9 was observed in the range 2–5wt.% Mn at 19wt.% Cr. The NieqMn value is zero at around 23wt.% Cr and becomes negative at higher Cr levels.

Experimental study and thermodynamic assessment of the Cu–Fe–Ti system

The Cu–Fe–Ti ternary system has been systematically studied through experimental investigation and thermodynamic modeling. Combining diffusion multiple technique with selected equilibrated alloys, equilibrium phase relations in the Cu–Fe–Ti system at 800°C have been established by means of SEM/EDS (Scanning Electron Microscopy/Energy Dispersive Spectrum) and EPMA (Electron Probe Micro-Analysis). DSC (Differential Scanning Calorimetry) analysis has been also employed to measure phase transformation temperatures in order to construct various vertical sections of the Cu–Fe–Ti system. Liquidus projection of the ternary system has been determined by identifying primary crystallization phases in as-cast alloys. Based on all available experimental information from literatures and this work, the Cu–Fe–Ti ternary system was modeled with the aid of the CALPHAD (CALculation of PHAse Diagram) method. Comprehensive comparisons made between experimental and calculated results shed light on reliability of the current thermodynamic description.

Composition Dependent Diffusivities in Multi-Component Systems

The modified Redlich-Kister approximation of the composition dependent intrinsic diffusivities in the multicomponent solid solution is presented. The effective computation method (the inverse problem) combines the Hierarchical Genetic Strategy with real number encoding (HGS-FP) with the modified Redlich-Kister approximation. The Cu–Ni–Fe alloys at 1271 K are analyzed. We show that the measured intrinsic diffusivities, the estimated from available diffusivity data and calculated by inverse method are in agreement. The presented method may become a very effective tool when the diffusion multiple technique is considered.

Mapping of 475 °C embrittlement in ferritic Fe–Cr–Al alloys

Embrittlement at 475 °C was mapped in ferritic ternary alloys with a wide composition range of Fe–(10–30)Cr–(0–20)Al (at.%) using a diffusion multiple technique. A large solid solution of Al suppresses the 475 °C embrittlement, while a small solid solution of Al promotes embrittlement. Transmission electron microscopy observations on aged samples suggest that suppression of the embrittlement due to Al addition can be attributed to the suppression of phase separation of the ferrite phase into the two phases Fe-rich ferrite and Cr-rich ferrite.

Phase Diagram Mapping of the Fe3Al-Cr-Mo-C Pseudo-Quaternary System at 800 °C Using a New Diffusion-Multiple Technique

A new diffusion-multiple technique was used for mapping the phase diagram in the pseudo-quaternary Fe3Al-Cr-Mo-C system at 800 °C. The following five carbide phases were formed in an Fe3Al matrix phase (B2) with composition gradients of Cr, Mo, and C in the diffusion-multiple samples: κ-Fe3AlC, M5C, M6C, Cr7C3, and M2C (M: Mo, Cr, Al, and Fe). It was assumed that B2 phase is in equilibrium with κ, M5C, M6C, and Cr7C3 but not with M2C phase at 800 °C. Complex phase equilibria among those phases were efficiently mapped by the diffusion-multiple technique. The results from the technique were consistent with those obtained from the conventional bulk alloy method.

Determination of phase equilibria in the Fe 3Al–Cr–Mo–C semi-quaternary system using a new diffusion-multiple technique

A new diffusion-multiple (DM) technique was proposed to allow us mapping of quaternary phase diagrams. This technique utilizes a combination of DM technique to introduce two-dimensional composition gradients in a matrix phase and a conventional annealing heat treatment to have precipitation reactions in the matrix. Phase equilibria at 800 °C in the semi-quaternary Fe 3Al–Cr–Mo–C system were determined with an assist from this technique. The following five carbide phases were precipitated in the Fe 3Al matrix phase (B2) with composition gradients of Cr, Mo and C: κ-Fe 3AlC, M 6C H, M 6C L, Cr 7C 3 and M 2C (M: Mo, Cr and Fe, the two M 6C phases are distinguished by their C and Cr contents.). It was found from our DM technique that the four-phase equilibrium of M 6C H + M 6C L + Cr 7C 3 + B2 exists. Microstructure analysis of several bulk alloys as well as DM samples revealed that the three-phase equilibrium of M 6C L + κ + B2 in the Fe 3Al–Mo–C system changes to that of M 6C L + Cr 7C 3 + B2 with increasing Cr content through the following three four-phase equilibria: (1) M 6C H + M 6C L + κ + B2, (2) M 6C H + Cr 7C 3 + κ + B2, (3) M 6C H + M 6C L + Cr 7C 3 + B2. The M 2C phase is thought to be not in equilibrium with the Fe 3Al matrix phase at 800 °C.