Liquidus Isotherms Research Articles

Directional and single-crystal solidification of Ni-base superalloys: Part I. The role of curved isotherms on grain selection

The development of crystallographic texture during directional solidification has been quantitatively analyzed in columnar castings of the Ni-base superalloys, CMSX4 and CM186LC, produced with a range of cooling rates and liquidus front curvatures. It is proposed that the more diffuse crystallographic texture developed in CMSX4 relative to CM186LC results from a combination of the differing local orientation stability condition and the alloys’ solidification characteristics. The implications of these additional factors on the evolution of the axial grain texture, the grain orientations produced in singlecrystal processing, and the stability of spurious grains in processing CMSX4 are discussed. An experimental method is presented to quantitatively analyze the grain selection process in the case of curved liquidus isotherms by retaining the stereology of the primary 〈001〉 dendrite growth direction and the local thermal gradient vector. This can account for the stability of spuriously nucleated edge grains in a single-crystal matrix.

Using tert-Butyl Alcohol as an Adductive Agent for Separation of an m-Cresol and 2,6-Xylenol Mixture

The solid−liquid equilibrium (SLE) phase boundaries of the ternary mixture of m-cresol, 2,6-xylenol, and tert-butyl alcohol and those of the three constituent binary mixtures were experimentally determined by means of the solid-disappearance method. Each of the m-cresol + 2,6-xylenol and tert-butyl alcohol + 2,6-xylenol mixtures exhibits one eutectic point, whereas the m-cresol + tert-butyl alcohol mixture exhibits one congruent point and two eutectic points. The approach proposed by Ott and Goates (J. Chem. Thermodyn. 1983, 15, 267) was used to represent the melting point temperatures as functions of the mole fraction of one of the components. The formulation developed by Stoicos and Eckert (Chem. Eng. Sci. 1987, 42, 1137) for SLE calculations was used with the NRTL activity coefficient model of Renon and Prausnitz (AIChE J. 1968, 14, 135) to correlate the experimental data for the binary systems. On the basis of the information presented in the phase diagram, which shows all the eutectic and congruent points and the liquidus isotherms for the ternary system, two conceptual possible processes involving the use of tert-butyl alcohol as the adductive agent for separating a mixture of m-cresol and 2,6-xylenol are proposed.

Dissolution origin and syn-entrapment compositional change of melt inclusion in plagioclase

In the system Di–Ab–An–H 2O, melt inclusions in plagioclase were reproducibly formed in a series of partial dissolution experiments, and the compositional differences from the surrounding matrix melt were evaluated. At 200 MPa and 1050−−1150°C, a seed crystal of An 59 was partially dissolved into the matrix melt, which was in equilibrium with more calcic plagioclase than the seed. The reaction proceeded inward from the crystal surface by a dissolution and recrystallization process to form a reaction zone composed of melt channels and recrystallized calcic plagioclase. The melt channels were choked (necked) off by the recrystallized plagioclase at the crystal surface to create melt inclusions. The experimentally formed inclusions, having square and zigzag shapes up to a few tens of micrometers in size, are similar in texture to some common types of natural melt inclusion. Since the partial dissolution of phenocrysts can occur during various magma mixing processes, it should be taken into consideration as one of the inclusion formation mechanisms when trying to interpret information from natural melt inclusions, especially for those in hydrous arc magmas. The chemical composition of the reproduced melt inclusions deviates from the matrix melt basically along the plagioclase liquidus isotherm. The molar ratio of Ca/(Ca + Na) and the MgO concentration in the synthesized melt inclusion are up to 17 and 61% (relative) lower than those in the matrix melt, respectively. This compositional difference is caused by a combination of factors: (1) supersaturation with dissolved plagioclase component; (2) insufficient diffusive homogenization in the melt channels due to rapid dissolution of plagioclase; and (3) the choking-off effect. On the basis of the experimental results, a model for diffusion in a growing melt channel in dissolving plagioclase was constructed which revealed that the concentration of incompatible elements with low diffusivities can be significantly lower in the melt inclusions than that in the matrix melt. These results demonstrate the importance of petrography for interpretation of inclusion data and of more experimental studies on melt inclusion origin.

Nucleation-controlled microstructural development in Al-Si alloys

When surface melting is conducted in a scanning mode, rapid resolidification can result in the loss of epitaxial regrowth. A columnar or epitaxial regrowth develops under the condition of low interfacial undercooling. At high beam scan velocities of several m s −1 or more, and/or for concentrated alloys, the lag of the solidification front behind the liquidus isotherm may be substantial and thus may allow for the nucleation of new grains within the undercooled liquid. The transition from constrained growth to nucleation control of microstructural evolution has been revealed in the solidification of laser-remelted Al-26wt.%Si alloys. An analysis of the transition has been formulated based upon the limiting solidification interface temperature at the transition and a heterogeneous volume nucleation model. The nucleation kinetics analysis indicates that the nucleation of primary silicon restricts the domain of the coupled eutectic zone for silicon compositions greater than 20 wt.%.

High Quality GaAs Epitaxial Layers Grown from Ga–As–Bi Solutions by Liquid Phase Epitaxy

The liquidus isotherms for the Ga–As–Bi system were determined at 973 and 923 K in the Ga–As–GaAs region. The liquid phase epitaxial growth of GaAs from Ga–As and Ga–As–Bi solutions were investigated. The addition of ten atomic percent of Bi to the Ga–As solution increase the growth rate of the grown epilayers nearly 4.4 times than in the case of GaAs layers from Bi solution. Above 9 at.% of Bi in Ga solution the problems associated with the edge growth were almost eliminated. Optical measurements at 4.2 K revealed that Bi does not alter the band gap energy value of the GaAs epitaxial layers. The photoluminescence (PL) intensity and full width at half maximum (FWHM) revealed the good quality of undoped GaAs epilayers from Bi solvents compared to that of Ga solvents even though the purity of the Bi was relatively less.

A scaling analysis of the unidirectional solidification of a binary alloy

A scaling analysis of the conservation equations for momentum, heat and species transport inside the solidifying mushy zone of a binary alloy is performed to examine systematically common assumptions and predict general behavior of the mixture during freezing. Several terms in the momentum equation are found to be negligible throughout the solidifying domain, and the use of D'Arcy's law to approximate the momentum equations in the mushy zone is found to be valid except in the region near the liquidus isotherm. A criterion is developed to define this region, and the dependence of the streamfunction and buoyancy driven velocity on material properties and fraction solid is determined. The energy equation is examined to provide scaling laws for the mushy zone and solid region thicknesses, as well as the transient chill wall temperature. Advection is shown to dominate solute transport throughout the mush, although, in the denser regions of the solid-liquid region, liquid velocities are so small as to have a negligible effect on macrosegregation. Numerical calculations performed for Pb-Sn and Al-Mg alloys at different cooling rates confirm trends suggested by the scaling analysis.

Inhomogeneities in single-crystal components

The temperature distribution during single-crystal solidification of the Ni-based superalloys SRR99 and CMSX-6 by the Bridgman process was measured at various withdrawal rates in dummy turbine blades. Asymmetric heat flux and cross-section transients influence the geometrical formation of the liquidus isotherm and consequently of dendritic growth. The probability of the formation of structural inhomogeneities such as microporosity, zebras, mosaic structures, etc. is largely dependent on the curvature of the solidification front, which in turn depends on the geometrical arrangement of the ceramic cluster and on the withdrawal rate. The proneness to recrystallization during γ′ solutioning at cross-section transients due to casting-induced deformation and misaligned dendrites was also examined. Recrystallization remains confined to highly deformed areas as long as microscopic inhomogeneities acting as obstacles are present during heat treatment. High cycle fatigue tests showed that defects such as porosity and local recrystallization reduce the fatigue strength to about half the fatigue strength of the defect-free materials.

Microsegregation of Silicon in Iron-Carbon Alloys

Residual microsegregation of silicon in hypoeutectic Fe-C alloys was shown to depend on the ratio of silicon to carbon. Concentration regions where direct and inverse microsegregation of silicon develops were established experimentally in the Fe-C-Si system. The behaviour of the third component changes in a similar manner in other systems, featuring a positive slope in the liquidus isotherms such as Fe-C-AI, Fe-C-Cu, and Fe-C-Ni. The concepts of para- and meta- equilibrium are defined, it being shown how geometric thermodynamic methods were employed to establish the equilibrium of the liquid and solid phases which was chosen as the criteria for describing the absence of silicon microsegregation in an alloy. X-ray spectrum analysis of the micro-segregation zones revealed that rules of dendritic segregation established for ternary alloys are applicable to real multi-component Fe-C alloys containing Si, Al, Cu and Ni within the range which is typical for unalloyed steels and irons. The peculiarities of silicon eutectic segregation, in relation to the valley geometry of double eutectics having stable and metastable phases, were considered. Finally, the microsegregation effect of major components, primarily silicon and manganese, on the formation of both structure and properties of irons and unalloyed steels is discussed.

Ga-As-Bi phase equilibrium study by LPE for thin solutions

Mixed solvents such as Ga+Bi are used to improve GaAs epilayer surface morphology and the growth control. Liquid phase epitaxy was carried out for the mixed solutions of 1.4 mm thickness. Substrates and reagents were placed in a graphite cassette. The growth was performed in an open quartz tube reactor in a resistive furnace under hydrogen atmosphere. Growth kinetics was studied for GaAs epitaxy. The liquidus isotherms for the Ga-As-Bi system were determined for T = 1013 K and T = 1073 K in the Ga-As-GaAs region. The average liquidus slope was determined for the investigated region along the arsenic diffusion coefficient D L As as a function of temperature and Bi content in the solution. The surface morphology was improved for layers grown from the mixed solutions in comparison with those from gallium solutions. Precise control of the epilayer thicknesses was achieved.

Effects of simplified enthalpy relations on the prediction of heat transfer during solidification of a lead-tin alloy

An investigation into the effects of enthalpy functions that vary with both concentration and temperature on the prediction of heat transfer during solidification using a volume-averaged mixture energy equation is presented. Results are presented for the solidification of a Pb-20 wt.% Sn alloy in a semi-infinite domain using both the Lever Rule and Scheil models to relate temperature and volume fraction. The effects of simplifying the enthalpy relations so that the derivatives of the phase enthalpies with respect to temperature and concentration are constant or zero are examined. The resulting predictions all underestimate the movement of the eutectic and liquidus isotherms in comparison with fully variable enthalpy terms. The additional simplifications of linearizing the phase diagram and using the same properties for the α-phase and eutectic solids introduce a small improvement in the predictions. In addition, the consequences of neglecting the effects of microscopic concentration profiles in the solid on the solid enthalpy are investigated, and the resulting predictions overestimate the movement of the eutectic and liquidus isotherms. The results should serve as an estimation of the magnitude of the differences in the modelling of heat transfer during solidification introduced by simplifying the enthalpy relations or ignoring microscopic concentration variations within the solid.

Determination of the liquidus lines and isotherms of the Hg-Zn-Te system by a modified direct observation method

The modified direct observation method is employed for the determination of the liquidus lines in the (Hg1_xZnx)1_yTey, ternary system. The liquidus temperatures of the ternary samples of various compositions withx from 0.05 to 0.30 andy from 0.5 to 0.9 are measured. The temperature-composition phase diagrams and some liquidus isotherms are established for this system.

Evaluation of InAs solubility in the InAsSn system

A theoretical investigation of InAs solubility in a two-component solvent (indium plus tin) is performed. The liquidus isotherms for the InAsSn system are calculated in the temperature range 710–1010 K, the tin content in the solvent being varied from 0 to 0.9 mole fraction. The theoretical curves are compared with experimental data. The results show that the liquid phase of the InAsSn system can be considered to be a quasi-regular solution only for the 830–890 K temperature range.

Phase diagram of the AlInSb system

The phase equilibria between the liquid and compound phases in the AlInSb system were studied experimentally and thermodynamically. The liquidus isotherms were determined over the entire composition range by differential thermal analysis, and the solidus composition in the AlSbInSb pseudobinary was obtained by electron microprobe analysis. The phase diagram was calculated on the basis of these results together with the thermochemical data reported in the literature. It was found that a three-phase region composed of the AlSbInSb ternary crystal and two molten phases appears in the AlIn-rich region below 750 °C.

Synthetic fluid inclusions: VIII. Vapor-saturated halite solubility in part of the system NaCl-CaCl 2-H 2O, with application to fluid inclusions from oceanic hydrothermal systems

Halite solubility along part of the vapor-saturated liquidus in the system NaCl- CaCl 2- H 2 O has been determined using the synthetic fluid inclusion technique. Data allow the construction of liquidus isotherms for temperatures up to 500°C and bulk compositions containing >60 wt% total salt and as much as 25 wt% CaCl 2. Combined with previous data for the binary system NaCl- H 2 O and for the ternary system NaCl- CaCl 2- H 2 O in the low-salinity, low-temperature region, a preliminary ternary phase diagram can be constructed that remains incomplete only in the CaCl 2-rich region. Results are applied to the interpretation of saline fluid inclusions from quartz veins in oceanic metagabbros, and can be applied to many other natural inclusions containing aqueous solutions with NaCl and CaCl 2 the dominant solutes. Microthermometric measurements at equilibrium of the melting temperature of ice [ Tm (ice)] and of the dissolution temperature of halite [ Tm (halite)] are sufficient to determine the bulk composition of the NaCl- CaCl 2- H 2 O fluid.

The phase diagrams of the pseudobinary Nd-(Fe<inf>14</inf>B) and the Fe-Nd-B ternary system

A pseudobinary phase diagram of the Nd- (Fe14,B) system and liquidus isotherms in the Nd 2 Fe 14 B(T 1 ) primary field of the Fe-Nd-B ternary system were determined by DTA, XRD, metallography and EDX techniques. The peritectic region for the appearence of T 1 phase is in the range of 3 % to 40 % Nd for the pseudobinary system, and hence part of the liquidus projection in the Fe-Nd-B ternary system is modified. It was found that there exists a homogeneity range for Nd in T 1 phase above 1000°C. It was determined to be 0.6, 1.0 and 1.5 at% Nd at 1000°C, 1090°C and 1145°C, respectively. A composition triangle of Fe-T 1 -T 2 (Nd 1.1 Fe 4 B 4 ) instead of Fe-T 1 -Fe 2 B at 1090°C was identified.

Some general properties of the liquidus surface of a “pseudobinary” solid solution (A 1 − uB u) 1 − δC 1 + δ

A ternary A-B-C system forming a narrow homogeneity-range solid solution (A 1 − u B u ) 1 − δC 1 + δ with congruently melting end members is considered. Two properties of the liquidus isotherms are proven that are independent of the detailed thermodynamic behavior of the liquid or solid solution phases. These are (1) the liquid coexisting with a solid of fixed u-value at its solidus temperature contains 50 at.% of component C, and (2) only when the liquid is ideal does the liquidus in a section of constant atomic ratio B A have its maximum at 50 at.% C. The properties are illustrated for the ideal case.

A Study on LPE Growth of In1-xGaxP1-yAsy(y ≃0) on (100) GaAs Substrate

The growth conditions have been studied in detail for InGaPAs LPE layers grown on (100) GaAs substrates using the two-phase melt technique. The accurate liquidus isotherms and iso-concentration curves have been obtained experimentally and are compared with the calculated ones. It has been found that the area of the successful growth of InGaPAs on GaAs shifts according to the degree of supercooling. The influences of variations of the As atomic fraction in the liquid, XAsl, on the liquidus and solidus compositions have also been investigated in detail. The diffusion coefficients of P and Ga in an In-rich melt at 800°C have been determined as 1.9×10-4 and 1.8×10-4 cm2/s, respectively. The influence of the degree of supercooling on crystal growth is discussed using a mass transport analysis in both liquid and solid phases, together with the equilibrium phase diagram.

Substrate Orientation Dependence of the In‐Ga‐As Phase Diagram for Liquid Phase Epitaxial Growth of In0.53Ga0.47As on InP

The liquidus isotherms of the In‐Ga‐As system were determined at 600° and 700°C by the improved seed dissolution technique. From the results of the liquidus isotherms and the lattice‐constant measurements, the substrate orientation dependence of solution compositions to grow lattice‐matched layers on the (100), (111)A, and (111)B substrates by liquid phase epitaxy (LPE) was exactly obtained in the temperature range 600°–790°C. The solution compositions of Ga for the (111)A and (111)B faces are always larger than those for the (100) face over the entire temperature range 600°–790°C. The solution compositions of As for the (111)A and (111)B faces are always smaller than those for the (100) face over the entire temperature range 600°–790°C. In order to study effects of the surface free energy on the In‐Ga‐As phase diagram which was determined by using the LPE method, the In‐Ga‐As phase diagram was calculated, for the first time, by adding the surface free energy to the chemical free energy of the solid phase. According to the calculated phase diagram, the composition of Ga in the solution to obtain the (111) oriented is smaller than the composition of Ga in the solution to obtain the (100)‐oriented . This tendency of the calculated results is contrary to the experimental results. That is to say, the difference in the surface free energy is not a main reason for the substrate orientation dependence of the In‐Ga‐As phase diagram.

Liquid phase epitaxial growth conditions of lattice-matched In 1- xGa xAs 1- yP y layers on (111)A and (111)B InP

Liquidus isotherms of the In-Ga-As-P quaternary system were determined at 650 and 700°C. On the basis of these, liquid phase epitaxial (LPE) growth conditions of lattice-matched In 1- x Ga x As 1- y P y layers on (111)A and (111)B InP were determined. Using these LPE growth conditions, lattice-matched In 1- x Ga x As 1- y P y layers can be grown on (111)A InP at 650 and 700°C and on (111)B InP at 700°C over the entire compositional range of the quaternary alloy.

Phase diagram and LPE growth rate in the Ga-As-Sn system

Liquidus isotherms of the Ga-As-Sn system have been measured and calculated. The experiments were carried out in the LPE domain, at 1073 K on the Ga side. The calculations using the available thermodynamic properties of the boundary systems Ga-As and Ga-Sn, provide a good description of the entire phase diagram. Then, the LPE growth rate of GaAs in this ternary system has been experimentally determined for 0 ≤ x Sn ≤ 0.8. These results have been analysed on the basis of a diffusion limited growth model using our phase diagram data. So, the values of the As diffusion coefficient in the GaSn melts were estimated to be equal to 4.4 (1 + 0.82 x L Sn) 10 -5 cm 2 s -1.