Equilibrium Phase Fraction Research Articles

Prediction of Solidification Paths in Al-Si-Fe Ternary System and Experimental Verification: Part I. Fe-Containing Hypoeutectic Al-Si Alloys

The effects of Fe content and cooling rate on the solidification path and formation behavior of the Al5FeSi (β) phase in Fe-containing hypoeutectic Al-Si alloys were studied based on thermodynamic analysis and pertinent experiments. The thermodynamic calculations were performed using the Thermo-Calc program. For analyses in the high alloy region of the Al-Si-Fe ternary system, a thermodynamic database for Thermo-Calc was correctly updated and revised by the collected up-to-date references. For thermodynamics-based predictions of the solidification path in Fe-containing hypoeutectic Al-Si alloys, liquidus projection (including various invariant, monovariant, and bivariant reactions and isotherms) and equilibrium phase fraction were calculated as functions of composition and temperature in the Al-Si-Fe ternary system. The calculated results were compared to experimental results using various casting runs. In order to analyze the solidification path as a function of Fe content, two representative hypoeutectic Al-Si alloys with different Fe levels were designed. To better understand the influence of cooling rate on the formation behavior of the β phase, the two alloys were solidified under slowly- and rapidly-cooled conditions, respectively. The cooling curves of the solidified alloys were recorded by thermal analysis and various important solidification events were detected using the first derivative of the cooling curves. Microstructures of the casting samples were studied by combined analyses of optical microscopy (OM) and scanning electron microscopy (SEM). For the slowly-cooled condition with the high Fe level, the primary β phase enveloping the Al8Fe2Si (α) phase was mainly formed by the quasi-peritectic reaction of L + α → (Al) + β (612°C). For the rapidly-cooled condition with the high Fe level, the primary β phase with morphology of a curved needle was mainly formed by the reaction of L → (Al) + β (579∼612°C).

Austenite stabilization through manganese enrichment

A model is proposed to predict austenite stabilization through manganese partitioning between ferrite and austenite. The model predicts retained austenite fractions as a function of intercritical annealing temperature based on equilibrium phase fractions and solute contents. Thermodynamic data are used to calculate the Ms temperature of the enriched austenite in order to predict fresh martensite formation upon cooling to room temperature. An intercritical annealing temperature resulting in the greatest retained austenite fraction is predicted which correlates to some experimental observations.

EFFECT OF COOLING RATES ON SEGREGATION AND DENSITY VARIATION IN THE MUSHY ZONE DURING SOLIDIFICATION OF SUPERALLOY INCONEL 718

The microstructure and segregation of experimental samples of the superalloy Inconel 718 solidified at different cooling rates have been investigated by SEM and EDAX. The equilibrium phase fraction diagrams of Inconel 718 and the segregated liquid composition were calculated by Thermo-Calc. The experimental and calculated results were in good agreement with those of an Inconel 718 ingot, and they indicated that, at a cooling rate less than 3°C/min, heavy Nb and Mo segregation resulted in Laves phase formation directly from the liquid. The density of the liquid surrounding the Laves phase decreased and the region between the two Laves precipitates (inter-precipitate) often had the lowest density. A density difference (or micro inter-precipitate density inversion) existed between the inter-precipitate liquid and the original liquid at the same or higher temperatures where there were no liquid-precipitated Laves.

Investigations on the growth kinetics of Laves phase precipitates in 12% Cr creep-resistant steels: Experimental and DICTRA calculations

The growth kinetics of Laves phase precipitates (type Fe 2W) in the early stage of creep (650 °C for 10,000 h) in two 12% Cr ferrite–martensitic steels has been investigated. In one alloy the Laves phase formed on tempering, while in the second alloy the Laves phase precipitated during creep. Kinetic simulations were performed using the software DICTRA. The particle size of the Laves phase was measured on transmission electron microscopy samples. The equilibrium phase fraction of the Laves phase was reached in the first thousand hours. Simulations of particle growth showed good agreement with the experimental results. Competitive growth between M 23C 6 and the Laves phase showed that M 23C 6 carbides reached their equilibrium after 12 days, whereas the Laves phase reached equilibrium after 3 months. Simulations of the influence of the interfacial energy and addition of Co, Cu and Si on Laves phase precipitation are presented.

Investigation into the effects of Fe additions on the equilibrium phase compositions, phase fractions and phase stabilities in the Ni–Cr–Al system

NiCrAl alloys are commonly used for the bond coat in thermal barrier coatings (TBCs). Previous work has investigated the effects of intentional chemical additions on phase stability, but there is also a need to consider the effects of unintentional additions. For instance, cryomilling of NiCrAlY powder, which has been demonstrated to increase TBC lifetime, results in unintentional Fe additions. In this study, the effects of Fe additions are evaluated both through experimentation and computational simulation. The combined results indicate that the presence of Fe stabilizes the high-temperature γ and β phases, corresponding to a decrease in the transformation temperature. These results are explained on the basis of Gibbs free energy for individual phases. Phase composition is also investigated, indicating that, even without Fe, the phases are more complex than typically assumed and that, at the low concentrations associated with cryomilling, the Fe goes into solution in the Ni-rich phases.

Equilibrium tuned by a magnetic field in phase separated manganite

We present magnetic and transport measurements forLa5/8−yPryCa3/8MnO3 with y = 0.3, a manganite compound exhibiting intrinsic multiphase coexistence of sub-micrometricferromagnetic and antiferromagnetic charge ordered regions. Time relaxation effectsbetween 60 and 120 K, and the obtained magnetic and resistive viscosities, unveil thedynamic nature of the phase separated state. An experimental procedure based on thederivative of the time relaxation after the application and removal of a magnetic fieldenables the determination of the otherwise unreachable equilibrium state of the phaseseparated system. With this procedure the equilibrium phase fraction for zero field as afunction of temperature is obtained. The presented results allow a correlation betweenthe distance of the system to the equilibrium state and its relaxation behavior.

Phases Equilibrium Study in Quaternary Iron-rich Fe-Al-Mn-C Alloys

High aluminium low manganese steels were elaborated in order to study the phase equilibrium in the range of 900–1 100°C. Two different quaternary alloys have been studied (Fe–9 to 10wt%Al–1.7wt%Mn–0.2wt%C and Fe–9 to 10wt%Al–8wt%Mn–0.2wt%C). Equilibrium phase’s nature was identified at four temperatures for two alloys. Equilibrium phase fraction and chemical compositions were determined at 900°C. Thanks to these equilibrium results, we tried to understand the non-equilibrium microstructure observed after different thermal histories (DTA cycles, isothermal treatment followed by quench, reception state) and identify DTA events in a coherent way.

Percolation of Diffusionally Evolved Two-Phase Systems

ABSTRACTAlthough the phase fractions in dual phase systems are often compared with the percolation threshold for a randomly-assembled composite, most two-phase systems are non-random by virtue of correlations introduced during processing or as a consequence of microstructural evolution. This study examines the two dimensional percolation threshold in systems with soft impingement, i.e., when the phase distribution is affected by diffusional interactions between growing second phase particles. Phase field modeling is used to simulate the nucleation and growth process, with many simulations conducted at various system sizes and equilibrium phase fractions to obtain percolation probabilities. The value of the percolation threshold in the thermodynamic limit is estimated based on the finite size scaling behavior of the system. The value of the critical exponent ν (the size scaling exponent) is also estimated.

Interfacial Stress, Interfacial Energy, and Phase Equilibria in Binary Alloys

A simple model is presented in order to explore the influence of interfacial stress, interfacial energy, and surface stress on the characteristics of phase equilibria in stressed, two-phase binary alloys. Two different system geometries are employed: concentric spheres and thin plates. The conditions for thermodynamic equilibrium are solved and equations of state for each geometry are obtained in terms of the phase fraction, alloy composition, system dimension, and several dimensionless materials parameters. Elastic stress introduces new equilibrium states that are further modified by the interfacial quantities. Those conditions for which interfacial quantities can induce significant changes in the equilibrium phase fraction and phase compositions are identified.

Modelling of phase transformations occurring in low activation martensitic steels

The main objective of this paper is to summarize modelling of on-heating and on-cooling phase transformations occurring in Low Activation Martensitic (LAM) steels. Calculations of thermodynamic equilibrium phase fractions and kinetic aspects of phase transformations have been performed by using different approaches from experimental data (CCT and TTT diagrams obtained by dilatometry). All the calculated data have been compared to an important and systematic set of experimental data obtained on different LAM steels of the 7.5–11% CrWVT a type.

New Inuyama classification; new criteria for histological assessment of chronic hepatitis

To investigate whether the iodine density of liver parenchyma in the equilibrium phase and extracellular volume fraction (ECV) measured by deep learning-based spectral computed tomography (CT) can enable noninvasive liver fibrosis staging.We retrospectively analyzed 63 patients who underwent dynamic CT using deep learning-based spectral CT before a hepatectomy or liver transplantation. The iodine densities of the liver parenchyma (I-liver) and abdominal aorta (I-aorta) were independently measured by two radiologists using iodine density images at the equilibrium phase. The iodine-density ratio (I-ratio: I-liver/I-aorta) and CT-ECV were calculated. Spearman's rank correlation analysis was used to evaluate the relationship between the I-ratio or CT-ECV and liver fibrosis stage, and receiver operating characteristic (ROC) analysis was used to evaluate the diagnostic performances of the I-ratio and CT-ECV.The I-ratio and CT-ECV showed significant positive correlations with liver fibrosis stage (ρ = 0.648, p < 0.0001 and ρ = 0.723, p < 0.0001, respectively). The areas under the ROC curve for the CT-ECV were 0.882 (F0 vs ≥ F1), 0.873 (≤F1 vs ≥ F2), 0.848 (≤F2 vs ≥ F3), and 0.891 (≤F3 vs F4).Deep learning-based spectral CT may be useful for noninvasive assessments of liver fibrosis.

Phase transitions in the ISM a source of dissipative behaviour

By considering a simple fluid model, we investigate the role of phase transitions in the ISM on the galaxy- scale gas dynamics. Cooling and heating timescales in the ISM are typically shorter than typical galactic rotation timescales, so the individual phases in the ISM can be assumed to be in temperature equilibrium with the radiation field. Using this approximation we can construct an equation of state which depends upon the average density and mass fractions in the individual phases. Previous studies suggest that there is an equilibrium phase fraction as a function of pressure. We incorporate evolution towards this equilibrium state as a relaxation term with a time to obtain equilibrium τ. We derive a condition in terms of a critical Mach number when one dimensional shocks should be continuous. For small values of the relaxation time τ we show that the relaxation term acts like a viscosity. We show with one dimensional simulations that increasing τ causes shocks to become smoother. This work suggests that phase changes can strongly effect the gas dynamics of the ISM across spiral arms and bars.