Journal articles: 'Phase equilibria'

1

Walther, J. V. "Phase Equilibria." Science 262, no. 5141 (December 17, 1993): 1911–12. http://dx.doi.org/10.1126/science.262.5141.1911.

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Ashirov, G. "PHASE EQUILIBRIA IN THE Ag8SiTe6–Ag8GeTe6 SYSTEM." Azerbaijan Chemical Journal, no. 1 (March 15, 2022): 89–93. http://dx.doi.org/10.32737/0005-2531-2022-1-89-93.

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Phase equilibria in the Ag8SiTe6–Ag8GeTe6 system were experimentally investigated by means of differential thermal analysis and powder X-ray diffraction techniques. It was established that continuous series of solid solutions with SiGe substitution are formed in the system. T–x-diagram of the title system and concentration dependence of lattice parameters of the obtained solid solutions were plotted

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Mekhdiyeva, I. F. "PHASE EQUILIBRIA IN THE TlTe-Tl9ErTe6 SYSTEM." Azerbaijan Chemical Journal, no. 2 (June 18, 2020): 74–77. http://dx.doi.org/10.32737/0005-2531-2020-2-74-77.

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Amundson, N. R., A. Caboussat, J. W. He, A. V. Martynenko, C. Landry, C. Tong, and J. H. Seinfeld. "A new atmospheric aerosol phase equilibrium model (UHAERO): organic systems." Atmospheric Chemistry and Physics Discussions 7, no. 3 (June 22, 2007): 8709–54. http://dx.doi.org/10.5194/acpd-7-8709-2007.

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Abstract. In atmospheric aerosols, water and volatile inorganic and organic species are distributed between the gas and aerosol phases in accordance with thermodynamic equilibrium. Within an atmospheric particle, liquid and solid phases can exist at equilibrium. Models exist for computation of phase equilibria for inorganic/water mixtures typical of atmospheric aerosols; when organic species are present, the phase equilibrium problem is complicated by organic/water interactions as well as the potentially large number of organic species. We present here an extension of the UHAERO inorganic thermodynamic model (Amundson et al., 2006c) to organic/water systems. Phase diagrams for a number of model organic/water systems characteristic of both primary and secondary organic aerosols are computed. Also calculated are inorganic/organic/water phase diagrams that show the effect of organics on inorganic deliquescence behavior. The effect of the choice of activity coefficient model for organics on the computed phase equilibria is explored.

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Amundson, N. R., A. Caboussat, J. W. He, A. V. Martynenko, C. Landry, C. Tong, and J. H. Seinfeld. "A new atmospheric aerosol phase equilibrium model (UHAERO): organic systems." Atmospheric Chemistry and Physics 7, no. 17 (September 14, 2007): 4675–98. http://dx.doi.org/10.5194/acp-7-4675-2007.

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Abstract. In atmospheric aerosols, water and volatile inorganic and organic species are distributed between the gas and aerosol phases in accordance with thermodynamic equilibrium. Within an atmospheric particle, liquid and solid phases can exist at equilibrium. Models exist for computation of phase equilibria for inorganic/water mixtures typical of atmospheric aerosols; when organic species are present, the phase equilibrium problem is complicated by organic/water interactions as well as the potentially large number of organic species. We present here an extension of the UHAERO inorganic thermodynamic model (Amundson et al., 2006c) to organic/water systems. Phase diagrams for a number of model organic/water systems characteristic of both primary and secondary organic aerosols are computed. Also calculated are inorganic/organic/water phase diagrams that show the effect of organics on inorganic deliquescence behavior. The effect of the choice of activity coefficient model for organics on the computed phase equilibria is explored.

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Tukmakova, Anastasiia, Anna Novotelnova, Sergey Taskaev, Hiroyuki Miki, and Vladimir Khovaylo. "Simulation of Fe-Ti-Sb Thernary Phase Diagram at Temperatures above 900 K." Key Engineering Materials 877 (February 2021): 114–19. http://dx.doi.org/10.4028/www.scientific.net/kem.877.114.

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Heusler alloys have been considered as one of the most promising thermoelectric materials for electrical power generation in a temperature range of 500–800 °C. Establishment of phase diagrams allows one to predict formation, equilibria, and stability of phases in of these ternary alloys. In this work we report on the simulation and investigation of phase diagram and phase equilibria in ternary Ti-Fe-Sb system which is of considerable interest for thermoelectric applications. The simulation was carried out using the CALPHAD method in Pandat software. The existence of the thermoelectric Heusler TiFe1.5Sb phase was revealed in a temperature range from 970 to 1070 K. The equilibria between TiFe1.5Sb and other phases were determined. The entropy of formation was calculated for the phases existing at 970, 1020 and 1070 K using a fitting approach. A narrow equilibrium region containing pure body centered cubic Fe and TiFe1.5Sb was found.

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Ismayilova, E. N., L. F. Mashadiyeva, I. B. Bakhtiyarly, and M. B. Babanly. "PHASE EQUILIBRIA IN THE Cu2Se–SnSE–Sb2Se3 SYSTEM." Azerbaijan Chemical Journal, no. 1 (March 15, 2022): 73–82. http://dx.doi.org/10.32737/0005-2531-2022-1-73-82.

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Phase equilibria in the Cu2Se–SnSe–Sb2Se3 quasi-ternary system has been studied by differential thermal analysis and powder X-ray diffraction. Some polythermal sections, isothermal sections at 300 K of the phase diagram and the projection of the liquidus surface are constructed. The regions of primary crystallization of phases, the nature and temperatures of non- and monovariant equilibria have been determined. The phase diagram of the SnSe–CuSbSe2 quasi-binary section has been refined. It was found that a quaternary compound CuSnSbSe3 is formed in the system by the peritectic reaction. This compound exists in a narrow range ~(650–723 K) temperatures. In addition, in the studied Cu2Se–SnSe–Sb2Se3 system, limited regions of solid solutions based on the SnSe, Sb2Se3, CuSbSe2 and SnSb2Se4 compounds have also been revealed

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Mansimova, Sh H., K. N. Babanly, L. F. Mashadiyeva, R. J. Mirzoyeva, and M. B. Babanly. "PHASE EQUILIBRIA IN THE Ag2Se-PbSe-AgSbSe2 SYSTEM." Chemical Problems 17, no. 1 (2019): 41–49. http://dx.doi.org/10.32737/2221-8688-2019-1-41-49.

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9

Alakbarzade, G. I. "SOLID-PHASE EQUILIBRIA IN THE TlBiТe2-TlTbTe2 SYSTEM." Chemical Problems 17, no. 4 (2019): 565–70. http://dx.doi.org/10.32737/2221-8688-2019-4-565-570.

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10

Mashadiyeva, L. F., Z. T. Hasanova, Yu A. Yusibov, and M. B. Babanly. "PHASE EQUILIBRIA IN THE Cu2Se–Cu3AsSe4–As2Se3 SYSTEM." Azerbaijan Chemical Journal, no. 3 (August 21, 2024): 83–93. http://dx.doi.org/10.32737/0005-2531-2024-3-83-93.

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Through experimental study of carefully crystallized via long-term thermal annealing alloys using powder X-ray diffraction and differential thermal analysis methods, as well as considering the evidence from the literature, a comprehensive picture of phase equilibria in the Cu2Se-Cu3AsSe4-As2Se3 system was obtained. The projection of the liquidus surface, the isothermal section at 500 K, and three vertical sections of the phase diagram are presented and discussed. The fields of primary crystallization of phases, types, and coordinates of invariant and monovariant phase equilibria are determined. The side Cu2Se-As2Se3 system was re-investigated and its refined phase diagram was constructed. It is shown that this system is quasi-binary and is characterized by the formation of ternary Cu3AsSe3 and CuAsSe2 compounds

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11

Ismailova, E. N., L. F. Mashadieva, I. B. Bakhtiyarly, V. A. Qasimov, R. J. Gurbanova, and F. M. Mammadova. "PHASE EQUILIBRIA IN THE Cu2Se - Cu3SbSe4 - Cu2SnSe3 SYSTEM." Chemical Problems 23, no. 1 (2025): 36–46. http://dx.doi.org/10.32737/2221-8688-2025-1-36-46.

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Copper-tin and copper-antimony chalcogenides have received increasing attention as promising thermoelectric materials due to their high efficiency and low toxicity. Many of these phases are synthetic analogues of natural copper chalcogenide minerals and have been drawing more interest for the development of new environmentally friendly materials. In this regarding, we studied phase equilibria in the Cu2Se - Cu3SbSe4 - Cu2SnSe3 system using Differential Thermal Analysis (DTA), Powder x-ray Diffraction (PXRD) and Scanning Electron Microscope (SEM). Based on experimental data, a number of polythermal sections, the solid-phase equilibria diagram at 600 K and a projection of the liquidus surface were constructed for the title system. The system has revealed limited regions of solid solutions based on ternary compounds Cu3SbSe4 (α) and Cu2SnSe3 (β). It has been established that the liquidus surface consists of three regions corresponding to primary crystallization (HT-Cu2Se), as well as α- and β-phases.

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12

Johnson, W. C., and J. Y. Huh. "Coherent Phase Equilibria." Defect and Diffusion Forum 129-130 (March 1996): 37–56. http://dx.doi.org/10.4028/www.scientific.net/ddf.129-130.37.

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13

Ruan, Jingjing, Yuyuan Chen, Kosei Kobayashi, Nobufumi Ueshima, and Katsunari Oikawa. "Investigations on the Phase Transformations, Equilibria and Athermal ω in Ni-Ga-Cr Ternary System." Materials 15, no. 21 (October 30, 2022): 7617. http://dx.doi.org/10.3390/ma15217617.

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In the present work, the phase equilibria of the Ni-Ga-Cr ternary system at 850, 1000 and 1150 °C were experimentally investigated to provide the essential data for developing the high-entropy shape memory alloys (HESMAs) containing Ni, Ga and Cr. At 850 °C, in the Ni-rich portion, the B2 phase shows equilibrium with the L12 phase when the Cr content is less than 10.49 at. %, while displaying the equilibrium with L12 and BCC phases when the Cr content increases. The B2 + L12 + BCC changes into B2 + FCC + BCC three-phase equilibria from 850 to 1150 °C, as the L12 phase region becomes narrow with rising temperature. The two-phase equilibrium, B2 + BCC, was found at all the isothermal sections investigated. Other three-phase equilibria were also discovered: B2 + α-Cr3Ga + BCC and Ni2Ga3 + α-Cr3Ga + L at 850 °C, and B2 + α-Cr3Ga + L at 1000 °C. Significantly, an athermal ω intermetallic compound with the space group of P3¯m1 was observed distributing at the B2 phase in the quenched Ni45.98-Ga25.50-Cr28.52, Ni42.23-Ga15.70-Cr42.07 and Ni16.54-Ga13.63-Cr69.83 (at. %) alloys after being annealed at 1150 °C for 10 days. The high-resolution transmission electron microscopy (HRTEM) results reveal that the ω shows a crystallographic orientation of [11¯0]B2//[112¯0]ω; (111)B2//(0001)ω with the B2 parent phase.

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14

Chiang, C. S., and William C. Johnson. "Coherent phase equilibria in systems possessing a consolute critical point." Journal of Materials Research 4, no. 3 (June 1989): 678–87. http://dx.doi.org/10.1557/jmr.1989.0678.

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The influence of coherency strains on phase equilibria in a two-phase microstructure is examined for a binary or pseudobinary alloy system possessing a consolute critical point (chemical miscibility gap). The qualitative features of phase equilibria, including the limits of metastability (chemical spinodal), are shown to depend critically on the mechanical loading conditions and the geometric arrangement of the phases in the microstructure. If the elastic state of a phase in a two-phase coherent system is independent of the presence of the other phase, then the equilibrium characteristics usually associated with fluid systems should be observed, even though the system is nonhydrostatically stressed. If the elastic state of a phase depends upon the presence of the other phase, then the equilibrium characteristics that have come to be associated with coherent systems should be observed; tie lines and field lines do not coincide, the common tangent construction is invalid, and Gibbs phase rule is not applicable.

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15

Haccuria, Elien, Peter C. Hayes, and Evgueni Jak. "Phase equilibria studies of the “MnO”–Al2O3–SiO2system in equilibrium with metallic alloy. Part 2: phase equilibria." International Journal of Materials Research 106, no. 3 (March 11, 2015): 225–36. http://dx.doi.org/10.3139/146.111181.

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16

Onderka, B., A. Dębski, and W. Gąsior. "Thermodynamic Assessment Of The Bi-In-Zn System." Archives of Metallurgy and Materials 60, no. 2 (June 1, 2015): 567–75. http://dx.doi.org/10.1515/amm-2015-0175.

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Abstract A thermodynamic description of the entire ternary Bi-In-Zn system was obtained by the CALPHAD modelling of the Gibbs energy of the liquid phase. The experimental data on the phase equilibria and the thermodynamic properties published and complemented by the authors’ own experiments were taken into account. In order to verify the phase equilibria in the Bi-In-Zn system, 15 different samples were studied in the temperature range of 300-900 K by the DTA technique during heating and cooling cycles. Coexisting phases and their composition were analyzed by the SEM and EDX techniques for 9 distinct samples after their thermal equilibration at 373 K and 473 K. Assessment and selected phase equilibrium calculations were performed with ThermoCalc and Pandat softwares, and compared with experimental data. The obtained results reproduce well the experimental data on both the phase equilibria and the thermodynamic properties in the optimized system.

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17

Orujlu, E. N., T. M. Alakbarova, and M. B. Babanly. "GeTe–Bi<sub>2</sub>Te<sub>3</sub>–Te System." Žurnal neorganičeskoj himii 69, no. 8 (August 15, 2024): 1144–54. https://doi.org/10.31857/s0044457x24080079.

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Alloys of the GeTe–Bi2Te3–Te system, synthesized using a special technique that makes it possible to obtain them in a state as close as possible to equilibrium, have been studied using the methods of differential thermal and X-Ray diffraction analysis, as well as scanning electron microscopy. A solid-phase equilibria diagram, a projection of the liquidus surface, some polythermal sections and an isothermal section at 300 K of the phase diagram were constructed. The fields of primary crystallization of phases, types and coordinates of non— and monovariant equilibria are determined. It has been established that monovariant equilibria on curves emanating from the peritectic and eutectic points of the GeTe–Bi2Te3 boundary system undergo transformations at certain transition points. Near the tellurium corner of the concentration triangle, a cascade of invariant transition reactions has been identified, characterizing the joint crystallization of two-phase mixtures of telluride phases and elemental tellurium.

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18

Sun, Lifeng, Zhengyue Liu, and Maofa Jiang. "Phase Equilibria of CaO-SiO2-La2O3-Nb2O5 System in Reducing Atmosphere." Metals 12, no. 5 (April 29, 2022): 768. http://dx.doi.org/10.3390/met12050768.

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In the current work, the phase equilibria of CaO-SiO2-La2O3-Nb2O5 system at 1200 °C in reducing atmosphere (PO2 = 10−15 atm) was investigated according to the melting separation process for extracting lanthanum and niobium resources from Bayan Obo tailing. High temperature equilibrium experiment, scanning electron microscope, and energy dispersive spectrometer (SEM-EDS) were used to determine the compositions of equilibrium phases. According to the experiment results, the phase equilibria of the CaO-SiO2-La2O3-Nb2O5 system in reducing atmosphere were ascertained and the 1200 °C isothermal phase diagram of CaO-SiO2-La2O3-Nb2O5 system in reducing atmosphere was constructed. The research results not only play an important role in guiding the development of the lanthanum and niobium extraction process, but also enrich the thermodynamic data of relevant silicate slag systems.

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19

Allazova, N. M., R. F. Abbasova, T. M. Ilyasli, I. I. Aliyev, and M. R. Allazov. "PHASE EQUILIBRIA IN THE CuInSe2-Ge-Se QUASİTERNARY SYSTEM." Chemical Problems 18, no. 2 (2020): 244–49. http://dx.doi.org/10.32737/2221-8688-2020-2-244-249.

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20

Frolov, T., and Y. Mishin. "Phases, phase equilibria, and phase rules in low-dimensional systems." Journal of Chemical Physics 143, no. 4 (July 28, 2015): 044706. http://dx.doi.org/10.1063/1.4927414.

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21

Seidzade, A. E., E. N. Orujlu, and M. B. Babanly. "EXPERIMENTAL STUDY OF THE PHASE EQUILIBRIA IN THE SnTe–Sb2Te3–Te SYSTEM." Azerbaijan Chemical Journal, no. 2 (May 7, 2024): 44–52. http://dx.doi.org/10.32737/0005-2531-2024-2-44-52.

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Phase equilibria of the SnTe–Sb2Te3–Te portion of the Sn–Sb–Te ternary system have been experimentally investigated using differential thermal analysis (DTA), powder X-ray diffraction (XRD), and microstructural analysis methods. Based on the measured experimental results and literature information, isothermal sections at 500 K, liquidus surface projection, and several vertical sections of the phase diagram were plotted. The 500 K phase diagram of this system consists of 2 single-phase regions, 2 two-phase regions, and 3 three-phase regions. The liquidus surface projection is represented by the primary crystallization fields of 5 phases. The primary crystallization fields of all phases, the types, and coordinates of non- and monovariant equilibria were determined. Obtained experimental data can be valuable input for design for Sn–Sb–Te-based alloys

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22

Yan, B., R. Guo, and J. Zhang. "A study on phase equilibria in the CaO-Al2O3-SiO2-“Nb2O5”(5 mass pct) system in reducing atmosphere." Journal of Mining and Metallurgy, Section B: Metallurgy 49, no. 2 (2013): 145–51. http://dx.doi.org/10.2298/jmmb120823013y.

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Phase equilibria in 5 mass% ?Nb2O5? plane of CaO-Al2O3-SiO2-?Nb2O5? system at 1873 K in an oxygen partial pressure of 1.78?10-6 Pa have been investigated through isothermal equilibration and quenching followed by EPMA examinations. In order to characterize the effect of niobium oxide on the phase relationship of the CaO-Al2O3-SiO2 system, Nb2O5-containing and Nb2O5-free samples with the same CaO/Al2O3/SiO2 weight ratio were investigated simultaneously. The ratios of CaO/Al2O3/SiO2 were selected from the CaO?2Al2O3-liquid two-phase equilibrium region in the CaO-Al2O3- SiO2 system at1873 K. It was found that the adding of 5 mass% Nb2O5 to the CaO-Al2O3-SiO2 system caused the original CaO?2Al2O3-liquid equilibrium to become three different new equilibria. The three equilibria were single liquid phase, CaO?6Al2O3-liquid and gehlenite-CaO?2Al2O3-liquid equilibrium respectively. The gehlenite phase may be a new solid solution of 2CaO?Al2O3?SiO2 and NbOx with melting point higher than 1873 K.

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23

Gokcen, N. A., and Z. Moser. "Thermodynamics of phase equilibria." Journal of Phase Equilibria 14, no. 3 (June 1993): 288–95. http://dx.doi.org/10.1007/bf02668226.

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24

Withers, Anthony C., Eric J. Essene, and Youxue Zhang. "Rutile/TiO2II phase equilibria." Contributions to Mineralogy and Petrology 145, no. 2 (March 6, 2003): 199–204. http://dx.doi.org/10.1007/s00410-003-0445-2.

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25

Cahn, Robert W. "Phase equilibria under stress." Advanced Materials 1, no. 8-9 (1989): 300–302. http://dx.doi.org/10.1002/adma.19890010812.

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26

Cahn, Robert W. "Phase Equilibria under Stress." Angewandte Chemie 101, no. 8 (January 13, 2006): 1154–56. http://dx.doi.org/10.1002/ange.19891010858.

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27

Cahn, Robert W. "Phase Equilibria under Stress." Angewandte Chemie International Edition in English 28, no. 8 (August 1989): 1128–30. http://dx.doi.org/10.1002/anie.198911281.

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28

Wetzel, Marius Holger, Tina Trixy Rabending, Martin Friák, Monika Všianská, Mojmír Šob, and Andreas Leineweber. "Phase Stability of Iron Nitride Fe4N at High Pressure—Pressure-Dependent Evolution of Phase Equilibria in the Fe–N System." Materials 14, no. 14 (July 15, 2021): 3963. http://dx.doi.org/10.3390/ma14143963.

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Although the general instability of the iron nitride γ′-Fe4N with respect to other phases at high pressure is well established, the actual type of phase transitions and equilibrium conditions of their occurrence are, as of yet, poorly investigated. In the present study, samples of γ′-Fe4N and mixtures of α Fe and γ′-Fe4N powders have been heat-treated at temperatures between 250 and 1000 °C and pressures between 2 and 8 GPa in a multi-anvil press, in order to investigate phase equilibria involving the γ′ phase. Samples heat-treated at high-pressure conditions, were quenched, subsequently decompressed, and then analysed ex situ. Microstructure analysis is used to derive implications on the phase transformations during the heat treatments. Further, it is confirmed that the Fe–N phases in the target composition range are quenchable. Thus, phase proportions and chemical composition of the phases, determined from ex situ X-ray diffraction data, allowed conclusions about the phase equilibria at high-pressure conditions. Further, evidence for the low-temperature eutectoid decomposition γ′→α+ε′ is presented for the first time. From the observed equilibria, a P–T projection of the univariant equilibria in the Fe-rich portion of the Fe–N system is derived, which features a quadruple point at 5 GPa and 375 °C, above which γ′-Fe4N is thermodynamically unstable. The experimental work is supplemented by ab initio calculations in order to discuss the relative phase stability and energy landscape in the Fe–N system, from the ground state to conditions accessible in the multi-anvil experiments. It is concluded that γ′-Fe4N, which is unstable with respect to other phases at 0 K (at any pressure), has to be entropically stabilised in order to occur as stable phase in the system. In view of the frequently reported metastable retention of the γ′ phase during room temperature compression experiments, energetic and kinetic aspects of the polymorphic transition γ′⇌ε′ are discussed.

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Kilpatrick, Peter K., L. E. Scriven, and H. T. Davis. "Thermodynamic Modeling of Quaternary Systems: Oil/Brine/Surfactant/Alcohol." Society of Petroleum Engineers Journal 25, no. 03 (June 1, 1985): 330–42. http://dx.doi.org/10.2118/11209-pa.

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Abstract Surfactant flooding for EOR results in multiphase oil/brine/surfactant/alcohol mixtures. Because alcohol and surfactant do not partition among the phases in constant proportion, thermodynamic modeling phases in constant proportion, thermodynamic modeling of quaternary systems is necessary in an accurate treatment of phase equilibria in these systems. We describe here the quaternary version of a free-energy-based equation of state (EOS). The systematic computation of phase equilibria in a quaternary system begins on the phase equilibria in a quaternary system begins on the binary edges and ternary faces and proceeds by numerical continuation through the higher dimensional composition space. We expedite the computation with knowledge of the limits of thermodynamic stability the spinodal surfaces and all critical points that lie on those surfaces. This preliminary calculation indicates those regions in which solution of the nonlinear equations of phase equilibria will suffer from slow numerical convergence. phase equilibria will suffer from slow numerical convergence. Multiphase equilibria are searched out by both parametric and compositional continuation. The results provide the basis for understanding the trends of three- and four-phase equilibria in oil/brine/surfactant/alcohol mixtures. Introduction At completion of secondary oil recovery, most of the residual petroleum is held in place in the reservoir pore space by capillary forces. The strength of these forces is dictated by the magnitude of the interfacial tension (IFT) between coexisting oleic and aqueous phases. In one method of tertiary oil recovery, the capillary forces are reduced by injection of formulations containing surfactant and alcohol, which with oil and brine form a microemulsion phase having, under the right conditions, ultralow (approximately 10–3 dyne/cm [10–3 mN/m]) IFT's against coexisting oil-rich and water-rich phases. When there axe ultralow tensions, flooding with the surfactant and alcohol formulation can result in substantial oil recovery. Whether ultralow tensions occur depends crucially on the equilibrium phase behavior of the surfactant and alcohol mixtures with the reservoir oil and brine. Although reservoir oil, brine, and commercial surfactant are multicomponent substances, it is common to treat the oil/brine/surfactant/alcohol system as a pseudoternary mixture in which the surfactant and alcohol, pseudoternary mixture in which the surfactant and alcohol, the oil, and the brine partition as pseudocomponents. This approach has been quite useful for qualitatively understanding the general patterns of phase behavior, but it suffers the disadvantage that alcohol and surfactant partition quite differently between oil-rich and water-rich partition quite differently between oil-rich and water-rich phases and are, therefore, poor pseudocomponents. Our phases and are, therefore, poor pseudocomponents. Our purpose here is to improve the situation by modeling purpose here is to improve the situation by modeling oil/brine/surfactant/alcohol systems as quaternary mixtures in which surfactant and alcohol are independent components. The preferred modeling technique is to fit limited data to the parameters of a free-energy-based EOS. The benefits of such a description are many:the free energy of the model dictates the number of phases and composition regions of metastable states, some possibly long-lived;the parameters of the model link directly the phase behavior and the molecular forces between constituent molecules; andthe topography of the free energy function in composition space is the primary determinant of IFT and wettability behavior. Rossen et al. used this approach to model pseudoternary oil/brine/surfactant mixtures with a modified version of the Flory-Huggins EOS. We describe here the quaternary version of this model, which should prove useful for quantitative predictions of phase splits and compositions. predictions of phase splits and compositions. The computational strategy for extracting phase equilibria from a quaternary thermodynamic model relies on known equilibria for binary edges and ternary faces, which serve as termini of and initial approximations for quaternary equilibria. As quaternary phase equilibria are computed by projecting from the edges and faces, the calculation is guided by supplementary determinations of the limit of thermodynamic stability or spinodal and the lines of critical points that fall on this limit. It is near the critical points that the iteration schemes for solving the nonlinear equations of phase equilibria begin to fail. Moreover, the computation of critical points is a simpler task requiring less effort than the points is a simpler task requiring less effort than the calculation of phase equilibria. Once the location of all critical points and their stability have been determined, the pattern of phase behavior with the quaternary compositional tetrahedron is determined easily. SPEJ p. 330

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30

Fedorov, Pavel P., and Elena V. Chernova. "Phase diagrams of zirconium dioxide systems with yttrium and scandium oxides." Kondensirovannye sredy i mezhfaznye granitsy = Condensed Matter and Interphases 25, no. 2 (May 11, 2023): 257–67. http://dx.doi.org/10.17308/kcmf.2023.25/11106.

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The literature data on the study of phase equilibria in systems zirconia with yttria and scandia are analysed. Possible schemes of low-temperature phase equilibria in ZrO2-Y2O3 and ZrO2-Sc2O3 systems are presented taking into account the third law of thermodynamics. The coordinates of non-variant transformations in these systems are tabulated. A sign of non-equilibrium states is the observation of non-diffusion processes of ordering of solid solutions. The modified cryoscopy method is used to calculate the distribution coefficients of scandia and yttria during the crystallization of the ZrO2 melt. The possibilities for the existence of a set of ordered phases in the ZrO2-Y2O3 system and diffuse phase transition in the cubic modification of zirconia are discussed.

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31

Ascani, Moreno, Gabriele Sadowski, and Christoph Held. "Simultaneous Predictions of Chemical and Phase Equilibria in Systems with an Esterification Reaction Using PC-SAFT." Molecules 28, no. 4 (February 13, 2023): 1768. http://dx.doi.org/10.3390/molecules28041768.

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The study of chemical reactions in multiple liquid phase systems is becoming more and more relevant in industry and academia. The ability to predict combined chemical and phase equilibria is interesting from a scientific point of view but is also crucial to design innovative separation processes. In this work, an algorithm to perform the combined chemical and liquid–liquid phase equilibrium calculation was implemented in the PC-SAFT framework in order to predict the thermodynamic equilibrium behavior of two multicomponent esterification systems. Esterification reactions involve hydrophobic reacting agents and water, which might cause liquid–liquid phase separation along the reaction coordinate, especially if long-chain alcoholic reactants are used. As test systems, the two quaternary esterification systems starting from the reactants acetic acid + 1-pentanol and from the reactants acetic acid + 1-hexanol were chosen. It is known that both quaternary systems exhibit composition regions of overlapped chemical and liquid–liquid equilibrium. To the best of our knowledge, this is the first time that PC-SAFT was used to calculate simultaneous chemical and liquid–liquid equilibria. All the binary subsystems were studied prior to evaluating the predictive capability of PC-SAFT toward the simultaneous chemical equilibria and phase equilibria. Overall, PC-SAFT proved its excellent capabilities toward predicting chemical equilibrium composition in the homogeneous composition range of the investigated systems as well as liquid–liquid phase behavior. This study highlights the potential of a physical sound model to perform thermodynamic-based modeling of chemical reacting systems undergoing liquid–liquid phase separation.

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Mamedov, E. I. "INVESTIGATION OF PHASE EQUILIBRIA AND PHYSICO-CHEMICAL PROPERTIES OF OBTAINED PHASES IN THE Sb2S3-Cr2Se3 SYSTEM." Azerbaijan Chemical Journal, no. 3 (September 19, 2023): 152–60. http://dx.doi.org/10.32737/0005-2531-2023-3-152-160.

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Using complex of physicochemical methods of analysis (DTA, XRD, MSA, as well as measurements of density and microhardness), the phase equilibria in the Sb2S3-Cr2Se3 system was studied and a phase diagram was constructed. It is established that the system is quasi-binary and has eutectic type T-x diagram. In the process of chemical interaction, a compound with composition Cr2Sb2S3Se3 is formed in the system. The Cr2Sb2S3Se3 compound melts incongruently at 6500C., A limited area of the solid solution based on the initial components of the system is formed. The coordinates of the eutectic formed between the α-solid solution and the Cr2Sb2S3Se3 compound is 17 mol % Cr2Se3 at 4500C. At room temperature, solid solutions based on Sb2S3 reach up to 5 mol % Cr2Se3, and based on Cr2Se3 up to – 3 mol % Sb2S3. According to the results of X-ray diffraction analysis, Cr2Sb2S3Se3 crystallizes in a tetragonal system with lattice parameters: a=16.37; c=11.69 Å, ρpuc.=5.40 q/sm3, ρX-ray=5.42 q/sm3. The temperature dependence of the electrical conductivity and thermo-EMF of the (Sb2S3)1-x(Cr2Se3)x (x=0.01; 0.02; 0.03;) solid solution has been studied

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Yen, Yee-wen, and Sinn-wen Chen. "Phase equilibria of the Ag–Sn–Cu ternary system." Journal of Materials Research 19, no. 8 (August 2004): 2298–305. http://dx.doi.org/10.1557/jmr.2004.0296.

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Phase equilibria of the Ag–Sn–Cu ternary system have been determined experimentally as well as using the calculation of phase diagram (CALPHAD) method. Various Ag–Sn–Cu alloys were prepared to study the isothermal sections of the Ag–Sn–Cu ternary system at 240 and 450 °C. No ternary compounds were found and all the binary compounds had only limited ternary solubility. The ∈1–Cu3Sn phase is a very stable phase. It is in equilibrium with the Ag, ζ–Ag4Sn, ∈2–Ag3Sn, η–Cu6Sn5, and Cu phases at 240 °C, and is in equilibrium with the Ag, ζ, ∈2, L, and δ–Cu4Sn phases at 450 °C. Thermodynamic models of the Ag–Sn–Cu ternary system were developed based on available thermodynamic models of the constituent binary systems without introducing ternary interaction parameters. The isothermal sections at 240 and 450 °C were calculated, and the results were in good agreement with those determined experimentally. In addition to the isothermal sections, stability diagrams of Sn and Cu were calculated as well.

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Burchakov, Alexander V., Ivan K. Garkushin, Sergey N. Milov, and Maria A. Sukharenko. "Forecasting of phase equilibria in the system NaCl-Na2MoO4-Na2WO4 at the liquid-solid interface." Butlerov Communications 60, no. 10 (October 31, 2019): 124–39. http://dx.doi.org/10.37952/roi-jbc-01/19-60-10-124.

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The paper presents the results of a theoretical study of the phase complex of a three-component system consisting of tungstates, molybdates and sodium chlorides for equilibrium "liquid - solid". Previously, a literature review was conducted on data on phase equilibria in the condensed state of individual salts, binary faceting systems. In two NaCl-Na2MoO4 and NaCl-Na2WO4 binary systems, a eutetic equilibrium is observed with the formation of solid phases corresponding to the system components and Na3ClMoO4 and Na3ClWO4, and in binary faceting system Na2MoO4 – Na2WO4, one phase of a continuous series of solid solutions crystallizes. Based on the mathematical model of the molar balance, one can uniquely determine the quantities of reaction products, the molecular formulas of solid solutions, and the equations of chemical reactions for an arbitrary mixture of system components. This model represents a set of algebraic equations by which the balance is calculated. To build a 3D computer model, the paper presents the equations for the conversion of coordinates from barycentric to Cartesian. The model is implemented in concentration-temperature coordinates using the KOMPAS-3D program using experimental data on the system. With 3D model it is possible to conduct a preliminary a priori forecast of phase equilibria in order to identify the structure of phase diagrams at the qualitative and quantitative levels. The projection of the crystallization polytherm onto the square of the compositions is represented by three fields of solid solutions – NaCl, Na3ClMoxW1-xO4 and Na2MoxW1-xO4. Isothermal and polythermal sections were constructed. The system implements di- and monovariant equilibria. A diagram of the material balance of crystallizing phases is constructed. The paper presents the calculation of the ratio of equilibrium phases, as well as their qualitative and quantitative composition for the two-phase and three-phase regions according to the coordinates of the points - the vertices of the conode segments and conode triangles, which are extracted from the 3D model. The calculation is implemented for a given composition and temperature.

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Drápala, Jaromír, Petr Kubíček, J. Vřeštál, and Monika Losertová. "Study of Reaction Diffusivity in the Copper–Indium–Tin Ternary System." Defect and Diffusion Forum 263 (March 2007): 231–36. http://dx.doi.org/10.4028/www.scientific.net/ddf.263.231.

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Interaction of lead-free solders with copper substrate represents an important phenomenon in the issue of reliability of solder joints. New experimental data describing phase equilibria in the Cu-In-Sn system after long-time diffusion annealing at the 400 °C/50 hours, 600 °C/310 hours and 600 °C/48 hours will be presented. The composition of solders was: 100 % Sn, 75 % Sn + 25 % In, 50 % Sn + 50 % In, 25 % Sn + 75 % In, 100 % In. The fast quenching method was employed to freeze thermodynamic equilibrium after annealing, followed by metallography, microhardness measurements, SEM (Scanning Electron Microscope) and WDX (Wave Dispersive X-ray) analysis. New phase equilibrium data, together with the data from literature, represent the best existing experimental description of phase equilibria in the system in question. The obtained experimental results of the phase equilibria were compared with the thermodynamic modelling by the CALPHAD (Calculation of Phase Diagrams) method and with other authors.

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Hoschek, Gert. "Phase equilibria of Hornblende Garbenschists from Hohe Tauern, Eastern Alps." Neues Jahrbuch für Mineralogie - Abhandlungen 173, no. 2 (July 7, 1998): 155–87. http://dx.doi.org/10.1127/njma/173/1998/155.

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Ghazi, Hala, Francois James, and Hélène Mathis. "Vapour-liquid phase transition and metastability." ESAIM: Proceedings and Surveys 66 (2019): 22–41. http://dx.doi.org/10.1051/proc/201966002.

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The paper deals with the modelling of the relaxation processes towards thermodynamic equilibrium in a liquid-vapour isothermal mixture. Focusing on the van der Waals equation of state, we construct a constrained optimization problem using Gibbs' formalism and characterize all possible equilibria: coexistence states, pure phases and metastable states. Coupling with time evolution, we develop a dynamical system whose equilibria coincide with the minimizers of the optimization problem. Eventually we consider the coupling with hydrodynamics and use the dynamical system as a relaxation source terms in an Euler-type system. Numerical results illustrate the ability of the whole model to depict coexistence and metastable states as well.

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Deiters, Ulrich K. "Modelling Supercritical Phase Equilibria: Problems and Pitfalls." Periodica Polytechnica Chemical Engineering 63, no. 2 (March 18, 2019): 261–69. http://dx.doi.org/10.3311/ppch.12757.

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This article addresses some recurring difficulties and problems of computing phase equilibria involving supercritical fluid phases. These difficulties prevent a full automatization of thermodynamic calculations and require human interference. Examples are the wrong interpretation of experimental data, phase inversion phenomena, or overlooking phases. While none of these insights are knew, publications dealing with them are scattered and sometimes hard to obtain. This article gives a short overview over some of the most common difficulties and pitfalls.

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Stephen Berry, R. "PHASES AND PHASE EQUILIBRIA: CLUSTERS TO BULK MATTER." International Journal of Modern Physics B 06, no. 23n24 (December 1992): 3695–707. http://dx.doi.org/10.1142/s0217979292001766.

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40

Wusatowska-Sarnek, Agnieszka M., Gautam Ghosh, Gregory B. Olson, Martin J. Blackburn, and Mark Aindow. "Characterization of the microstructure and phase equilibria calculations for the powder metallurgy superalloy IN100." Journal of Materials Research 18, no. 11 (November 2003): 2653–63. http://dx.doi.org/10.1557/jmr.2003.0371.

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The microstructure of the Ni-based superalloy IN100 processed by a powder metallurgy route was evaluated to reveal the structures, volume fractions, distributions, and chemistries of the various phases present. These data were compared with those predicted by computational thermodynamics. It is shown that the microstructural parameters expected on the basis of global equilibrium conditions differ significantly from those measured experimentally. However, modification of these calculations by use of constrained and successive equilibria compensated for kinetic effects and led to accurate (or better) predictions of phase volume fractions and chemistries in this alloy. This demonstrated that such modified phase equilibria calculations could be powerful tools for modeling microstructures, even in complex multicomponent alloys processed under nonequilibrium conditions.

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Lacroix-A-Chez-Toine, Bertrand, and Yan V. Fyodorov. "Counting equilibria in a random non-gradient dynamics with heterogeneous relaxation rates." Journal of Physics A: Mathematical and Theoretical 55, no. 14 (March 10, 2022): 144001. http://dx.doi.org/10.1088/1751-8121/ac564a.

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Abstract We consider a nonlinear autonomous random dynamical system of N degrees of freedom coupled by Gaussian random interactions and characterized by a continuous spectrum n μ (λ) of real positive relaxation rates. Using Kac–Rice formalism, the computation of annealed complexities (both of stable equilibria and of all types of equilibria) is reduced to evaluating the averages involving the modulus of the determinant of the random Jacobian matrix. In the limit of large system N ≫ 1 we derive exact analytical results for the complexities for short-range correlated coupling fields, extending results previously obtained for the ‘homogeneous’ relaxation spectrum characterised by a single relaxation rate. We show the emergence of a ‘topology trivialisation’ transition from a complex phase with exponentially many equilibria to a simple phase with a single equilibrium as the magnitude of the random field is decreased. Within the complex phase the complexity of stable equilibria undergoes an additional transition from a phase with exponentially small probability to find a single stable equilibrium to a phase with exponentially many stable equilibria as the fraction of gradient component of the field is increased. The behaviour of the complexity at the transition is found only to depend on the small λ behaviour of the spectrum of relaxation rates n μ (λ) and thus conjectured to be universal. We also provide some insights into a counting problem motivated by a paper of Spivak and Zyuzin of 2004 about wave scattering in a disordered nonlinear medium.

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Rovetto, L. J., C. J. Peters, and E. A. Brignole. "Phase equilibrium behavior for hydrogenolysis components: three-phase equilibria LLV and retrograde behavior." Journal of Supercritical Fluids 34, no. 2 (June 2005): 183–87. http://dx.doi.org/10.1016/j.supflu.2004.11.013.

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Promkotra, Sarunya. "Phase Equilibria of Condensate and Natural Gas." Advanced Materials Research 746 (August 2013): 529–32. http://dx.doi.org/10.4028/www.scientific.net/amr.746.529.

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Condensate and natural gas from a gas field in the northeast of Thailand are examined for their physical and chemical properties, and phase behaviors referring to phase equilibria. The physical properties of condensate are analyzed based on API gravity, density, Reid vapor pressure, true vapor pressure, pressure and temperature, viscosity and specific energy. Chemical components of natural gas are grouped depending on the amount of organic hydrocarbons which are methane, light hydrocarbons, heavy hydrocarbons, aromatic and cyclic compounds and non-hydrocarbon contents in the mole per cent of 97.15, 1.16, 0.22, 0.019 and 1.50, respectively. Pristane and phytane ratio is 1.73 which refers to an oxidizing environment during the deposition of the petroleum reservoir. Phase behavior of condensate is found only one phase, liquid phase at 15°C and 101.327 kPa, which indicates the critical temperature of 592.13 K and the critical pressure of 2,372.96 kPa. However, natural gas can be separated in two phases, vapor and liquid phases. The results show that the cricondentherm and cricondenbar of natural gas are 326.36 K and 1,295.28 kPa, respectively. These results can be useful for controlling and managing condensate and natural gas.

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Omelchuk, Anatoliy, Igor Skryptun, Nikolay Zakharchenko, Olha Bosenko, Ruslan Savchuk, and Larisa Gritsay. "PHASE EQUILIBRIA IN THE NaCl–CaCl2–CaO SYSTEM." Ukrainian Chemistry Journal 87, no. 2 (March 19, 2021): 77–86. http://dx.doi.org/10.33609/2708-129x.87.02.2021.77-86.

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The phase equilibria of the ternary system CaCl2 – NaCl – CaO in the area which enriched of calcium and sodium chloride were investigated by the methods of differential-thermal analysis and powder X-ray phase analysis. In the systems were determined the equilibrium concentration of calcium oxide and the composition of the phases, which at the same time exist in an equilibrium state at different temperatures. The surfaces of liquidus and solidus were established, the compositions of the sections of the ternary system CaCl2–NaCl–CaO were defined, which recommended for electrochemical reduction of refractory metal oxides (titanium, zirconium and other), which allow electrolysis in the temperature range from 550 to 1000 °С. Five polythermal sections of the NaCl – CaCl2 – CaO ternary system were studied. For each polythermal section the regions of existence of the liquid and solid phases were established. For each polythermal section state diagrams were constructed. Used X-Ray phase analyses it was established the compositions of liquid and solid phases for each polythermal sections. The phases of which the system consists were determined. At a constant ratio of components [NaCl]:[CaCl2] = 1.06 (mol.) in the melts of the ternary system CaCl2 – NaCl – CaO, the equilibrium content of calcium oxide reaches 12.0 mol.%, while their crystallization temperature does not exceed 550 °C. This allows us to recommend mixtures of this composition for electrochemical reduction of refractory metal oxides in a wide range of temperatures (from 550 to 1000 °C) with a high content of both calcium and sodium chlorides (not less than 40 mol.%) and oxide. calcium (up to 12.0 mol.%). The eutectic of this ternary system has a melting point of 480 ° C and corresponds to he composition (mol.%): CaCl2 (45.8) – NaCl (47.0) – CaO (7.2).

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Anisimov, Mikhail, and Olga Petrova-Bogdanova. "Eutectic and Peritectic Lines for Diagrams of Quasi Equilibria of Binary Systems with Partially Soluble Components." Siberian Journal of Physics 8, no. 1 (March 1, 2013): 65–72. http://dx.doi.org/10.54362/1818-7919-2013-8-1-65-72.

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Topologies of the nucleation rate surfaces over phase equilibria diagrams with eutectic and peritectic points are constructed schematically. Theoretical methods to obtain the topology of these surfaces are not yet available. Individual eutectic and peritectic points, empirically observed previously in non-equilibrium conditions, are following as particular cases of the common results of the present paper. It is shown that there are lines of eutectic and peritectic compositions in general, depending on the mother phase invasion depth into the region of the coupled phase equilibria

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IWAI, Yoshio, and Yasuhiko ARAI. "Phase Equilibria for Polymer Systems." Journal of The Japan Petroleum Institute 34, no. 5 (1991): 416–26. http://dx.doi.org/10.1627/jpi1958.34.416.

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IWAI, Y., T. FURUYA, T. ISHIDAO, and Y. ARAI. "Phase equilibria for polymer systems." International Journal of the Society of Materials Engineering for Resources 3, no. 1 (1995): 211–18. http://dx.doi.org/10.5188/ijsmer.3.211.

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Fleet, M. E. "Phase Equilibria at High Temperatures." Reviews in Mineralogy and Geochemistry 61, no. 1 (January 1, 2006): 365–419. http://dx.doi.org/10.2138/rmg.2006.61.7.

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Stapleton, M. R., D. J. Tildesley, and N. Quirke. "Phase equilibria in polydisperse fluids." Journal of Chemical Physics 92, no. 7 (April 1990): 4456–67. http://dx.doi.org/10.1063/1.457756.

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Chatterjee, A., and B. Widom. "Model lamellar-lamellar phase equilibria." Molecular Physics 80, no. 4 (November 1993): 741–54. http://dx.doi.org/10.1080/00268979300102611.

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Journal articles on the topic 'Phase equilibria'

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