Solidus Curves Research Articles

The Binary Alkali Nitrate and Chloride Phase Diagrams: NaNO3-KNO3, LiNO3-NaNO3, LiNO3-KNO3, and NaCl-KCl

LiNO3-NaNO3, LiNO3-KNO3, NaNO3-KNO3, and NaCl-KCl phase relations were formulated using the regular solution model to obtain desired compositions for their potential application as a heat transfer fluid. The simultaneous nonlinear equations formed were solved numerically using a contour plot technique in Matlab. An algorithm was developed to determine the real roots of the coupled nonlinear equations and subsequent phase diagrams were constructed. The phase diagrams were compared with those predicted using FactSage thermochemical package and literature data from experimental studies. The calculated NaNO3-KNO3 phase diagram shows that this system has a eutectic point at 0.5 mole fraction of KNO3 with a eutectic temperature of 220.85 °C, while the LiNO3-KNO3 system was found to have a eutectic point at 0.44 mole fraction LiNO3 at 137 °C. The LiNO3-NaNO3 system shows a eutectic at 0.524 mole fraction LiNO3 at 192.8 °C, and finally the NaCl-KCl system has a eutectic point at 0.48 mole fraction NaCl at 634 °C. The liquidus and solidus curves obtained fitted close against values obtained from the quasi-chemical model used in FactSage and experimental values from the literature. This study showed that the regular solution model combined with the contour plots approach can sufficiently describe the liquidus–solidus curves of the alkali binary nitrate and chloride systems and could be a useful method for predicting the phase diagrams for higher order alkali nitrates and chlorides.

Morphological Stability of the Solid–Liquid Interface during Melt Crystallization of Ca1–xSrxF2 Solid Solution

The stability function of the solid‒liquid interface for PbF2–CdF2 solid solution with respect to constitutional supercooling is calculated using the phase diagram of the system. The calculated curve is typical of the systems with continuous solid solutions, having minima points in the liquidus and solidus curves. This dependence can be used to estimate the technological parameters of the process which are required for growing crystals with the high optical quality.

Effect of macro- and micro-segregation on hot cracking of Inconel 718 superalloy argon-arc multilayer cladding

The hot cracking sensitivity dramatically increases because of the longitudinal macro-segregation of craters and the transverse macro-segregation of welding center in pre-layers. Statistical analysis of the total area, average size and Nb concentration of interdendritic low-melting point Laves phase, the Nb concentration of the γ phase in the dendritic core, and the arm spacing of different sub-regions was used to explore the effects of macro- and micro-segregation of Nb. Solidus and liquidus curves were used to determine the temperature at which solid and liquid phases coexist in different sub-regions, which were combined with Scheil equation curves to identify Nb sources and interlayer transfer, so as to develop a model for the molten pool of subsequent layers. This model explains the effect of transversal and longitudinal macro-segregation in the pre-layer on the Nb concentration of the melt pool of subsequent layers, the dynamic balance of the solidification interface and the relative area of Laves phase in the macro-segregated sub-region of the solidified metal.

Phase Equilibria in LiYF4–LiLuF4 System and Heat Conductivity of LiY1–xLu x F4 Single Crystals

Single crystals of LiY1–xLu x F4 (x = 0, 0.25, 0.5, 0.65, 0.9) solid solution were grown by Bridgman–Stockbarger technique. Melting points determined by DSC monotonically varied with composition from 831 to 841 K when x increased. Interval between liquidus and solidus curves is not larger 1°C. This feature extremely favors to the growth of homogeneous single crystals from melt. Heat conductivity (κ) of solid solution is lower than that of LiYF4 and LiLuF4 components. In the region 0.25 ≤ x ≤ 0.65 at 300 K, κ = 4 ± 0.1 W/(m K).

Partition of metallic cations between aqueous solutions and mixed crystals of hydrated cobalt and nickel nitrates: Modelling of the influence of temperature and composition

Abstract A systematic study of the solid-liquid equilibria of the H2O-Co(NO3)2-Ni(NO3)2 ternary system enabled to define the liquidus and the solidus curves of the isotherms at 287.15 K and 313.5 K. Two widespread solid solutions, Co(1-σ)Niσ(NO3)2.6H2O and Ni(1-ω)Coω(NO3)2.6H2O, were observed. They were formed by the substitution of Co2+ cations by Ni2+ cations in the monoclinic structure of the cobalt nitrate hexahydrate and the substitution of Ni2+ by Co2+ in the triclinic structure of the nickel nitrate hexahydrate. Two series of tie-lines for each crystallographic structure of these hexahydrates were obtained. The analyses of these tie-lines and those of the previous studies at 258.15 K and 303.15 K enabled a thermodynamic modelling of the solid-liquid equilibria within a temperature range from 258.15 K to 313.15 K. The simple equation system obtained allows to calculate the accurate composition of the mother solution, at a defined temperature, to reach the appropriate cationic ratio in the crystallised solid solution.

The melting of subducted banded iron formations

Banded iron formations (BIF) were common shelf and ocean basin sediments 3.5–1.8 Ga ago. To understand the fate of these dense rocks upon subduction, the melting relations of carbonated BIF were determined in Fe–Ca–(Mg)–Si–C–O2 at 950–1400 °C, 6 and 10 GPa, oxidizing (fO2 = hematite–magnetite, HM) and moderately reducing (fO2∼CO2-graphite/diamond, CCO) conditions. Solidus temperatures under oxidizing conditions are 950–1025 °C with H2O, and 1050–1150 °C anhydrous, but 250–175 °C higher at graphite saturation (values at 6–10 GPa). The combination of Fe3+ and carbonate leads to a strong melting depression. Solidus curves are steep with 17–20 °C/GPa. Near-solidus melts are ferro-carbonatites with ∼22 wt.% FeOtot, ∼48 wt% CO2 and 1–5 wt.% SiO2 at fO2∼HM and ∼49 wt.% FeOtot, ∼20 wt% CO2 and 19–25 wt.% SiO2 at fO2∼CCO.At elevated subduction geotherms, as likely for the Archean, C-bearing BIF could melt out all carbonate around 6 GPa. Fe-rich carbonatites would rise but stagnate gravitationally near the slab/mantle interface until they react with the mantle through Fe–Mg exchange and partial reduction. The latter would precipitate diamond and yield Fe- and C-rich mantle domains, yet, Fe–Mg is expected to diffusively re-equilibrate over Ga time scales. We propose that the oldest subduction derived diamonds stem from BIF derived melts.

Melting relations in the Fe\u2013S\u2013Si system at high pressure and temperature: implications for the planetary core

The phase and melting relations in the Fe–S–Si system were determined up to 60 GPa by using a double-sided laser-heated diamond anvil cell combined with X-ray diffraction. On the basis of the X-ray diffraction patterns, we confirmed that hcp/fcc Fe–Si alloys and Fe3S are stable phases under subsolidus conditions in the Fe–S–Si system. Both solidus and liquidus temperatures are significantly lower than the melting temperature of pure Fe and both increase with pressure. The slopes of the Fe–S–Si liquidus and solidus curves determined here are smaller than the adiabatic temperature gradients of the liquid cores of Mercury and Mars. Thus, crystallization of their cores started at the core–mantle boundary region.

Czochralski growth of the mixed halides BaBrCl and BaBrCl:Eu

We present results from the growth of BaBrCl and BaBrCl:Eu single crystals, using the Czochralski method. Cubic inch crack-free crystals of both undoped and 5% Eu doped BaBrCl were obtained. The BaBr2–BaCl2 phase diagram was acquired by differential thermal analysis revealing that the system forms a solid solution at all concentrations with no significant separation between the solidus and liquidus curves. Details of the Czochralski process used to prevent cracking are presented. The scintillation performance of the Czochralski grown crystals is presented.

Stability of the solid–liquid interface under constitutional undercooling in the crystal growth of TlCl–TlBr and TlBr–TlI solid solutions

Using phase diagram data for the TlCl–TlBr and TlBr–TlI systems, we have calculated the stability functions of the solid–liquid interface under constitutional undercooling for solid solutions of these systems. The curves thus obtained are typical of systems containing continuous series of solid solutions and having minima in their liquidus and solidus curves. The curves can be used to evaluate technologically important process parameters necessary for the growth of crystals of high optical quality.

Thermodynamic modeling of the UO2–CaO phase diagram

A thermodynamic modeling of the UO2–CaO phase diagram was performed with experimental data available in the literature. A relatively simple approach is used to model the solution phases, which are treated as the regular and the sub-regular solutions of the end-members. A consistent set of optimized interaction parameters was derived for describing the Gibbs energy of each phase in this system leading to a good fit between calculation and experimental data. A tentative phase diagram was presented by calculating the liquidus, solidus, and solvus curves. Also, the lattice stabilities and the activities of each component were evaluated from the present thermodynamic modeling.

The liquidus surface of the Cr–Al–Nb system and re-investigation of the Cr–Nb and Al–Cr phase diagrams

The liquidus surface and corresponding reaction scheme of the ternary Cr–Al–Nb system were determined experimentally. The solidification paths of a series of more than 40 ternary alloys were deduced from investigation of their as-cast microstructures and measurement of all reaction temperatures applying scanning electron microscopy (SEM), electron probe microanalysis (EPMA), X-ray diffraction (XRD), and differential thermal analysis (DTA). The hexagonal C14-type Laves phase Nb(Cr,Al)2, which is not stable in any of the binary boundary systems and which is the only ternary compound, forms the most extended primary crystallization field of the ternary system dominating the centre of the liquidus surface. A ternary eutectic was found near the Al–Nb boundary composed of the three intermetallic phases C14+Nb2Al+NbAl3. Besides the ternary liquidus surface, the solidus and liquidus curves of the Cr–Nb boundary system and of the Cr-rich part of the Al–Cr system were determined resulting in revised binary phase diagrams.

Melting and Phase Relations of Carbonated Eclogite at 9-21 GPa and the Petrogenesis of Alkali-Rich Melts in the Deep Mantle

The melting and phase relations of carbonated MORB eclogite have been investigated using the multi-anvil technique at 9–21 GPa and 1100–1900°C. The starting compositions were two synthetic mixes, GA1 and Volga, with the CO2 component added as CaCO3 (cc): GA1 + 10%cc (GA1cc) models altered oceanic crust recycled into the convecting mantle via subduction, and Volga + 10%cc (Volga-cc) models subducted oceanic crust that has lost some of its siliceous component in the sub-arc regime (GA1 minus 6·5 wt % SiO2). The subsolidus mineral assemblage at 9 and 13 GPa includes garnet, clinopyroxene, magnesite, aragonite, a high-pressure polymorph of TiO2 (only at 9 GPa) and stishovite (only at 13 GPa). At 17–21 GPa clinopyroxene is no longer stable; the mineral assemblage consists predominantly of garnet with subordinate magnesite (only at 17 GPa), Na-rich aragonite, stishovite, Ca-perovskite (mostly at 21 GPa), and K-hollandite (mostly at 17 GPa). Na-carbonate with an inferred composition (Na,K)2(Ca,Mg,Fe)(CO3)2 was present in Volga-cc at 21 GPa and 1200°C. Diamond (or graphite) crystallized in most runs in the GA1cc composition, but it was absent in experiments with the Volga-cc composition. In Volga-cc, the solidus temperatures are nearly constant between 1200 and 1300°C over the entire pressure range investigated. In GA1cc, the solidus is located at similar temperatures at 9–13 GPa, but at higher temperatures of 1300–1500°C at 17–21 GPa. The difference in solidi between the GA1cc and Volga-cc compositions can be explained by a change in Na compatibility between 13 and 17 GPa as omphacitic clinopyroxene disappears, resulting in the formation of Na-carbonate or Na-rich melt in Volga-cc. The solidus temperature in GA1cc also increases with increasing pressure as a consequence of carbonate reduction and diamond precipitation, possibly brought on either via progressive Fe2+–Fe3+ transition in garnet at higher pressures or by a decrease of the activity of the diopside component in clinopyroxene. The low-degree melts are highly alkalic (K-rich at 9–13 GPa and Na-rich at 17–21 GPa) carbonatites, changing towards SiO2-rich melts with increasing temperature at constant pressure. The solidi of both compositions remain higher than typical subduction pressure–temperature (P–T) profiles at 5–10 GPa; however, at higher pressures the flat solidus curve of carbonated eclogite may intersect the subduction P–T profile in the Transition Zone, where carbonated eclogite can produce alkali- and carbonate-rich melts. Such subduction-related alkali-rich melts can be potential analogues of kimberlite and carbonatite melt compositions and important agents of mantle metasomatism and diamond formation in the Transition Zone and in cratonic roots. Melting of carbonated eclogite produces a garnet-bearing refractory residue, which could be stored in the Transition Zone or lower mantle.

Defect structure and the phase diagram of uranium dioxide

Positions of the phase boundaries of pure uranium dioxide UO2 − x are calculated under the assumption that damage (melting) of the crystal lattice is caused by filling it with defects. The conditions of complete filling of the crystal lattice with individual defects are analyzed. The equilibrium reaction rate constants are determined for the high-temperature forms of interaction of the crystal with oxygen of ambient gaseous medium. The position of the monotectic point is found for x > 0. The melting point parameters are determined for stoichiometric uranium dioxide and uranium dioxide with the maximum dense packing of the defects. A retrograde behavior of the solidus curve in the region x > 0 and anisotropy of properties near the point of congruent melting are predicted. The complex character of the behavior of the boundaries of U4O9 and U3O8 phases is explained. The reason of discrepancy between the results of two different measurements of solidus temperature in the region x < 0 is explained qualitatively, and the possibility of the existence of solid uranium dioxide up to 3400 K under certain conditions is predicted.

Berthollide formation conditions

Possible routes to generate berthollide phases are considered, specifically, via the separation of part of a component-based solid solution due to morphotropic transitions and as a result of the intersection of the binodal line with the solidus curve. Particular example phase diagrams are given for binary systems containing berthollides. Experimental data on berthollide phase formation in systems of MF2-RF3 and NaF-RF3 (where R stands for rare-earth elements) are summed up.

Experimental and Thermodynamic Studies of the Fe–Si Binary System

Phase equilibria in the Fe–Si binary system were investigated experimentally and thermodynamic assessment was carried out. The αFe (A2) + αFe3Si (D03) two-phase microstructures at 600°C and 650°C were obtained, whose grain sizes were sufficiently coarsened to be analyzed by FE-EPMA with a spatial resolution below 0.5 μm under the condition of 6 kV accelerating voltage. α'FeSi (B2) + αFe3Si (D03) two-phase equilibria above 700°C were detected for the first time and equilibrium compositions were determined by the diffusion couple method. The horn-shaped two-phase miscibility gap extends from the low temperature αFe + αFe3Si equilibrium along the B2/D03 second-order transition boundary and closes below 1000°C. Four-sublattice split compound energy formalism was applied to calculate the Gibbs energy of the bcc phases, A2(αFe), B2(α'FeSi) and D03(αFe3Si), and the thermodynamic parameters in the Fe–Si binary system were evaluated. Equilibrium relations in the binary system were well reproduced, especially the effect of the B2 and D03 ordering on the liquidus and solidus curves and the miscibility gap between bcc phases. Optimized thermodynamic parameters as well as the experimental results are expected to be helpful for developing higher multi-component systems for practical steels.

A thermodynamic analysis of native point defect and dopant solubilities in zinc-blende III–V semiconductors

A thermodynamic model is used to analyze available experimental data relevant to point defects in the binary zinc-blende III–V compounds (Ga,In)-(P,As,Sb). The important point defects and their complexes in each of the materials are identified and included in the model. Essentially all of the available experimental data on dopant solubility, crystal density, and lattice parameter of melt and solution grown crystals and epilayers are reproduced by the model. It extends an earlier study [Hurle, J. Appl. Phys. 85, 6957 (1999)] devoted solely to GaAs. Values for the enthalpy and entropy of formation of both native and dopant related point defects are obtained by fitting to experimental data. In undoped material, vacancies, and interstitials on the Group V sublattice dominate in the vicinity of the melting point (MP) in both the phosphides and arsenides, whereas, in the antimonides, vacancies on both sublattices dominate. The calculated concentrations of the native point defects are used to construct the solidus curves of all the compounds. The charged native point defect concentrations at the MP in four of the six materials are significantly higher than their intrinsic carrier concentrations. Thus the usually assumed high temperature “intrinsic” electroneutrality condition for undoped material (n=p) is not valid for these materials. In GaSb, the GaSb antisite defect appears to be grown-in from the melt. This contrasts with the AsGa defect in GaAs for which the concentration grown-in at the MP is negligibly small. Compensation of donor-doped material by donor-Group III vacancy complexes is shown to exist in all the compounds except InP where Group VI doped crystals are uncompensated and in InSb where there is a lack of experimental data. The annealing effects in n+ GaAs, including lattice superdilation, which were shown in the earlier paper to be due to Group III vacancy undersaturation during cooling, are found to be present also in GaSb and InAs. Results for native point defects are compared with reported “first principles” calculations for GaAs. It is seen that, while there is some accord with experimental findings for low temperature molecular beam epitaxial (MBE) growth, they fail totally to predict the behavior under high temperature growth conditions. The analysis of data on liquid phase epitaxy (LPE) growth of GaAs from Bi solution in the earlier paper has been re-calculated in the light of experimental data that showed that the model used in that paper to represent the Ga–As–Bi phase equilibria was inadequate. An improved model reveals that Ga vacancies exert a greater effect in controlling the extent of the linear range of donor dopant solubility than previously predicted. It has also led to a re-evaluation of the equilibrium EL2 and Ga vacancy concentrations in GaAs during MBE growth under As-rich conditions at low temperatures (∼500 K). The amended model predicts that the very high concentrations of EL2 and of Ga vacancies observed experimentally are near equilibrium values. The predicted increase in the equilibrium concentrations of these defects at low temperatures results from coulombic attraction between the two defects. At temperatures somewhat lower than 500 K the rate of increase becomes catastrophic.

Phase equilibria in binary subsystems of urea–biuret–water system

Joint results of the differential scanning calorimetry (DSC) and thermogravimetry (TG) experiments were the basis for the fusion enthalpy and temperature determination of the biuret (NH2CO)2NH (synthesis by-product of the urea fertilizer (NH2)2CO). Recommended values are Δm H = (26.1 ± 0.5) kJ mol−1, T m = (473.8 ± 0.4) K. The DSC method allowed for the phase diagrams of “water–biuret,” “water–urea,” “urea–biuret” binary systems to be studied; as a result, liquidus and solidus curves were precisely defined. Stoichiometry and decomposition temperature of the biuret hydrate identified, composition of the compound in “urea–biuret” system was suggested.

Physical properties of (1−x)K0.5Na0.5 NbO3–(x/5)NaK2Li2Nb5O15 composite ceramics

Alkaline niobate ANbO3 (A=K, Li and Na) ceramics were fabricated into the composites of K0.5Na0.5NbO3 (KNN) and NaK2Li2Nb5O15 (NKLN) phases. The NKLN phase was composed of completely filled tetragonal tungsten-bronze and LiNbO3 structures. The (1−x)KNN–(x/5)NKLN composite ceramics displayed alloy effects with changing x. The NKLN phase was expected to be solidified into the KNN phase through the liquidus–solidus curve of the (1−x)KNN–(x/5)NKLN composite ceramics. The (1−x)KNN–(x/5)NKLN composite ceramics showed the ferroelectric distortions with orthorhombic symmetry. We discussed the ferroelectric and dielectric properties of the (1−x)KNN–(x/5)NKLN composite ceramics.

The solidus of carbonated eclogite in the system CaO–Al2O3–MgO–SiO2–Na2O–CO2 to 32 GPa and carbonatite liquid in the deep mantle

Melting phase relations have been determined in a model carbonated eclogite (5wt.% CO2) at 10.5–32.0GPa and 1300–1850°C. The assemblage of silicate minerals coexisting with partial melts changes with pressure from garnet–omphacite–kyanite–stishovite at 10GPa via garnet–corundum–stishovite at 16–20GPa to Mg–perovskite–Ca–perovskite–CF phase–stishovite at 27–32GPa. Magnesite is the only carbonate stable in this system through the studied pressure range. The solidus temperature was defined by the appearance of partial melt. The solidus of carbonated eclogite is bracketed at 1380–1460°C at 10.5GPa, 1460–1560°C at 16.5GPa, 1530–1630°C at 20GPa, and 1600–1790°C at 27 and 32GPa. The slope of solidus curve is less steep at 10–32GPa than at lower pressures. The solidus curve of Fe-free carbonated eclogite roughly coincides with an average mantle geotherm. Partial melts formed by melting of carbonated eclogite at 10.5–32.0GPa have magnesiocarbonatite compositions with Ca/Mg ratios higher than in similar melts in peridotite assemblages, and contain high Na2O-contents. It has been demonstrated that carbonatite-like melt can be generated by partial melting of carbonated eclogites at pressure up to at least 32GPa, i.e. to lower mantle depths.

Studies on the phase diagram of CaCl 2–CaBr 2 system

A study on pseudo-binary CaCl 2–CaBr 2 system was carried out using differential thermal analysis (DTA) technique covering the complete composition range of the constituents between room temperature and 1073 K. From the DTA results the contour of solidus and liquidus temperatures with composition are plotted and the phase diagram of CaCl 2–CaBr 2 system is constructed. The solidus and liquidus curves exhibit a minimum at 971 K and at a composition of 56.5 mol% CaBr 2. Below 971 K, the system exhibits complete solid solution. Long-term equilibration of samples of several compositions was carried out at 923 and 673 K and the phases were characterized by XRD. The XRD results supported solid solution formation in the CaCl 2–CaBr 2 system between 673 and 923 K.