Nb/Sn Liquid-Solid Reactive Diffusion Couples and Their Application to Determination of Phase Equilibria and Interdiffusion Coefficients of Nb-Sn Binary System

Nb3Sn plays an irreplaceable role in superconducting parts due to its stable performance under high field conditions. Accurate phase equilibria and interdiffusion coefficients are of great significance for designing novel Nb3Sn superconductors. However, the related experimental information is still in a state of scarcity because of the difficulty in fabrication of Nb-Sn alloys caused by the large difference in melting points of Nb and Sn. In this paper, a simple but pragmatic approach was first proposed to prepare the Nb/Sn liquid-solid reactive diffusion couples (LSDCs) at 1100 °C and 1200 °C, of which the phase identification of the formed layer and the measurement of composition-distance profiles were conducted. The formed layer in Nb/Sn LSDCs was confirmed to be Nb3Sn compound. While the measured composition profiles were employed to determine the phase equilibria according to the local equilibrium hypothesis and the interdiffusion coefficients with an aid of the latest version of HitDIC software. The determined phase equilibria of Nb3Sn, (Nb) and liquid show good agreement with the assessed phase diagram. While the calculated interdiffusion coefficients and activation energy for diffusion in Nb3Sn are consistent with both experimental and theoretical data in the literature. Moreover, the growth of the formed Nb3Sn layer in Nb/Sn LSDCs was also found to be diffusion controlled. All the obtained phase equilibria and interdiffusion coefficients are of great value for further thermodynamic and kinetic modeling of the Nb-Sn system. Furthermore, it is anticipated that the presently proposed approach of fabricating liquid-solid reactive diffusion couple should serve as a general one for various alloy systems with large differences in melting points.

The Interdiffusion Behavior of NiCoCrAlYHf Coating Deposited by Arc Ion Plating on Carburized Ni-Based Single Crystal Superalloy

In the present study, arc ion plating (AIP) was used to prepare a NiCoCrAlYHf coating (HY5 coating) on a carburized third-generation single-crystal superalloy DD10. The interdiffusion behavior of the carburized superalloy with an HY5 coating was investigated for a 1000 h oxidation time at 1100 °C. Carburization enhanced the interfacial bonding force and improved the microstructure of the NiCoCrAlYHf coating. An interdiffusion zone (IDZ) formed after a 300 h oxidation time, and the formation of a carburized layer effectively suppressed an inward diffusion of cobalt, aluminium, and chromium to the DD10 superalloy as well as an outward diffusion of nickel and refractory elements for instance rhenium and tungsten to the HY5 coating that occurred in static air at 1100 °C. The roles of the carburized layer in affecting thermal cyclic oxidation and element interdiffusion were studied. Subsequently, a modified form of the Boltzmann–Matano analysis was used to present the interdiffusion coefficients of aluminium.

New Analyzing Approaches for In Situ Interdiffusion Experiments to Determine Concentration-Dependent Diffusion Coefficients in Liquid Al–Au

Interdiffusion coefficients are key parameters for the solidification process of liquid alloys. However, the determination of interdiffusion coefficients in liquid metals at high temperatures is a challenging and extensive task, due to a variety of potential systematic errors. In recent years we have developed an X-ray in situ shear cell method for the measurement of interdiffusion coefficients in binary metallic melts. This technique enables the monitoring of the experiment in order to exclude fatal errors. Utilizing X-ray contrast, the method also provides a time-resolved concentration distribution. Such an in situ data set contains significantly more information than ex situ evaluated experiments. Available analyzing strategies do not fully exploit this potential yet. We present three new analyzing approaches that are able to retrieve a concentration-dependent interdiffusion coefficient from only one in situ data set. In that way, larger concentration differences become accessible for an experiment, which considerably decreases efforts. Using simulations, the approaches are checked for robustness. Furthermore, the approaches are run on real in situ data from a binary (0 to 9 at% Au-content) Al–Au alloy at 1000 °C which results in a concentration-dependent interdiffusion coefficient within the measured concentration range.

Phase Equilibrium and Interdiffusion in Blends of Polystyrene with Polyacrylates

The solubility and interdiffusion of polystyrene (PS) with polymethyl acrylate (PMA), polyethyl acrylate (PEA), polybutyl acrylate (PBA), and polyethylhexyl acrylate (PEHA) have been studied by the optical interferometry method. Phase state diagrams are plotted. It is shown that they are characterized by the upper critical solution temperatures (UCST), which are localized in the temperature range above 450 K. Pair interaction parameters and their temperature dependences are determined and analyzed. Extrapolation of the temperature dependence of the interaction parameter was used to construct the dome of binodal curves and determine the spinodal curves in the framework of the Flory–Huggins theory. The diffusion coefficients of polystyrene into polyacrylates and polyacrylates into polystyrene are calculated. The dependences of the interdiffusion coefficients on the concentration, temperature, polystyrene molecular weight, and the number of carbons in the side chain of polyacrylate are analyzed. The numerical values of the interdiffusion coefficients of PS-1 into polyacrylates at 433 K change as −8.5 → −6.7 → −6.4 in the homologous series PMA → PEA → PBA. The coefficients of friction are calculated and the effect of change in the matrix structure on the diffusion of polystyrene in them is estimated.

InfPolyn, a Nonparametric Bayesian Characterization for Composition-Dependent Interdiffusion Coefficients

Composition-dependent interdiffusion coefficients are key parameters in many physical processes. However, finding such coefficients for a system with few components is challenging due to the underdetermination of the governing diffusion equations, the lack of data in practice, and the unknown parametric form of the interdiffusion coefficients. In this work, we propose InfPolyn, Infinite Polynomial, a novel statistical framework to characterize the component-dependent interdiffusion coefficients. Our model is a generalization of the commonly used polynomial fitting method with extended model capacity and flexibility and it is combined with the numerical inversion-based Boltzmann–Matano method for the interdiffusion coefficient estimations. We assess InfPolyn on ternary and quaternary systems with predefined polynomial, exponential, and sinusoidal interdiffusion coefficients. The experiments show that InfPolyn outperforms the competitors, the SOTA numerical inversion-based Boltzmann–Matano methods, with a large margin in terms of relative error (10x more accurate). Its performance is also consistent and stable, whereas the number of samples required remains small.

An Effective Approach to Acquire the Impurity Diffusion Coefficients in Binary Alloys with Quantified Uncertainties

In this paper, we started from the composition-dependent interdiffusion coefficients with quantified uncertainties in binary alloys by integrating the Matano-based method, distribution functions, and uncertainty propagation approach. After carefully defining the numerically stable region for the interdiffusion coefficients, the suitable pre-set functions were screened to achieve the reasonable fit to the D-c and μ-c data according to the Akaike information criterion. With the fitted D-c and μ-c curves, the impurity diffusion coefficients with uncertainties can be directly determined. Benchmark tests in five hypothetical binary systems with different preset D-c relations were then utilized to validate the presently effective approach, followed by practical applications in five real cases, i.e., fcc Ni-Co, fcc Cu-Al, fcc Pt-Ni, hcp Mg-Zn, and bcc Ti-V alloys. The impurity diffusion coefficients with uncertainties derived by the presently effective approach were found to be in excellent agreement with the data by tracer experiments, indicating that this effective approach can serve as a standard one for acquiring the high-quality impurity diffusion coefficients in binary alloys with quantified uncertainties, especially for the noble metals and the cases without suitable radioactive tracer isotopes.

Novel Interdiffusion Analysis in Multicomponent Alloys - Part 2: Application to Quaternary, Quinary and Higher Alloys

A novel study of analysis interdiffusion in multicomponent alloys is investigated by means of closed form solutions and numerical simulations. Quaternary as well as selected CoCrFeMnNi (HEAs) quinary metallic systems are analysed using one, two and three diffusion couples with the full set of interdiffusion coefficients being calculated. A custom written Matlab fitting program (MFP) is used as the main tool for the simultaneous fitting into multiple composition profiles in both systems. The retrieved interdiffusion matrices are obtained using a newly developed approach that is interlinked with composition vectors, eigenvalues and eigenvector. On average, it can be concluded that the accuracy of the obtained matrices steadily improves with the increase of the number of couples used in the analysis.

Novel Interdiffusion Analysis in Multicomponent Alloys - Part 1: Application to Ternary Alloys

A novel study of interdiffusion analysis in multicomponent alloys is presented. A custom written Matlab fitting program (MFP) is used as the main tool for the present study. The interdiffusion matrices are obtained using a newly developed mathematical approach based on the fitting into the closed form solution for the composition profiles. Overall, the new fitting method gives very good outcomes and allows the probing of multiple solutions (validated by back tests) that exist when a single diffusion couple is used in a multicomponent system. An important finding of the present investigations is that small differences in composition profiles may lead to large differences in the interdiffusion coefficients.

Automation of diffusion database development in multicomponent alloys from large number of experimental composition profiles

Nowadays, the urgency for the high-quality interdiffusion coefficients and atomic mobilities with quantified uncertainties in multicomponent/multi-principal element alloys, which are indispensable for comprehensive understanding of the diffusion-controlled processes during their preparation and service periods, is merging as a momentous trending in materials community. However, the traditional exploration approach for database development relies heavily on expertize and labor-intensive computation, and is thus intractable for complex systems. In this paper, we augmented the HitDIC (high-throughput determination of interdiffusion coefficients, https://hitdic.com) software into a computation framework for automatic and efficient extraction of interdiffusion coefficients and development of atomic mobility database directly from large number of experimental composition profiles. Such an efficient framework proceeds in a workflow of automation concerning techniques of data-cleaning, feature engineering, regularization, uncertainty quantification and parallelism, for sake of agilely establishing high-quality kinetic database for target alloy. Demonstration of the developed infrastructures was finally conducted in fcc CoCrFeMnNi high-entropy alloys with a dataset of 170 diffusion couples and 34,000 composition points for verifying their reliability and efficiency. Thorough investigation over the obtained kinetic descriptions indicated that the sluggish diffusion is merely unilateral interpretation over specific composition and temperature ranges affiliated to limited dataset. It is inferred that data-mining over large number of experimental data with the combinatorial infrastructures are superior to reveal extremely complex composition- and temperature-dependent thermal–physical properties.