Liquidus Curves Research Articles

New correlative method of thermodynamic analysis of the inorganic compounds

The present paper is the result of the fundamental thermodynamic study, which started with the experimental and review papers [1-5]. The main idea is based on the periodic law. The Russian scientist Kapustinsky established by calorimetry a linear relation between the enthalpies of formation and the logarithm of the total electrons’ number of the compounds for the first time. He called this relation “the rule of thermochemical logarithmics” [6]. We developed this rule and established a strict relation between the enthalpies of formation, the melting temperatures and the sum of A and B atomic numbers for isostructural A III B V phases of sphalerite and wurtzite types [3, 5]. We applied our model to develop the thermodynamic calculation of the properties for isostructural compounds. Every binary system A III -B V , apart from B-As system, has only one compound A III B V with a congruent melting point. Most of the known A III B V compounds crystallize in a cubic system, of the ZnS type, except the nitrides of aluminum, gallium, indium and thallium, which have a hexagonal cell, ZnS wurtzite type. Boron nitride (hBN) is isostructural to graphite under normal conditions, and its high-pressure modification (cBN) is of blend ZnS type above 10 GPa. The selection of A III and B V standard state is rather simple. Under standard conditions (P = 101325 Pa) at T = 298 K, all these elements are solid, but nitrogen which is a gas, while at some temperatures and pressures it may be solid. The experimental study of nitride systems is extremely complicated due to the fact that nitrogen gas is formed before its fusion. The liquidus curve depends on nitrogen pressure. It is necessary to maintain a nitrogen pressure between 6 and 10 GPa for nitrides [7]. It must be mentioned that nitrogen is solid at such pressures and at room temperature. The transition from solid to liquid takes place at T = 308 K and P = 2.8 GPa according to reference [8]. In view of the fact that phosphorus has ten forms allotropic forms [5] we selected the white phosphorus as standard state. According to obtained results the white form is more suitable for our correlation model. The relationship between the reduced enthalpies

Solvation phenomena and revision of solid–liquid equilibria in aqueous solutions of two precursors of mixed oxides, the hydrates of cobalt and nickel nitrates

The hydrates of cobalt and nickel nitrates are highly relevant as precursors for the preparation of mixed ceramics. In order to verify the numerous bibliographical data, systematic solubility measurements in aqueous medium under atmospheric pressure and a critical evaluation have been undertaken. By taking solvation phenomena into account, it has proved possible to correlate all the phenomena observed, to obtain equations representative of the liquidus curves, and to refine and extrapolate the experimental curves. The whole stable and metastable coordinates of the invariant transformations in both binary systems have been calculated or more accurately determined.

Thermodynamic analysis of solubility data 1: phase diagrams of systems salt hydrate + water

Solubility equilibria between solid salts, salt hydrates, and water have been analyzed on a thermodynamic basis. Fitting equations with three or four adjustable parameters suffice to describe the temperature dependence of solubility adequately when the latter is expressed in ionic (species) mole fractions. Phase diagrams, temperature versus mole fractions, summarize and deal concisely with equilibrium solubility properties of the systems. Comparison of experimental and estimated ratios of slopes to liquidus curves intersecting at isobaric invariants, such as, for example, eutectic or peritectic points, provides a thermodynamic consistency test.

Al-Bi-Sn (Aluminum-Bismuth-Tin)

The Al-Bi phase diagram depicts a liquid miscibility gap with the critical temperature at 1037 C. A monotectic reaction occurs at 658 C, where an Al-rich liquid L1 decomposes to (Al) and a Bi-rich liquid L2. The final solidification is at the Bi-end through the eutectic reaction at 270 C: L2 M (Al) + (Bi). The Al-Sn phase diagram is of the simple eutectic type, with the eutectic reaction at 228 C and 97.6 at.% Sn. The shape of the liquidus curve suggests the presence of a metastable liquid miscibility gap in the AlSn system. The Bi-Sn system is of the simple eutectic type, with the eutectic reaction at 139 C and 43 at.% Bi. See [Massalski2] for the above phase diagrams.

Experimental calibration of the effect of H2O on plagioclase crystallization in basaltic melt at 200 MPa

Crystallization experiments were conducted at 200 MPa to determine the effect of small amounts of H 2 O on the liquidus temperature of basaltic melts in which plagioclase is the liquidus phase. The H 2 O concentrations in the quenched glasses, determined by infrared spectroscopy and Karl-Fischer titration, ranged from 0.02 to 4.2 wt% H 2 O. The dry liquidus temperature at 200 MPa was estimated from experiments at 1 atm (H 2 O-free) and from the known pressure dependence of plagioclase crystallization temperature. The effect of water (expressed as wt% H 2 O) on the plagioclase liquidus temperature is nonlinear and diminishing with increasing melt H 2 O concentrations. According to our new experimental data, it can be empirically predicted with following equation: ( T DRY - T WET ) = 76.99 · C H 2 O 0.71 where C H 2 O is the water concentration in the melt (wt%), T DRY , and T WET are plagioclase crystallization temperatures in water-free and water-bearing systems, respectively. The relationship between C H 2 O and liquidus temperature worked out in this study is valid for a range of basaltic compositions, ranging from high-alumina basalts to basaltic andesites. The combination of the empirical equation predicting the liquidus depression of plagioclase with previous models predicting the olivine liquidus curve is useful to determine the liquidus temperature in various H 2 O-bearing basaltic systems in which either plagioclase or olivine is the liquidus phase.

Decompression-induced Crystallization in Hydrated Silica-rich Melts: Empirical Models of Experimental Plagioclase Nucleation and Growth Kinetics

Isothermal and isobaric crystallization of plagioclase in a water-saturated synthetic rhyolitic melt is investigated through time series of decompression experiments. The experimental variables are the rate at which samples are initially decompressed (30, 150, and 1200 MPa/h) from 200 MPa and 875°C, final pressure (25 to 160 MPa), and holding time at final pressure (up to 17 days). Through textural measurements of the crystals, plagioclase crystallization kinetics has been characterized in terms of nucleation lag and rates of nucleation and growth. Plagioclase crystallization is markedly dependent on effective undercooling, Teff, and holding time at crystallization pressure. With Teff increasing from 55 to 110°C, (i) nucleation lag decreases from 1-2 days to ~15 min, (ii) maximum nucleation rates increase from ~10-3 to 10-2 mm-2.s-1, and (iii) maximum growth rates decrease from ~10-6 to 5x10-7 mm.s-1. The initial decompression rate (30, 150, and 1200 MPa/h) has no systematic control on crystallization at final pressure, except for the 1200-MPa/h series in which samples show nucleation difficulties. From the experimental data of Teff-constrained plagioclase number density, proportion, and morphology, we provide means to assess conditions of nucleation and growth of natural plagioclase microlites from rapidly-ascended rhyolitic melts, through the determination of plagioclase liquidus curve and Teff prevailing during crystallization.

Solubility of ionic liquids in water and octan-1-ol and octan-1-ol/water, or 2-phenylethanol/water partition coefficients

The solubility of 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate, [EMIM][FAP] and 1-hexyl-3-methylpyridinium triflate, [HM3Py][CF3SO3] in octan-1-ol, water, and 2-phenylethanol have been determined at ambient pressure. A dynamic method was used over a broad range of mole fractions and temperatures from 270K to 360K. The immiscibility in the liquid phase with an upper critical solution temperature (UCST) was observed in ([EMIM][FAP]+octan-1-ol, or water). The complete miscibility in the liquid phase was observed for the binary system ([EMIM][FAP]+2-phenylethanol). The simple liquidus curves with complete miscibility in the liquid phase were observed for the binary systems ([HM3Py][CF3SO3]+1-octanol, or 2-phenylethanol) and with miscibility gap in water. The octan-1-ol/water, Kow and 2-phenylethanol/water, KPhw partition coefficients in ternary liquid-liquid phase equilibrium were determined for the systems {[EMIM][FAP], or [HM3Py][CF3SO3], or N-octylisoquinolinium bis{(trifluoromethyl)sulfonyl}imide, [OiQuin][NTf2] (1)+octan-1-ol (2) +water (3)} at temperature T=298.15K.

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.

Molecular dynamics simulations of gold-catalyzed growth of silicon bulk crystals and nanowires

Abstract

Liquidus of Silicon Binary Systems

Thermodynamic knowledge about liquid silicon is crucial for the production of solar-grade silicon feedstock from molten silicon. In the current study, liquidus for silicon binary alloys is formulated using a previously developed method in which the liquidus curve is calculated using two constants. The liquidus measurements for the silicon portion of the silicon alloys with Al, Ca, Mg, Fe, Ti, Zn, Cu, Ag, Au, Pt, Sn, Pb, Bi, Sb, Ga, In, Ni, Pd, Mn, and Rh are reviewed, and the consistent data were used to determine the liquidus constants. The liquidus curves for silicon binary systems are calculated and plotted. It is indicated that the calculated liquidus curves fit well with the experimental data. A correlation between the determined liquidus constants is also observed, which can be used to gain a better understanding of the thermodynamics of the silicon binary melts.

An isothermal (30 °C) study of heterogeneous equilibria in the sucrose (C 12H 22O 11)–calcium hydroxide (Ca(OH) 2)–water system

Solid–liquid equilibria in the C 12H 22O 11–Ca(OH) 2–H 2O system have been determined at 30 °C. Two phases C 12H 22O 11·3Ca(OH) 2 and C 12H 22O 11·2Ca (OH) 2 have been evidenced, and solubility (liquidus) curves have been determined. It is thus shown that these ternary phases exhibit incongruent solubilities at 30 °C. These solid phases were characterized using Infrared Spectroscopy (IR), Scanning Electron Microscopy (SEM) and Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES).

Solid−Liquid Equilibria in Fatty Acid/Triglycerol Systems

Used for biofuel production, fatty acids and their corresponding triglycerols are stored in most plants. At room temperature, saturated fatty acids and their triglycerols are solid, whereas unsaturated fatty acids and their triglycerols are liquid. Solid−liquid equilibrium data were measured for various binary systems of fatty acids and their triglycerols by differential scanning calorimetry. The freezing temperatures from liquidus curves for the binary systems containing tripalmitine were higher than those for systems containing palmitic acid. At the eutectic point, the melting temperatures for binary systems containing tripalmitine or palmitic acid were similar. The liquidus curves from the solid−liquid equilibrium data were compared with the predicted values obtained by using the LLE-UNIFAC model, and good agreement between the experimental and calculated results was found.

Solidus and liquidus profiles of chondritic mantle: Implication for melting of the Earth across its history

We investigated the melting properties of a synthetic chondritic primitive mantle up to core–mantle boundary (CMB) pressures, using laser-heated diamond anvil cell. Melting criteria are essentially based on the use of X-rays provided by synchrotron radiation. We report a solidus melting curve lower than previously determined using optical methods. The liquidus curve is found between 300 and 600 K higher than the solidus over the entire lower mantle. At CMB pressures (135 GPa), the chondritic mantle solidus and liquidus reach 4150 (± 150) K and 4725 (± 150) K, respectively. We discuss that the lower mantle is unlikely to melt in the D″-layer, except if the highest estimate of the temperature profile at the base of the mantle, which is associated with a very hot core, is confirmed. Therefore, recent suggestions of partial melting in the lowermost mantle based on seismic observations of ultra-low velocity zones indicate either (1) a outer core exceeding 4150 K at the CMB or (2) the presence of chemical heterogeneities with high concentration of fusible elements. Our observations of a high liquidus temperature as well as a large gap between solidus and liquidus temperatures have important implications for the properties of the magma ocean during accretion. Not only complete melting of the lower mantle would require excessively high temperatures, but also, below liquidus temperatures partial melting should take place over a much larger depth interval than previously thought. In addition, magma adiabats suggest very high surface temperatures in case of a magma ocean that would extend to more than 40 GPa, as suggested by siderophile metal–silicate partitioning data. Such high surface temperature regime, where thermal blanketing is inefficient, points out to a transient character of the magma ocean, with a very fast cooling rate.

Microstructure and Wear Properties of TiC/7075 Composites by <i>In Situ</i> Reaction Liquidus Curve Casting Method

7075 matrix alloy was fabricated by in-situ reaction liquidus curve casting method, and its as-cast microstructure was analyzed, the wear properties of these composites and matrix alloy were studied under the different conditions. The results show that the wear resistance of TiC/7075 composites is superior to 7075 matrix alloy in the same conditions (with same load or rotating velocity). Because of introduction of particle reinforcements, the wear resistance of the composite is enhanced by 1.5～4 times than that of its matrix. In addition, the wear mass loss of TiC/7075 composites increases almost with increase of load, but decreases with increase of rotating velocity. The wear resistance of the composites increases slightly at low load and high rotating velocity. The SEM analysis of the worn-out surface indicates that the wear mechanism of TiC/7075 composites is mainly abrasive wear.

Dy-Mn (Dysprosium-Manganese)

TheDy-Mnphasediagram in [Massalski2]was redrawn from [1967Kir]. [1994Oka] pointed out that the liquidus curves of the intermetallic compounds DyMn2; Dy6Mn23; and DyMn12 in this phase diagram appear to be unusually flat when they are extrapolated to their metastable congruent melting points. Figure 1 shows the Dy-Mn phase diagram calculated by [2009Wan]. This phase diagram is based on the same phase boundary data reported by [1967Kir], but the interpretation of the data points seems to be better because the problem described above was alleviated. Table 1 shows Dy-Mn crystal structure data quoted from [Massalski2]. The composition column has been modified for consistency with Fig. 1.

Evaluation of Softening, Shrinking and Melting Reduction Behavior of Raw Materials for Blast Furnace

To evaluate influences on the softening and melting behavior of blast furnace raw materials, the examinations of high temperature properties in various types of raw materials for blast furnaces were executed. Shrinking behavior before reaching approximately 1300°C is estimated by using softening viscosity taking into consideration pores of particles, and void ratio as well as liquid phase ratio of the layer. The softening viscosity of the solid phase of approximately 1010 Pa·s was obtained and the influence of the mineral species of the solid phase or temperature is small. Melting reduction sharply progresses through expanding the liquid phase deriving from FeO and gangue. And this behavior is affected with position of the reduction curve and the liquidus curve. Sinter forms a solid phase from FeO and gangue due to a rise of reduction degree according to melting reduction. This solid obstructs contact of the liquid phase including FeO with coke, which restricts the progress of melting reduction. On the other hand, with lumpy ore and pellet, melting reduction rapidly progresses without interruption, since no solid phase is formed even when FeO decreases due to melting reduction.

Liquidus Temperatures of Cryolite Melts With Low Cryolite Ratio

The effect of calcium fluoride on liquidus temperatures of the cryolite melts with a low cryolite ratio (CR) was studied. The systems KF-NaF-AlF3 and KF-LiF-AlF3 with CRs of 1.3, 1.5, and 1.7 have been investigated. The liquidus curves of systems containing CaF2 are different and depend on the K/(K + Na) and K/(K + Li) ratios. In potassium cryolite with CRs of 1.3 and 1.5, the calcium fluoride solubility is low and increases with NaF (LiF) concentration.

Melting point equations for the ternary system water/sodium chloride/ethylene glycol revisited

Partial phase diagrams are of considerable utility in the development of optimized cryobiological procedures. Recent theoretical predictions of the melting points of ternary solutions of interest to cryobiology have caused us to re-examine measurements that our group made for the ethylene-glycol–sodium chloride–water phase diagram. Here we revisit our previous experiments by measuring melting points at five ethylene-glycol to sodium chloride ratios (R values; R = 5, 10, 15, 30, and 45) and five levels of concentration for each ratio. Melting points were averaged from three measurements and plotted as a function of total solute concentration for each R value studied. The new measurements differed from our original experimental values and agreed with predicted values from both theoretical models. Additionally, the data were fit to the polynomial described in our previous report and the resulting equation was obtained: T m = ( 38.3 - 2.145 × 10 - 1 R ) w + ( 81.19 - 2.909 × 10 - 1 R ) w 2 , where w is the total solute mass fraction. This new equation provided good fits to the experimental data as well as published values and relates the determined polynomial constants to the R value of the corresponding isopleths of the three dimensional phase diagram, allowing the liquidus curve for any R value to be obtained.

Liquidus in the CO2 + and N2O + Hydrofluorocarbon Systems

The present paper summarizes and reinterprets the results for a series of measurements of solid−liquid equilibria for binary systems formed by carbon dioxide or nitrous oxide with a series of hydrofluorocarbons (fluoromethane, difluoromethane, trifluoromethane, pentafluoromethane, 1,1,1,2-tetrafluoroethane, 1,1,1-trifluoroethane, and 1,1-difluoroethane). All of the systems form eutectics. The contribution from heat capacity and activity coefficients to the liquidus courses represented by the Schröder equation were analyzed for each system included in the present study. The performed analysis showed that both mentioned contributions are small and, to a great extent, are mutually compensating each other and thus could be disregarded. The results showed that, for the systems under study, the liquidus curve down to the eutectic point may be represented by the Schröder equation involving two quantities only: the temperature at triple point and the enthalpy of fusion of the system components.

New intermetallic compounds in the Ce–Pt system

Abstract The Ce-rich part of Ce–Pt phase diagram has been investigated by means of differential thermal analysis (DTA), X-ray diffraction (XRD), optical and electron microscopy (SEM) and energy dispersive X-ray analysis (EDX). Two new intermediate phases, Ce5Pt3 and Ce5Pt4, have been discovered and found to crystallize with tetragonal Pu5Pd3-type structure and orthorhombic Ge4Sm5-type structure, respectively. All the Ce-rich compounds of the system were found to crystallize with a peritectic type formation. We have determined the temperatures of the peritectic plateaus and established the liquidus curves up to 1500 °C.