Section Of Phase Diagram Research Articles

Investigation of the effect of aluminum on the phase composition of Ti–Al–Nb–Mo gamma alloys

A quantitative analysis of the influence of aluminum concentration on the phase composition of TNM-type Ti–Al–Nb–Mo γ-alloys has been carried out using the Thermo-Calc software and experimental methods. Isothermal and polythermal sections of the corresponding phase diagram have been calculated; the critical temperatures of phase transformations in the alloys of the system, and the chemical compositions of phases formed in them (β, α, α2, γ) have been determined. The influence of the annealing temperature on the microstructure and phase composition of the alloys containing 43 and 40% Al has been studied.

Specific Features of Phase Formation and the Crystal Structures of Compounds in the Ternary Tm–Cu–Si System

The methods of X-ray phase diffraction and structural diffraction analyses and, partially, the method of microstructural analysis are used to study the phase equilibria in the ternary Tm–Cu–Si system and plot the isothermal section of the phase diagram of this system at 870°K. The existence of seven ternary compounds at this temperature, namely, Tm3Cu11Si4 , TmCu2Si2 , Tm6Cu8Si8, TmCuSi, TmCu0.5Si1.5 , TmCu0.39–0.09Si1.61–1.91, and TmCu0.05Si1.66 is established. It is shown that solely the TmCu2 binary compound dissolves 5 at.% Si. At the same time, we did not detect any noticeable solubility of the third component in the other binary compounds. The structural parameters are determined for the following ternary compounds: Tm3Cu11Si4 (ST Sc3Ni11Si4 , SG P63 /mmc , PS hP36, a = 8.3898(6), c = 8.6425(7) A, R B = 0.0606, R F = 0.0442, R P = 0,0351, R wp = 0.0570, and χ2 = 1.74), TmCuSi (ZrBeSi, P63 /mmc , hP36, a = 4.1399(3), c = 7.1471(7) A, R B =0.0493, R F = 0.0449, R P = 0.0698, R wp = 0.0930, and χ2 = 1.98), and TmCu0.5Si1.5 (AlB2 , P6/mmm , hP3, a = 3.9799(3), c = 3.9197(4) A, R I = 0.0543, R P = 0.0293, and χ2 = 1.01). The specific features of the Tm–Cu–Si system and its relationship with the previously studied R–Cu–Si systems are analyzed.

Solidification sequence of Ni-Si-Cr ~3wt% B brazing alloys

Various Ni-Si-Cr-B brazing alloys with a similar boron content (3 wt%) are investigated. Alloy compositions cover a section of the quaternary phase diagram that connects BNi-3 to BNi-9 ternary alloys for industrial use. Samples were melted and solidified at low cooling rate (1 K/min) under secondary vacuum to minimize oxidation and the metastable phase formation. Transformation temperatures, microstructures, and chemical analyses are reported. Experimental conditions were found to play a significant role on the accuracy of obtained data. Thermodynamic data were collected upon heating. Before analyzing quaternary alloys, the results of investigated ternary alloys were compared with the literature and discussed.

Formation and preservation of fresh lawsonite: Geothermobarometry of the North Makran Blueschists, southeast Iran

ABSTRACTA low‐grade metamorphic “Coloured Mélange” in North Makran (SE Iran) contains lenses and a large klippe of low temperature, lawsonite‐bearing blueschists formed during the Cretaceous closure of the Tethys Ocean. The largest blueschist outcrop is a >1,000 m thick coherent unit with metagabbros overlain by interlayered metabasalts and metavolcanoclastic rocks. Blueschist metamorphism is only incipient in coarse‐grained rocks, whereas finer grained, foliated samples show thorough metamorphic recrystallization. The low‐variance blueschist peak assemblage is glaucophane, lawsonite, titanite, jadeite±phengitic mica. Investigated phase diagram sections of three blueschists with different protoliths yield peak conditions of ~300–380°C at 9–14 kbar. Magnesio‐hornblende and rutile cores indicate early amphibolite facies metamorphism at >460°C and 2–4 kbar. Later conditions at slightly higher pressures of 6–9 kbar at 350–450°C are recorded by barroisite, omphacite and rutile assemblages before entering into the blueschist facies and finally following a retrograde path through the pumpellyite–actinolite facies across the lawsonite stability field. Assuming that metamorphic pressure is lithostatic pressure, the corresponding counterclockwise P–T path is explained by burial along a warm geothermal gradient (~15°C/km) in a young subduction system, followed by exhumation along a cold gradient (~8°C/km); a specific setting that allows preservation of fresh undecomposed lawsonite in glaucophane‐bearing rocks.

STUDY OF THE METAMORPHIC EVOLUTION OF A CARBONATE-BEARING METAPERIDOTITE FROM THE SIDIRONERO COMPLEX (CENTRAL RHODOPE, GREECE) USING P-T AND P(T)-XCO2 PSEUDOSECTIONS

The carbonate-bearing metaperidotite from Sidironero Complex, north of the Xanthi town is composed primarily of olivine and orthopyroxene megacrysts and of Ti-clinohumite, tremolite, chlorite, dolomite, magnesite, talc, antigorite and spinel group minerals. The metaperidotite underwent a prograde HP metamorphism probably isofacial with the neighboring amphibolitized eclogites. Calculated P-T and P(T)-XCO2 phase diagram sections (pseudosections) for the bulk rock composition showed that XCO2 in the fluid phase was extremely low (≤0.008) at the first stages of the metamorphism and increased up to 0.022 at the peak P-T conditions ~1.5 GPa and 690 0C. The prograde metamorphism probably started from a hydrated and carbonated assemblage including talc+chlorite+magnesite+dolomite and proceeded with tremolite and antigorite formation before olivine growth, and orthopyroxene formation after olivine growth (Ol-1). Matrix dolomite, breakdown of chlorite (Chl-1) to Cr spinel+olivine and of Ti-clinohumite to olivine+Mg-ilmenite occurred during decompression. The P-T path is constrained by the absence of clinopyroxene in the metaperidotite.

Critical Evaluations and Thermodynamic Optimizations of the MnO-Mn$$_{2}$$O$$_{3}$$-SiO$$_{2}$$ and FeO-Fe$$_{2}$$O$$_{3}$$-MnO-Mn$$_{2}$$O$$_{3}$$-SiO$$_{2}$$ Systems

A critical evaluation and thermodynamic modeling for thermodynamic properties of all oxide phases and phase diagrams in the Fe-Mn-Si-O system (MnO-Mn\(_{2}\)O\(_{3}\)-SiO\(_{2}\) and FeO-Fe\(_{2}\)O\(_{3}\)-MnO-Mn\(_{2}\)O\(_{3}\)-SiO\(_{2}\) systems) are presented. Optimized Gibbs energy parameters for the thermodynamic models of the oxide phases were obtained which reproduce all available and reliable experimental data within error limits from 298 K (25 \(^{\circ }\)C) to above the liquidus temperatures at all compositions covering from known oxide phases, and oxygen partial pressure from metal saturation to 0.21 bar. The optimized thermodynamic properties and phase diagrams are believed to be the best estimates presently available. Slag (molten oxide) was modeled using the modified quasichemical model in the pair approximation. Olivine (Fe\(_{2}\)SiO\(_{4}\)-Mn\(_{2}\)SiO\(_{4}\)) was modeled using two-sublattice model in the framework of the compound energy formalism (CEF), while rhodonite (MnSiO\(_{3}\)-FeSiO\(_{3}\)) and braunite (Mn\(_{7}\)SiO\(_{12}\) with excess Mn\(_{2}\)O\(_{3}\)) were modeled as simple Henrian solutions. It is shown that the already developed models and databases of two spinel phases (cubic- and tetragonal-(Fe, Mn)\(_{3}\)O\(_{4}\)) using CEF [Kang and Jung, J. Phys. Chem. Solids (2016), vol. 98, pp. 237–246] can successfully be integrated into a larger thermodynamic database to be used in practically important higher order system such as silicate. The database of the model parameters can be used along with a software for Gibbs energy minimization in order to calculate any type of phase diagram section and thermodynamic properties.

Topology of subsolidus sections of phase diagrams of quaternary reciprocal systems without solid solutions

A problem of constructing subsolidus isobaric–isothermal sections of phase diagrams of quaternary reciprocal systems with constant-composition compounds and limited solid solutions was considered. Relations between the topological characteristics of such sections were derived. Their topological classification was proposed. An algorithm for constructing sections using the theory of finite graphs was developed. A problem of enumerating sections for diagrams with a given set of classification characteristics was solved.

Studies on the phase diagram of Bi-Cr-O system

Isothermal cross sections of the ternary phase diagram of Bi-Cr-O system have been established at 500 and 750 °C. Existence of a new compound Bi22Cr18O60 was identified and it was characterized by XRD, SEM and TEM. Ternary phase diagram at 500 °C shows that no ternary compounds would coexist with liquid Bi at 500 °C. Only Cr2O3 and Bi2O3 would coexist with liquid Bi at this temperature. Equilibrations at 750 °C show that two ternary compounds, namely Bi22Cr18O60 and Bi38CrO60 can coexist with liquid Bi at this temperature and no other ternary compound would be stable in liquid Bi.

Phase diagram of the Fe-Sn-Zr system at 800 °C

New experimental results on the Fe-Sn-Zr phase diagram at 800 °C are presented, particularly in the central, Fe rich and Sn rich regions of the Gibbs triangle. Seven ternary alloys were designed, produced and examined by different techniques: optical and scanning electron microscopy, semi-quantitative microanalysis, quantitative microanalysis and X-ray diffraction. The results of this work and previous experimental data were used to determine the phase diagram section at 800 °C which contains at least five ternary compounds: Fe6Sn6Zr, Y, X′, θ and C36.

Key experiments and challenging thermodynamic modeling of the Li-Si-C system

The phase equilibria and thermodynamic properties of the ternary Li-Si-C system are crucial for developing new anode materials containing Si and/or C for Li-ion batteries. We carried out the long time annealing experiments and confirmed the key three-phase equilibrium of βLi2C2+SiC + Li7Si3 at 630 °C–650 °C. A consistent thermodynamic description of the Li-Si-C ternary system has been constructed based on the recently published Li-Si system, and the Li-C and Si-C binary systems that we revised in this work. The revision requires a more negative Gibbs energy for the αLi2C2 and βLi2C2 phases in the Li-C system, and a more positive Gibbs energy for the SiC phase in the Si-C system. The more negative Gibbs energy of the βLi2C2 phase requires an associate solution model to be introduced for the liquid phase. Calculated partial pressures from the revised thermodynamic description of the Li-C binary system show better agreement with the experimental data. The calculated phase diagram sections of the Li-Si-C ternary system are not only in good agreement with the key annealing experiment results, but also with differential scanning calorimetry results.

Complementary thermodynamic and dilatometric assessment of phase transformation pathway in new β-stabilized TiAl intermetallics

New Ti-44Al-5Nb-3Cr-1.5Zr(at%) intermetallic alloy, microstructured by float zone (FZ) processing, was subjected to slow dilatometric heating from the room temperature (RT) up to solidus. The evolution of linear thermal expansion coefficient (LTEC) has been compared with the phase transformation path of the alloy within the polythermal section of phase diagram calculated with ThermoCalc®. Thus, the characteristic temperatures of predicted phase transitions were experimentally verified. Results from dilatometry, EDX microanalysis, scanning and transmission electron microscopy have shown that thermodynamic database used is poorly describe the phase transformations in β-stabilized TiAl alloy at the temperatures lower than ~1000°C. While at higher temperatures the perfect correspondence was observed between the ThermoCalc® predictions and dilatometric data. The features of verified phase transformation behavior are discussed in view of comparison with those of “classic” Ti-43.5Al-4Nb-1Mo-0.1B TNM™ alloy. It is assumed that TiAl(Nb, Cr, Zr) alloy is fundamentally more favorable for high-temperature FZ-microstructuring and performance.

Thermodynamic stability of LuRhO3 in a photoelectrochemical cell

Long term stability of lutetium rhodite (LuRhO3) as an electrode for photoelectrochemical decomposition of water is investigated. The thermodynamic properties of LuRhO3 are determined in the temperature range from 875 to 1300 K using an electrochemical cell incorporating calcia–stabilized zirconia as the solid electrolyte. The standard Gibbs energy of formation of LuRhO3 from its constituent binary oxides Lu2O3 with C-type rare earth oxide crystal structure and Rh2O3 with orthorhombic structure is obtained:ΔGf,oxo(±135)/Jmol−1=−40106+3.282(T/K)The standard entropy of LuRhO3S298.15Ko(LuRhO3)/JK-1mol-1=89.54(±0.35) and standard enthalpy of formation from elements ΔHfo(298.15K)/kJmol−1=−1181.97(±3.86) are derived. The phase relations and stabilities of phases in the LuRhO system are computed from thermodynamic data. An isothermal section of the ternary phase diagram, a 2–D oxygen potential diagram and a 3–D chemical potential diagram at 1200 K are presented along with temperature–composition phase diagrams at various oxygen partial pressures of oxygen. LuRhO3 (p-type) is thermodynamically unstable as a photocathode in contact with hydrogen gas. However, n-type LuRhO3 can be used as a photoanode in the presence of oxygen.

Partition of the composition tetrahedron during construction of subsolidus isobaric-isothermal sections of the phase diagrams of quaternary systems

A problem of constructing subsolidus isobaric-isothermal sections of phase diagrams with constant-composition compounds and limited solid solutions was considered. Relations between the topological characteristics of such sections were derived. Their topological classification was proposed. An algorithm for constructing sections using the theory of finite graphs was developed. A problem of enumerating sections for diagrams with a given set of classification characteristics was solved.

Critical evaluation and thermodynamic optimization of the Na2O–FeO–Fe2O3–Al2O3–SiO2 system

A critical assessment and thermodynamic optimization of phase diagrams and thermodynamic properties of the entire Na2O–FeO–Fe2O3–Al2O3–SiO2 system were carried out at 1atm total pressure. A set of optimized model parameters obtained for all phases present in this system reproduces available and reliable thermodynamic property and phase equilibrium data within experimental error limits from 298K to above liquidus temperatures for all compositions and oxygen partial pressures from metallic Fe saturation to 1atm. The Gibbs energy of liquid solution was described based on the Modified Quasichemical Model considering the possible formation of NaAlO2 and NaFeO2 associates in the liquid state. The solid solutions wüstite, spinel, feldspar, nepheline, carnegieite, mullite, corundum, clino-pyroxene, meta-oxides and Na-β″-alumina were treated within the framework of Compound Energy Formalism. The database of model parameters can be used to calculate any thermodynamic property and phase diagram section of the present system.

Analytic Approach to Alloys Thermodynamics: Ternary Cu-Ga-Ni system

In this paper are presented the results of the calculation of thermodynamic properties in liquid state for ternary Cu-Ga-Ni alloys using the newest version of general solution model. Calculation was carried out in temperature interval 1473-2073 K, along 3 cross sections from corner of each metal, with ratios between two other metals 1:3, 1:1 and 3:1. Partial and integral molar thermodynamic properties in liquid phase for the Cu-Ga-Ni ternary system are determined, presented and discussed. Calculated data is compared with data available from literature and good agreement between these two sets of data was observed. Additionally, isothermal section of phase diagram at 298 K is calculated using Thermo-Calc software and presence of eleven different phases is detected. Presented thermodynamic data for the Cu-Ga-Ni alloys could be useful for the further assessment of this system and its phase diagram as well as for completing thermodynamic description of these alloys.

Thermodynamic modeling of oxide phases in the Fe–Mn–O system

A critical evaluation and thermodynamic modeling for thermodynamic properties of all oxide phases and phase diagrams in the Fe–Mn–O system are presented. Optimized Gibbs energy parameters for the thermodynamic models of the oxide phases were obtained which reproduce all available and reliable experimental data within error limits from 298K to above the liquidus temperatures at all compositions covering from known oxide phases, and oxygen partial pressure from metal saturation to 0.21bar. The optimized thermodynamic properties and phase diagrams are believed to be the best estimates presently available. Two spinel phases (cubic and tetragonal) were modeled using Compound Energy Formalism (CEF) with the use of physically meaningful parameters. The present Fe–Mn spinel solutions can be integrated into a larger spinel solution database, which has been already developed. The database of the model parameters can be used along with a software for Gibbs energy minimization in order to calculate any type of phase diagram section and thermodynamic properties.

Ultra-reducing conditions in average mantle peridotites and in podiform chromitites: a thermodynamic model for moissanite (SiC) formation

Natural moissanite (SiC) is reported from mantle-derived samples ranging from lithospheric mantle keel diamonds to serpentinites to podiform chromitites in ophiolites related to suprasubduction zone settings (Luobusa, Dongqiao, Semail, and Ray-Iz). To simulate ultra-reducing conditions and the formation of moissanite, we compiled thermodynamic data for alloys (Fe–Si–C and Fe–Cr), carbides (Fe3C, Fe7C3, SiC), and Fe-silicides; these data were augmented by commonly used thermodynamic data for silicates and oxides. Computed phase diagram sections then constrain the P–T–fO2 conditions of SiC stability in the upper mantle. Our results demonstrate that: Moissanite only occurs at oxygen fugacities 6.5–7.5 log units below the iron–wustite buffer; moissanite and chromite cannot stably coexist; increasing pressure does not lead to the stability of this mineral pair; and silicates that coexist with moissanite have X Mg > 0.99. At upper mantle conditions, chromite reduces to Fe–Cr alloy at fO2 values 3.7–5.3 log units above the moissanite-olivine-(ortho)pyroxene-carbon (graphite or diamond) buffer (MOOC). The occurrence of SiC in chromitites and the absence of domains with almost Fe-free silicates suggest that ultra-reducing conditions allowing for SiC are confined to grain scale microenvironments. In contrast to previous ultra-high-pressure and/or temperature hypotheses for SiC origin, we postulate a low to moderate temperature mechanism, which operates via ultra-reducing fluids. In this model, graphite-/diamond-saturated moderately reducing fluids evolve in chemical isolation from the bulk rock to ultra-reducing methane-dominated fluids by sequestering H2O into hydrous phases (serpentine, brucite, phase A). Carbon isotope compositions of moissanite are consistent with an origin of such fluids from sediments originally rich in organic compounds. Findings of SiC within rocks mostly comprised by hydrous phases (serpentine + brucite) support this model. Both the hydrous phases and the limited diffusive equilibration of SiC with most minerals in the rocks indicate temperatures below 700–800 °C. Moissanite from mantle environments is hence a mineral that does not inform on pressure but on a low to moderate temperature environment involving ultra-reduced fluids. Any mineral in equilibrium with SiC could only contain traces of Fe2+ or Cr3+.

On the General Material Balance Equation(S) to Calculate Quasi-Binary Sections of Multi-Component Phase Diagrams

A general form of material balance equations to be used to calculate quasi-binary sections of multi-component phase diagrams is derived here. When this general equation is reduced to ternary systems, it coincides with those, given in the Thermo-Calc manual. For a k-component system, altogether only (k-2) such independent equations should be written from the list of k(k-1)/2 possible equations.

Stability study of gear meshing area considering friction of tooth surface

In order to study the spur gear's dynamic characteristics under the condition of considering tooth surface friction, tooth surface friction model is established based on Stribeck model and the change rule of friction coefficient is obtained. The vibration differential equations of single meshing area and double meshing area are established based on the friction coefficient and the numerical simulation of the vibration differential equations is carried out by using Runge-Kutta method, and the influence of various parameters on the system dynamic characteristics is obtained. It can be seen from the phase diagram and Poincare section that in the single meshing area and double meshing area, the following measures can enhance the stability of the system: increase the damping ratio, exciting frequency away from the resonance region, increase the load and reduce the gear backlash.

O79] The isothermal section of the phase diagram of Gd–Fe–Mn system at 773K

O79] The isothermal section of the phase diagram of Gd–Fe–Mn system at 773K