Liquidus Isotherms Research Articles

Influence of alloy solidification path on melt pool behavior in additive manufacturing

Numerical models used to study transport phenomena in laser-powder bed fusion processes often rely on assumptions and simplifications to reduce their computational expense. One common simplification is in the description of latent heat evolution during the solid-liquid phase change (i.e., the solidification pathway), justified by the fact that the mushy zone thickness is similar to the numerical grid spacing used for continuum transport models. The lack of resolution of transport phenomena in the mushy zone motivates the use of computationally convenient solidification paths such as linear or sigmoidal relationships over pathways derived from fundamental solidification theory such as equilibrium or Scheil models. In the present work, an uncertainty quantification (UQ) framework is used to analyze the influence of solidification pathway selection on the solidification dynamics and melt pool geometries in laser based additive manufacturing (AM) of IN625. Results show the solidification pathway has a quantifiable influence on the cooling rate at the liquidus isotherm, mushy zone thickness, and solidification time. Due to similarities in the latent heat evolution at the beginning of solidification, the equilibrium and Scheil models predict similar cooling rates near the liquidus isotherm, however the wider freezing range of Scheil leads to a wider mushy zone compared to equilibrium. The non-physical latent heat release profiles of sigmoidal and linear paths lead to significant overpredictions of cooling rates at the liquidus isotherm compared to equilibrium and Scheil. These results indicate that careful consideration should be given to the choice of solidification pathway to ensure reliable model predictions.

Phase equilibria in the NiO-ZnO-SiO2 and PbO-NiO-ZnO-SiO2 systems

Experimental investigation and thermodynamic modeling of the phase equilibria in the (PbO)-NiO-ZnO-SiO2 system has been undertaken to characterize Ni behavior in high-Zn slags. Phase equilibria data at 790–1700 °C were obtained through equilibration of synthetic mixtures in sealed silica ampoules or Pt-Ir / Au foils, rapid quenching, and electron probe X-ray microanalysis. Phase equilibria and liquidus isotherms of the NiO-ZnO-SiO2 system in the tridymite/cristobalite SiO2, monoxide (Ni,Zn)O, zincite (Zn,Ni)O, olivine (Ni,Zn)2SiO4 and willemite (Zn,Ni)2SiO4 phase fields were measured and the extent of the 2-liquid immiscibility gap over cristobalite was determined. Additional solid solutions: larsenite Pb(Zn,Ni)SiO4 and melilite Pb2(Zn,Ni)Si2O7 were measured in the PbO-NiO-ZnO-SiO2 system. It was found that NiO partially substitute ZnO in larsenite and melilite and may form a complete range of solubility in barysilite Pb8(Zn,Ni)Si6O21. New data were used for developing a thermodynamic database to describe the Pb/Cu-containing complex system for characterizing Ni behavior in Zn-containing slags.

Solidification of quaternary X5CrNi18-10 alloy after laser beam welding: A phase-field approach

The austenitic stainless steel (X5CrNi18-10) is the most commonly used chrome-nickel steel, due to its high corrosion resistance. However, it faces the challenge of cracking events during post-laser-beam-welding dendritic solidification. These microstructural changes significantly impact the final mechanical properties. To contribute to a more precise understanding of the physical mechanisms of the appearance of cracking, the goal of this research is to investigate various aspects at the microscale influenced by process-specific extreme thermal conditions. A thermodynamic model of quaternary alloy configuration is used to study the micro-segregation behavior of alloying elements and resulting morphology based on the local thermal conditions. For this purpose, a multi-component and multiphase-field-based grand chemical potential model is used. It is observed that in addition to global processing conditions, local conditions are also important to consider and classify the morphology changes from columnar-dendritic to cellular along the liquidus isotherm of the weld pool.

Eliminating Equiaxed Grain Defects in a Ni‐Based Single‐Crystal Blade Platform by Flattening the Liquidus Isotherm

The article presents a mechanism for the formation of equiaxed grain defects and a new approach to eliminate them during the directional solidification of single‐crystal CMSX‐4 nickel‐based superalloy blades. The standard Bridgman method produces blade castings with clusters of equiaxed grains in platform areas above the root corners containing long freckle chains. The mechanism proposed considers the curvature of the liquidus isotherm and suggests that isolated dendrite fragments move upward from the freckle channel to the melt of the platform area. The floating surviving grains settle at the columnar dendrite tips, where they continue to grow into large equiaxed grains that block the development of the single‐crystal structure in the platform area located above the root corners. To eliminate these defects from the platform, a new approach is proposed, which involves introducing inner radiation baffles along the mold height to control the liquidus isotherm curvature in the blade. This stops the movement of small dendritic fragments from the root corner to the platform area, resulting in a significant reduction of freckles at the root and obtaining a typical single‐crystal structure free of equiaxed grains in the platform.

Experimental and thermodynamic modeling study of phase equilibria in the PbO–NiO–SiO2 system

AbstractAn integrated experimental and thermodynamic modeling investigation of the phase equilibria in the PbO–NiO–SiO2 system in air and also in equilibrium with liquid metal has been undertaken to better characterize the chemical reactions taking place in the Ni‐containing Pb processing slags. New experimental phase equilibria data at 720°C–1740°C were obtained for this system using high‐temperature equilibration of synthetic mixtures with predetermined compositions in sealed silica ampoules or in Au/Pt–Ir foils, a rapid quenching technique, and electron probe x‐ray microanalysis of the equilibrated phase compositions. Phase equilibria and liquidus isotherms in the quartz/tridymite/cristobalite (SiO2), olivine (Ni2SiO4), monoxide (NiO), Ni‐barysilite (Pb8NiSi6O21), massicot (PbO), and di‐lead silicate (Pb2SiO4) primary phase fields were revealed and the extent of the high‐SiO2 two‐liquid immiscibility gap in equilibrium with cristobalite was determined. New experimental data were used in the development of a thermodynamic database describing this ternary system. Also, modeling revision of the NiO–SiO2 binary system was conducted, resulting in a smaller miscibility gap in ternary systems that was closer to the experimental results.

Extending the inverse sequential quasi-Newton method for on-line monitoring and controlling of process conditions in the solidification of alloys

This work introduces the sequential quasi-Newton method (SQNM) to solve the inverse design problem of estimating the transient boundary heat fluxes that produce desired evolutions of the solidus and liquidus isotherms in alloys’ solidification processes. This is an unprecedented application for sequential gradient-based methods. The final goal is monitoring and controlling the evolution of the mushy zone in a near real-time fashion, which is of high technological interest to the foundry industry. We assess the performance of the SQNM in solving several inverse design problems in one- and two-dimensional domains. The method satisfactorily estimates the boundary heat fluxes using relatively few future measurements. However, some instabilities have been detected in the SQNM-predicted heat fluxes. To alleviate this issue, we proposed a modified version of SQNM, say mSQNM, that employs an inexact line search strategy to find the optimal step length during the iterative estimation procedure. We finally show how mSQNM improves the estimation of the boundary heat fluxes.

Integrated Experimental and Thermodynamic Modeling Investigation of Phase Equilibria in the PbO\u2013MgO\u2013SiO2 System in Air

Magnesium oxide-based refractory materials are used industrially to contain the chemically aggressive slags present in lead smelting systems. In the present study an integrated experimental and thermodynamic modeling approach was taken to provide fundamental information on the chemical reactions taking place in these systems. New experimental phase equilibria and liquidus data were obtained for the PbO–MgO–SiO2 system in air in the temperature range 750 °C to 1740 °C. In the MgO–SiO2 binary, new experimental results were obtained at 1550 °C to 1740 °C and compared to the available thermodynamic data in the literature. The experiments were carried out using the high-temperature equilibration of oxide powder mixtures followed by rapid quenching of the samples. Electron probe X-ray microanalysis (EPMA) was used to determine the compositions of the solid and liquid phases present at equilibrium conditions. Phase equilibria and liquidus isotherms in the cristobalite and tridymite (SiO2), pyroxene (protoenstatite MgSiO3), olivine (forsterite Mg2SiO4), barysilite (Pb8MgSi6O21), massicot (PbO) and periclase (MgO) primary phase fields were measured, and the extent of the high-silica two-liquid immiscibility gap in equilibrium with cristobalite was determined. The experimental results were used to optimize the parameters in a thermodynamic database that was subsequently used to describe this multi-component, multi-phase system and predict the liquidus for the PbO–MgO–SiO2 system. The new data were used to characterize the chemical interactions of magnesia-based refractory with PbO–MgO–SiO2 slags.

Experimental phase equilibria studies in the “CuO0.5”-CaO-SiO2 ternary system in equilibrium with metallic copper

Phase equilibria studies were undertaken on the “CuO0.5”-CaO-SiO2 system in equilibrium with metallic copper to provide fundamental information on the reactions taking place between slags and refractory materials in metallurgical furnaces. The liquidus isotherms between 1160 and 1706 °C in the tridymite and cristobalite (SiO2), cuprite (Cu2O), pseudowollastonite (CaSiO3), rankinite (Ca3Si2O7) and dicalcium silicate (Ca2SiO4) primary phase fields, and the 2-liquid miscibility gaps in the silica-rich corner and low-silica area of the system, were experimentally determined using the equilibration and quenching technique, followed by the electron probe X-ray microanalysis (EPMA) of phase compositions. The liquidus surface of the “CuO0.5”-CaO-SiO2 system has been constructed. The dissolution of copper oxide in the tridymite and cristobalite (SiO2) was shown to be negligible. The data obtained are used for the optimization of the thermodynamic database for the copper-containing systems.

Experimental study of “CuO0.5”-“FeO”-SiO2 and “FeO”-SiO2 systems in equilibrium with metal at 1400–1680 °C

The phase equilibria of the “CuO0.5”-“FeO”-SiO2 slag system in equilibrium with metallic copper and tridymite/cristobalite (SiO2), and the “FeO”-SiO2 slag system in equilibrium with metallic iron and tridymite/cristobalite (SiO2) were investigated between 1400 and 1680 °C. High temperature equilibration in closed silica ampoules, followed by quenching and the direct measurement of the phase compositions with the electron probe X-ray microanalysis (EPMA) was used. The liquidus isotherms in the tridymite and cristobalite (SiO2) primary phase fields were measured, and the shape of the two liquid slags miscibility gap over cristobalite was determined for the “CuO0.5”-“FeO”-SiO2 and “FeO”-SiO2 systems in equilibrium with metallic copper and iron respectively. The two liquid slags miscibility gap over cristobalite was found to be present at all Cu/(Cu+Fe) molar ratios in the slag. However, the difference in the SiO2 concentration between the low- and high-SiO2 slag was found to decrease as the Cu/(Cu+Fe) molar ratio in slag approached 0.5, with the minimal difference assessed to be approximately 4 mol.%. Additionally, new phase equilibria data obtained for the “FeO”-SiO2 subsystem in equilibrium with metallic iron suggested that the monotectic temperature of the subsystem is 1673 ± 3 °C, and that the low- and high- SiO2 slags contain 59.7 mol.% and 96.4 mol.% SiO2 respectively. The present study was a continuation of previous investigations by the authors into the Cu-Fe-Si-O multicomponent slag system, aimed at providing information for improving the thermodynamic models for all phases in this system.

The effect of 15 wt%Al2O3 addition on the equilibrium phase relations of CaO–SiO2–TiO2 system at 1400 °C in air

The combined processing of industrial wastes of titania-bearing slags with coal fly ash is an important part of the circular economy. In the present work, the effect of Al2O3 on the 1400 °C liquidus isotherms of the perovskite, rutile and tridymite primary phase fields in the CaO–SiO2–TiO2–Al2O3 system has been determined by employing a high-temperature equilibration-quenching technique, followed by X-ray Photoelectron Spectroscopy and Scanning Electron Microscopy-Energy Dispersive X-ray Spectrometry. Titanium was confirmed to be stable as TiO2 in the present equilibria. The equilibrium solid phases of perovskite CaO·TiO2, rutile TiO2 and tridymite SiO2 were confirmed to be coexisting with the liquid oxide phase. The comparison of the addition of 0–15 wt% Al2O3 was beneficial for expanding the primary phase field of perovskite to lower TiO2 concentrations. Comparisons of the experimental 1400 °C isotherm with the predictions using FactSage and MTDATA databases confirmed some differences to the present experimental data, thus demonstrating the direction for updating the present thermodynamic titania-bearing oxide databases.

Numerical modelling and experimental validation of the effect of ultrasonic melt treatment in a direct-chill cast AA6008 alloy billet

In this work, we study how ultrasonic cavitation melt treatment (UST) affects the temperature distribution, sump profile, and resulting microstructure in the direct-chill (DC) casting of an AA6008 aluminum alloy. Two 152 mm diameter billets were cast; one was treated with UST (UST-DC casting) in the hot top while the other was not (conventional DC casting). To investigate the temperature distribution, temperature was measured at multiple points in both billets. The sump profile was visualized by pouring Zn into the sump during casting. The microstructure was analyzed by measuring the grain size of as-cast billets. A numerical model of DC casting and UST-DC casting has been validated with the temperature measurements across the billets, and the experimental results agrees well with the numerical model. It is found that the sump profile quantification with thermocouple measurements is more accurate and less prone to interpretation than with Zn tracing. Numerical simulation results show that UST application in the hot top with sonotrode position at 20 mm above the graphite ring level depresses the liquidus isotherm but does not affect the solidus isotherm, resulting in a thinner transition region compared with conventional DC casting. Grain structure analysis verifies that structure refinement with UST has been achieved at the given sonotrode position. The strongest grain refinement was at the center of the billet with the average grain size 50% smaller than that without UST. The results are discussed in terms of the known mechanisms of UST, i.e. dendrite fragmentation and deagglomeration of nucleating substrates.

A front-tracking measurement technique for in-situ columnar and equiaxed structure growth with controlled solidification

Growth rate is an important consideration in solidification as it influences features of the micro and macrostructure such as morphology and the columnar to equiaxed transition. Thus, accurately quantifying the growth rate is key to understanding the solidification process as well as verifying numerical simulations. In this work, an experimental apparatus has been developed to investigate in-situ directional solidification using a transparent analogue material, neopentyl glycol-35 wt%(D)camphor. The facility enables the control of the mushy zone growth rate as well as the imposed temperature gradient during solidification, similar to Bridgman type furnaces. Image processing techniques were developed for automated tracking of position and growth rate of the solidification front (SF) using background subtraction on photographic image sequences captured in experiments. Growth rate measurements using this technique and the traditional method (liquidus isotherm speed) have been benchmarked against manual measurements of position and growth rate. Results show that automatically tracked growth rate compares well throughout experiments with errors less than 2.7%. Contrastingly, isotherm speed was in error up to 19%. Three columnar and two equiaxed morphologies were investigated and SFs were characterised for their growth rates and thermal conditions.

Performance gains prompt leach expansion at Pinto Valley

The phase equilibria of the “CuO0.5”-“FeO”-SiO2 slag system in equilibrium with metallic copper and tridymite/cristobalite (SiO2), and the “FeO”-SiO2 slag system in equilibrium with metallic iron and tridymite/cristobalite (SiO2) were investigated between 1400 and 1680 °C. High temperature equilibration in closed silica ampoules, followed by quenching and the direct measurement of the phase compositions with the electron probe X-ray microanalysis (EPMA) was used. The liquidus isotherms in the tridymite and cristobalite (SiO2) primary phase fields were measured, and the shape of the two liquid slags miscibility gap over cristobalite was determined for the “CuO0.5”-“FeO”-SiO2 and “FeO”-SiO2 systems in equilibrium with metallic copper and iron respectively. The two liquid slags miscibility gap over cristobalite was found to be present at all Cu/(Cu+Fe) molar ratios in the slag. However, the difference in the SiO2 concentration between the low- and high-SiO2 slag was found to decrease as the Cu/(Cu+Fe) molar ratio in slag approached 0.5, with the minimal difference assessed to be approximately 4 mol.%. Additionally, new phase equilibria data obtained for the “FeO”-SiO2 subsystem in equilibrium with metallic iron suggested that the monotectic temperature of the subsystem is 1673 ± 3 °C, and that the low- and high- SiO2 slags contain 59.7 mol.% and 96.4 mol.% SiO2 respectively. The present study was a continuation of previous investigations by the authors into the Cu-Fe-Si-O multicomponent slag system, aimed at providing information for improving the thermodynamic models for all phases in this system.

Design of variable withdrawal rate for superalloy single-crystal blade fabrication

Stray grains bring great challenges to the production of superalloy single-crystal blades using the Bridgman method. The height difference between the liquidus isotherms in the airfoil and platform, which is induced by the difference between liquidus isotherm advancing velocity and withdrawal rate, provides undercooling for the nucleation and the growth of stray grains. The height range of liquidus isotherm is used for the first time to describe the asymmetric distribution of temperature and radiation, and to estimate the probability of stray grain formation. A real-time adjustment of withdrawal rate method is proposed to design the withdrawal rate-time curve aiming to fabricate superalloy single-crystal blades with complex geometry. The obtained withdrawal rate curve is then validated by numerical simulation and hence applied to the fabrication of single-crystal blades. The simulation results show that with obtained withdrawal rate curve the distribution of radiation and temperature are significantly improved and the undercooling in the platform is largely reduced. The observed macrostructure in the experiments proves that the stray grains in the platform can be avoided through the designed withdrawal rate curve. The proposed method for designing withdrawal rate can provide a reliable strategy for the research and manufacture of stray-grain-free single-crystal blades.

Investigation of macrosegregation for different dendritic arm spacing, casting temperature, and thermal boundary conditions in a direct-chill casting

The study of macrosegregation for different dendritic arm spacing, casting temperature, and cooling conditions in a Direct-Chill (DC) casting was investigated in the present study. The velocity variance-elliptic relaxation ( $$ \overline{{v^{2} }} - f $$ ) turbulence model was used to account for the turbulence effect in the bulk liquid and slurry region. The thermosolutal effect was implemented in the bulk liquid and slurry flow. The Scheil’s solute redistribution model was used to account for solute partitioning at the solidification interfaces. The pressure-based segregated time-dependent solver was used in the solution method to solve the flow equations. The model validation indicates loawer transition thickness due to: (1) efficient damping of the flow in the slurry zone by the turbulence viscous forces, (2) effective handling of the kinematic wall blocking effects in the vicinity of the slurry zone, and (3) strong mixing of the turbulent fluid motion that tends to decrease the distance between the solidus and liquidus isotherm. In all the cases investigated, it was evident that the thermal boundary condition at the secondary cooling zone, casting inlet temperature and secondary Dendritic Arm Spacing (DAS) affect the segregation ratio both at the centerline and the billet surface.

Study of the Phase Equilibria of the Co-Fe-Ni Ternary System in the High-Temperature Range

The research is devoted to the study of the high-temperature phase equilibria within the complete compositional range of the Co-Fe-Ni ternary system using the differential thermal analysis, scanning electron microscopy, energy-dispersive x-ray spectroscopy, and x-ray diffraction analysis. The liquidus isotherms were evaluated on the basis of the experimental data and plotted in the concentration triangle. The position of the monovariant peritectic line in the ternary system was specified.

Upward Unsteady-State Solidification of Dilute Al–Nb Alloys: Microstructure Characterization, Microhardness, Dynamic Modulus of Elasticity, Damping, and XRD Analyses

Aluminium alloys form many important structural components, and the addition of alloying elements contributes to the improvement of properties and characteristics. The objective of this work is to study the influence of thermal variables on the microstructure, present phases, microhardness, dynamic modulus of elasticity, and damping frequency in unidirectional solidification experiments, which were performed in situ during the manufacturing of Al–0.8 Nb and Al–1.2 Nb (wt.%) alloys. Experimental laws for the primary (λ1) and secondary (λ2) dendritic spacings for each alloy were given as a function of thermal variables. For Al–0.8%wt Nb, λ1 = 600.1( T ˙ )−1.85 and λ2 = 186.1(VL)−3.62; and for Al–1.2%wt Nb, λ1 = 133.6( T ˙ )−1.85 and λ2 = 55.6(VL)−3.62. Moreover, experimental growth laws that correlate the dendritic spacings are proposed. An increase in dendritic spacing influences the solidification kinetics observed, indicating that metal/mold interface distance or an increase in Nb content lowers the liquidus isotherm velocity (VL) and the cooling rate (Ṫ). There is also a small increase in the microhardness, dynamic modulus of elasticity, and damping frequency in relation to the composition of the alloy and the microstructure.

Defect Creation in the Root of Single-Crystalline Turbine Blades Made of Ni-Based Superalloy.

An analysis of the defects in the vicinity of the selector–root connection plane occurring during the creation of single-crystalline turbine blades made of CMSX-6 Ni-based superalloy was performed. X-ray diffraction topography, scanning electron microscopy, and positron annihilation lifetime spectroscopy were used. Comparing the area of undisturbed axial growth of dendrites to the area of lateral growth concluded that the low-angle boundaries-like (LAB-like) defects were created in the root as a result of unsteady-state lateral growth of some secondary dendrite arms in layers of the root located directly at the selector–root connection plane. Additional macroscopic low-angle boundaries (LABs) with higher misorientation angles were created as a result of concave curvatures of liquidus isotherm in platform-like regions near selector–root connections. Two kinds of vacancy-type defects, mono-vacancies and vacancy clusters, were determined in relation to the LABs and LAB-like defects. Only mono-vacancies appeared in the areas of undisturbed axial growth. Reasons for the creation of macroscopic LABs and LAB-like defects, and their relationships with vacancy-type defects were discussed.

On Consonance between a Mathematical Method for the CET Prediction and Constrained / Unconstrained Solidification

Abstract Some properties of the functions yielding from the temperature field have been employed as a tool to determine the structural zones’ localization in a large static steel ingot. Thus, a numerical simulation was performed to generate the temperature field converged subsequently into the thermal gradient field. As a result, the selection of a zone, in which a columnar into equiaxed structure transformation (CET) is expected, is possible. It is shown that the CET - zone is formed when the thermal gradient becomes temporarily constant. Moreover, the CET localization can be easily controlled / shifted by the mold thickness selection. Both temperature and thermal gradient fields were also calculated to predict mathematically the creation of some structural zones in the continuously solidifying brass ingot. The columnar structure resulting from the constrained growth seems dominant in these ingots. However, when the s/l interface rate and velocity of the liquidus isotherm movement are subjected to a separation then the birth of the equiaxed structure is to be expected. In the industrial practice, the following structural zones are evinced in a continuously cast brass ingot: chilled columnar grains-, (CC), fine columnar grains-, (FC), columnar grains-, (C), equiaxed grains zone, (E), and eventually the single crystal, (SC), situated axially. The current innovative method for the mathematical predictions of the CET appearance in the static ingot turns out also useful in the reproduction of the all mentioned structural zones’ localization. In particular, a study of the behavior of the velocity of the liquidus isotherm movement and thermal gradient changes versus solidification time delivers a precise information about these structural zones’ situation.

Effect of Processing Parameters and Shape of Blade on the Solidification of Single-Crystal CMSX-4 Ni-Based Superalloy

The effect of mold withdrawal velocity, heater and pouring temperatures and the thickness of blade root on the solidification parameters and shape of the liquidus isotherm as well as microstructure of single-crystal CMSX-4 nickel-based superalloy, manufactured by the Bridgman method, has been analyzed in the article. The temperature gradient G, solidification rate v and location of the liquidus isotherm were determined in relation to the radiation baffle on the basis of temperature measurements conducted in nine test points along the height of castings (140 mm) with different thicknesses of root (27, 15 and 7 mm) and withdrawal velocities of 3 and 5 mm/min. The increase of root thickness, relative to the airfoil, resulted in the rise of inhomogeneity of solidification parameters as well as the primary dendrite arm spacing and unsteady state solidification along the whole blade height. However, in the case of blade with constant thickness, the steady-state solidification was created at the distance of 65 to 130 mm from its base. The increase of mold withdrawal velocity caused the decrease of temperature gradient. However, the solidification rate was different from the mold withdrawal velocity, especially in the root and middle part of the airfoil. The increase of heater temperature resulted in a rise of temperature gradient and reduction of the curvature of the liquidus isotherm, whereas the pouring temperature did not affect the solidification parameters in the blade. Particularly unfavorable conditions of the solidification process could occur in the middle part of the airfoil and root because of the lowest value of G/v and the largest primary dendrite arm spacing.